8th european workshop on numerical modeling of...

8th EUROPEAN WORKSHOP ON NUMERICALMODELING OF MANTLE CONVECTION AND

LITHOSPHERIC DYNAMICS

Castle of Hruba Skala, Czech RepublicSeptember 13—18, 2003

Organizers:

Ondrej Cadek (Charles University, Prague, Czech Republic)Ales Spicak (Institute of Geophysics, Academy of Sciences of the Czech Republic)Ondrej Sramek (Charles University, Prague, Czech Republic & ENS Lyon, France)Yanick Ricard (ENS Lyon, France)Harro Schmeling (University of Frankfurt, Germany)

MAGMA

Address:

Zamek Hruba Skala511 01 TurnovCzech Republic

Tel.: +420 481 389 681Fax.: +420 481 389 683www: http://www.hrubaskala.cz

Director:

Mr. Vladimır [email protected]

The Castle

HotelStekl

Hotel Jana

Reception

Registration

Lecture

Room

Dining

RoomPosters Tower

Terrace (2

nd courtyard

)

1st courtyard

Valdstejn

Wing White

Wing

Black

Wing

Moat

Moat

Bridge I

Bridge II"Kastel

an" Wing

Church

A c c e s s Ro a d

Garden

Garden

Cars can be parked free of charge in the 1st courtyard.

Meals are served in the dinning room.Breakfast is served from 7:30 am to 9 am.Lunch is served at 1 pm.Dinner is served at 7 pm.Morning coffee is served close to the lecture room at around 11 am.Afternoon coffee is served in the poster area during the poster session.

One of the first geodynamic models of the Earth’s interior.

Reprinted from ”Mundus subterraneus, in quo universae naturae

majestas et divitiae demonstratur” by Athanasius Kircher (1664).

Castle of Hruba Skala, Czech Republic, September 13–18, 2003 PROGRAM

Program of the workshop

Saturday, September 13

12:00–19:00 Registration

20:00 Welcome party

Sunday, September 14

Chairperson:

08:45 Opening of the workshop

09:00 Invited lecture — David Bercovici

10:00 Invited lecture — Nicolas Coltice:

Mantle chemical evolution: constraints and models

11:00 — coffee break —

11:30 Invited lecture — Klaus Regenauer-Lieb:

The physics of subduction: statics, kinematics and dynamics

13:00 — lunch —

15:00 Students’ meeting (chairperson: Thorsten Becker)

16:00 Micropresentation of posters

16:30 Poster session (for the list of presented posters see p. 8)

18:30 Summary of the day (possible continuation after dinner)

19:00 — dinner —

Monday, September 15

Chairperson: Craig Bina

09:00 Invited lecture — Luce Fleitout:

Phase transitions and mantle dynamics

10:00 Invited lecture — Paul Tackley:

Modeling the coupled chemical and thermal evolution of terrestrial planets

using mantle convection models with geochemical tracking


11:30 Invited lecture — Anne Davaille:

Experimental investigation of mantle convection and chemical mixing

13:00 — lunch —

15:00 Students’ meeting



18:30 Summary of the day (possible continuation after dinner)

19:00 — dinner —

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8th European Workshop on Numerical Modeling of Mantle Convection and Lithospheric Dynamics

Tuesday, September 16

Chairperson: Yanick Ricard

09:00 Invited lecture — Giorgio Spada:

From sealevel to space geodesy: the past and the future of postglacial re-

bound

10:00 Invited lecture — Tilman Spohn:

Planetary interior dynamics


11:30 Invited lecture — Ulrich Christensen:

Convection in the Earth’s core from the perspective of a mantle convection

modeller

13:00 — lunch —

afternoon — walking trip to the castle of Valdstejn, barbecue in the evening

Wednesday, September 17

Chairperson: Harro Schmeling

09:00 Invited lecture — Raffaella Montelli:

Finite frequency tomography reveals a variety of plumes in the mantle

10:00 Invited lecture — Ulli Hansen:

The fluid dynamics of plumes


11:30 Invited lecture — Edouard Kaminski:

Building the bridge between seismic anisotropy and upper mantle convection

13:00 — lunch —

15:00 Students’ meeting



18:30 Summary of the day

19:00 — farewell party —

Thursday, September 18

morning Departure for Prague

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Castle of Hruba Skala, Czech Republic, September 13–18, 2003 INVITED LECTURES

Invited lectures

Sunday, September 14

Nicolas COLTICEUniversite Claude Bernard Lyon 1, France

Mantle chemical evolution: constraints and models (abstract p. 17)

Klaus REGENAUER-LIEBETH Zurich, Switzerland & CSIRO Perth, Australia

The physics of subduction: statics, kinematics and dynamics (abstract p. 37)

Monday, September 15

Luce FLEITOUTENS Paris, France

Phase transitions and mantle dynamics (abstract p. 20)

Paul TACKLEYUCLA, USA

Modeling the coupled chemical and thermal evolution of terrestrial planets using mantle convectionmodels with geochemical tracking (abstract p. 42)

Anne DAVAILLEIPG Paris, France

Experimental investigation of mantle convection and chemical mixing (abstract p. 18)

Tuesday, September 16

Giorgio SPADAUniversity of Urbino, Italy

From sealevel to space geodesy: the past and the future of postglacial rebound (abstract p. 39)

Tilman SPOHNUniversity of Munster, Germany

Planetary interior dynamics (abstract p. 39)

Uli CHRISTENSENMax-Planck-Institut fur Aeronomie, Katlenburg-Lindau, Germany

Convection in the Earth’s core from the perspective of a mantle convection modeller(abstract p. 16)

Wednesday, September 17

Raffaella MONTELLIPrinceton, USA

Finite frequency tomography reveals a variety of plumes in the mantle (abstract p. 31)

Ulli HANSENUniversity of Munster, Germany

The fluid dynamics of plumes (abstract p. 24)

Edouard KAMINSKIIPG Paris - Universite Paris 7, France

Building the bridge between seismic anisotropy and upper mantle convection (abstract p. 27)

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Poster session, Sunday, September 14

Micropresentations of posters: 16:00–16:30Poster session (authors in attendance): 16:30–18:30

Posters can be displayed from Saturday evening to Monday morning.

Subducting slabs and related topics

Diane Arcay: Effect of slab dehydration on mantle wedge dynamics in subductionzones

S01

Craig Bina: Seismic velocity and density anomalies from subducted basalts S02Roberta De Franco: Consequences of different rheologies on numerical models of sub-

ductionS03

Alwina Enns: The dynamics of the slab rollback effect S04Francesca Funiciello: Role of lateral mantle flow in the evolution of subduction system:

insight from laboratory experimentsS05

Rob Govers: Dynamics of slab-transform plate boundaries: preliminary finite el-ement models of the south-central Mediterranean uppermost man-tle and lithosphere

S06

Ritske Huismans: Factors controlling slab roll-back and back-arc extension S07Martin Kukacka: The role of crustal properties in the slab detachment S09

Nick Kusznir: Mass balance of the subducted slab under the Central Andes, dy-namic topography and its isostatic implications

S09

Fred Marton: Variable thermal conductivity in subducting slabs: olivine metasta-bility and the mechanisms of deep earthquakes

S10

Gabriele Morra: On the curvature of oceanic arcs S11Lars Ruepke: Dynamic implications of mantle serpentinization for intra-slab seis-

micityS12

Eh Tan: The role of slabs on plume development S13

Other topics

Andrey Babeyko: Effect of frictional and viscous softening in the cruston the lithospheric-scale deformation in Central Andes

S14

Thorsten Becker: Constraints on the mechanics of the Southern San Andreas faultsystem from velocity and stress observations

S15

Susanne Buiter: Numerical models of the formation of extensional sedimentarybasins: sensitivity to rheology and surface processes

S16

Frederic Deschamps: Mantle tomography and its relation to temperature and composi-tion

S17

Boris Kaus: Eulerian spectral/finite difference method for large deformationmodelling of visco-elasto-plastic geomaterials

S18

Gabriele Marquart: Viscosity and S-wave conversion factor for the Earth’s mantle basedon CHAMP gravity data and new tomography models

S19

Michael Riedel: Modeling shear instabilities with block sliders: brittle and ductile S20

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Castle of Hruba Skala, Czech Republic, September 13–18, 2003 POSTER SESSIONS

Poster session, Monday, September 15


Posters can be displayed from Monday morning to Tuesday afternoon.

Mantle convection and chemical mixing

Gael Choblet: A cell model for mixed heating convection M01Hana Cızkova Generation of slab-like downwellings in a layered model with an in-

terface at a depth of 1000 kmM02

Caroline Dumoulin: Small-scale convection below oceanic lithospheres: scaling lawsof onset time, influence of transform faults and 3-D geometry

M03

Cinzia Farnetani: Seismic velocity anomalies and anticorrelation in the lowermostmantle: the role of chemical heterogeneities

M04

John Hernlund: Small-scale asthenospheric convection and cenozoic extensional tec-tonics of the basin and range province

M05

Satoru Honda: Small scale convection under the island arc? M06Yann Krien: The accommodation of volume changes in phase transition zones:

implications for mantle dynamicsM07

Claire Perry: Modelling continental roots in a convecting mantle M08Claudia Stein: A self-consistent mantle convection model: generation of a low-

viscosity zone and plate-like featuresM09

Jeroen van Hunen: Three-dimensional small scale convection below the oceanic litho-sphere

M10

Ludek Vecsey: Ultra-high Ra convection and applications of wavelet M11

Other topics

David Bercovici: The mantle transition-zone water filter model M12Miroslav Cada: Benchmark of numerical codes used for subduction modeling M13

John Hopper: Mantle melting during continental breakup M14Kristian Mueller: The effect of the stress field on the melt channel instability M15

Karen Niehuus: Geodynamic interpretation of temporal geoid variations M16Martin Pauer: Constraining Venus structure by gravity and topography: global

methods; Gravity field and topography of Venus: localization meth-ods

M17,18

9


Poster session, Wednesday, September 17


Posters can be displayed from Tuesday afternoon to Thursday morning.

Plumes and related phenomena

Attila Galsa: The number of hotspots in numerical models of mantle convection W01Saskia Goes: Synthetic seismic signature of thermal mantle plumes W02

Damien Jurine: Penetration of mantle plumes through the lithosphere W03Frank Lohman: Analogue and numerical modelling of sub-lithospheric plume-

breakout processesW04

Peter Mihalffy: The influence of the large-scale mantle flow field on the interactionof the mid-Atlantic ridge and the Iceland plume

W05

Marc Monnereau: Clustering of plumes and small-scale convection in the upper man-tle: consequences of lower-mantle plume dynamics

W06

Thomas Ruedas: The effect of hydrous melting on plume dynamics W07Harro Schmeling: Modelling crustal accretion above the Iceland plume W08

Balint Sule: The structure and the surface manifestation of mantle plumes indepth-dependent three-dimensional models

W09

Postglacial rebound

Andrea Antonioli: FE modeling of post glacial rebound with complex viscosity struc-ture

W10

Ondrej Cadek: Postglacial rebound with laterally variable viscosity W11Emanuele Casarotti: A synthetic fault system in a spherical and viscoelastic Earth model W12

Giulio Dal Forno: Finite elements modeling of postglacial rebound in North America:predominance of nonlinear creep

W13

Kevin Fleming: The influence of the rheology underlying Iceland on glacial isostaticadjustment

W14

Jan Hagedoorn: A time-domain method of implementing the sea-level equation inglacial-isostatic adjustment for a rotating Earth

W15

Ladislav Hanyk: Viscous heating in the mantle induced by glacial forcing W16Gilles Pelfrene: A model of kinetics effects in the transition zones: application to

the postglacial reboundW17

Hugo Schotman: Model sensitivity of GIA induced high resolution gravity anomaliesand geoid heights

W18

Paolo Stocchi: Using TABOO for postglacial rebound predictions W19

Other topics

Andrey Babeyko: 2.5-D thermomechanical modelling of the Dead Sea transform W20Thorsten Becker: Global azimuthal anisotropy from Rayleigh waves and flow models W21Ritske Huismans: Asymmetric lithosphere extension: factors controlling rift mode se-

lectionW22

Takashi Nakagawa: Effects of magnetic field and radioactive heating in the core onthermal evolution of the convecting mantle and core

W23

Ondrej Sramek: Melt extraction in two-phase flows W24

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Castle of Hruba Skala, Czech Republic, September 13–18, 2003 SUBMITTED ABSTRACTS

Submitted abstracts (in alphabetical order)

FE modeling of post glacial rebound withcomplex viscosity structure

Andrea Antonioli1, Spina Cianetti1,Carlo Giunchi1and Giorgio Spada2

1Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy2Istituto di Fisica, Universita di Urbino, Italy

The response of the Earth to the late Pleistocene ice sheetsmelting, is usually modeled by spherically symmetric mod-els. In this work we approach the GIA problem by FEmodeling in two stages. In the first we compute the post-glacial displacements for a 2D axis-symmetric Earth modelincluding a lithospheric thickening (craton), which consti-tutes the simplest departure from the 1D spherical symme-try. These computations are a necessary step to understandthe first order role of lithospheric depth variations and toperform benchmark comparisons with solutions provided byother research groups which employ spectral approaches.The effects of the craton on the displacement field aremainly evident during the relaxation following the ice melt-ing, as confirmed by previous findings. In the second stagewe present the preliminary results of our FE 3D models,where we employ a realistic ice distribution and we accountfor lateral variations of the lithospheric thickness and mantleviscosity constrained by the ocean-continent distribution.The relative sealevel curves for sites close to the margins ofthe ice load, such as New York, exhibit the larger sensitivityto the presence of lateral viscosity variations, as it occurs inthe 2D case. The direction of horizontal rates of displace-ment, which are currently monitored by geodetic surveys,are affected by the presence of lateral viscosity variationson large spatial scales.

Effect of slab dehydration on the mantlewedge dynamics in subduction zones

Diane Arcay1, Emmanuel Tric1and

Marie-Pierre Doin2

1Laboratoire Geosciences Azur, Universite de Nice-SophiaAntipolis, France

2Laboratoire de Geologie, Ecole normale superieure,

Paris, France

In oceanic subduction zones, dehydration of slab’s miner-als might partly explain back-arc spreading and its initia-tion within the volcanic arc. While the slab enters the as-thenosphere, it releases water which hydrates the astheno-sphere and might significantly decrease its viscosity. Thisshould develop the corner flow, and warm the overridinglithosphere. If the induced thermal erosion lasts, an exten-sive stress will locally appear.

In our dehydration modelling, the released water comesfrom the oceanic crust, and the altered peridotite of the slab.This peridotite is believed to be serpentinized at the mid-ocean ridge and along normal faults during bending nearthe trench, and can be 5 to 20 km thick. We use accuratephase diagrams for H2O-satured mantle peridotite and agabbroic crust to determine at each time step the amount of

water released or absorbed by each unit of rock. Transitionphases are supposed to be not metastable. We assume thatthe rock viscosity decrease depends on the concentration inwater. The viscosity of a H2O-satured asthenospheric rockis at least 100 times less than that of a dry one, at a pressureof 3 kbars (Hirth and Kohlstedt, 1996).

For cold subductions, simulations show a three-step de-hydration of the subducting lithosphere. The crust releasesits water at 74 km (blue schists destabilisation) and the toppart of peridotite at 150 km (chlorite destablisation). Inthe bottom peridotite part serpentine transforms into phaseA at 200 km whitout losing water. As P-T-t paths remainquite cold, only a small amount of water is liberated. How-ever this water seems to be sufficient to hydrate the over-lapping lithosphere over a significant volume (about 100km wide and 50 km high) and increases the mantle cornerconcentration in water. Introducing a decrease in viscos-ity associated to the hydrated corner, the viscosity contrastvisco(dry)/visco(wet) must be at least equal to 50 to obtaina developed thermal erosion. In these cases, the overlappinglithosphere is eroded on a wide region (between 151 and 271km of the trench) and deeply (about 50 km of eroded mate-rials). This specific position corresponding to the back-arcregion, with longer simulations it wouldn’t be impossible toobserve back-arc spreading in some cases of subduction.

Effect of frictional and viscous softening inthe crust on the lithospheric-scale

deformation in Central Andes

Andrey Yu.Babeyko and Stephan V. Sobolev

GeoForschungsZentrum Potsdam, Germany

The Altiplano plateau in the Central Andes is the secondgreatest plateau in the world after Tibet with an average el-evation of about 4 km formed as a result of ocean-continentcollision between subducting Nasca plate on the west andBrazilian shield on the east. According to the classicalIsacks (1988) scenario, the Cenozoic evolution of the plateaustarted ca. 30 Ma in response to the retreat of the flat-subducted Nasca plate. Astenospheric material, which re-placed the retreated plate, thermally thinned and soft-ened the overlying lithosphere. Continuing relative west-wards motion of the cold Brazilian shield was first accomo-dated by distributed shortening of the softened lithosphereof the present-day plateau (pure-shear mode of shorten-ing). However, at ca. 8–10 Ma deformation style abruptlychanged into a simple-shear mode. Upper crustal shorten-ing was ceased at the plateau and migrated eastwards, ontothe margin of the Brazilian shield, while the plateau itselfcontinued to grow due to the continuing shortening of itslower crust.

We employ numerical 2D thermomechanical modellingto test the above scenario and to evaluate key parameters,which account for the transition from pure- to simple-shearstyle of the lithosphere-scale deformation under pure-shearboundary condition. As numerical tool we use explicit finiteelement lagrangian code that originates from well-knownPARAVOZ. Material and historical properties are trackedby markers. The code is parallelized for sheared-memorymachines (OMP), MPI-paralellization is in progress.

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The starting model is composed of rheologically differ-ent layers representing sediments, felsic and mafic crust,lithospheric mantle, and astenosphere. Rheological lawsare Mohr-Coloumb elasto-plastic and Maxwell visco-elasticwith nonlinear power-law creep. Both plastic and viscoussoftening is implemented. Initial and boundary conditionssimulate thermal activation of the Altiplano lithosphere byupwelling astenosphere as well as its westward pushing bythe cold Brazilian shield with constant velocity.

We found that model shortening always occurs in a pure-shear mode unless the uppermost crust of the margin ofBrazilian shield becomes during the deformation consider-ably weaker than the Altiplano upper crust (drop of frictioncoefficient down to 0.05–0.1). Viscous softening in the mid-dle and lower crust of the plateau is not strictly required,but its presence gives more ”clear” simple-shear mode. Theweakening in the uppermost part of the Brazilian shield maybe attributed to pronounce plastic softening in the thicklayer of Paleozoic sediments covering the shield. The phys-ical mechanism of the abrupt and strong plastic softeningin sediments remains an open question. One explanationcould be fluid overpressure due to hydrocarbon generation.

2.5-D thermomechanical modelling ofthe Dead Sea transform

Stephan V. Sobolev1, Andrey Yu.Babeyko1,

Zvi Garfunkel2, Alexey Petrunin1andDESERT Working Group

1GeoForschungsZentrum Potsdam, Germany2Hebrew University, Jerusalem, Israel

The Dead Sea transform system (DST) is the boundarybetween the Arabian and African plates, where left-lateraltransform motion has largely accommodated the opening ofthe Red Sea basin during the last 15–20 My. General ge-ometry of the system is, to a first approximation, two andhalf dimensional, i.e., variations along the strike are muchsmaller than that across the transform. Taking this intoaccount, we extent the well-known two-dimensional explicitfinite-element code PARAVOZ to 2.5-D. We solve the full3-D system of conservation equations (momentum, mass,energy) assuming no variations along the third axis (d/dz= 0). This simplification allows us to perform calculationson a 2D-grid. Explicit calculation scheme allows us to oper-ate with realistic visco-elasto-plastic rheology of lithospherewithout any predefined faults. Faults are generated in aself-consistent way due to the strain localization processassociated with the strain softening in plastic deformationmode. Material and history properties are tracked by mark-ers. The algorithm was parallelized for sheared-memory ma-chines (OMP), MPI-paralellization is in progress.

Modelling results suggest that the DST lithosphericstructure is controlled by the plate-scale transform displace-ment within a relatively cold lithosphere. In such a litho-sphere, shear strain is localized in a narrow (20–40 km wide)vertical decoupling zone, which crosses the entire litho-sphere. In the upper crust the deformation localizes at oneor two major faults located at the top of this zone. The loca-tion of the vertical decoupling zone is controlled by the tem-perature of the uppermost mantle prior to the transform mo-tion. The lithospheric structure imaged along the DESERTseismic line is consistent with the 105 km transform motion

combined with less than 4 km transform-perpendicular ex-tension. Uplift of the Arabian Shield adjacent to the DSTcan be explained by young (< 20 Ma) thinning of the litho-sphere at and east of the plate boundary. Such lithosphericthinning is consistent with seismological observations aswell as with low present-day surface heat flow and withhigh temperatures derived from mantle xenoliths broughtup by Neogene-Quaternary basalts. The modelling sug-gests that the lithospheric thinning in the southern partof the DST have enabled transform motion at the DST bylowering the strength of the otherwise too strong Arabianlithosphere.

Constraints on the mechanics ofthe southern San Andreas fault systemfrom velocity and stress observations

Thorsten W. Becker1, Jeanne Hardebeck2andGreg Anderson3

1IGPP, SIO, UC San Diego, La Jolla, USA2USGS Menlo Park, USA3USGS Pasadena, USA

We use GPS and stress-orientation observations to studythe distribution of slip on the system of faults comprisingthe southern California plate boundary region. Of particu-lar interest is how slip is partitioned between the San An-dreas Fault (SAF), the San Jacinto Fault (SJF) and theEastern California Shear Zone. Some prior work placesthe majority of slip on the SAF. Other studies, however,find that the SJF accommodates much slip in the south,implying a low slip rate on the San Bernardino segment ofthe SAF.

Two new data sets are used to address this question.The first is the Southern California Earthquake Center’sgeodetic velocity field (version 3), which includes much im-proved coverage over prior models. The second is a regionalmap of stress field orientations at seismogenic depths, asdetermined from earthquake focal mechanisms. While GPSdata has been used in similar studies, this is the first appli-cation of stress field observations to this problem.

We construct a simplified version of the southern Cali-fornia fault system, and model the surface velocities usinga block model with elastic strain accumulation, followingMeade et al. (2002). Additionally, we model the stress ori-entations at seismogenic depths, assuming that the stressfield results from the loading of active faults. An inver-sion for fault slip rates is performed to simultaneously fitthe GPS and stress observations. The model fit to the datais good in general, indicating that a simple mechanicalmodel can capture both observed interseismic strain andstress accumulation. We evaluate the sensitivity of the sliprate solutions to the different datasets and identify ‘anoma-lous’ fault segments with stresses that deviate from our sim-ple loading model.

Global azimuthal anisotropy fromRayleigh waves and flow models

Thorsten W. Becker1, James B. Kellogg2, GoeranEkstroem2and Richard J. O’Connell2

1IGPP, SIO, UC San Diego, La Jolla, USA2EPS, Harvard University, Cambridge, USA

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We model the development of finite strain in three-dimensional mantle-circulation models and compare ourmodel predictions with azimuthal anisotropy as derivedfrom Rayleigh waves. The flow models are simplified; weuse a Newtonian viscosity that is only allowed to vary withdepth. However, the predicted circulation includes the effectof plate motions and density anomalies as derived from to-mography. Flow fields are thus representations of the large-scale upper mantle currents and either steady-state or evolv-ing with time based on tectonic reconstructions of plateboundaries. Differences in the predicted strain for thesetwo cases are small, however, since saturation strains of or-der unity accumulate in a few Myr at all but the shallowestdepths. By using synthetic anisotropy based on the flowcalculations as input for the Rayleigh wave inversions, weexplore the resolving power of the seismologic data. We es-tablish that structure can be resolved reliably and observedregional patterns are hence stable features of the inver-sion. The predicted longest axes of the finite-strain ellipsoid(FSE) from our flow models match the observed fast propa-gation orientations for anisotropy within most oceanic litho-sphere and some young continental regions well. We findthat alignment of seismically fast axes with the FSE leadsto substantially smaller deviations from observed anisotropythan alignment with absolute plate motions, as is commonlyassumed. Regions of large misfit might be indicating in-traplate deformation for which our geodynamic model doesnot yet account for. These findings lend support to the hy-pothesis that seismic anisotropy is due to lattice-preferredorientation (LPO) of olivine crystals due to shearing in non-trivial mantle flow. We further explore how the model pre-dictions are affected when the infinite strain axis (ISA) isconsidered alongside the FSE. The ISA was proposed byKaminski & Ribe (2002) as a high-strain, limit-case indi-cator for LPO as expected for a path-dependent treatmentof fabric development that includes dynamic recrystalliza-tion. Our models contribute to the verification of theoriesabout anisotropy formation and establish anisotropy as aquantitative indicator of mantle convection.

The mantle transition-zone water filtermodel

David Bercovici

Department of Geology and Geophysics, Yale University,

New Haven, USA

The chemical distinction between ocean island and mid-ocean ridge basalts (OIB and MORB, respectively) sug-gests that the mantle contains relatively isolated geochem-ical reservoirs which are due either to chemical layering orpoor mixing. All mantle-reservoir theories, however, intro-duce various problems of their own, and geochemical con-straints are often satisfied at the expense of seismologicaland geodynamical ones. Here we propose and explore analternative hypothesis that mantle convection is not layeredbut instead undergoes a filtering mechanism at the 410km-deep olivine-wadsleyite phase tranformation. We arguethat as the broad background of upwelling ambient man-tle (forced up by the downward flux of subducting slabs)moves out of the high-water-solubility transition zone (be-tween the 660km and 410km discontinuities) into the low-solubility upper mantle above 410km, it undergoes watersupersaturation and partial melting that removes water and

filters out incompatible elements; the remaining solid phasecontinues to ascend and supplies relatively dry and depletedmaterials to the MORB source region. The residual melt islikely denser than the surrounding solid and is thus trappedat the 410km boundary; however, slab entrainment providesan effective means for recirculating this enriched and hy-drated material back into the transition zone and lower man-tle. Mass balance (“box-model”) calculations predict thatsufficient melt is produced at 410km to filter incompatibleelements, and the resulting melt layer is of order 1-10kmthick. The filtering effect, however, is likely suppressed forhotter mantle plumes, because of lower transition-zone sol-ubility at higher temperature; the plumes would thereforegenerate more enriched OIBs. The filter mechanism couldalso have been suppressed globally in the hotter Archaeanduring peak crustal production, thereby allowing for chem-ically enriched continental crust. Observations suggestingseparate isotopic evolutions of MORB and OIB source re-gions could be explained by homogenization of mantle iso-topic signatures as the ambient upwelling passes through the410km melt zone, followed by several hundred million yearsof isolation as the solid-residue material rises slowly acrossthe upper mantle. Although segregation of incompatibleelements occurs, bulk elements and heat are transportedacross the mantle as if in whole-layer circulation, therebyavoiding the geophysical problems with layered convection(such as build up of internal thermal boundary layers andthe resulting anomalously strong plumes). Seismic evidencefor a melt zone above the 410km discontinuity provides par-tial support for our hypothesis. Overall, the transition-zonewater-filter model explains the chemical variability betweenocean islands and mid-ocean ridges, yet avoids the manyproblems of invoking isolated mantle reservoirs and layer-ing.

Seismic velocity and density anomaliesfrom subducted basalts

Craig R. Bina

Dept. of Geological Sciences, Northwestern University,

Evanston, USA

Products of chemical differentiation near the surface, suchas oceanic crustal basalts and gabbros, may be transporteddownward by subduction to give rise to chemical hetero-geneity at depth. In the shallow upper mantle, anhydrousmetabasalts (e.g., eclogites) should be slightly fast rela-tive to ambient peridotite mantle, with a signature aris-ing primarily from the thermal anomaly rather than com-position. Hydrous metabasalts (e.g., lawsonite blueschists,lawsonite eclogites), on the other hand, should be signifi-cantly slow in the 100-250 km depth range, becoming faster(e.g., stishovite eclogites) below 250 km. The propertiesof observed seismic reflectors along the upper surfaces ofsubducting slabs are consistent with phase relations in hy-drothermally altered basalts [Helffrich et al., 1989; Helffrich& Stein, 1993; Peacock, 1993; Hacker, 1996; Helffrich, 1996;Connolly & Kerrick, 2002].

In the lower mantle, anhydrous metabasalts (e.g., per-ovskitites) should be fast, growing progressively more sowith increasing depth. This signature arises from the com-positional contrast, as the temperature-dependence of seis-mic velocities falls with increasing depth in the lower man-tle, and the magnitude of temperature anomalies from sub-ducted material should also fall with increasing depth due

13


to thermal assimilation [Bina & Wood, 2000; Mattern etal., 2002; Bina, 2003]. Thus, subducted metabasalts canexplain many apparently fast seismic scatterers in the lowermantle, but how can some apparently slow scatterers (e.g.,at ∼1115 km) be explained [Kawakatsu & Niu, 1994; Niu& Kawakatsu, 1997; Hedlin et al., 1997; Kaneshima & Helf-frich, 1998, 1999; Vinnik et al., 1998, 2001; Castle & Crea-ger, 1999; Kruger et al., 2001; Niu et al., 2003]? Possiblecauses of such low velocity features include dense hydroussilicate phases and post-stishovite phases of free silica.

If dense hydrous phases persist to such depths, theymay decrease the predicted velocity anomaly (as in the caseof hydrous metabasalts in the upper mantle). However,dense hydrous silicates are unstable below ∼1200–1300 kmdepth [Shieh et al., 1998; Ohtani et al., 2001]. Furthermore,the elasticity of these phases appears to depend primarilyupon density rather than upon water content, so that anyassociated slow velocity anomalies should be small [Angelet al., 2001]. Thus, significantly slow seismic anomalies inthe lower mantle may be difficult to generate from densehydrous silicate phases in subducted material.

An unusual shear-mediated phase transition in silica,from rutile-structured stishovite to a CaCl2-structuredphase, occurs at high pressures. As a result, the shear mod-ulus of SiO2 should drop by ∼20 % in the pressure interval∼40–47 GPa before rising again subsequently [Karki et al.,1997; Shieh et al., 2002]. This transition thus has the po-tential to generate slow VS anomalies in the ∼1200–1500km depth range which are accompanied by positive den-sity anomalies but small VP anomalies, in accord with re-cent seismic observations below 1100 km [Niu et al., 2003].At greater depths, such high-pressure silica phases maybe expected to yield fast anomalies. It has recently beensuggested, however, that mantle temperatures may possi-bly depress this transition in silica to greater depths, per-haps ∼1900 km, rendering it unsuitable to explain veloc-ity anomalies at shallower levels [Ono et al., 2002]. Thus,the temperature-dependence of this transition pressure insilica remains an important topic for further study. In sum-mary, slow shear velocity anomalies at ∼1200–1500 km mayarise from a post-stishovite phase change in silica (as maylarge fast anomalies at greater depths) unless dP/dT forthe transition proves to be large.

It is important to note that both fast and slow anoma-lies in material subducted into the lower mantle arise largelyfrom the presence of free silica in metabasaltic mineralo-gies. Hence, such anomalies depend upon the survival offree silica phases, which are unstable in contact with the sur-rounding peridotite. In the lower mantle, for example, silicareacts with ferropericlase to form perovskite. Thus, thesemetabasalt mineralogies (free silica + perovskite) can per-sist only to the extent that they are preserved as armoredrelics (with perovskite rinds) from contact with surround-ing metaperidotite (perovskite + ferropericlase). Therefore,high temperatures and efficient mixing in the deep mantlemay induce decay in such velocity anomalies, due not onlyto volumetric averaging but also to chemical reaction.

Subducted metagabbro/basalt should remain negativelybuoyant (relative to peridotite) throughout the lower mantle[Bina & Wood, 2000; Mattern et al., 2002; Bina, 2003; Mat-tern, pers. comm. 2003; Ohtani et al., 2003]. While it hasbeen suggested that an abundance of low-density (Ca-ferritestructured) Na-Al phase in sodic compositions may allow fordensity crossover (to neutral buoyancy) near ∼1500–2000

km [Ono et al., 2001], high-pressure alkali phase behaviorremains a complex puzzle for further study [Miyajima et al.,2001].

References:

Angel R. J., Frost D. J., Ross N. L. and Hemley R. (2001)Stabilities and equations of state of dense hydrous magne-sium silicate. Phys. Earth Planet. Inter. 127, 181–196.

Bina C.R. (2003) Seismological constraints upon mantlecomposition. In Treatise on Geochemistry, Elsevier Science,in press.

Bina C.R. and Wood B. J. (2000) Thermal and composi-tional implications of seismic velocity anomalies in the lowermantle. Eos Trans. AGU 81 (22), Western Pacific Suppl.,WP193-WP194, Abstract T32B-03.

Castle J. C. and Creager K.C. (1999) A steeply dip-ping discontinuity in the lower mantle beneath Izu-Bonin.J.Geophys. Res. 104, 7279–7292.

Connolly J. A.D. and Kerrick D.M. (2002) Metamorphiccontrols on seismic velocity of subducted oceanic crust at100–250 km depth. Earth Planet. Sci. Lett. 204, 61–74.

Hacker B. R. (1996) Eclogite formation and the rheology,buoyancy, seismicity, and H2O content of oceanic crust. InSubduction Top to Bottom (eds. G. Bebout, D. Scholl, S.Kirby and J. Platt), pp. 337–346. AGU Geophys. Monog.96.

Hedlin M.A.H., Shearer P.M. and Earle P. S. (1997)Seismic evidence for small-scale heterogeneity throughoutthe Earth’s mantle. Nature 387, 145–150.

Helffrich G. (1996) Subducted lithospheric slab velocitystructure: Observations and mineralogical inferences. InSubduction Top to Bottom (eds. G. Bebout, D. Scholl, S.Kirby and J. Platt), pp. 215–222. AGU Geophys. Monog.96.

Helffrich G. and Stein S. (1993) Study of the structure ofthe slab-mantle interface using reflected and converted seis-mic waves. Geophys. J. Int. 115, 14–40.

Helffrich G., Stein S. and Wood B. J. (1989) Subduc-tion zone thermal structure and mineralogy and their re-lationship to seismic wave reflections and conversions atthe slab/mantle interface. J.Geophys. Res. 94, 753–763.

Kaneshima S. and Helffrich G. (1998) Detection of lowermantle scatterers northeast of the Mariana subduction zoneusing short-period array data. J.Geophys. Res. 103, 4825–4838.

Kaneshima S. and Helffrich G. (1999) Dipping low-velocitylayer in the mid-lower mantle: Evidence for geochemical het-erogeneity. Science 283, 1888–1892.

Karki B.B., Stixrude L. and Crain J. (1997) Ab initioelasticity of three high-pressure polymorphs of silica. Geo-phys. Res. Lett. 24, 3269–3272.

Kawakatsu H. and Niu F. (1994) Seismic evidence for a920-km discontinuity in the mantle. Nature 371, 301–305.

Kruger F., Banumann M., Scherbaum F. and Weber M.(2001) Mid-mantle scatterers near the Mariana slab detectedwith a double array method. Geophys. Res. Lett. 28, 667–670.

Mattern E., Matas J. and Ricard Y. (2002) Computing den-sity and seismic velocity of subducting slabs. Eos Trans.AGU 83 (47), Fall Meet. Suppl., Abstract S51A-1011.

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Miyajima N., Yagi T., Hirose K., Kondo T., Fujino K.and Miura H. (2001) Potential host phase of aluminum andpotassium in the Earth’s lower mantle. Amer. Mineral. 86,740–746.

Niu F. and Kawakatsu H. (1997) Depth variation ofthe mid-mantle seismic discontinuity. Geophys. Res. Lett.24, 429–432.

Niu F., Kawakatsu H. and Fukao Y. (2003) Seismic evi-dence for a chemical heterogeneity in the mid-mantle: Astrong and slightly dipping seismic reflector beneath the Mar-iana subduction zone. J.Geophys. Res., in press.

Ohtani E., Sano A., Litasov K., Kubo T. and Kondo T.(2003) Phase transformation in wet oceanic crust and sub-duction dynamics of the slab. Goldschmidt Conference Ab-stracts 2003, A354.

Ohtani E., Toma M., Litasov K., Kubo T. and Suzuki A.(2001) Stability of dense hydrous magnesium silicate phasesand water storage capacity in the transition zone and lowermantle. Phys. Earth Planet. Inter. 124, 105–117.

Ono S., Hirose K., Murakami M. and Isshiki M. (2002)Post-stishovite phase boundary in SiO2 determined by insitu X-ray observations. Earth Planet. Sci. Lett. 197, 187–192.

Ono S., Ito E. and Katsura T. (2001) Mineralogy ofsubducted basaltic crust (MORB) from 25 to 37 GPaand chemical heterogeneity of the lower mantle. EarthPlanet. Sci. Lett. 190, 57–63.

Peacock S. M. (1993) The importance of blueschist eclog-ite dehydration reactions in subducting oceanic crust.Geol. Soc. Am.Bull. 105, 684–694.

Shieh S.R., Duffy T. S. and Li B. (2002) Strengthand elasticity of SiO2 across the stishovite-CaCl2-typestructural phase boundary. Phys. Rev. Lett. 89 (25),doi:10.1103/PhysRevLett.89.255507.

Shieh S.R., Mao H.K., Hemley R. J. and Ming L.C.(1998) Decomposition of phase D in the lower mantle andthe fate of dense hydrous silicates in subducting slabs. EarthPlanet. Sci. Lett. 159, 13–23.

Vinnik L., Kato M. and Kawakatsu H. (2001) Search forseismic discontinuities in the lower mantle. Geophys. J. Int.147, 41–56.

Vinnik L., Niu F. and Kawakatsu H. (1998) Broad-bandconverted phases from midmantle discontinuities. EarthPlanets Space 50, 987–990.

Numerical models of the formation ofextensional sedimentary basins: sensitivity

to rheology and surface processes

Susanne Buiter, Ritske Huismans and ChristopherBeaumont

Geodynamics Group, Department of Oceanography,

Dalhousie University, Halifax, Canada

Extensional sedimentary basins are an expression of locali-sation of crustal deformation during extension of continentallithosphere. The geometry of extensional basins can evolvein a symmetric or asymmetric manner, which in a purelykinematic description would result from pure shear or simpleshear, respectively. Here we use dynamic models to studyfactors controlling the geometrical evolution of extensional

sedimentary basins. We focus specifically on the effectsof crustal rheology, strain softening of the frictional-plasticcrust, and sedimentation and erosion.

For our experiments we use a thermo-mechanical nu-merical model on a crustal scale. All materials have aviscous-plastic rheology where brittle behaviour is governedby the frictional-plastic Coulomb criterion and viscous flowfollows a temperature-dependent creep law for quartz. Vari-ations in crustal strength are obtained by scaling the vis-cous creep law or through changes in the extension velocity.Shear zones develop dynamically (i.e., are not prescribed)and can weaken through strain softening of the frictional-plastic crustal material. The models are isostatically com-pensated through flexure of an underlying elastic beam.

Our models show how extension of the continental crustleads to the formation of sedimentary basins bounded bynarrow shear zones. An asymmetric basin geometry is pro-moted by a weak lower crust and frictional-plastic strainsoftening. Extension of weak crust with a thin frictional-plastic domain is compensated by upwelling of the lowercrust. This causes an outward propagation of small half-graben basins. A strong (i.e., frictional-plastic) crust leadsto the formation of a deep, initially symmetric, sedimen-tary basin. In general, we observe that if sedimentation isincluded basins tend to be narrower and deeper. Our re-sults illustrate that surface processes have the potential toinfluence crustal tectonics directly.

Benchmark of numerical codes used forsubduction modeling

Miroslav Cada1, Gabriele Morra1,Fabio A. Capitanio1, Klaus Regenauer-Lieb2,

Saskia Goes1, Louis Moresi3andDomenico Giardini1

1Institute of Geophysics, ETH Hoenggerberg, Zurich,Switzerland

2CSIRO Division of Exploration and Mining, Bentley, Australia3School of Mathematical Sciences, Monash University, Clayton

Victoria, Australia

Modeling of subduction has long been attempted with var-ious numerical codes, each with its own limitation. Fromthe numerical point of view, a self-consistent model of asubducting slab is very challenging. We do not have fullknowledge of slab rheology, i.e. the dominance of differ-ent creep mechanisms and the role of elasticity. Differentassumptions on the controlling factors of lithosphere rhe-ology have resulted in development of different numericalcodes. Most of the codes were developed to simulate mantleconvection, focusing on sharp viscosity variations and, re-cently, plasticity. However, the rheology of the lithosphereis different from the mantle. New results have shown theimportance of elasticity for modeling lithosphere dynamics.

To document the strength and limitations of differentapproaches a benchmark comparison was proposed at theGeodynamical Workshop in September 2002 at the ETHZurich. Here we compare codes comprising commercialpackages and university-developed codes. We use a simplegeometrical setup published on http://www.Geobench.org.We compare passive subduction of a purely viscous rheol-ogy with a prescribed or thermally controlled density field.Four codes were used namely: ELLIPSIS, a particle-in-cell

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finite element code based closely on the standard finite ele-ment method, a finite-volume multigrid code based on themethod developed by Trompert and Hansen (1996 [1]), AN-SYS/Flotran a fluid-dynamic commercial code (CFD) andABAQUS Explicit an Arbitrary Lagrangian Eulerian (ALE)commercial code.

References:

[1] R.Trompert and U.Hansen, The application of a finitevolume multigrid method to three-dimensional flow prob-lems in a highly viscous fluid with variable viscosity, Geo-phys. Astrophys. Fluid Dynamics, 83: 261–291, 1996.

Postglacial rebound with laterally variableviscosity

Ondrej Cadek1and Luce Fleitout2

1Department of Geophysics, Charles University, Prague, CzechRepublic

2Ecole normale superieure, Paris, France

We present a new time-domain spectral method to modelviscoelastic deformation of spherical Earth with a 3-dimensional (3d) viscosity structure. The method gives sta-ble results for lateral contrasts in viscosity up to 2-3 ordersof magnitude. The use of the method is especially efficientfor cut-off degree < 100, thus for a low and intermadiateresolution modeling. We apply the method to investigatethe effects of viscosity changes associated with lateral vari-ations of the lithospheric thickness. Comparison of relativevertical displacements predicted for various 1d and 3d vis-cosity models suggests that the postglacial uplift is mainlysensitive to the viscosity profile below the observing siteand basically insensitive to the lateral viscosity variationsin the remote areas. This indicates that the traditional in-versions of the uplift data for 1d viscosity may give correctresults provided that the data come from a region of con-stant lithospheric thickness and they were obtained suffi-ciently far from the border between the lithospheric blocksof different thickness.

A synthetic fault system in a sphericaland viscoelastic Earth model

Emanuele Casarotti and Antonio Piersanti

Instituto Nazionale di Geofisica e Vulcanologia, Roma, Italy

In order to improve the knowledge about the fault interac-tion at long distances due to the postseismic stress trans-fer, we have developed a synthetic fault system based on aspherical, viscoelastic, selfgravitating Earth model. Thoughseismicity in our simulation is controlled mainly by tectonicloading, our results highlight the significant role played bypostseismic stress transfer in assessing the spatio-temporalpattern of the earthquakes.

A cell model for mixed heating convection

Gael Choblet

Planetologie et Geodynamique, Universite de Nantes, France

Solid-state thermal convection in planetary mantles is gen-erated by both volumetric heating (radiogenic elements, sec-ular cooling, tidal heating) and heating from below (coolingof the metallic core). However, the relative importance ofplumes emanating from both boundary layers and their in-teraction is yet poorly understood. A simple scaling canbe achieved for fluid layers bounded by rigid horizontal sur-faces, based on the observation that the structure of the topcold boundary layer does not depend on the heating distri-bution but simply on the global amount of heating (internalplus basal). In the case of free-slip boundaries, however,variations of the relative bottom heat flux (0: pure volu-metric heating; 1: pure basal heating) induce modificationsin the cold boundary layer that may have a significant in-fluence on the geological history of the planet.

The proposed scaling is based on the classical boundarylayer theory for a 2D cell structure, modified in order to takeinto account the heating distribution: the cell’s rotation cen-ter is shifted toward an upper corner due to an asymmetryof the flow (cold plumes associated with a larger velocitythan hot ones when internal heating is present); the heat-ing of plumes during their ascent/descent is also modeled; inaddition, the asymmetry due to a different impact of the im-pinging plume on the boundary layer is also described. Therelationships issued from the derivations mentioned aboveproduce an efficient framework to analyze numerical resultscarried out in a 2D Cartesian geometry.

— INVITED —Convection in the Earth’s core from

the perspective of a mantle convectionmodeller

Ulrich Christensen

Max-Planck-Institut fur Aeronomie, Katlenburg-Lindau,

Germany

During the past eight years numerical simulations of the geo-dynamo found a lot of attention and the field has attractedresearchers also from the mantle convection community.The time delay of 25 years in the development of the twofields has several reasons. Most important is that Cowling’stheorem does not allow the generation of purely axisymmet-ric magnetic fields by self-sustained dynamo action. Hencea self-consistent dynamo model must be three-dimensionalfrom the outset. While mantle flow is simply governed byStokes law, i.e. a balance between buoyancy and viscousfriction, the force balance for core flow is much more com-plex. Inertia cannot be neglected on short time scales al-though it is not of prime importance. The Coriolis forceplays a key role in structuring the flow and is balanced bythe electromagnetic Lorentz force to first order. Viscousforces are almost negligible in the core, which creates largeproblems for the stability of numerical methods. Because ofthe competing symmetries of buoyancy forces (radial) andCoriolis forces (axial), spherical models are essential. Planelayer dynamo models, which are computationally simpler,miss important aspects. In addition to the familiar (in man-tle convection) advection-diffusion equation for temperaturand/or composition, a similar equation must be solved forthe magnetic field (i.e. for a vector rather than a scalar).While the fundamental physical laws governing core flow aremore complex than those for mantle convection, complexi-ties of the material properties that are very important for

16


mantle rock, such as the strong temperature dependence ornonlinearity of viscosity, are irrelevant in liquid iron.

Mantle convection models can today be calculated atthe appropriate parameter values (correct Rayleigh number)even in 3D, but this is not possible for core convection. Keyparameters, such as the Ekman number describing the ra-tio of viscous forces to the Coriolis force or the magneticPrandtl number, the ratio of viscosity to thermal diffusiv-ity, are off by many orders of magnitude. As a consequencethe hierarchy of forces acting on the flow is not necessarilythe same in the models as it is in the Earth’s core and re-sults must be interpreted with care. Dynamo models havebeen calculated with two different purposes in mind. Oneis the fundamental understanding of how magnetic field isgenerated, in particular the dominant dipole part. Herethe helical structure of the convective flow in columns thatare aligned with the rotation axis seems to play the key role.Another aim is to reproduce the characteristic structure inspace and time of the geomagnetic field as faithfully as possi-ble. Some models are successful to a surprising degree. Theycreate not only a dipole-dominated field of about the rightstrength but also agree in the characteristic morphology ofthe multipole components and exhibit stochastic dipole re-versals closely resembling to what is known for the Earthfrom paleomagnetism. Given the discrepancies in modelparameters it is not clear if the agreement is fortuitous orif this indicates that the models contain all the essentialphysics nonetheless.

Mantle flow and core convection meet at the core-mantleboundary. Their interaction is predominantly thermal. Thecore is the slave and the mantle is the master who imposesa condition of non-uniform heat flow on core convection.Non-zonal differences in heat flow break the axial symme-try of the dynamo and should lead to a longitudinal bias inthe statistical properties of the geomagnetic field. The ques-tion whether deviations from axisymmetry exist in the time-average geomagnetic field or in the distribution of paths ofthe virtual geomagnetic pole during reversals is discussedcontroversally in the paleomagnetic community. Dynamomodels, in which the pattern of heat flow is related to seis-mic velocities anomalies in the lowermost mantle from to-mography, predict longitudinal differences in geomagneticproperties in agreement with suggested pattern from pale-omagnetic data. If this can be substantiated it would sup-port a thermal rather than a compositional interpretationof seismic velocity anomalies in the D”-layer.

Generation of slab-like downwellings ina layered model with an interface at

a depth of 1000 km

Hana Cızkova and Ctirad Matyska

Department of Geophysics, Charles University, Prague, Czech

Republic

We investigate the stability of hypothetical layered convec-tion in the mantle and the mechanisms how the downwellingstructures originating in the lower layer are generated. Thestability is studied by means of numerical simulations of thedouble-diffusive convection in a 2-D spherical model with ra-dially dependent viscosity. We demonstrate that the stabil-ity of the layering strongly depends not only on the densitycontrast between the layers but also on the heating mode

and the viscosity profile. In the case of the classical Boussi-nesq model with an internally heated lower layer, the densitycontrast of about 4 % between the compositionally differentmaterials is needed for the layered flow to be maintained.The inclusion of the adiabatic heating/cooling in the modelreduces the temperature contrast between the two layersand, thus, enhances the stability of the layering. In thiscase, a density contrast of 2–3% is sufficient to preservethe layered convection on a time scale of billions of years.The generation of the downvelling structures in the lowerlayer occurs via mechanical or thermal coupling scenarios.If the viscosity dependent on depth and average temper-ature at each depth is considered, the low viscosity zonedevelops at a boundary between the two convecting layerswhich suppresses mechanical coupling. Then the downvel-ling structures originating in the lower layer develop beneathupper layer subductions, thus resembling continuous slab-like structures observed by seismic tomography.

— INVITED —Mantle chemical evolution:

constraints and models

Nicolas Coltice

Universite Claude Bernard Lyon 1, France

Progresses in geochemistry, geophysics and numerical mod-eling have significantly improved our understanding of man-tle convection. Though, the chemical structure and evo-lution of the mantle still remain puzzling problems. Somegeophysical and geochemical data cannot be unambiguouslyinterpreted and the physics of mantle differentiation is notwell understood. In this context, several end-member mod-els of mantle dynamics have been proposed and some havebeen partly tested through numerical models.

Reviewing and criticizing the data is the first step toestablish a set of constraints on the evolution of the mantle.The second step is to use modeling to focus on the relevantphysics and parameters of the problem. The last step is tolook back at the data and to identify future observationsneeded to better constrain mantle models. Following thisprocedure shows that, today, the major limitation towardsan accurate modeling of mantle chemical evolution is ourlack of understanding of early Earth history.

Finite elements modeling of postglacialrebound in North America:

the predominance of nonlinear creep

Giulio Dal Forno, Paolo Gasperini andEnzo Boschi

Dipartimento di Fisica, Universita di Bologna, Italy

Several finite elements simulations of postglacial reboundwe run, showed how the employment of a composite (lin-ear plus nonlinear) mantle rheology (Gasperini et al., 1992)could reproduce Relative Sea Level (RSL) time histories inNorth America more accurately than a pure linear rheol-ogy. Moreover, the power-law creep component came outto account for 55% up to 85% of the total strain-rate dur-ing the numerical analysis (Fig. 1). We evaluated modelsreproduction of RSL sequences through a chi-square anal-ogous statistics (Wu, 1999) and we tested fitting improve-ment significance of composite rheology by the analysis ofvariance.

17


−18000 −16000 −14000 −12000 −10000 −8000 −6000 −4000 −2000 00

200000

400000

600000

800000

1e+006

1.2e+006

1.4e+006

1.6e+006

TIME (yr)

EFF

EC

TIV

E S

HE

AR

ST

RE

SS (

Pa)

STRESS VARIATION AT 670 KM OF DEPTH IN THE AXIAL REGION

1.7110x106−18000 −16000 −14000 −12000 −10000 −8000 −6000 −4000 −2000 0

0

10

20

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70

80

90

100

PER

CE

NT

AG

E O

F N

ON

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EA

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OM

PON

EN

T(%

)

Fig. 1: Stress induced in the mantle by glacial forcing. Thesolid line represents the effective shear stress produced byglacial forcing during our simulation at the depth of 670

Km; the dash-dotted line, instead, the percentage ofnonlinear component we estimated for the model having

σB = 1.6 MPa and σT = 1.5 MPa.

The main limit of the whole modeling procedure is the ax-ially symmetric geometry together with the restriction oftested datasets to RSL variations. Thus we are currentlyimplementing 3D flat models having rheological parame-ters values in ranges which better performed in axisym-metric analysis; at this stage the best-fitting linear modelperformed strongly better than the corresponding axisym-metric model, while the improvement was much smaller forcomposite rheology. This difference with respect to the ax-isymmetric results can be partially ascribed to the fact thatlocal time histories of the glacial model ICE-3G (Tushing-ham and Peltier, 1991, 1992) were deduced under the as-sumption of a linear mantle rheology and thus the lattercould overfit the deglaciation details especially in the pe-riphery of the ice load. Furthermore, we did not exploredthe full parameter space of composite rheology for the tridi-mensional case. However, the slightly better fit (Fig. 2)of the composite rheology appears to confirm the findingsobtained in axially symmetric geometry.

1020

1021

1022

1023

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30

40

50

60

70

80

VISCOSITY(Pas)

CH

I−SQ

UA

RE

(1.9x1021, 8.1) (5.5x1021, 7.9)

Fig. 2: Chi-square values versus viscosity for linear (dashedline) and composite (solid line) models.

— INVITED —Experimental investigation of mantle

convection and mantle mixing

Anne Davaille

Laboratoire de Dynamique des Systemes Geologiques,

IPG Paris, France

The surface of terrestrial planets shows signatures ofstrongly episodic phenomena such as intense volcanism(e.g. Mars, Venus and Earth), complete resurfacing(Venus), plate tectonics and continental growth (Earth).On the other hand, geochemical and sismological data showthat the Earth’s mantle is also heterogeneous in composi-tion, density, and viscosity, on a wide range of lengthscales.To explain those phenomena, we therefore need a betterunderstanding of the convective dynamics of a planetarymantle. Thermal convection is known to produce episod-icity (e.g. transient 3D cells, plumes), which is furtherenhanced by the presence of an endothermic phase tran-sition, or when the fluid is heterogeneous. However, strongepisodicity, or/and generation of sharp interfaces and finescale motions are still difficult to study systematically withnumerical methods. Hence, laboratory experiments, usinganalogous fluids such as aqueous polymers and sugar syrups,offer a good complement to numerical and theoretical stud-ies, being a good tool to map and characterize the differentregimes of thermal convection and mixing.

Since Plate Tectonics-like convection remains to be pro-duced in a laboratory, this review focuss on the generation ofupwellings in a mantle with various initial degree of hetero-geneities, and the figures of mixing which can be generated.In a homogeneous mantle, we shall see that the classicalimage of a plume with a long conduit connecting its sourcein a bottom thermal boundary layer, to the lithosphere isvalid only during a short time compared to the entire life ofthe plume. Scaling laws further show that the typical life-time of hotspots produced by such plumes should be under40–50 Myr. To create fixed, long-lived plumes, a mecha-nism to anchor them is needed. A fluid initially stratifiedin density and viscosity is capable of producing such long-lived features, a well as more episodic and dramatic motions,depending on the buoyancy ratio B (ratio of the stabiliz-ing chemical density anomaly to the destabilizing thermaldensity anomaly). Indeed, two regimes are found: at highB, convection remains stratified and fixed, long-lived ther-mochemical plumes are generated at the interface; whileat low B, hot domes oscillate vertically through the wholetank while thin tubular plumes can rise from their uppersurfaces. Under certain conditions, the initial configura-tion can even be completely reversed. Scaling laws derivedfrom laboratory experiments allow predictions of a numberof characteristics of the convective features, such as theirgeometry, size, thermal structure, and temporal and chem-ical evolution. Convection acts to destroy the stratificationthrough mechanical entrainment and instabilities. There-fore, both regimes are transient and a given experiment canstart in the stratified regime, evolve towards the domingregime, and end in well-mixed classical one-layer convection.In a heterogeneous fluid, figures of mixing are complicated,since convection creates compositional heterogeneities withtwo different typical size and topology: (a) thin filamentsare generated by mechanical entrainment through viscouscoupling, either in the thermochemical plumes on top ofthe domes, or during the doming sequence. The two initialreservoirs therefore quickly become ”marble cakes”, eventhough they remain dynamically separated for a long time.(b) domes, and blobs encapsulated in the domes, are gener-ated by instabilities.

Those fluid mechanics results will then be applied toplanetary mantle convection, in an attempt to explain 1)

18


the present-day global tomographic images, 2) the episodicgeneration of intense volcanism, such as hot spots and floodbasalts, on Venus, Mars and Earth, and 3) the resurfacingof Venus.

Consequences of different rheologies onnumerical models of subduction

Roberta De Franco and Rob Govers

Faculty of Earth Sciences, Utrecht University,

The Netherlands

In a subduction process, the collision of two continents mayresult in one of two different modes; either the subductedslab breaks off and the plate boundary ceases to be ac-tive or the plate boundary reorganizes to continue plateconvergence. Our aim is to use a 3D numerical model toidentify the parameters that act as the switches betweenthe two different modes of collision, and to test them inthe Timor region, where continental collision is occurringfollowing subduction of Tethyan oceanic lithosphere. Toinvestigate the subduction process we use finite elementmodels that solves mechanical equilibrium, diffusion anddiffusiom-advection heat equations in a Lagrangian domain.The first problem that we address is how different rheologiesaffect the subduction process. In this preliminary step weinvestigate a simpler 2D model in which the oceanic thin-ner lithosphere is subducting under a continental plate. Wedid that using different rheologies. We put particular at-tention on the role of the viscosity which is in some casestemperature and stress dependent.

Mantle tomography and its relation totemperature and composition

Frederic Deschamps and Jeannot Trampert


The Netherlands

A method is provided to constrain lateral variations oftemperature and composition in the lower mantle fromglobal tomographic models of shear- and compressional-wave speed. We assume that the lower mantle consists ofa mixture of perovskite and magnesio-wustite, and we usedrecent mineral physics data together with a careful equa-tion of state modeling to compute sensitivities of velocitiesto temperature and composition. In a first stage, we directlyinvert VP- and VS-anomalies for variations of temperatureand composition, using the appropriate sensitivities of ve-locities to temperature and composition. However, uncer-tainties in the tomographic models and in the sensitivitiesare such that variations in composition are not robust. Atpresent knowledge, a deterministic determination of lateralvariations of temperature and composition seems thereforeunfeasable. We then turn to a statistical approach, whichallow us to infer some robust features. We compute syn-thetic histograms of the ratio R of the relative shear-to-compressional velocity anomalies for a large variety of cases,including different combinations of the anomalies of temper-ature and composition. Comparisons of these complete his-tograms (not only averages) with those predicted by globaltomography show that the origin of seismic anomalies can-not be purely thermal. In the bottom of the mantle, strong

anomalies of composition, due to changes in the amount ofperovskite and/or iron, are clearly present. The ratio Ralone is however unable to resolve all existing trade-offs be-tween anomalies of temperature and composition. An accu-rate determination of temperature and composition requiresknowledge of density variations. We show that anomaliesof iron can be resolved from the additional analysis of his-tograms of the relative shear-velocity to density anomalies.Preliminary comparison with robust observed histogramsobtained using a neighbourhood algorithm suggest that ironanomalies ±2 % at the bottom of the mantle.

Small-scale convection below oceaniclithospheres: scaling laws of onset time,influence of transform faults and 3-D

geometry

Caroline Dumoulin1, Marie-Pierre Doin2,Diane Arcay2and Luce Fleitout2

1Laboratoire de Planetologie et Geodynamique,Universite de Nantes, France

2Ecole normale superieure, Paris, France

Numerical simulations of two-dimensional Rayleigh-Benardconvection are designed to study lithospheric cooling abovea convective mantle. We model transient lithospheric cool-ing by imposing a zero temperature at the surface ofthe mantle with an initially homogeneous temperature. Astrongly temperature-dependent viscosity fluid is heatedfrom within, in order to avoid internal temperature drift.For a while the lithosphere cools approximatively as a con-ductive half-space and lithospheric isotherms remain flat.As instabilities progressively develop at the base of the litho-sphere, lithospheric cooling departs from the half-spacemodel.

We propose two different parameterizations of the ageof the first dripping instability, using boundary layermarginal stability or quantifying the characteristic timescaleof the exponential growth of instabilities as a functionof the Rayleigh number and of the viscous temperaturescale.Both account very well for our numerical estimates ofonset times, within their error bounds. The absolute valueof the onset time depends on the amplitude and locationof initial temperature perturbations within the box, and onthe initial temperature structure of the thermal boundarylayer.

Furthermore, thermal perturbations of finite amplitudelocated within the lithosphere (such as the ones inducedby transform faults, for example) strongly reduce the ageof the first dripping instability. This study emphasizesthe role of the lithospheric isotherms topography on the de-velopment of instabilities. To developp our analyse, a workin collaboration with G. Choblet (University of Nantes) isstarted. We will use a 3-D convection code in order to studythe influence of transform faults, and therefore lithosphericisotherms topography, on small-scale convection.

The dynamics of the slab rollback effect

Alwina Enns1, Harro Schmeling1andThorsten W. Becker2

1Institute of Meteorolgy and Geophysics,J.W.Goethe-University Frankfurt am Main, Germany

2IGPP, SIO, UC San Diego, USA

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Subduction influences plate tectonics by modifying the sur-face area and velocities of plates, and plates connected toslabs move faster than plates without slabs. Most of the sub-duction zones on Earth show the trench retreat effect, whichinfluences the subduction process and geologic deformationat the surface. To investigate the trench retreat effect weused the 2D finite differences code FDCON (Schmeling &Marquart, 1993). In order to start subduction, we as-sumed that initially one edge of the subducting plate dipsinto the mantle. An overriding plate was not included inthe models. The models are isotherm and viscous (Stokesflow) with a visco-plastic subducting lithosphere. The plas-tic rheology of the plate is described by the Byerlee law,mimicking brittle deformation in the shallow lithosphere.The density and viscosity of the mantle and the lithosphereare advected with the tracer approach. We used periodicand reflective free slip boundary conditions. Numerical ex-periments were done to analyze the relationship betweenthe trench retreat and various subduction parameters us-ing different viscosity structures: (1) homogeneous mantleviscosity and (2) stratified viscosity to model the upper andthe lower mantle. The viscosity of the plate and the mantle,the thickness and the length of the lithosphere were varied.We found that the flow in the lower part of the model box forthe models with periodic and reflective boundary conditionsinfluences the way in which the slabs are folded. For thetrench retreat, we observed that it depends predominantlyon the viscosity of the mantle, rather than on the viscosityof the slab. The velocity of trench retreat decreases whenthe slab touches the boundary between the upper and lowermantle.

Seismic velocity anomalies andanticorrelation in the lowermost mantle:

the role of chemical heterogeneities

Henri Samuel, Cinzia G. Farnetani andDenis Andrault

Institut de physique du globe de Paris, France

Recent seismological observations cannot be explained bythermal anomalies alone, but suggest the existence of chem-ical heterogeneities in the lowermost mantle. Our objectifis to investigate the dynamics of chemically denser mate-rial and to constrain its composition by using seismologicalobservations.

We solve the equations governing convection of a com-pressible viscous fluid, and use active tracers to modelchemically denser heterogeneities. We consider a twophases mantle: (Fe,Mg)SiO3 perovskite + (Fe,Mg)O mag-nesiowustite and assume that the reference mantle has apyrolitic composition. For the denser material we inves-tigate a plausible range of mineralogical compositions byvarying: (i) the silica molar ratio, (ii) the iron molar ra-tio, (iii) the iron-magnesium partition coefficient betweenperovskite and magnesiowustite.

The calculated seismic velocity anomalies for P- and Swaves and for the bulk sound speed are compared with seis-mic observations. Moreover, the obtained anticorrelationbetween bulk sound speed and S wave velocity shows thatanticorrelation is associated with upwelling regions, whilewe find almost no anticorrelation in subducting areas, ingood agreement with recent observations. We also show

that in order to satisfy both geodynamical and seismologi-cal constraints, the (1–2 %) denser material in the lowermostmantle may result from a simultaneous enrichment in Fe andSi, with respect to a pyrolitic composition. A decrease ofthe iron-magnesium partition coefficient, due to a pressureincrease and to the presence of Al-perovskite, would reducethe required Fe and Si enrichment.

— INVITED —Phase transitions and mantle dynamics

Luce Fleitout

Ecole normale superieure, Paris, France

In studies of mantle convection, phase transition zones, inparticular those at 670km depth have been considered eitheras a barrier between upper and lower mantle, as the site forlateral mass anomalies hampering the flow or merely as ar-eas of potential increase in viscosity as function of depth,without much impact on mantle dynamics. The possibilityof a petrological change through the phase transition zonewas invoked in some ancient studies but is rarely proposedsince seismological studies have shown the slabs to pene-trate in the lower mantle. Here, we shall attempt to discussvarious mechanisms linked with phase transitions and ableeither to affect the vigor of mantle convection or to inducecompositional variations as function of depth.

The most widely studied mechanism through whichphase transitions can affect mantle dynamics is the potentialeffect of a negative Clapeyron slope at 670km depth. Theglobal buoyancy of colder material around 670km depth willdepend strongly upon the phase changes in the non olivinecomponents of the mantle (i.e. upon the Majorite-garnettowards perovskite phase change). The ’Effective Clapey-ron slope’ will depend upon the background mantle tem-perature and upon details of the phase diagram which arenot perfectly known but it is unlikely to be so negative thatthe avalanche regime prevails.

Two types of compositional variations associated withthe 670km phase transition have been proposed: a denser(iron rich) lower mantle has been invoked. Ringwood sug-gested that the crustal and non crustal components ofthe mantle had their relative densities varying as a functiondepth, the crustal material being less dense in a thin layerbelow 670km. He inferred that crustal material may remaintrapped above the 670km discontinuity. Tests of these ideasusing convection models show that phase transitions may in-deed induce segregation as function of depth in the mantle.A negative Clapeyron tends to segregate the denser crustalmaterial in the lower mantle, but a difference in depth ofthe phase changes of the olivine vs pyroxene (crustal) com-ponents tends to induce accumulation of crust above and ofdepleted material below the 670km depth discontinuity.

Kinetic effects induce a delay in the phase transforma-tions. This corresponds to deflections of the phase transitionzones and therefore to lateral density variations hamperingthe flow. The release of latent heat is at the origin of oneof these kinetic effects. It may hinder convection whateverthe sign of the Clapeyron slope but can play a significant rolein mantle dynamics only for thin transition zones (ringwood-ite to perovskite plus magnesio-wustite at 670km depth?).A phase transition implies a change of volume which will oc-cur only if it is accompanied by creep. This is true both ona global scale and on a local scale. This introduces a delay

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in phase transitions inversely proportional to the viscosityin the zone of phase change. If there is no ’transforma-tion plasticity’, this effect linked to the volume change atthe 670km phase change could significantly hamper convec-tion. On a macroscopic scale, the grain growth of the newlyformed phase can also be delayed because of the creep nec-essary to accommodate the volume change. As most mantlephase changes are divariant, the diffusion of elements {Fe,Al}can also be a cause of kinetic delay but the diffusioncoefficients are poorly known. This mechanism is howeverimportant for preventing short term, small amplitude vari-ations of the love numbers.

Is-there a viscosity reduction in the zones of phase tran-sition? These low viscosities could affect the flow, bothdirectly and also because they would strongly trigger petro-logical segregation. The viscosity reduction may be linkedeither to internal stresses because of inhomogeneous changeof volume on a microscopic scale or to grain size reduction.Experimental investigations concerning these viscosity re-duction mechanisms are difficult: The phase changes occurwithin a few minutes in the lab (usually in specimens withmicron grain sizes), but over 1Ma in nature.

In summary, several processes linked with phase transi-tions can potentially hamper mantle convection and also in-duce major elements variations as function of depth. Geoiddata seem indeed to favor models involving mass anoma-lies hampering convection in the transition zone. There arepresently uncertainties in the values of the physical param-eters involved in each of the processes described above. Seis-mological studies, bringing constraints on the thickness andvelocity jump across phase transitions, more sophisticatednumerical models of mantle convection and also more datafrom high pressure physics (phase diagram for non olivinephases, diffusion coefficients of Fe, Al, grain size as functionof speed of reaction... ) should improve our understandingof the dynamic and petrologic effect of phase transitions.

Contemporary changes in the geoid aboutGreenland: predictions relevant to gravity

space missions

Kevin Fleming, Zdenek Martinec, Jan Hagedoornand Detlef Wolf


Contempory spatial and temporal changes in the geoidabout Greenland are the sum of several contributions.We have examined those from glacial-isostatic adjustment.These may be divided into changes in ice loading occuringoutside of Greenland, particularly North America, followingthe last glacial period, and those resulting from the Green-land Ice Sheet (GIS). Concerning the GIS’s contribution,this may be further divided into past and current changesin the ice sheet. The spatial variability in the GIS’s present-day mass balance affects the geoid power spectrum signif-icantly and results in a signal that may be better resolvedby measurements from gravity space missions than has beenproposed by other authors.

Stagnant lid convection with an icerheology

Justin Freeman1,3, Louis Moresi1,2,3 andDavid May4

1Scool of Mathematical Sciences, Monash University, Australia2Scool of Geosciences, Monash University, Australia

3Monash Cluster Computing, Monash University, Australia4Victorian Partnership for Advanced Computing (VPAC),

Australia

Numerical investigations of thermal convection withstrongly temperature dependent Newtonian viscosity (dif-fusion creep) and extremely large viscosity contrasts havedemonstrated the existence of three convective regimes.These are the small viscosity contrast regime, transitionalregime and the stagnant lid regime. The strong temper-ature dependence of water ice suggests that convectionoperating within the mantle of an icy satellite should bewithin the stagnant lid regime. We study the evolution intothe stagnant lid regime with a water ice rheology by solvingthe equations of thermal convection for a creeping fluid withthe Boussinesq approximation and infinite Prandtl number.The viscosity is non-Newtonian (dislocation creep). We fixthe Rayleigh number at the base (Ra1) to be 1 × 104 andsystematically increase the viscosity contrast (as determinedby ∆T ) over the region from ∆η = 1 to 1014. The transi-tion to the stagnant lid regime occurs at a viscosity con-trast greater than 104 for Newtonian viscosity convection,whilst non-Newtonian viscosity convection accommodatesthe stagnant lid regime at larger viscosity contrasts. For astress exponent, n, equal to 3, the stagnant lid regime isachieved at a viscosity contrast greater than 108. Disloca-tion creep of water ice is characterized by a larger stressdependence (n = 4) than silicates (n = 3), and with thiswater ice rheology, the stagnant lid regime is attained at aviscosity contrast greater than 1010.

Role of lateral mantle flow inthe evolution of subduction system:insights from laboratory experiments

Francesca Funiciello1, Claudio Faccenna1andDomenico Giardini2

1Dip. di Scienze Geologiche, Univ. ”Roma Tre”, Italy2Insitut fur Geophysik, ETH Zurich, Switzerland

Subduction zones are complex 3-dimensional (3-D) struc-tures. They vary both in lateral and depth extent andhave irregular vertical and horizontal geometry. Never-theless these geodynamic structures have been always in-terpreted on the basis of laboratory and numerical mod-els bearing a fundamental 2-dimensional (2-D) geometry.We present here the first systematic laboratory setup thatfocuses on the feedback of mantle flow and slab dynam-ics as constrained by 3-D boundary conditions. These ex-periments are conducted with a composite silicone-honeysystem. The velocity of the incoming plate is varied withthe aim of exploring the widest field of conditions in the sub-duction system. We find that the behavior of the slabduring the fall into a stratified mantle is always charac-terized by three distinct phases, independently by appliedboundary conditions: 1) the fall of the slab into the up-per mantle; 2) the dynamic interaction phase with the 660km discontinuity; 3) the final phase of steady state whenthe slab lies flat on the upper/lower mantle transition zone.Forces active into the system, whose distribution is influ-enced by the choice of the adopted boundary conditions,

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govern the nature of these phases Nevertheless our resultshighlight also that the highly dynamic behavior of subduc-tion is strongly function of the effects of slab-mantle in-teractions and of the possible mantle flow restrictions bothvertically and horizontally.

The number of hotspots in numericalmodels of mantle convection

Attila Galsa

Department of Geophysics, Eotvos University, Budapest,

Hungary

Numerical calculations have been carried out to study the ef-fect of the Rayleigh number, viscosity distribution and in-ternal heating on the areal density of upwellings in three-dimensional Cartesian models of mantle convection. Modeldomain with large aspect ratio (661) has been applied toensure a robust upwelling statistics and to minimize the dis-torting effect of the sides of the box. Model parame-ters were chosen to simulate physical processes occurringin the Earths mantle according to available computationalresources. The Rayleigh number varied in the domain ofRa = 105–5 · 107, the viscosity increased exponentially withdepth by a factor of γ =1, 10, 30 or 100, additionally amantle-like depth-dependent viscosity profile has been stud-ied. The value of internal heating corresponds to the chon-dritic abundance of radioactive elements, nondimensionalinternal heating was H = 10. Horizontal boundaries wereisothermal and stress-free, vertical boundaries had mirrorsymmetry.

It was found that by increasing the Rayleigh num-ber the flow velocity becomes faster (ν ∼ Ra2/3), convec-tive cooling intensifies, thus the surface heat flow increases(Nu ∼ Ra1/3), the characteristic length of the horizontaland vertical boundary layers decreases (δ ∼ Ra−1/3). Ob-tained exponents are in accordance with results from scal-ing analysis [Solomatov 1995]. By increasing the viscos-ity contrast between the bottom and the top of the boxthe flow slows down especially in the lower regions re-sulting in the decrease of the heat transport and causingthe strengthening (in thermal sense) of the bottom bound-ary layer. Therefore, the symmetry of the convective pat-tern deforms, upwellings are represented as axisymmetricascending currents (plumes), while downwellings have slab-like feature.

On the basis of the numerical investigation of the arealdensity of upwellings the number of plumes increases withgrowing Rayleigh number [Parmentier and Sotin 2000], butdecreases with the increase of the viscosity contrast (Fig.1). It has been established, that the number of upwellingsis related to the thickness of the bottom boundary layer asits inverse proportion, N ∼ δ−1

1 (Fig. 2). It is supported byboth numerical models and scale analysis.

In the presence of internal heating the form of the con-vection modifies substantially. The average temperaturein the model domain increases leading to the strengthen-ing of the upper and the weakening of the bottom thermalboundary layer. As a consequence, downwellings will ap-pear as cold plumes, upwellings as passively ascending dif-fuse, hot zones. However, by increasing the Rayleigh num-ber the model domain cools, temperature difference acrossthe bottom boundary layer increases. Increasing viscositycontrast decreases more the average temperature of the box

making stronger the bottom thermal boundary layer. Thehigh Rayleigh number and the viscosity increasing withdepth results in the main forms of convective motion asupwelling plumes and downwelling slabs. Since the internalheating weakens the bottom boundary layer, thus increasesthe number of plumes (Fig. 3). On the basis of flow pa-rameters calculated from numerical models (average surfaceheat flux, velocity of the lithosphere, thickness of lithosphereand D” zone, diameter of plumes) mantle convection occursrather in one- than two-layered form. The type of the con-vective flow system (one- or two-layered) can be inferredfrom the relation between the areal density of upwellingsand surface hotspots, as well. If the convection occurs inone-layered form, the density of plumes beneath hotspotswill be about 2–3 (using the depth of the mantle as a unit)[Steinberger 2000]. However, if the flow system were two-layered separated by the phase boundary at the depth of 660km, it would yield the density of upwellings of 0.04–0.06 inthe upper mantle (using the depth of the upper mantle asa unit). Whereas the areal density of plumes obtained fromour realest numerical models lies in the domain of 0.8–1,which is between the two values, a coexisting one- and two-layered flow regime is supported. This form of the mantleconvection is not a new hypothesis, such a flow system hasbeen suggested by both geochemical investigations of extru-sive basalts and numerical models including mineral phasetransition at 660 km [Cserepes and Yuen 1997].

References:

Cserepes, L., D. A. Yuen, Dynamical consequences of mid-mantle viscosity stratification on mantle flows with an en-dothermic phase transition, Geophys. Res. Lett., 24, 1997,181–184.

Parmentier, E. M., C. Sotin, Three-dimensional numericalexperiments on thermal convection in a very viscous fluid:Implications for the dynamics of a thermal boundary layer athigh Rayleigh number, Phys. Fluids, 12/3, 2000, 609–617.

Solomatov, V. S., Scaling of temperature- and stress depen-dent viscosity convection, Phys. Fluids, 7/2, 1995, 266–274.

Steinberger, B., Plumes in a convecting mantle: Models andobservations for individual hotspots, J. Geophys. Res., 105,2000, 11127–11152.

Fig. 1. The areal density of upwellings as a function ofthe Rayleigh number and the viscosity exponentially

increasing with depth in a model box of 661 in the absenceof internal heating (H = 0). At high Ra the averagedensity of upwellings is indicated with its standard

deviation. Viscosity contrast is marked in the figure bysymbols.

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Fig. 2. The number of upwellings in a model box of 661plotted against the thickness of the bottom boundary

layer, H = 0. The fitted curve: N = 0.48 · δ−1.061 .

Fig. 3. The areal density of upwellings in a model box of661 as a function of Ra with different viscosity

distributions in the presence of internal heating (H = 10).At high Ra the average density of upwellings is indicatedwith its standard deviation. It is emphasized by dashed

line that hot plumes do not form at γ = 1.

Synthetic seismic signature of thermalmantle plumes

Saskia Goes1, Fabio Cammarano1and Ulli Hansen2

1Institute of Geophysics, ETH Zurich, Switzerland2Institute of Geophysics, University of Muenster, Germany

The first seismic images of mantle plumes have been a sourceof significant debate. To interpret these images, it is usefulto have an idea of a plume’s expected seismic signature. Weperform a set of numerical experiments to obtain dynamicthermal whole mantle plumes, with temperature contrastsbelow the lithosphere that are consistent with those inferredfrom surface observations. The plume thermal structure isconverted to seismic structure by accounting for the effectsof temperature, pressure, an average mantle composition in-cluding phase transitions, and anelasticity. With depth- de-pendent expansivity and temperature- and depth-dependentviscosity, these relatively weak plumes have lower-mantlewidths of 300-600 km at one half of the maximum tempera-ture anomaly. To attain the narrow upper mantle plumes in-ferred from surface observations and tomography, viscosityreduction by a factor 30-100 is necessary, either as a jump ora strong gradient. All model plumes had buoyancy fluxes of

at least 4 Mg/s and it seems difficult to generate whole man-tle thermal plumes with fluxes much lower. Due to changingseismic sensitivity to temperature with depth and mineral-ogy, variations in the plumesseismic amplitude and width donot coincide with those in their thermal structure. Velocityanomalies of 2–4 % are predicted in the uppermost mantle.Reduced sensitivity in the transition zone as well as complexvelocity anomalies due to phase boundary topography mayhamper the imaging of continuous whole mantle plumes. Inthe lower mantle, our plumes have seismic amplitudes ofonly 0.5–1 %. Unlike seismic velocities, anelasticity reflectsthermal structure closely, and yields plume anomalies of 50–100 % in dln(1/Qs).

Dynamics of slab-transform plateboundaries: preliminary finite element

models of the south-central Mediterraneanuppermost mantle and lithosphere.

Rob Govers and Rinus Wortel


The Netherlands

Slab edges are currently a relatively common geometricalfeature in plate tectonics. We use finite element models toinvestigate the consequences of vertical slab edges on the dy-namics of the lithosphere and uppermost mantle. In thisstudy, we focus on the south-central Mediterranean region.The three-dimensional dynamic models are constrained bytomography, and by geological, geophysical and geodetic ob-servations. The preliminary models we present are based ona linear visco-elastic rheology. We investigate the responseto variations in the shear strength of major faults.

A time-domain method of implementingthe sea-level equation in GIA for a rotating

earth

Jan M. Hagedoorn, Zdenek Martinec andDetlef Wolf


The implementation of the sea-level equation (SLE) de-scribing the redistribution of melt water in the oceansis complicated in conjunction with the Laplace-transformmethod conventionally used to model glacial-isostatic ad-justment (GIA). The recently developed spectral-finite el-ement method (Martinec, 2000) solves the field equationsgoverning GIA in the time domain and, thus, eliminatesthe need of applying the Laplace-transform method. More-over, the spectral finite-element approach allows us to solvethe SLE when modeling GIA for a 3-D self-gravitating, in-compressible, viscoelastic earth model.

The solution of the field equations in the time domainalso makes it possible to use the MacCullagh formula inthe time domain and to compute the incremental inertia ten-sor. This allows us to solve the linearized Liouville equationgoverning the variation of earth rotation. From the varia-tion of earth rotation the incremental centrifugal potentialcan be calculated, which enters into he SLE.

The present test is restricted to radially symmetric earthmodels consisting of a fluid core, a Maxwell-viscoelasticlower and upper mantle and an elastic lithosphere. The

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last Pleistocene glaciation is simulated using two differ-ent scenarios, with different glaciation histories followed bythe deglaciation history of the global ice model ICE-3G(Tushingham & Peltier, 1991). We investigate the influenceof variable earth rotation on sea level and the influence ofdifferent viscosity models and glaciation histories on earthrotation.

References:

Martinec, Z., 2000. Spectral-finite element approachto three-dimensional viscoelastic relaxation in a sphericalearth. Geophys. J. Int., 142, 117-141.

Tushingham, A.M., Peltier, W.R., 1991. Ice-3g: a newglobal model of late Pleistocene deglaciation based upon geo-physical predictions of post-glacial relative sea level change.J. Geophys. Res., 96, 4497–4523.

— INVITED —The fluid dynamics of plumes

Ulli Hansen

Institut fuer Geophysik, Universitaet Muenster, Germany

In geodynamics plumes play an important role for phenom-ena on different scales, ranging from local hot-spots to largescale features like superswells. Plumes evolve from thermalboundary layers if a critical paramter (similar to a localRayleigh numbea) exceeds a critical value. In that senseplumes can be viewed as threshold phenomena. By meansof numerical experiments various aspects of plume structure- and evolution will be demonstrated in this presentation.

The shape and the evolution of plumes is strongly in-fluenced by the viscosity of the material. Especially astrong temperature dependence pf the viscosity leads toepisodic bursts of hot material from the thermal boundarylayer following a previously established path of low viscos-ity. Episodicity is a common feature of plumes in fluids withtemperature dependent viscosity, even if the forcing is notvarying with time. If plumes are evolving self-consistentlyfrom a thermal boundary layer they hardly entrain mate-rial during ascent, i.e. material reaching the top is verysimilar to the material of the source region. Besides thetemperature dependence also the pressure dependence ofthe viscosity significantly influences the behavior of plumes.The symmetry, between the upwelling and downgoing cur-rents is destroyed by pressure dependence of the viscosity.Strong upwellings exists while the downwellings are weak-ened. The effect of the viscosity increasing with pressureon the flow dynamics is further enhanced by the decrease ofthe thermal expansion coefficient with pressure. Both, actto increase the strength of upwelling plumes, thus leadingto flows of large horizontal scales. In two dimensions, flowswith aspect ratios greater than 30 have been observed.

Under appropriate conditions (combinations of pres-sure and depth dependence) small plumes from the thermalboundary layer gather to form massive upwellings. This is apossible scenario relevant for the formation of superplumes.Under the same condition the net viscosity profile exhibits alocal maximum in the lower mantle, as indicated by recentstudies.

Viscous Heating in the Mantle Induced byGlacial Forcing

Ladislav Hanyk1, Ctirad Matyska1and

David A.Yuen2

1Department of Geophysics, Charles University, Prague, CzechRepublic

2Department of Geology & Geophysics and Minnesota

Supercomputing Institute, University of Minnesota,

Minneapolis, USA

We have studied the possibility of energy transfer fromglacial forcing to the Earth’s interior via viscous dissipa-tion of the transient flow. We applied our initial-value ap-proach to the modelling of viscoelastic relaxation of spher-ical compressible self-gravitating Earth models with a lin-ear viscoelastic Maxwellian rheology. We have focussed onthe magnitude of deformations, stress tensor componentsand corresponding dissipative heating for glaciers of Lauren-tide extent and cyclic loading with a fast unloading phaseof various lengths.

We have surprisingly found that this kind of heatingcan represent a non-negligible internal energy source withexogenic origin. The volumetric heating by fast deforma-tion can be locally higher than the chondritic radiogenicheating during peak events. In the presence of an abruptchange in the ice-loading, its time average of the integralover the depth corresponds to equivalent mantle heat flowof milliwatts per m2 below the periphery of ancient glaciersor below their central areas. However, peak heat-flow valuesin time are by about two orders of magnitude higher. Notethat nonlinear rheological models can potentially increasethe magnitude of localized viscous heating.

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To illustrate the spatial distribution of the vis-cous heating for various Earth and glacier models,we have invoked the 3-D visualization system Amira(http://www.amiravis.com). Our file format allows to an-imate effectively time evolution of data fields on a movingcurvilinear mesh, which spreads over outer and inner man-tle boundaries and vertical mantle cross-sections. Two at-tached snapshots of the Amira movies show examples ofnormalized dissipative heating of the PREM model witha lower-mantle viscosity hill at the end of the instanta-neous unloading of glaciers with rectangular (Fig. 1a) andparabolic (Fig. 1b) cross-sections.

Small-Scale Asthenospheric Convectionand Cenozoic Extensional Tectonics

of the Basin and Range Province, WesternU.S.A.

John W. Hernlund1and Paul J. Tackley1,2

1Department of Earth and Space Sciences, Universityof California, Los Angeles, USA

2Institute of Geophysics and Planetary Physics, University

of California, Los Angeles, USA

Cenozoic extension in the Western U.S. is broadly asso-ciated with widespread volcanism, high heat flow, exten-sive thinning or removal of mantle lithosphere, and uplift.While there is no universally straightforward temporal rela-tion between the onset times of extension and volcanism inthe basin and range province, these phenomena appear tobe related to, or at least partly controlled by, dynamic pro-cesses occurring in the upper mantle. Because the mantlelithosphere is denser than the underlying asthenosphere, itis gravitationally unstable and may give rise to small-scaleconvective motions that result in lithospheric thinning, vo-luminous melt production, and high heat flow. Numericalsimulations of this process, including the effects of melt-ing, indicate that the occurrence of partial melting dramat-ically increases the propensity for small-scale convection.Two distinct styles of small-scale convection are observedin these models: 1) large amplitude (up to ∼300 K) slug-gish convection that results in substantial convective re-moval of mantle lithosphere (the ”drippy” mode), and 2)small amplitude (∼100 K) rapid convection which tends toleave the lithosphere largely intact (the ”compact” mode).The occurrence of these two styles is regulated by the vis-cosity contrast between asthenosphere and lithosphere. Thedrippy mode occurs when the viscosity contrast is low (i.e.a soft mantle lithosphere), while the compact mode oc-curs when the viscosity contrast between lithosphere and as-thenosphere is large (i.e. a stiff mantle lithosphere). Thus adrippy style of small-scale convection, producing silicic vol-canism at the surface and resulting in substantial thinningof mantle lithosphere, is expected to accompany a ”wet”mantle. A hot and ”dry” mantle, on the other hand,would give rise to a compact mode of small-scale convectionthat will most likely produce effusive basaltic volcanism atthe surface. A temporal transition from drippy mode small-scale convection associated with the mid-Tertiary ignimbriteflare-up and removal of the wet Farallon flat slab to a com-pact mode beginning at roughly mid-Miocene times appearsto be a viable mechanism for unifying Cenozoic mantle andcrustal dynamics in the Western U.S..

Small scale convection under the islandarc?

Satoru Honda1and Mitsunobu Saito2

1Earthquake Research Institute, University of Tokyo, Japan2Department of Earth and Planetary Systems Science,

Hiroshima University, Japan

(now at Keishin High School, Japan)

Recently Billen and colleagues (e.g. Billen et al. (2003))extensively studied the subduction zones based on the dy-namic modeling of subduction zones and proposed the ex-istence of the low viscosity wedge (LVW), which may beproduced by the water dehydrated from subducting slabs.Meanwhile, in northeast Japan, Tamura et al. (2002) foundalong-arc variations of distribution of volcanoes, low veloc-ity anomalies and Bouger anomalies. They can be grouped10 lineaments with a wavelength of ∼80 km, which are per-pendicular to the trend of trench. They called these ”HotFingers”, since those features are suggestive of high temper-ature in the upper mantle. The morphology akin to this haspreviously been expected for small-scale convection beneathmoving oceanic plates. We might expect such a small-scaleconvection under the back-arc, if the wedge mantle viscos-ity is low enough. This small-scale convection may be apossible origin of Hot Fingers. We explore this possibilityusing both 2-D and 3-D modeling with/without pressureand temperature dependent viscosity of wedge mantle. 2-D models without pressure and temperature dependence ofviscosity show that, with a reasonable geometry of the LVWand subduction speed, the small-scale convection is likely tooccur, when the viscosity of the LVW is less than 1019 Pasec. Corresponding 3-D model studies reveal that the wave-length of rolls depend on the depth of the LVW. An inclusionof temperature dependent viscosity requires an existence offurther low viscosity in the LVW, since temperature depen-dence suppresses the instability of cold thermal boundarylayer. A pressure (i.e. depth) dependence combined witha temperature dependence of the viscosity produces a low-viscosity zone, and, thus, it promotes short wavelength in-stabilities. The model, which shows a relatively moderateviscosity decrease in the LVW (most of the LVW viscosity is1018 - 1019 Pa sec) and the wavelength of roll ∼80 km, hasa rather small activation energy and volume (∼130 kJ/moland ∼4 cm3/mol) of the viscosity. This small activation en-ergy and volume may be possible, if we regard them as aneffective viscosity of non-linear rheology.

References:

M. I. Billen. M. Gurnis, M. Simons, Multiscale dynamicsof the Tonga-Kermadec subduction zone, Geophys. J. Int.,153 (2003), 359-388.

Y. Tamura, Y. Tatsumi, D. Zhao. Y. Kido, H. Shukuno,Hot fingers in the mantle wedge: new insights into magmagenesis in subduction zones, Earth Planet. Sci. Lett., 197(2002), 105-116.

Mantle melting during continentalbreakup

John R. Hopper∗and Thomas K. Nielsen

Danish Lithosphere Center, Copenhagen, Denmark∗ now at GEOMAR, Marine Geodynamics, Kiel, Germany

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Despite the fact that volcanic rifted margins have been stud-ied intensively for more than a decade, controversies oversome of the most fundamental issues remain. Although de-tails between different provinces vary, volcanic rifted mar-gins generally show a short lived pulse of exteme magma-tism that quickly abates to steady-state, plate-driven, mid-ocean ridge accretion. The generation of thick igneous crustrequires either melting of hotter than normal mantle, orsmall scale convection so that larger amounts of mantle ma-terial are processed in the melting region than is the casefor plate-driven passive flow. To assess under what condi-tions buoyantly driven upwelling (or small-scale convection)at rifted plate boundaries is important, we use a numericalmodel of convection based on the CITCOM code that incor-porates feedback from melting on the physical properties ofthe mantle. The viscosity function is both temperature andpressure dependent, includes increases due to dehydrationduring initial melting, and decreases due to grain boundarysliding, which is enhanced by the presence of melt. Ignoringdehydration strengthening, we show that to induce signif-cant small-scale convection and anomalous melt production,we must assume a viscosity structure that is inconsistentwith steady-state oceanic accretion. Including the viscosityincrease from dehydration does not fundamentally changethis conclusion. It serves only to exacerbate the prob-lem by suppressing buoyant upwelling above the depth tothe dry solidus and restricting shallow flow to plate drivenupwelling. This is critical since most melt is generated abovethis depth. Models that assume an abrupt change in preriftlithospheric thickness suffer the same deficits. The smallscale convection induced is primarily below the depth ofmelting and does not lead to anomalous melt productivity.To produce a single volcanic pulse followed by plate-drivenoceanic accretion, we require an exhaustable sublithosphericlayer at the time of breakup. Although this layer could bea chemical anomaly of highly fertile mantle, a temperatureanomaly seems more likely. Observations along SE Green-land can be matched if a 50 km thick layer with a ∆T 100–200 ◦C.

Asymmetric lithosphere extension: factorscontrolling rift mode selection

Ritske Huismans, Susanne Buiter andChristopher Beaumont

Geodynamics Group, Department of Oceanography, Dalhousie

University, Halifax, Canada

To a large part extension of the crust and mantle lithosphereis accommodated by brittle faults and viscous shear zones.In previous work we have focused on the roles of frictional-plastic and viscous strain softening and surface processes ingenerating asymmetry at the lithosphere scale during ex-tension. Here the focus is the behaviour of simple two-layermodels with a frictional plastic strain-softening layer overly-ing a uniform viscous layer. We use estimates of the rate ofenergy dissipation and forward numerical mechanical mod-elling to investigate factors that lead to different styles ofextension. Our focus is the behaviour of simple two-layersystems with a frictional- plastic strain-softening layer over-lying a uniform viscous layer.

We derive criteria that control mode selection by com-paring the respective rate of dissipation for each riftingmode. The mode with the least dissipation is favoured.

The primary controls are the relative rates of dissipation inthe frictional-plastic and viscous layers. The dissipation inthe plastic layer is determined by the yield strength and itsstrain dependence, both of which are independent of veloc-ity. The dissipation in the viscous layer is partly determinedby the viscosity and the strain rate, and is, therefore, de-pendent on the rifting velocity. The remaining control isthe traction coupling between the layers.

The dissipation analysis predicts that at low viscousstresses, arising from low viscosities and/or low exten-sion velocities, the fundamental asymmetry promoted bythe strain softening frictional-plastic layer is fully expressedand rifting of the lithosphere may be asymmetric. At higherviscous stresses this tendency is suppressed and symmetricor pure shear lithosphere extension is predicted. The resultsfrom the forward mechanical models are well in agreementwith the dissipation analysis.

Factors controlling slab roll-back andback-arc extension

Ritske Huismans, Christopher Beaumont andPhilippe Fullsack

Geodynamics Group, Department Oceanography, Dalhousie

University, Halifax, Canada

Although subduction is a first order plate tectonic process,the factors controlling the dynamics of slab roll-back andback-arc formation are still not very well understood. Themajor driving forces for subduction and slab roll-back arewell established as the slab pull (Fsp) and ridge push (Frp)forces, their relative importance and the relative impor-tance of forces modifying and interacting with these driv-ing forces is, however, not very clear. A number of forcesmay resist subduction and roll-back of the slab. 1) Normaland tangential forces resisting downwelling of the slab (Fn,Fs), 2) Bending resistance in the slab at the trench andat the 660 km discontinuity (Fb), 3) Resistance to lateralflow of the upper mantle below and above the subductingslab. To investigate the relative contribution of these resist-ing forces we use 2D plane strain thermo-mechanical finiteelement models. The model evolution is calculated using anArbitrary-Lagrangian-Eulerian (ALE) method for the finiteelement solution of incompressible viscous-plastic creepingflows (Fullsack, 1995).

In a first set of models we test the relative roles of bend-ing resistance (Fb) and upper mantle viscosity (i.e. Fn,Fs) with a subducting plate where an overlying plate is notincluded. The models extend from the surface to 660 kmdepth. The upper surface of the model is free to move. Up-per mantle rheology is linear viscous, whereas the rheologyof the subducting slab is either linear viscous or combinedlinear viscous and von Mises plastic. Reflective and peri-odic boundary conditions are used. The slab is allowed tosink in the underlying mantle under its own weight. The re-sults are very similar to recent analogue studies of Faccenna(2001) and Funiciello et al. (2003). The models indicatethat the resisting forces (Fn, Fs) form the primary controlon the rate of subduction and roll-back where the velocity oftrench retreat depends linear on the viscosity of the uppermantle. Variation of roll-back with viscosity of the subduct-ing slab is minor. Interaction of the slab with the 660 kmdiscontinuity results in a small, < 5 %, decrease in roll-back

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velocity. This suggests a subordinate role of bending forces.The results are compared with a scaling analysis of relativeimportance of contribution forces.

In a second set of models we investigate interaction ofthe subducting slab with the overlying plate and specifi-cally focus on factors that may control the opening of aback-arc basin. The down going plate is driven by a kine-matic boundary condition, far from the zone of subduction.After an initial stage of far-field driven contraction, the neg-ative buoyant down welling of the mantle lithosphere maydrive continued formation of the subduction zone leadingto mature subduction. The models suggest that two ma-jor factors control whether the subducting system developsan extensional back-arc system: 1) The relative contribu-tion of the imposed far-field velocity and roll-back veloc-ity, 2) The strength of the overlying plate. We investigatethe roles of small scale convection, enhanced by corner flowabove the subducting plate, and far field plate velocity onthe opening of the back arc basin.

Penetration of mantle plumes throughthe lithosphere

Damien Jurine, Claude Jaupart andGenevieve Brandeis

Laboratoire de Dynamique des Systemes Geologiques, Institut

de physique du globe de Paris, France

The interaction between thermal mantle plumes and litho-sphere is still poorly known and controversial. Differentmodels are necessary to explain the complexity of their ef-fects on Earth. Two different types of lithosphere exist :oceanic and continental lithospheres. They differ by theirviscosity, density and thickness. Continental lithosphere isthicker, chemically different and therefore more viscous andless dense. In order to quantify the effect of these differences,we have developed an experimental approach to the prob-lem: two layers of fluid with different density and viscosityare superimposed in a tank. The thermal plume is thensuddenly generated by a point source of heat at the baseof the tank. We study the effects of the power input ofthe heater, the density difference, the viscosity ratio, andthe thickness of the layers.

We follow the thermal structure of the flow with ther-mocouples and we film the evolution in time of the interfacebetween the two fluids. We also measure the height andwidth of the plume intrusion into the upper layer. Experi-ments show that the flow reaches a quasi permanent statewhere the height of the intrusion and the temperature atthe axis of the plume are constant. At constant viscosity ra-tio, there are two end-member cases: (1) horizontal spread-ing of the plume at the base of the lithosphere or (2) upwardpenetration through the lithosphere. It is therefore impor-tant to characterize the degree of penetration of the plumewhich is controlled by two parameters: the buoyancy num-ber and the viscosity ratio.

We also perform numerical simulations with the pro-gram STAG3D developed by Paul Tackley. We solvethe equations governing the convective motion in a non-compressible viscous fluid and use active tracers to modelthe upper layer which is chemically less dense and moreviscous. Simulations allow to vary all the parameters in awide range and show a good agreement with experiments.

— INVITED —Building the bridge between seismic

anisotropy and upper mantle convection

Edouard Kaminski

Institut de physique du globe de Paris, France

The interpretation of seismic anisotropy in the mantle re-quires a knowledge of the relationship between the latticepreferred orientation (LPO) of crystals and the convectiveflow field. In order to understand this link, one needs amodel for the evolution of LPO in olivine aggregates thatdeform by both intracrystalline slip and dynamic recrystal-lization. In this presentation, we will first give a reviewof the pioneer works on the subject and will then focus onthe most recent advances dealing with dynamic recrystal-lization.

Deformation mechanisms are the corner stone of anytheory on LPO development. Dislocation creep is respon-sible of the development of LPO by slip on slip systemsand induced rotation of the crystallographic axes. To cal-culate the plastic deformation of the crystals, three familiesof model are available: stess equilibrium based, strain equi-librium based, and kinematic ones. All the models predictthat the LPO due to plastic deformation follows the finitestrain ellipsoid (FSE).

For large deformation, an extra deformation mechanismis triggered: dynamic recrystallization. This process de-pends on the dislocation density of the grains, which is afunction of the applied local stress and of the rate of nucle-ation in the grains. Depending on their density of disloca-tions, grains will grow or shrink so to minimize the strainenergy of the aggregate. A new LPO then appears, relatedto the orientation of the grains with the lower density ofdislocations.

Models of LPO development are constrained by ob-served LPO patterns in experimentally deformed olivineaggregates and by the temporal evolution of the strengthof the LPO. The plastic flow/recrystallization models canthen used to study systematically the relationship betweenolivine lattice preferred orientation (LPO) and the mantleflow field that produces it.

Numerical solutions for the mean orientation of an ini-tially isotropic aggregate deformed uniformly show thatthe LPO evolves in three stages: (1) for small deforma-tions, recrystallization is not yet active and LPO followsthe FSE; (2) for intermediate deformations, the LPO ro-tates towards the orientation corresponding to the maxi-mum slip on the softest slip system; (3) for large deforma-tion, LPO is controlled by plastic deformation and rotatestowards the orientation of the long axis of the finite strainellipsoid corresponding to an infinite deformation (the ”infi-nite strain axis” or ISA). In more realistic nonuniform flows,LPO evolution depends on a dimensionless ”grain orienta-tion lag” (GOL) parameter, defined locally as the ratio ofthe intrinsic LPO adjustment time scale to the time scalefor changes of the ISA along pathlines in the flow. Explicitnumerical calculation of the LPO evolution in simple fluiddynamical models for ridges and for plume-ridge interactionshows that the LPO aligns with the flow direction only inthose parts of the flow field where GOL parameter is muchsmaller than 1. Calculation of this parameter provides asimple way to evaluate the likely distribution of LPO in a

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candidate flow field. Dense seismic data are required in areawith high values of the GOL parameter, in which the com-parison to the prediction is both more complex and moreinformative.

Eulerian spectral/finite difference methodfor large deformation modelling ofvisco-elasto-plastic geomaterials

Boris J. P.Kaus1, Yuri Y. Podladchikov1andDani W. Schmid2

1Earth science department, ETH Zurich, Switzerland2Geomodeling Solutions GmbH, Zurich, Switzerland

Many problems that occur in geodynamics can be reducedto the solving of visco-elasto-plastic rheological equations.Here a spectral/finite-difference method is described thatcan deal with these rheologies in an eulerian framework.The method approximates derivatives in vertical directionby finite-differences and in horizontal direction(s) by a pseu-dospectral approach. Material boundaries are tracked bymarker chains that are moved through a fixed euleriangrid and allow large deformations. It is demonstrated thatthe Gibbs effect is avoidable, the method is reliable upto large viscosity contrasts of 5x105 and is able to resolvestrongly localised solutions like shear bands. Examples thatare given range from folding instabilities, to mohr coulombplasticity and viscoelastic convection.

The accomodation of volume changesin Phase transition zones; implications for

mantle dynamics

Yann Krien and Luce Fleitout


The change of volume associated with phase transitionsneeds to be accompanied by creep. Otherwise, a pres-sure anomaly impeding the phase change is induced. Phasetransformations in mantle flows are therefore delayed by thisprocess. The delay depends upon the thickness and the lo-cal viscosity of the zone of phase transition and is associatedwith deflections of the transition zone which tend to hamperthe flow. This phenomenon is studied, first with the help ofa simple analytical model, then for harmonic load functionsin a self-gravitating mantle. This process is shown to be po-tentially important (deflections of the 670km discontinuityby several km) but only if transformational plasticity doesnot take place within the phase transformation zone.

This effect can also occur on a microscopic scale as ithampers grain growth. We show that it can induce a de-flection of the phase transition zones by several kilometerseven in the case of non-newtonian rheologies.

The role of crustal properties in the slabdetachement

Martin Kukacka and Ctirad Matyska


Republic

Numerical models of subducting processes usually glanceover the detachement of the subducted oceanic plate fromthe continental one. In fully dynamic models the detache-ment of the plates is achieved by prescribing a fault [e.g.van Hunen et al. 2000, Billen and Gurnis 2001, Cizkova etal. 2002]. These models demonstrate well that sinking plateis driven by the buyoancy force. On the other hand, kine-matic models deal with prescribed velocity of the slab toobtain the temperature distribution of the subducted slab[e.g. Ponko and Peacock 1995] and to study phase changesin the deeper part of the subduction. Recently, the thirdgroup of models takes place: the velocity and the dip angleof the subduction remains prescribed, but in the overly-ing mantle wedge the fully dynamic problem is solved [vanKeken et al. 2002, Gerya and Stockhert 2002].

We present a different model, where both the tempera-ture and the velocity field as well as the shape and the po-sition of the boundary-line between the plates are the out-puts from the modeling. The model is based on the streamfunction formulation that easily enables the stratification ofthe inflowing oceanic lithosphere. Due to a viscosity depen-dent on the stream function, the problem is strongly non-linear and an iterative process is used to obtain the solution.The temperature field is calculated using the heat transferequation with the dissipation term in the whole box, whichcan lead to some problems with convergency. Such problemscan be overcome by introducing adaptive iteration scheme:

Xi = Kx(i)Xi−1 + (1 − Kx(i))Xi

where Xi denotes quantity (temperature, stream function,stress) in the i-th iteration and Kx(i) is the function ofthe iteration number specific for each quantity.

We present the steady-state solution in the box 300 x100 km with different creep properties of the lithosphreand the oceanic crust. Composite rheology including bothdislocation and diffusion creep is used; the non-viscous be-havior of the crust and the lithosphere is modeled by in-troducing the yield stress [Tackley 1998]. The ouput fromthe modeling gives some constraints on the magnitudes ofthe yield stresses - the dip of the lithosphere is proportionalto the ratio between the yield stress in the crust and inthe lithosphere. The subduction plate with dip about 45degrees requires the crustal yield stress to be 10-100 timessmaller than the yield stress of the lithosphere. Such a de-crease can be caused by high water content [Escartin et al.2001].

References:

M. I. Billen, M. Gurnis, A low viscosity wedge in subductionzones, Earth Planet. Sc. Lett. 193 (2001) 227–236.

H. Cizkova, J. van Hunen, A. P. van den Berg, The influ-ence of rheological weakening and yield stress on the inter-action of slabs with 670 km discontinuity, Earth Planet. Sc.Lett. 199 (2002) 447–457.

J. Escartin, G. Hirth, B. Evans, Strength of slightly serpen-tinized peridotites: Implication for the tectonics of oceaniclithosphere, Geology 29 (2001) 1023–1026.

T. V. Gerya, B. Stockhert, Exhumation rates of high pres-sure metamorphic rock in subduction channels: The effectof Rheology, Geophys. Res. Lett. 29 (2002) art. no. 1261.

J. van Hunen, A. P. van den Berg, N. J. Vlaar, A thermo-mechanical model of horizontal subduction below an overrid-ing plate, Earth Planet. Sc. Lett. 182 (2000) 157–169.

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P. E. van Keken, B. Kiefer, S. M. Peacock, High-resolutionmodels of subduction zones: Implications for mineral dehy-dration reactions and the transport of water into deep man-tle, Geochem. Geophy. Geosy. 3 (2002) art. no 1056.

S. C. Ponko, S. M. Peacock, Thermal modeling of the south-ern Alaska subduction zone: Insight into the petrology ofthe subducting slab and overlying mantle wedge, J. Geophys.Res. 100 (1995) 22117–22128.

P. J. Tackley, Self-consistent generation of tectonic platesin three-dimensional mantle convection, Earth Planet. Sc.Lett. 157 (1998) 9–22.

Mass balance of the subducted slab underthe Central Andes, dynamic topography

and its isostatic implications

Nick Kusznir and Carlos Izarra

Department of Earth Sciences, Liverpool University,

United Kingdom

A comparison of this observed mantle residual gravityanomaly with that predicted by simple thermal models ofthe subducted Nazca plate under the Central Andes showsthat the modelled gravity anomaly from the subduction pro-cess appears to be substantially greater than that observedby approximately 125 mgal. Key uncertainties in the predic-tion of the gravity anomaly from a thermal model of the sub-ducted slab arise from uncertainties in the thermal expan-sion coefficient, and subduction geometry and dip. Sensi-tivity tests to model parameters show that the discrepancybetween observed and modelled gravity anomaly may be asgreat as 300 mgal or as little as 40 mgal. This discrepancybetween observed and modelled mantle gravity anomaly be-neath the Central Andes may be resolved by the inclusionof other subduction related mass anomalies, in addition tothat of the cold descending Nazca plate, as suggested by geo-physical observations and thermo-dynamic considerations.Dynamic fluid flow modelling of the preferred mantle den-sity model predicts a dynamic subsidence at the base ofthe Central Andean crust that deviates the crust from localisostasy by as much as 6–10 km and 4–6 km in the Easternand Western Cordilleras respectively. The inclusion of thisdynamic subsidence in the determination of the observedresidual gravity anomaly greatly improves the fit betweenobserved and predicted mantle residual gravity anomaliesfrom the mantle over the Central Andes. This suggests thatdynamic topography and the depression of the Moho be-neath the Central Andes may be important in compensat-ing part of the mass excess arising from the cold subductingslab. Apart from the slab itself, the most important bodyaffecting the wavelength and amplitude of the dynamic to-pography is the asthenospheric wedge.

Viscosity and S-wave Conversion Factorfor the Earth’s Mantle based on CHAMP

Gravity Data and New TomographyModels

Gabriele Marquart and Radboud Koop

Utrecht University and SRON (National Institute for Space

Research), The Netherlands

The viscosity structure and the internal buoyancy forces ofthe Earth’s mantle are essential for understanding the con-vective flow pattern. These buoyancy forces are directlyrelated to density inhomogeneities. With the use of seismictomography it is possible to determine the seismic velocitydistribution in the Earth - but the conversion factor be-tween the seismic velocity and density is still not properlyknown. This is mainly due to uncertainties in the chemicalcomposition of the mantle. If the origin of lateral hetero-geneities in seismic wave velocity is purely thermal, the con-version factor should be around 0.2 to 0.4 as deduced frommineral physics. However, recent studies to relate mantledynamics and gravity data reported even negative valuesfor the conversion factor in the uppermost and lowermostmantle. For the uppermost mantle this finding has beenexplained by depletion in iron during partial melting.

In the presented study we solved the equation of mo-tion for an incompressible, self gravitating 6-layer shell anddetermined the response function for geoid, dynamic to-pography, and surface velocity (which can be compared tothe poloidal part of plate velocities). The internal load wasdetermined from 4 different tomography models (sb4l18,Masters et al., 1999; s362d1, Gu et al., 2001; s20rts, Rit-sema & van Heijst, 2000; saw24b16, Megnin & Romanowicz,2000). In a large Monte Carlo search we determined modelswith a correlation > .87 between the synthetic geoid andthe CHAMP hydrostatic geoid for L < 16. Successful mod-els show small, but not negative conversion factors in the up-per 300 km and a roughly constant value of ∼0.28 below.The viscosity is slightly reduced (compared to the scalingvalue of 1021 Pa·s) in the asthenosphere and even strongerreduced in the mantle transition zone between 410 and 670km where major changes in mineral geometry occur andthe release of water was recently proposed in the upper partof the transition zone. Resolution for both, viscosity andconversion factor, is poor below the transition zone down toabout 1500 km, but well confined in deeper parts of the man-tle. Here we find a viscosity between 30 to 40 ×1021 Pa·sand a conversion factor of 0.28 to 0.32.

Variable thermal conductivityin subducting slabs: olivine metastabilityand the mechanisms of deep earthquakes

Fred C. Marton1, David C. Rubie1,Tom J. Shankland2, Yousheng Xu3

1Bayerisches Geoinstitut, Universitat Bayreuth, Germany2EES-11, Los Alamos National Laboratory, USA

3Department of Geology and Geophysics, Yale University, New

Haven, USA

The mineralogical make-up of subducting lithosphere ishighly dependent upon its thermal state. This, in turn, isa function of the thermodynamic, kinetic, and heat trans-port properties of the minerals making up the lithosphere.Our understanding of slab mineralogy is therefore depen-dent upon accurate experimental measurements of thesedata, particularly for the polymorphs of (Mg,Fe)2SiO4. Thefirst have been available for quite some time; the secondhave progressed from analogue systems of Ni2SiO4 andMg2GeO4 (e.g., Rubie and Ross, 1994) to recent refinementsof the kinetics of (Mg,Fe)2SiO4 phase transitions themselves(Mosenfelder et al., 2001). As the last have been, until re-cently, lacking, subduction zone models used constant values

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of thermal conductivity, isobaric heat capacity, and densityin solving the heat flow equation (e.g., Minear and Toksz,1970; Kirby et al., 1996). Hofmeister (1999) developed amodel of thermal conductivity for mantle minerals as a func-tion of pressure and temperature based on phonon lifetimes.In turn, Hauck et al. (1999) incorporated this model intothermal models of subducting slabs. Their results predictedthat slowly subducting (< 8 cm/yr) slabs would be slightlycooler and faster/steeply-dipping slabs would be warmerthan slabs with constant conductivities. There are now,however, high P and T measurements of the thermal diffu-sivities of San Carlos olivine, wadsleyite, and ringwoodite(Xu et al., 2003) that allow more realistic thermal conduc-tivities to be used in thermo-kinetic models of subductingslabs.

Mineralogy is computed in subducting slabs usingthe thermodynamic data of Fei et al. (1991) for the MgO-FeO-SiO2 system and the model of olivine transformationkinetics of Mosenfelder et al. (2001) in which growth is as-sumed to be rate limiting. Latent heats of transformationare fed back into our model, significantly affecting the extentof olivine metastability (Daessler and Yuen, 1993; Devauxet al., 1997; Marton, 2001). A simplified single-componentsystem is used with a fixed composition of Fo90 that re-sults in univariant phase boundaries, i.e. without two-phaseloops, and the occurrence of the α → β transition at shal-lower depths than the α → γ transition at low temperature.Temperatures are computed via a finite difference algorithm(Minear and Toksioz, 1970) that solves the heat flow equa-tion using the conductivities from the experimental work ofXu et al. (2003). A plate model with the GDH1 parameters(Stein and Stein, 1992) was used for the initial lithospherictemperature distribution. Mantle temperatures at depthsbelow the lithosphere were determined by using a geother-mal gradient of 0.27 ◦C/km.

Simulations were done on 25 slabs in three groups withthermal parameters (φ = vertical subduction rate × ageof lithosphere at the trench) (Molnar et al., 1979) rangingbetween 3500–17000 km. When only lattice conductivitieswere used, cross-sectional areas of the metastable olivinewedges do not change much when compared with modelsrun with fixed conductivities of 3.138 W/mK (Stein andStein, 1992). Slabs that have significant wedges with fixedconductivity have reductions of no more than 5%. In termsof the maximum depths of the wedges, there is practically nochange at all in slabs which are moving slow enough for heatto be conducted in, thus enhancing the phase transitions andpreventing wedges from extending past 475 km. The wedgesof slabs which are subducting more rapidly extend to depths5-15 km shallower than in fixed-conductivity models. Whenradiative transfer is included, the results are significantlydifferent. The cross-sectional areas of the wedges shrink by20–30% for all slabs. This translates into metastable olivinewedges that extend to depths 30–50 km shallower than thosefor fixed conductivity slabs, with the differences increasingwith φ. These results agree with the results of Hauck et al.’s(1999) thermal model.

The presence of deep earthquakes, between 300 and 700km, contained within sinking slabs, suggest that the slabmaterial should be colder, denser, and stronger than the sur-rounding mantle material, a supposition supported by ob-servations of the maximum depth of earthquakes increas-ing with increasing thermal parameter and hence decreas-ing temperature inside the slab (Molnar et al., 1979). The

correspondence of deep earthquakes with the cold interi-ors of the subducting slabs suggests an association withthe kinetically inhibited olivine phase transformations. Onesuggested mechanism for the earthquakes is faulting occur-ring along superplastic aggregations of β or γ in the slabs(transformational faulting) (Kirby, 1987; Green and Burn-ley, 1989). If this is the mechanism responsible for deepearthquakes then the metastable olivine must extend atleast to the maximum depths of deep seismicity. However,thermal erosion of metastable wedges in our models indicatethat the olivine should be completely transformed well be-fore the depths of deepest seismicity. This indicates that fordeep earthquakes, other mechanisms should be considered.

References:

Daessler, R., Yuen, D.A., 1993. Geophys. Res. Lett. 20,2603–2606.

Devaux, J.P., Schubert, G., Anderson, C., 1997. J. Geo-phys. Res. 102, 24627–24637.

Fei, Y., Mao, H.-K., Mysen, B.O., 1991. J. Geophys. Res.96, 2157–2170.

Green, H.W. II, Burnley, P., 1989. Nature 341, 733–737.

Hauck, S. A. II, Phillips, R.J., and Hofmeister, A.M., 1999.Geophys. Res. Lett. 26, 3257–3260.

Hofmeister, A. M., 1999. Science 283, 1699–1706.

Kirby, S.H., 1987. J. Geophys. Res. 92, 13789–13800.

Kirby, S.H., Stein, S., Okal, E.A., Rubie, D.C., 1996. Rev.Geophys. 34, 261–306.

Marton, F.C., 2001. Eos Trans. Amer. Geophys. Union82, Abstract T41C–0872.

Minear, J.W., Toksz, M.N., 1970. T J. Geophys. Res. 75,1397–1419.

Molnar, P., Freedman, D., Shih, J.S.F., 1979. Geophys. J.R. astron. Soc. 56, 41–54.

Mosenfelder, J.L., Marton, F.C., Ross, C.R. II, Ker-schhofer, L., Rubie, D.C., 2001. Phys. Earth Planet. Int.127, 165–180.

Rubie, D.C., Ross, C.R. II, 1994. Phys. Earth Planet. Int.86, 223–241.

Stein, C.A., Stein, S., 1992. Nature 359, 123–129.

Xu, Y., Shankland, T.J., Linhardt, S., Rubie, D.C., Lan-genhorst, F., Klasinski, K. submitted. Phys. Earth Planet.Inter.

The influence of the large-scale mantleflow field on the interaction

of the mid-Atlantic ridge and the Icelandplume

Peter Mihalffy1, Bernhard Steinberger2and Harro

Schmeling1

1Institut fur Meteorologie und Geophysik,J.W.Goethe-Universitat Frankfurt am Main, Germany

2Institute for Frontier Research on Earth Evolution, Japan

Marine Science and Technology Center

The interaction of the Iceland plume with a global mantleflow field is investigated by 3D numerical models. The ap-proach consists of two steps. First the large-scale mantleflow field was calculated in a global modal, which includesthe whole volume of the mantle. This global and robust flow

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field served as a background flow in the regional model, inwhich the interaction of the mid-Atlantic ridge and the Ice-land plume was calculated.

A time-dependent model of the large scale mantle flowfield was obtained by using paleogeometries of the Atlanticand Eurasian plates reconstructed from magnetic anomalies[1] and by advecting density anomalies backward in time.The motion of the plume source on the bottom of the modelbox is calculated according to the distortion of an initallyvertical plume conduit in the large-scale mantle flow field [2].In the regional model the changing large-scale flow field andthe moving plume source are introduced as time dependentboundary conditions. In this way, the interaction of the Ice-land plume and the mid-Atlantic ridge is investigated in a3D model containing detailed ridge geomtery.

Results with time independent boundary conditionsshow that the large-scale mantle flow field is an importantfactor which controls the development of the plume. Inthe regional model the plume is tilted in the upper mantle,which is also shown by seismology. However, the northwardchanneling of the plume material in the model does not ex-plain the geochemical anomalies, which show an increasedplume influence south of Iceland.

Simulations with time dependent boundary conditions(time dependent ridge geometry and plume source position)may modify this channelling of plume material and give amore precise view of plume-ridge interaction

[1] Mueller et al. 1997. Digital isochrons of the world’socean floor, J. Geophys. Res.,103, 3211–3214.

[2] Steinberger, B. and O’Connell, R. J. 1998. Advectionof plumes in mantle flow: implications for hotspot motion,mantle viscosity and plume distribution, Geophys. J. Int.132, 412–434.

Clustering of plumes and small-scaleconvection in the upper mantle:

consequences of lower-mantle plumedynamics

Marc Monnereau1and David A. Yuen2

1CNRS/UMR5562, Observatoire Midi-Pyrenees, Toulouse,France



Minneapolis, USA

The clustering of plumes in the South Pacific and ev-idence for small-scale upper-mantle convection are long-standing issues in geodynamics, which have been aroundfor a long time. These features may be explained by con-sidering the interaction of the upper-mantle flow structuresto the lower-mantle plume dynamics. The key to this prob-lem is the presence of a low-viscosity channel in the vicinityof the 660 km phase transition. We have employed high-resolution 3-D spherical shell convection model in whichPREM like density has been used along with other depth-dependent thermodynamic and transport properties, suchas the Grueneisen parameter, thermal expansivity and vis-cosity. We have imposed an endothermic phase change at660 km depth with a Clapeyron slope of 3 MPa/K. Wehave examined a suite of viscosity profiles, ranging fromconstant viscosity to complicated depth-dependent viscosityprofile with a viscosity peak in the mid lower-mantle (Mitro-vica an Forte, 2002) and a low viscosity zone in the vicin-ity of the 660 km transition zone, first noted by Kido and

Cadek (1997). We have employed 256 points in the radialdirection and 256 spherical harmonics, which can resolve allof the small-scale features, generated in the flow in whichthe total power emanated from the mantle is around 35 TWand is internally heated with a strength about two timesthe chondritic abundance. The two features of clusteringof plumes and small-scale (Richter-like) rolls are manifestedonly in the models in which a low viscosity zone around 660km depth is present. They are absent in all other viscos-ity models. In the figure below we show the lateral ther-mal anomalies associated with the lower mantle which isbared to visual inspection (left panel). This panel can becontrasted to the right panel in which the lower mantle isnow covered by an opaque veil at 660 km depth. These re-sults show clearly the dynamical consequences in the upper-mantle features from interacting with the lower-mantle dy-namics. Both clustering of plumes and small-scale convec-tion in the upper mantle can be observed simultaneously inthe bottom panel. These results underscore the dynamicalimportance of the presence of a low viscosity zone under660 km, which can be caused by grain-size reduction dueto phase transition or lubrication by impinging hot lower-mantle plumes which fail to penetrate through the 660 kmphase change

Kido, M. and O. Cadek, Inferences of viscosity fromthe oceanic geoid: Indication of a low viscosity zone be-low the 660-km discontiuity, Earth Planet. Sci. Lett., 151,125-138, 1997.

Mitrovica, J.X. and A.M. Forte, On the radial profileof mantle viscosity, in Ice Sheets, Sea Level and the Dy-namic Earth, Geodynamics Series, 20, 187-199, J.X. Mitro-vica and B.L.A. Vermeersen (Eds.), American GeophysicalUnion, Washington, D.C., 2002.

— INVITED —Finite-frequency tomography reveals

a variety of plumes in the mantle

Raffaella Montelli1, Guust Nolet1, Guy Masters2,Francis A. Dahlen1and S.-H. Hung3

1Department of Geosciences, Princeton University, Princeton,NJ, USA

2IGPP, U.C. San Diego, La Jolla, CA, USA3Department of Geosciences, National Taiwan University,

Taipei, Taiwan

Morgan (1972) proposed that hotspots are due to plume-like upwelling from the lower mantle. Despite the abun-dance of evidence in support of Morgan’s idea, there is an-other current of thinking that believes hotspots originate

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from the upper mantle as a by-product of plate tectonics(Anderson, 1998, 2000; Foulger & Natland, 2003). Seismictomography has been so far unable to detect such narrowdeep rooted features. If plumes would appear in seismictomographic images, we would finally have a direct visualverification of the plume theory, and we will have a meanfor determining their origin in the mantle.

Our first global finite-frequency tomography of compres-sional waves shows unambigous evidence that at least 5hotspots originate in the deep lower mantle: Hawaii, EasterIsland, MacDonald, Samoa and Tahiti, and suggest thatfew others, such as Kerguelen and Cape Verde might beconnected to the core-mantle boundary (Montelli et al.,2003). Major hotspots which do not seems connected toa deep lower mantle plume include Afar, Ascension, Gala-pagos, Kilimanjaro, Madeira, Reunion and Tristan. Theseseem to originate in the mid mantle. Iceland originates ata shallow depth, confirming the results of Ritsema et al.(1999); Foulger & Pearson (2001); Foulger et al. (2001) andFoulger (2003) and clearly contradicting the finding of Bi-jwaard & Spakman (1999), who proposed a plume extendingall the way to the core-mantle boundary. Thus, what wasthe problem with the previous tomographic studies?

Almost all global P-wave tomographic models have beenso far obtained by applying the approximation of ray theory.The traveltime is only in by the Earth’s properties along aninfinitesimally narrow path that follows Snell’s law. Thissimplifies the mathematics, but it is quite far from physi-cal reality, in which rays have a given thickness dependingon the frequency content of the propagated wavefield. Thetraveltime of a finite-frequency wave is sensitive to velocitystructure off the geometrical ray within a volume known asthe Fresnel zone. Classical ray theory predicts that even asmall heterogeneity on the raypath would in the traveltime.But physics teaches us that small scale objects do not re-ally in the propagation of waves. They only do when theirscale length is comparable to the width of the Fresnel zone.Dahlen et al. (2000) and Hung et al. (2000) show that abroadband P traveltime is sensitive to anomalies in a hollowbanana-shaped region surrounding the unperturbed path,with the sensitivity being zero on the ray. The banana-doughnut kernel is thinner near the source and receiver butthe cross-path width extends up to about 1000-1300 kmnear the turning point, where the region of insensitivityaround the geometrical ray can reach hundreds of kilome-ters. Because of the minimax nature, surface reflected PPwaves show a much more complicated shape of the sensi-tivity region, with the ”banana-doughnut” shape replacedby a ”saddle-shaped” region region upon passage of a caus-tic. Not surprisingly, the introduction of such complicatedsensitivity has consequences for the final tomographic im-ages. Mantle plumes are narrow and therefore the mostaffected by an inappropriate modeling of finite-frequencyeffects. Because of their size, plume tails could partially behidden in the region of insensitivity around the unperturbedray. Wavefront healing is neglected by classical ray theory,but is properly accounted for in our finite-frequency mod-eling; this enhances the capability to detect such Earth’sstructures.

We present the final results of our inversion of finite fre-quency P, PP and pP waves with a dominant period of 20 s,whose travel time sensitivity kernels are modeled by usingthe formalism derived by Dahlen et al. (2000); combinedwith short period P and pP extracted from the ISC data

set (Engdahl et al., 1998) modeled by using standard raytheory. The velocity structure is sampled using an irregu-lar distribution of points to form a Delaunay mesh (Wat-son, 1981, 1992; Sambridge et al., 1995). Node spacing isadapted to the expected resolving length of our data andranges from about 200 km in the upper mantle to about600 km in the lower mantle. This gives an additional im-provement in the tomographic images.

An anisotropic viscous representation ofMohr-Coulomb failure

Louis Moresi1and Hans Muhlhaus2

1Monash Cluster Computing, School of Mathematical Sciences,Monash University, Melbourne, Australia

2Department of Earth Sciences, The University of Queensland,

Brisbane, Australia

In mantle convection models it has become common to makeuse of a modified (depth sensitive, Boussinesq) von Misesyield criterion to limit the maximum stress the lithospherecan support. This approach allows the viscous, cool ther-mal boundary layer to deform in a relatively plate-like modeeven in a fully Eulerian representation. In large-scale modelswith embedded continental crust where the mobile bound-ary layer represents the oceanic lithosphere, the von Misesyield criterion for the oceans ensures that the continentsexperience a realistic broad-scale stress regime.

In detailed models of crustal deformation it is, however,more appropriate to choose a Mohr-Coulomb yield criterionbased upon the idea that frictional slip occurs on whicheverone of many randomly oriented planes happens to be favor-ably oriented with respect to the stress field. As coupledcrust/mantle models become more sophisticated it is impor-tant to be able to use whichever failure model is appropriateto a given part of the system.

We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantleconvection problems coupled to large-scale crustal deforma-tion. Our approach uses an orthotropic viscous rheology (adifferent viscosity for pure shear to that for simple shear)to define a prefered plane for slip to occur given the localstress field. The simple-shear viscosity and the deformationcan then be iterated to ensure that the yield criterion is al-ways satisfied. An additional criterion is required to ensurethat deformation occurs along the plane aligned with maxi-mum shear strain-rate rather than the perpendicular planewhich is formally equivalent in any symmetric formulation.

It is also important to allow strain-weakening of the ma-terial. The material should remember both the accumu-lated failure history and the direction of failure. We haveincluded this capacity in a Lagrangian-Integration-point fi-nite element code and will show a number of examples ofextension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation is general andapplies to 2D and 3D problems, although it is somewhatmore complicated to identify the slip plane in 3D.

On the curvature of oceanic arcs

Gabriele Morra, Klaus Regenauer-Lieb andDomenico Giardini

Geophysics Institute, ETH Zurich, Switzerland

32


The key feature of plate tectonics is the subduction of coldoceanic plates into a hot convective mantle. These sub-ducting plates, as seen from the surface, mostly portray adistinct concave arc shape at the trench with respect tothe leading edge of subduction. The origin of arc curvatureis not yet understood. A common belief is that it is proba-bly an effect of the Earth’s sphericity. However, the spher-ical effect of the Earth creates convex, long-wavelength arcshapes. We thus investigate whether concave arc curvaturecan be explained by: (1) Exogenic feedback between the mi-grating lithosphere and the secondary induced mantle flow,(2) Endogenic heterogeneities within the lithosphere itself,e.g. owing to differences in cooling ages of the plate atthe trench. Although both mechanisms create concave arcs,for isolate subduction systems, only the endogenic effects aresufficient to explain the magnitude of observed arc curva-ture. We compare our results to the Aleutian and Sandwicharcs.

Our method is based on a novel 3-D numerical tool. Wemodel the subduction process as a solid (lithosphere) - fluid(mantle) interaction. Two different numerical methods areused to solve for the constituents: Implicit Finite Element(FEM) for the lithosphere and Implicit Boundary Elements(BEM) for the mantle. This joint approach extends the 2-Dsetup of Funiciello et al., (JGR, 2003) into 3-D by addingthe BEM solution as a semi-analytical solution for the man-tle drag. The BEM solution builds on the Stokeslet theory,which shows that the drag force mainly depends on the in-tegration of the singularities at the extremities of the slab.A short summary of the Stokeslets theory and its possibleapplication in geodynamics is given.

The effect of the stress field on the meltchannel instability

Kristian Muller and Harro Schmeling

Institut fur Geophysik, Universitat Frankfurt am Main,

Germany

We investigate melt transportation in partially molten rocksunder different stress fields above the head of a mantleplume or beneath a spreading mid-oceanic ridge. We modelsuch aggregates in a 2D-FD code by means of a porous de-formable matrix with melt under the influence of a givenstress field to clarify the following key questions:

• Could channeling occur in a matrix containing a ran-dom melt distribution under a given stress field?

• Which orientation does it take?

• Is it possible to achieve a focusing of melt towards aMOR (dykes)?

• Does applying simple or pure shear to the matrix re-sult in a difference in the formation and orientationof channels?

• How does the channel instability evolve during finitesimple shear?

Numerical solution of the problemThe 2D-FD code FDCON [1] solves the relevant fluid-dynamic equations (conservation of mass and momentum,according to McKenzie [2]) for melt and matrix respectively.

These equations are solved assuming the CompactionBoussinesq Approximation (CBA), using a stream functionformulation for the momentum equation and an ADI schemewith upwind for the energy equation. For the time being,the calculations are isothermal, so the energy equation is notsolved. Lately, the conservation of water has been includedand is presently being tested.

The boundary conditions in the code are: Pure shearwith free slip and simple shear with no slip.

The initial porosity field consists of a random distribu-tion of 3.5 ± 0.6 % porosity.

Melt Channel InstabilityIn a deforming partially molten aggregate, weakening ofthe solid matrix due to the presence of melt creates an in-stability in which melt is localized by the following mech-anism: regions of initially high melt fraction are areas oflow viscosity and pressure, so that melt is drawn into theseregions from higher pressure surroundings. This further en-hances the melt weakening, producing a self-excited local-ization mechanism [3].

Results and ConclusionsThe channeling developing (under the conditions of simpleshear) in a random melt distribution shows that melt is ac-cumulated preferably in inclined channels. For both, simpleas well as pure shear, the growth rate is highest for an orien-tation parallel to the direction of the maximum compressivestress and proportional to applied stress and the reverse ofthe Melt Retention Number.

This also confirms the theoretical growth rate found byStevenson [3].

Comparing different viscosity rheologies [1,2,4], we areable to clarify the influence of the CBA. The CBA influencesonly the growth rate at high wave numbers in the way ofshifting them constantly to higher values.

In the isothermal models we found that the influence ofwater reduces the growth rate. However Hall’s models [5]with water and constant melting rate show higher growthrates, which suggests it may play a major role.

Under simple shear melt channels evolve from an irregu-lar melt distribution at angles of 45 degrees to the directionof shear. Upon further straining they rotate out of the ori-entation of maximum growth rate and partly disrupt.

We further seek to clarify which physical quantities mayaffect the orientation of channels and their wavelengths.Possible factors are the compaction length and the nature ofthe stress field. The latter assumption will be tested com-bining pure and simple shear and defining different stressgradients.

References:

[1] H. Schmeling. Partial melting and melt segregationin a Convecting mantle. Physics and chemistry of par-tially molten rocks; N. Bagdassarov and D. Laporte and A.B. Thompson, Kluwer Academic Publishers, Dordrecht,141-178, 2000

[2] D. McKenzie. The generation and compaction of par-tially molten rock. Journal of Petrology, 25:713-765, 1984

[3] D.J. Stevenson. Spontaneous small-scale melt segrega-tion in partial melts undergoing deformation. GeophysicalResearch Letters, 16(9):1067-1070, 1989

[4] D.L. Kohlsted. Rheology of partially molten rocks.Physics and chemistry of partially molten rocks; N. Bagdas-sarov and D. Laporte and A. B. Thompson, Kluwer Aca-

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demic Publichers, Dordrecht, 1-28, 2000

[5] C.E. Hall and E.M. Parmentier. Spontaneous melt lo-calization in a deforming solid with viscosity variations dueto water weakening. Geophysical Research Letters, 27:9-12,2000

Effects of magnetic field and radioactiveheating in the core on thermal evolution of

the convecting mantle and core

Takashi Nakagawa

Department of Earth and Space Sciences, University


A couple of our previous studies have investgated the avail-ability for parameterized convection models in the hetero-geneous mantle and possible scenarios of thermal evolutionof the core by using the heat flux through the CMB which isestimated from complicated mantle convection model [Nak-agawa and Tackley 2002, AGU Fall Meeting; Nakagawa andTackley, 2003, IUGG General Assembly]. In recent progressof thermal evolution of the Earths core, the importance ofradioactive heat source in the core and heating by magneticfield (ohmic dissipation) is focused on by various researchers[Labrosse, 2003; Buffett, 2002; Buffett, 2003; Gubbins et al.,2003]. In this study, several preliminary results obtainedfrom thermally coupled model between convecting mantleand core including ohmic dissipation in the core are showedfor proposing other possible scenarios of thermal evolutionof the Earths interior.

Numerical model of mantle convection is based on Tack-ley and Xie[2002], which includes material differentiation,multiple phase change, plate-like behavior and partial melt-ing. Thermal evolution of the core as a bottom thermalboundary condition of mantle convection is based on Buf-fett [2002], which includes compositional convection, innercore growth and ohmic dissipation.

Three criteria for possible thermal evolution are checkedin this study: (1) Radius of the inner core, (2) Surface heatflux and (3) Heat flux through the CMB. In addition tothese criteria, the ohmic dissipation as a function of timeis also checked for understanding the magnetic evolution ofthe Earth’s core.

Geodynamic interpretation of temporalgeoid variations

Karen Niehuus and Harro Schmeling

Institut fur Meteorologie und Geophysik,

J.W.Goethe-Universitat Frankfurt am Main, Germany

IntroductionDensity distributions derived from highly resolved seismictomography and viscosity models of Earth’s mantle are in-vestigated in analytical and numerical flow models. Theaim of this project is to fit the models’ predicted observ-ables to the GRACE satellite-mission’s gravity and geoidmeasurements and the field’s variation with time, with spe-cial focus on lateral variations of the viscosity in the regionof the lithosphere and asthenosphere.

Advection of a given density field yields temporal vari-ations in the geoid and dynamic topography. In order to

investigate whether identifiers of such mantledynamic pro-cesses may be discerned from other signals contained inGRACE-data, these quantities will be analyzed in the spa-tial and spectral domain. This permits predictions for re-gional mantledynamic contributions and renders variationsof the harmonic coefficients with time, thus providing cor-rective fields to apply to GRACE-data.

ModellingAdvection of mantle density distributions derived from seis-mic tomography drives a flow.

The variables of the governing flow equations are ex-pressed in terms of products of radial functions and scalarspherical harmonics, yielding a set of coupled first orderdifferential equations. Spheroidal and toroidal terms decou-ple, the initial solutions for a set of boundary conditions arepropagated through a series of shells of constant values forthe sought variables by the propagator matrix [Panasyukand Hager, 1996]. This in turn yields solutions in the formof boundary vectors that give the fluid velocities, stresses,gravitational potential and its radial derivative at any radiallevel in the earth.

We plan to implement lateral viscosity variations intoour analytical code [Zhang and Christensen, 1993]. Whilethey report no significant improvement of the geoid fit, al-lowing for lateral viscosity variations within the lithosphereand asthenosphere yielded best fits according to most recentpublishings [Cadek and Fleitout, 2003].

Temporal geoid variationsAdvection of tomography-based mantle densities yields firstestimates of the magnitute of temporal geoid variations.Additionally, we determine the signal’s change caused bysubducting slabs or mantle plumes employing geoid kernels.Geoid kernels represent the geoid produced by a unit massanomaly of a given wavelength at a given depth, includingthe effects of dynamic topography. The geoid anomaly δNlm

caused by any assumed density distribution in the mantleis obtained by a convolution of these kernels with the den-sity field [Turcotte et al., 2001]. Advection of a densitydistribution (substituting δρ with the equation of state forincompressible fluids) with a vertical velocity of vz yieldsthe temporal geoid variation

∂δNlm

∂t=

4πGre

(2l + 1) g

∫ re

rc

∂Gl(r)

∂rαρ0δTlmδrvz. (1)

Fig. 1: Expected resolution of temporal geoid changes for a1 - and 5 - year GRACE mission duration and an estimate

of geoid variations for mantledynamic processes. Thelatter were calculated with a slab sinking model

(Marquart, pers. comm.) (bars), estimated using eq. (1)

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(dots) and obtained by advecting density distributionsderived from seismic tomography (solid line).

ConclusionsMantle-dynamic processes produce time-dependent geoidsignals which, according to preliminary results, reach or ex-ceede the resolution limits of the 5 - year GRACE mission.While the results shown are preliminary, an iterative searchof the parameter space should yield models of good fit tothe observed geoid and its variation. Estimates of the mod-els’ dynamic topography provide an additional constraint.

References:

O. Cadek and L. Fleitout. Effect of lateral viscosity varia-tions in the top 300 km on the geoid and dynamic topogra-phy. Geophysical Journal International, 152:566-580, 2003.

S.V. Panasyuk and B.H. Hager. Understanding the ef-fects of mantle compressibility on geoid kernels. GeophysicalJournal International, 124:121-133, 1996.

Donald L. Turcotte, Gerald Schubert, and Peter Olson.Mantle Convection in the Earth and Planets. CambridgeUnviversity Press, 2001.

S. Zhang and U. Christensen. Some effects of lateral vis-cosity variations on geoid and surface velocities induced bydensity anomalies in the mantle. Geophysical Journal In-ternational, 114:531-547, 1993.

Constraining Venus structure by gravityand topography: global methods

Martin Pauer


Republic

We examine on the global scale two different principles ofa topographic support. Our goal is to find such an inte-rior structure of planet which best predicts the geoid data.Both venusian geoid and topography are represented bythe most recent spherical harmonic models (MGNP180Uand GTDR.3 respectively). The predicted data are com-pared with observed ones on the basis of common spectralmethods. First, we apply the principle of isostasy and welook for an average apparent depth of compensation (ADC).For the whole spectrum, dominated by the low degrees, a165 km depth is found which might correspond to a bot-tom of the lithosphere. However, the predicted geoid doesnot fit well to the observed data in the whole spectral inter-val. Studying the degree-dependent ADC and the admit-tance function we obtain a uniform depth of compensationaround 35 km for degrees higher than 40. For the geoid atdegrees lower than 40 we propose a dynamic origin. Thishypothesis is investigated in the framework of the internalloading theory. Assuming that the buoyancy force does notvary with depth (which roughly corresponds to a plume-likestyle of mantle convection) we can well explain about 90 %of both geoid and topography (see below). The best fit tothe data and the observed admittance function is found forthe viscosity profile with a ∼100 km thick lithosphere anda viscosity increase by factor 10–100 through the mantle.

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Gravity field and topography of Venus:localization methods

Martin Pauer


Republic

Localization of the geophysical fields is a useful tool for fil-tering the full-spectra signal. In comparison with the spheri-cal harmonics the wavelet base (or some other suitable func-tion) is well localized (i.e. has non-zero amplitudes only ina vicinity of the point of interest). So using this method weobtain true field anomalies without artificial oscillations. Inour study of geoid and topography of Venus we also look atlocalized ”qualitative” fields: correlation and admittance.There are two major approaches - spectral one presented bySimons et al. (1997) and spatial one presented by Kido etal. (2003). We use the later one motivated by a possibleimprovement of resolution in the selected regions. For anintermediate and short wavelengths the spherical harmonicexpansions of the geoid contain too much of global signaturewhich makes the local features unreadable. In contrast,the use of a localization function gives us a clear picturewith individual features (see below). This could be a basefor intuitive comparison of structures on the given scale.Localization of the qualitative functions as of correlation oradmittance could give us information about observed geo-physical models as well as about degree of agreement withour results.

References:

Kido, M., Yuen, D.A. and Vincent, A.P. (2003): Continu-ous wavelet-like filter for a spherical surface and its applica-tion to localized admittance function on Mars, Phys. EarthPlanet. Inter., 135, 1–16.

M. Simons, S. C. Solomon, and B. H. Hager (1997): Local-ization of gravity and topography: Constraints on the tecton-ics and mantle dynamics of Venus, Geophys. J. Int., 131,24–44.

A model of kinetics effects inthe transition zones: application to

the postglacial rebound

Gilles Pelfrene and Luce Fleitout


The type of mantle convection strongly depends on differ-ent kinetics effects such as heat transfers across the transi-tion zones, chemical diffusion during phase transformationor stress relaxation occuring in response to volume changes.At a macroscopic scale, we model these effects through asingle parameter which is a frequency-dependent compress-iblity in the transition zones, in order to see its influence onpostglacial rebound observables. A realistic axisymmetricand compressible Earth model based on PREM parame-ters and on a viscoelastic rheology is submitted to the lastLaurentide ice-sheet glacial load (110 ky cycle). Becauseof the lack of data, a wide range of time characteristicsof phase transformations is tested (10ky-10My). It showsthat the viscosities of the upper and lower-mantle are notmuch affected by kinetics effects but that the pressure-fieldis strongly delayed in the transition zones during loading.This indicates a specific rheological behaviour of the tansi-tion zones depending on both their thickness and their timecharacteristics.

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Modelling continental rootsin a convecting mantle

Claire Perry1, Claude Jaupart1and Paul Tackley2

1Laboratoire de Dynamique des Systemes Geologiques, Institutde physique du globe de Paris, France

2Department of Earth and Space Sciences, University


Continental roots represent extensive regions of seismicallyfast, cold, and buoyant material compared to the surround-ing mantle. The fact that they are cold undoubtedly pro-duces large lateral variations in temperature, and hence vis-cosity in the mantle below. The effects of continental rootson the mode of mantle convection are studied using a 2-D Cartesian viscous flow model in which both the mantleand lithosphere are described as compressible, Newtonianfluids. Rayleigh numbers between 105 and 107 are consid-ered. Viscous dissipation, adiabatic heating, and internalheating are incorporated into the energy equation. The ra-diogenic heat produced by the decay of radiactive elementsin the mantle and the lithosphere respectively are incorpo-rated into the model. The heat production in these tworegions is distinct, as determined by studies of mantle xeno-liths and heat flow. The freely-moving continental root ismodelled as a highly viscous, undeformable region with aviscosity 102–103 times higher than that of the surroundingmantle. The presence of the continental root is shown toimpose time-dependent behaviour in the mantle circulationbelow. The continental heat flow, displacement, and strainrates vary significantly depending on the combination of pa-rameters listed above. Investigation of the time-dependenceof the results requires the consideration of both conductiveand convective timescales.

— INVITED —The physics of subduction: statics,

kinematics and dynamics

Klaus Regenauer-Lieb1,2, Gabriele Morra1and

Francesca Funiciello3

1Institute of Geophysics, ETH Zurich, Switzerland2CSIRO Perth, Exploration and Mining, Australia

3Dip. di Scienze Geologiche, Univ. ”Roma Tre”, Italy

The subduction problem has been tackled by many differ-ent methods. The simplest method is analytical/numericalmodelling of static stress equilibrium assuming elastic orelasto-plastic subducting slabs in steady state emphasizingon flexural topography; the next is analytical and fluid dy-namic kinematic solutions for corner flow style models em-phasizing on temperature solutions derived from kinemati-cally prescribed mantle flow; another is the laboratory ana-logue modelling of idealized scenarios which display partof the elasto-plastic or visco-elastic dynamics; the last ap-proach is numerical fluid dynamic modelling of stratified vis-cous fluids aiming to solve dynamical modes of subductionwhich arise in (1) subduction initiation, (2) interaction withdiscontinuities (660 km), (3) slab breakoff, (4) solid slab-fluid mantle interaction, (5) deep earthquakes, (6) dynamictopography and lastly (7) interaction of subduction withoverriding plate with implications for orogeny. While each

method has its individual advantage, we show that fluid dy-namical modelling of subduction is chiefly useful for kine-matics. However, dynamical fluid dynamic Rayleigh-Taylormodes do not correctly describe the physics of Earths sub-duction. Elasticity must be incorporated as a key ingredientof subduction. It is non-dissipative and the energeticallyfavoured mode of deformation. Therefore it is imperativeto investigate dynamic modes 1) to 7) with consideration ofelasticity. We will give a few examples highlighting the roleof elasticity in dynamics of subduction and show the limi-tations of purely viscous modelling.

Modeling shear instabilities with blocksliders: brittle and ductile

Michael R. Riedel

Institute of Geosciences, University of Potsdam, Germany

Block slider-type models have been succesfully used foralmost 35 years to describe the spatio-temporal develop-ment of shear instabilities in the brittle crust (Burridge& Knopoff, 1967; Olami et al., 1992). More recently, in-creasing attention is paid on the extension of the classicalBurridge-Knopoff model (based on a pure Mohr-Coulombrheology) with a viscous component, either to include depth-dependent properties into the model or aiming at a moreaccurate description of fore- and aftershock sequences of amain earthquake event (e.g. Hainzl et al., 1999). In ad-dition, the development of shear-localization in the ductilemantle lithosphere has become an increasingly attractivemechanism for the generation of intermediate-depth anddeep-focus earthquakes. Heat generated during viscous de-formation provides a positive feedback to creep and even-tually faulting under high pressure (Karato et al., 2001,Bercovici and Karato, 2003).

The present paper discusses the specific properties ofblock slider-type models that are extended with a viscouscomponent and compare their behaviour with the pure brit-tle (”classical”) case. It is shown, that block slider-typemodels for ductile instabilities in the mantle lithosphereare numerically much less demanding than solutions basedon the corresponding, thermal-mechanically coupled con-tinuum equations. Furthermore, they allow to include eas-ily possible non-equilibrium effects associated with mineralphase transformations in a subducting slab (kinetic over-shoot, grainsize reduction) into the rheological model.

References:

D. Bercovici and S. Karato, Theoretical Analysis of ShearLocalization in the Lithosphere, in: Reviews in Mineral-ogy and Geochemistry 51, eds. S. Karato and H.-R. Wenk,Chapter 13 (2003) 387–421.

R. Burridge and L. Knopoff, Model and theoretical seismic-ity, Bull. Seism. Soc. Am. 57 (1967) 341–371.

S. Hainzl and G. Zoller and J. Kurths, Similar Power-Lawsfor Fore- and Aftershock Sequences in a Spring-Block Modelfor Earthquakes, J. Geophys. Res. 104 (1999) 7243–7253.

S. Karato, M. R. Riedel, D. A. Yuen, Rheological Structureand Deformation of Subducted Slabs in the Mantle Transi-tion Zone: Implications for Mantle Circulation and DeepEarthquakes, Phys. Earth Planet. Inter. 127 (2001) 83–108.

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Z. Olami and H. J. S. Feder and K. Christensen, Self-organized criticality in a continuous, nonconservative cel-lular automaton modeling earthquakes, Phys. Rev. Lett. 68(1992) 1244–1247.

The effect of hydrous melting on plumedynamics

Thomas Ruedas1∗, Harro Schmeling1,Gabriele Marquart1,2

1Institute of Meteorology and Geophysics, Universityof Frankfurt am Main, Germany

2Vening Meinesz School of Geodynamics/SRON, Universityof Utrecht, The Netherlands

∗ now at Dansk Lithosfærecenter, København, Denmark

Convection models including the effect of melting normallyassume that the mantle is anhydrous, because water con-tents seem to be very low in the upper mantle. On the otherhand, it is known that hydrous damp melting occurs e.g. be-neath the principal melting zone of mid-oceanic ridges andresults in the extraction of even the small water contentin mantle rock after a few percent melting and a concomi-tant stiffening of the residue. We use a recent parameter-ization of hydrous and anhydrous melting, available datafor partitioning of water and the water content of normalmantle and plumes in the frame of a combined convection–melting numerical model to calculate the effect of hydrousmelting and dehydration stiffening on the convection andmelting dynamics of a plume in the upper mantle. Themodels confirm that dehydration leads to a strong viscos-ity increase over a depth range of a few tens of kilometersduring initial melting, at a depth which would be treatedas rheologically weak in a model with only pressure andtemperature-dependent viscosity. As this region lies deeperin the mantle in a plume, there is a depth interval, wherethe plume actually has a greater viscosity than normal man-tle despite its higher temperature. If the plume containsmore water than average MORB-source mantle, the depthof this high-viscosity region could lie as deep as 200–250 km.The viscosity increase results in a strongly reduced activeupwelling, so that the crust produced above the center ofa hydrous plume is less thick than that above an otherwisesimilar dry plume; on the other hand, the crustal anomaly ismore pronounced over a larger along-ridge interval in the hy-drous case. The differences in viscosity structure also resultin different stress fields for anhydrous and hydrous models.Several authors have proposed that the stress field controlsthe orientation of dikes and/or melt channels in the melt-ing region of the mantle. Using the mantle velocity fieldfrom the convection models, an attempt is made to predictthe orientation of tabular tensile dikes in anhydrous andhydrous plume-ridge settings and the resulting direction ofmelt migration. Comparison of both cases reveals notabledifferences especially in the shallower parts of the melting re-gion, where dike orientation in the hydrous plume resemblesmore the pattern also determined for normal MOR. Further-more, dike orientation seems to support defocussing of meltaway from the plume center in several parts of the plumehead, especially at greater depths.

Dynamic implications of mantleserpentinization for intra-slab seismicity

Lars Rupke1, Jason Phipps Morgan1,

Gabriele Morra2, Klaus Regenauer-Lieb2,James Connolly2and Matthias Hort3

1GEOMAR Research Center / SFB 574 Fluids in SubductionZones

2ETH Zurich, Switzerland3Universitat Hamburg, Germany

Subduction zones commonly show inclined seismic zonesthan can extend down to ∼ 670km depth. The origin ofsubduction related intermediate and deep earthquakes re-mains, however, not fully understood. Many studies em-phasize the importance of dehydration reactions (dehydra-tion embrittlement). Released fluids may increase the porepressure which decreases the effective confining pressure andthereby facilitates seismic rupture. An additional – less wellunderstood – factor promoting intra-slab seismicity may besudden volume/density changes during metamorphic reac-tions.

This process may be most important during the de-watering of serpentinized mantle where volume/densitychanges are high (up to 40 %). The incoming plate’s litho-spheric mantle may become significantly serpentinized be-tween the outer rise and the trench axis. Here the bend-ing plate develops normal faults that potentially providethe conduits for sea water to reach the slab’s mantle to makeserpentine. Deeper within the subduction zones, both slabdeserpentinization and the gabbro-to-eclogite transition areassociated with a strong volume reductions. The poten-tial dynamic implications of volume/density changes duringsubduction have, however not yet been thoroughly studiedusing numerical models with most current models treatingslabs as an incompressible viscous fluid.

Here we further explore the potential dynamic impli-cations of slab metamorphism (i.e. serpentinization, de-serpentinization, eclogitization) using a coupled analytical-solid-mechanical FEM model. We treat the subducting slabas a visco-elasto-plastic plate using a realistic, experimen-tally based, rheology. The model solves the implicit coupledtemperature-deformation problem; metamorphic reactionsare modelled using look-up tables calculated with the PER-PLEX program. We account for volumetric changes byadding a volumetric strain component to the ‘visco-elasto-plastic’ strain rate decomposition.

We find that slab deserpentinization significantlychanges the stress state of a subducting slab. The volumereduction during deserpentinization leads to very high strainrates. These high strain rates may lead to seismic failure byeither (1) reactivating pre-existing hydrated ‘bend-faults’or (2) producing new rupture planes. These findings sug-gest that dehydration reactions and the associated volumechanges may be important for triggering intermediate anddeep intra-slab earthquakes.

Modelling crustal accretion abovethe Iceland plume

Gabriele Marquart1and Harro Schmeling2

1SRON & Dep. of Earth Science, Utrecht University,The Netherlands

2Institute of Geophysics, University of Frankfurt, Germany

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The Icelandic crust, though oceanic in origin, is distinc-tively different from normal oceanic crust. Excess tem-peratures of the mantle plume generate anomalously highamounts of melts resulting in crustal thickness on an aver-age of 24 km, with a maximum value of 50 km. Seismicvelocities of the crust are high, and have to be explained bythermal or chemical effects.

We model crustal accretion in Iceland by a two fold ap-proach. In a 2D spreading model with anomalous mantletemperature beneath the ridge we solved the Navier-Stokes-, the heat tansport, the mass conservation and the meltingequations to determine the enhanced melt production be-neath the ridge. This melt was extracted and emplacedon top of the model to form the crust. Two cases are dis-tinguished: a) Extruded crustal material is taken out ofthe model and is only advected according to the spreadingof the plate, b) extruded material is fed back into the modelfrom the top to mimic isostatic subsidence of extruded crust.We find that the feed back of case b) is only moderate. Forexample, if extruded crustal material as thick as 40 km is fedback into the model, the melting region is depressed only byas much as 10km, and the total amount of generated meltis reduced by about 20 %. On the other hand, upper 30 kmof the model is cooled considerably by several 100 degrees.

A second set of models focuses on the details of crustalaccretion without explicitly solving for the melting and ex-traction. Knowing the spreading rate, the rate of crustalproduction can be estimated, but the site of emplacementis not obvious. For Iceland we define four source regionsof crustal accretion: surface extrusion, intrusion in fissureswarms at shallow depth connected to volcanic centres,magma chambers at shallow to mid-crustal level, and adeep accretion zone, where crust is produced by widespreaddyke and sill emplacement and underplating. We solvedthe Navier-Stokes-, the heat tansport and the mass con-servation equations and prescribed different functions inspace and time for crustal production in the four defined re-gions. The temperature of the imposed material depends onthe source region and the process of accretion is monitoredby identifying material from different source regions by amarker approach. After some time of spreading and accre-tion, a characteristic temperature distribution and crustallayering evolves, which is compared to observation data.

Model sensitivity of GIA induced highresolution gravity anomalies and geoid

heights

Hugo Schotman1,2 and Bert Vermeersen1

1Delft Institute for Earth-Oriented Space Research (DEOS),

Delft University of Technology, The Netherlands2SRON National Institute for Space Research, The Netherlands

Glacial Isostatic Adjustments (GIA) models compute the re-sponse of a model Earth to an ice loading history, for ex-ample using normal mode or finite element models. Com-mon results are sea-level curves, free air gravity anomaliesand geoid heights. We have investigated the influence of anumber of model assumptions on the high resolution free-air gravity and geoid signal, using a semi-analytical normalmode technique and a pseudo-spectral sea level code. Wehave focussed on coast line migration and the influx of meltwater, the layering of the Earth, including crustal low veloc-ity zones, and the use of different ice loading histories. The

results can be compared with sensitivities of future satel-lite gravity missions as GOCE, which is expected to mapthe static gravity field with an accuracy of 1 mgal for grav-ity anomalies and 1 cm for geoid heights, at a resolution of100 km or less. This research is a first step in the direc-tion of using a high resolution finite element model to studythe influene of lateral heterogeneities on GIA.

— INVITED —From sealevel to space geodesy: the past

and the future of postglacial rebound

Giorgio Spada

University of Urbino, Italy

Since the pioneering work of Haskell (1935), the approachto the postglacial rebound problem has varied considerably.The flat, homogeneous, newtonian fluid half space has beennon substituted by modern 2D and 3D models of the Earth,which can deal with both linear and non linear mantle rhe-ologies and with lateral variations in the mechanical proper-ties of the lithosphere and of the mantle. The overtaking ofMD models has been generally motivated by the increasedamount and quality of the data available, which now includegeodetic GPS and VLBI observations along with the classi-cal relative sealevel data. A great effort has been made toimprove modeling, with considerable success, but our knowl-edge on the Earth interior as inferred by postglacial reboundobservations is still imperfect. We review some of the mile-stones of the development of postglacial rebound studies,the physical and geological observations available, and wegive a few examples of interesting case studies.

— INVITED —Planetary interior dynamics

Tilman Spohn

Institut fur Planetologie, Munster, Germany

The dynamics of the interiors of earthlike planets and satel-lites is most likely governed by interior convective flow. Butin allmost all cases this flow does not extend to the sur-face as on Earth (plate tectonics) but is confined to themantle below the lithosphere. The coronae on Venus, largecircular domes, have been speculated to be either causedby plume heads extending to the surface or by the roots ofdownwelling cold plumes. There is also debate about earlyphases of plate tectonics or plate-like tectonics possibly onMars and on the Jovian Moon Ganymede and about litho-sphere delamination. But for the present day plate tecton-ics on these planets can be excluded. Heat transfer to thesurface is then by conduction through the lithosphere andthrough volcanic vents piercing through the lithosphere. Inthe early evolution mantle melting and extensive volcanismled to the differentitaion of the mantle and the formation ofthe crust. This differentiation probably occurred simulta-neously but extended beyond the more rapid formation ofthe core. Mars is the planet of which the early evolutionis best understood thanks to the isotope data from SNCmeteorites and the remnant magnetization of the very earlycrust. The isotopic evidence suggests that this differentia-tion occurred very early on Mars, in the first few 100 millionyears, and left reservoirs that have experienced very little if

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any mixing thereafter leading some researchers to speculatethat may be the Martian mantle has not been convectingsince. Isotopic evidence also suggests that core formationon Mars was very rapid and occured in the first few 10 mil-lion years. The formation of the gigantic volcanic Tharsisdome occurred together with crust formation but the vol-canic activity remained focussed there and extended albeitat an ever decreasing rate until the geologically recent past.

The magnetic properties of the planets is best under-stood by applying the theory of hydromagnetic dynamosdriven by thermal and compositional convection in thecores. Thermally driven dynamos appear to be confined tothe early cooling phases of the planets when vigorous man-tle convection cooled the cores. Mars, Moon and Venus arelikely to have had these early dynamos. In these planets,dynamo activity stopped when core cooling by the man-tle failed to keep the core convecting and, moreover, failedto freeze inner cores. On Earth and Mercury inner coregrowth is thought to have kept the dynamos alive to thepresent day. On Earth this is almost certainly due to platetectonics effectively cooling the deep interior. On Mercurycore freezing is attributed to the core being comparativelylarge and the mantle being comparatively thin. The puzzlein this model is Ganymede which should be similar to theMoon and Mars but which appears to have a self-sustainedmagnetic field.

The Jovian system provides a laboratory for studyingadditional features of planetary dynamics and evolutionsuch as tidal heating and coupled thermal- orbital evolutions(Io and Europa), heat transfer in partially molten interiors(Io), internal oceans (Europa, Ganymede and Callisto), anddifferentiation that failed to run to completion (Callisto).

Melt extraction in two-phase flows

Ondrej Sramek and Yanick Ricard

Ecole normale superieure de Lyon, France

Melt extraction in two-phase flows is often modelized us-ing equations developped by McKenzie (1984). RecentlyBercovici et al. (2001) proposed a somewhat different setof equations where, for example, the isotropic compactiondepends on the porosity and where the two phases (ma-trix and melt) are submitted to different pressures. Weextended these equations to take into account the phasechange in the case of a univariant phase diagram. We showhow the pressure difference between the two phases is re-lated to the melting rate and the rate of porosity change.We suggest that as the two phases undergo different pres-sure conditions, the melting does not occur under the usualthermodynamic static conditions (a single pressure field).Although preliminary, this study will show various simula-tions of 1D melting.

A self-consistent mantle convection model:generation of a low-viscosity zone and

plate-like features

Claudia Stein and Ulli Hansen

Institute of Geophysics, University of Muenster, Germany

A numerical mantle convection model with a temperature-,pressure- and stress-dependent rheology can generate differ-ent tectonic styles as they are observed for various terres-trial planets. The temperature dependence of the viscosity,

the basis of the rheological model, prescribes a viscositychange between the cold material at the surface and the hotmaterial at the bottom of the three-dimensional Cartesianbox regarded. Thus, the assumption of a strong temper-ature dependence leads to a highly viscous surface. Thedegree of deformation in this rigid surface (‘stagnant lid)is controlled by the applied yield stress. The variation ofthe yield stress for a constant pressure dependence resultsin four different regimes. For a high value stagnant lid con-vection like on Mars and Mercury maintains, i.e. convectionis confined beneath a rigid and immobile surface. For inter-mediate values an episodic behaviour as assumed for Venusappears. In this case deformation is limited to narrow zones.Parts of the surface behave like a rigid plate, but as sub-duction is faster than conductive cooling from above, inter-mittent behaviour is a consequence. For relatively low yieldvalues plate-like behaviour is found. Extended plates movecontinuously in time, because the influence of stress com-pared to that of pressure is diminished allowing for slowersubduction. Finally, for even lower values of the yield stressthe surface shows strong internal deformation in such a waythat the surface can be regarded as fluid-like.

Besides plate-like features as for example cylindrical up-wellings, sheet-like downwellings and trench migration, alow-viscosity zone (LVZ) arises self-consistently. The LVZ,however, only appears under a certain parameter combina-tion. In the four regimes described above, only the plate-like regime displays a viscosity drop at shallow depths. Thusthe existence of continuously moving plates and the presenceof a low-viscosity zone are two coupled phenomena. Thereason for the formation of the LVZ is definitely the appliedpressure dependence. Without a pressure-dependent vis-cosity neither plate-like behaviour nor a low-viscosity zoneis observed at all. However, pressure-dependent viscosityconvection does not necessarily form a low-viscosity zone.Only on a narrow range of parameters the self-consistentgeneration of a low-viscosity zone and plate-like behaviouris achieved.

Using TABOO for postglacial reboundpredictions

Paolo Stocchi and Giorgio Spada

Istituto di Fisica, Universita di Urbino, Italy

TABOO is a simple postglacial rebound calculator writtenin Fortran 90, which allows for the computation of displace-ment, velocity fields, and variations of the Stokes coefficientsforced by surface loads. TABOO, which has been mainlydeveloped for pedagogical purposes and is freely available,can be employed to compute the response of layered (1D),incompressible, self-gravitating, Maxwell viscoelastic Earthmodels to surface loads of various geometries and time-histories. In this poster we illustrate its basic features andwe give examples of interesting geophysical applications.

The structure and the surfacemanifestation of mantle plumes in

depth-dependent three-dimensional models

Balint Sule

40


Geodetic and Geophysical Research Institute of the Hungarian

Academy of Sciences, Seismological Observatory, Budapest,

Hungary

Thermal convection has been modeled in a 3-D model box,in order to study the structure (diameter and temperatureanomaly) of mantle plumes and their surface manifestation(topography, geoid anomaly, heat flow).

The variable parameters in the different models are

the Rayleigh number (it varies between 5·106and 108),the depth-dependent viscosity and the rate of internal heat-ing. In the simplest models the viscosity is assumed sim-ply exponential increasing with depth by a factor of 10 and100. Trying to model the real mantle viscosity distributionin some cases a narrow high and a low viscosity layer wasadded to model the lithosphere and the asthenosphere. Insome models the possible bottom boundary layer of mantleconvection, the D” layer is also included. In some modelsinternal heating was added with a non-dimensional valueof H=10 corresponding to the concentration of radioactiveelements in chondrite meteorites.The upper and the lowerboundaries are supposed to be isothermal and stress-free.The sides of the box are reflecting boundaries. The size ofthe box was chosen to allow the evolution of only one plumein the corner of the box. Applying these conditions, the boxrepresents one quarter of the whole convective cell. To cal-culate the anomalies, both upper and whole mantle scalingwere used.

Summarizing and comparing the result with the obser-vations, the following remarks can be drawn:

• The interior of the convective cell had a lower tem-perature in the case of high viscosity contrast. There-fore, the temperature anomaly of the plume becamehigher. In the topographic anomalies, there were nosignificant differences between the models of differentviscosity contrast. The addition of the asthenospheredecreases the geoid and topographic anomalies. Thelithosphere makes higher the temperature of the in-terior of the convective cell and reduces the surfaceheat flow anomaly leading towards better agreementwith the observed values.The high viscosity layer atthe CMB (D” layer) has no effect on the surfacemanifestations, but changes the structure of the con-vection. The interior of the convective cell will bewarmer.

• Basal heating dominates in every model, but the effectof internal heating on the studied features suggeststhat it cannot be neglected. It decreases the topo-graphic, geoid and temperature anomalies.

• Seismic tomographic studies (Bijwaard and Spak-man, 1999, Wolfe et al., 1997) suggest lower tem-perature anomalies of the upwellings than the cal-culated ones (Fig. 2). The most complex wholemantle model has the most similar value to the ob-servations. The diameter of the plume (Fig1.) alsoindicates rather a whole mantle convection, becausethe values at upper mantle convection are very low(< 80 km).The calculated values of heat flow anomaly

(50–600 mW/m2) are much higher than the observed

values (10–20 mW/m2, Courtney and White, 1986).In general, the amplitudes of the calculated anoma-lies (geoid, topography, Fig. 4 and Fig. 5) fit better

to the observations, when upper mantle convection issupposed. Usually all modeled topographic heightsare larger than the observations, except the lowestvalues. Geoid heights lie in the range of the realanomalies for almost every upper mantle model. Theproblematical part of these models is the horizontalextent of the anomalies, which is significantly smallerthan the observations. The horizontal extent (Fig.3) suggests whole mantle convection, but the ampli-tude of the topography in these models is significantlylarger than the observed values. The geoid anomaliesin these models are higher than the observed ones, ex-cept the models with asthenosphere and lithosphere.

References:

Bijwaard,H., and Spakman,W., 1999. Tomographic evi-dence for a narrow whole mantle plume below Iceland. EarthPlanet. Sci. Lett. 166: 121–126.

Courtney, R.C. and White,R. S., 1986. Anomalous heatflow and geoid across the Cape Verde Rise: evidence fordynamic support from a thermal plume in the mantle. Geo-phys. J. R.Astron. Soc., 87: 815–867.

Monnereau,M. and Cazenave, A. 1990. Depth and geoidanomalies over oceanic hotspot swells: a global survey.J.Geophys. Res., 95: 15 429–15 438.

Fig. 1. The half-widths of the fitted Gaussian curves tothe temperature distribution of the plume as the function

of the Rayleigh number in the case of whole mantleconvection (continuous line) and upper mantle convection

(dashed line). Notation: v10 - simple exponentiallyincreasing viscosity from the top to the bottom by a factor

of 10; v100 - simple exponentially increasing viscosityfrom the top to the bottom by a factor of 100; H v10 -

the same as v10, but internal heating is added; H v100 -the same as v100, but internal heating is added; AL1 -

lithosphere and asthenosphere was added to v100; AL2 -same like AL1, but the lithosphere is narrower; ALD -

the same as AL2, but also D” layer is included; H ALD -viscosity distribution is the same as ALD, but internal

heating is added.

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Fig. 2. The dimensionless temperature difference betweenthe center of the plume and the interior of the convectivecell plotted against the Rayleigh number. (Notation can

be seen at Fig 1.)

Fig. 3. The horizontal extent of topographic anomaliesabove plumes as a function of the Rayleigh number in

the case of whole mantle convection (continuous line) andupper mantle convection (dashed line). The lateral size ofanomalies is characterized by the half-width of the fittedGaussian curve. The extent of real hotspot swells variesbetween 500 and 1000 km (Monnereau and Cazenave,

1990). (Notation can be seen at Fig 1.)

Fig. 4. Topographic anomalies above the plumes asthe function of the Rayleigh number in the case of wholemantle convection (continuous line) and upper mantleconvection (dashed line). The height of hotspot swellsranges from 350 to 2200 m (Monnereau and Cazenave,

1990). (Notation can be seen at Fig 1.)

Fig. 5. Geoid anomalies above the plumes as the functionof the Rayleigh number in the case of whole mantle

convection (continuous line) and upper mantle convection(dashed line). The geoid height of hotspot swells ranges

from 1 to 150 m (Monnereau and Cazenave, 1990).(Notation can be seen at Fig 1.)

— INVITED —Modeling the coupled chemical and

thermal evolution of terrestrial planetsusing mantle convection models with

geochemical tracking

Paul J. Tackley1,2 and Shunxing Xie1

1Department of Earth and Space Sciences, Universityof California, Los Angeles, USA

2Institute of Geophysics and Planetary Physics, University


To investigate dynamical mechanisms that have been pro-posed to explain geochemical observations, a model ofmantle convection is presented that combines a treatmentof major and trace-element geochemical evolution witha dynamically-consistent mantle convection-plate tectonicsmodel. Melting is simulated using an experimental solidusand assumed to erupt instantly, forming a crust, therebygenerating chemical heterogeneity including the partitioningof trace elements between oceanic crust and residue. Traceelements studied are the U-Th-Pb and Sm-Nd isotope sys-tems, helium and argon. Both olivine and pyroxene-garnetsystem phase transformations are included, with the rel-ative density profiles of basalt, pyrolite, and harzburgitefollowing those of Ringwood (1990) and Ono et al (2001)up to 800km depth, but varied in the deeper mantle to re-flect present uncertainties. A suite of numerical experimentshas been run to systematically investigate the sensitivity ofthe results to uncertain physical properties such as the den-sity of subducted crust in the deepest mantle and elementalpartition coefficients.

If eclogite is denser than pyrolite or residue in the deepmantle, the system becomes chemically stratified, with abasal layer of subducted crustal material enriched in heat-producing elements and an upper mantle dominated by de-pleted residuum. Local stratification occurs across the 660-700 km region due to the compositionally-dependent phasetransitions. Results indicate that the system can self-consistently evolve regions that have a HIMU-like signature(by segregation of subducted crust at the CMB) and regions

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with high 3He/4He. Here we focus particularly on 3He/4Heratio distributions, and on the isotopic ’age’ that is associ-ated with U-Th-Pb and Sm-Nd system.

The system self-consistently evolves regions with the ob-served range of 3He/4He, but the exact distribution dependsstrongly on physical parameters. Furthermore, the distribu-tion depends on sampling method, with the distribution inerupted material often being different from mantle-averageddistributions. Some parameter combinations simultane-ously lead to MORB-like distributions of 3He/4He ratiosin erupted material, and ∼50 % outgassing of radiogenic40Ar consistent with geochemical constraints. MORB-like3He/4He histograms are produced in erupted material eitherwhen the shallow mantle has a high proportion of residuethat evolves MORB-like 3He/4He due to the high incom-patibility of He, or when sufficient recycled crust mixes backinto the shallow mantle to suitably reduce its 3He/4He.

Isotopic measurements on Mid Ocean Ridge Basalts andOcean Island Basalts indicate effective ’ages’ (from e.g., Pb-Pb or Sm-Nd systems) in the range 1-2 billion years- muchless than the age of the Earth, even though melting shouldhave been much more vigorous early on, skewing the meantime since melting to older values. This relatively young’age’ has generally been explained in terms of stretchingof heterogeneities by mantle convection, which might re-duce them to dimensions too small to be individually dis-tinguishable in short timescales of less than 1 Gyr. Onthe other hand, published numerical models that use tracersto track differentiated material (Christensen and Hofmann,1994, Davies, 2002) suggest that Earth-like ’ages’ can be ob-tained without taking stretching-induced erasure of tracersignatures into account, although this might effectively hap-pen if the lengthscale for sampling the isotope systems waslarge enough. In those models, the only explicit mechanismfor resetting isotope systems was re-melting, but for this toexplain the isotopic ages observed for basalts, the globalrate of melting in the recent past would have had to bevery much higher than present-day values. We investigatestretching vs. re-melting in these numerical experiments.The time of last melting and the total strain is tracked oneach tracer (in addition to isotopic information). The re-sults confirm that a model matching today’s crustal pro-duction rate and with a reasonable secular cooling historygenerates ’ages’ that are substantially larger than those ob-served, with the extent of crustal settling above the CMBmaking some difference but not enough. The effect of sam-pling lengthscale on observed ’age’ is also tested and foundto be insufficient to explain the data. Thus, these resultsreaffirm the importance of stretching as a key mechanismfor effectively deleting older heterogeneities. From analysisof strain vs. age and matching of the observed ages, it isestimated that erasure of heterogeneities occurs at strainsof 103–104, somewhat larger than has often been assumed.

The role of slabs on plume development

Eh Tan and Michael Gurnis

Seismological Laboratory, Caltech, Pasadena, USA

We show that with a wide range of reasonable plate kine-matics and material properties, slabs can reach the core-mantle boundary in models; even for cases with a high-viscosity lower mantle, a phase transition at 660 km depth,depth-dependent thermal expansivity, and depth-dependent

thermal diffusivity, we find that ancient slabs could be asso-ciated with lateral temperature anomalies ∼ 500 ◦C coolerthan ambient mantle. Plausible increases of thermal con-ductivity with depth will not cause slabs to diffuse awayin the lower mantle. There are important consequencesof deeply penetrating slabs. Plumes preferentially developon the edge of slabs. In slab-free areas, plume formationand eruption is frequent, and the basal thermal boundarylayer is thin; while in areas beneath slabs, the basal ther-mal boundary layer is thicker and plume formation infre-quent. Beneath slabs, a substantial amount of hot mantlecan be trapped over long periods of time, leading to ‘mega-plume’ formation. We predict there may be large volumes ofmantle with low seismic velocity directly beneath large-scalehigh seismic velocity structures at the core-mantle bound-ary, structures interpreted as ancient slabs. The predictedstructure has been found in the Caribbean region.

Three-dimensional small scale convectionbelow the oceanic lithosphere

Jeroen van Hunen, Jinshui Huang andShijie Zhong

University of Colorado, Boulder, USA

Sublithospheric small scale convection (SSC) has been pro-posed to explain the deviation in oceanic topography andheatflow from the cooling half-space model for oceanic platesspreading away from the mid-ocean ridge. The dynamicsof this SSC process have been previously studied in sev-eral numerical and laboratory experiments. Most numeri-cal studies use a two-dimensional setup, either parallel orperpendicular to the plate motion.

Here, we present results of a 3-D study, which com-bines the characteristics of each of the 2-D models. Weuse a realistic, strongly temperature-dependent rheology.First, we present detailed comparison between earlier 2-Dresults for Newtonian rheology and the new 3-D results, andshow that SSC dynamics are fundamentally different: in 2-D roll/convection cell orientation is predicted by the modelsetup, while in 3-D longitudinal ’Richter’ rolls are dominant.Background shearing due to plate motion enhances longitu-dinal rolls, but prohibits SSC in 2-D. The behaviour of anon-Newtonian fluid is differs significantly from a Newto-nian one: for comparable mantle viscosities, onset is earlierfor increasing powerlaw exponent n, and downwellings aremore vigorous.

Thermal structure of lithosphere above SSC can be com-pared to the cooling halfspace model, which leads to a ’ther-mal age’ that deviates from the real plate age due to SSC.Comparison of numerical results with a surface wave to-mography model show a large degree of agreement, whichprovides strong support for the existence of SSC.

We modeled the effect of a sudden change in the platemotion, such as suggested by the bend in the Hawaii-Emperor volcanic chain, on the development of SSC undervarious thermal and rheological conditions. Results showthat rapid alignment of rolls with the new plate motion doesnot easily occur, which suggests that SSC will not presentitself as Richter rolls.

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Ultra-high Ra convection and applicationsof wavelet

Ludek Vecsey1, David A.Yuen2,

Erik Olaf D. Sevre2and Fabien Dubuffet2

1Geophysical Institute, Academy of Science of the CzechRepublic



Minneapolis, USA

Thermal convection is a nonlinear phenomenon, the qualita-tive changes of its behavior can occur while increasing con-troling parameters. To understand the fundamental physics,we conducted a convection model in the Bousinesq approxi-mation for infinite Prandtl number and a 2-D axisymmetri-cal spherical shell geometry. When scaled to the Earth’smantle, the computational domain of this model has anaspect-ratio of around six. For comparing with 3-D sit-uation, we have also used a three-dimensional Boussinesqmodel taken from Dubuffet et al. (2000) with an aspect-ratio of 5 × 5 × 1.

We have found different convection regimes for increas-ing Rayleigh number Ra. Two convection cells with raisingsecondary instabilities (Ra = 106) will change to three andmore celled convection regimes (Ra = 107 and more). Ther-mal plumes are starting to be ubiquitous at high Rayleighnumber convection. Secondary instabilities (called alsoWhitehead instabilities, see Skilbeck and Whitehead, 1978,and Whitehead, 1982) will occur. We have also found thatsecondary Whitehead instabilities can develop naturally in3-D large aspect-ratio convection.

At a higher Rayleigh number between 109 and 1010the system goes to a layered convective state, as the plumesbecome more feeble and cannot reach the top bounday layer.Such a transition may be important in the high Rayleighnumber regime of a young planet and in magma cham-bers. For non-Newtonian rheology this transition from sin-gle cell to layered convection would take place at lower ef-fective Rayleigh numbers. Malevsky and Yuen (1992) hadshown that non-Newtonian rheology could lower the thresh-old Rayleigh number for secondary instabilities to developby at least an order of magnitude or a factor of 2 in the sur-face Nusselt number.

Wavelet transform is a powerful tool for data analysis.The 1-D wavelet transform is useful for time-frequency rep-resentation of signals in low Rayleigh number convection

(Vecsey and Matyska, 2001). As the high Rayleigh num-ber convection is more complex, we prefer the 2-D wavelettransform, with a nice ability to detect structures of differ-ent scales (Vecsey et al., 2003).

References:

Dubuffet, F., Rabinowicz, M., and M. Monnereau, Multi-scales in mantle convection, Earth Planet. Sci. Lett., 178,351–366, 2000.

Malevsky, A.V. and D.A. Yuen, Strongly chaotic non-Newtonian mantle convection, Geophys. Astro. Fluid Dyn.,65, 149–171, 1992.

Murphy M.S., Vecsey L., Sevre E.O.D., and D.A. Yuen,Secondary upwelling instabilities developed in high Rayleighnumber convection: Possible applications to hot spots, Elec-tronic Geosciences, 5, 2000.

Skilbeck, J.N. and J.A. Whitehead, Formation of discreteislands in linear chains, Nature, 272, 499–501, 1978.

Vecsey, L. and C. Matyska, Wavelet spectra and chaos inthermal convection modelling, Geophys. Res. Lett., 28,395–398, 2001.

Vecsey L., Hier Majumder, C.A., and D.A. Yuen, Mul-tiresolution tectonic features over the Earth inferred froma wavelet transformed geoid, Vis. Geosci., 8, 26–44, 2003.

Whitehead, J.A., Instabilities of fluid conduits in a flowingearth – are plates lubricated by the astenosphere, Geophys.J. R. Astron. Soc., 70, 415–433, 1982.

Fig.: Examples of Whitehead instabilities developed intemperature fields. The used Rayleigh numbers: (a)

3 · 106, (b) 3 · 107, (c) 3 · 108, and (d) 109. The red arrowspoint to (a) Whitehead-like instability and (b)-(d)

Whitehead instabilities (Murphy et al., 2000).

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Castle of Hruba Skala, Czech Republic, September 13–18, 2003 REGISTERED PARTICIPANTS

List of registered participants (in alphabetical order)

Andrea ANTONIOLIINGV, Via di Vigna Murata, 605, 00143 ROMA, [email protected]

Diane ARCAYUniversite de Nice-Sophia Antipolis, LaboratoireGeosciences Azur, 250, rue Albert Einstein, 06560 Val-bonne, [email protected]

Dr. Andrey BABEYKOGeoForschungsZentrum, Potsdam (GFZ), Telegrafen-berg, D-14473 Potsdam, [email protected]

Dr. Thorsten BECKERIGPP, Scripps Institution of Oceanography, Universityof California San Diego, La Jolla, CA 92093-0225, [email protected], [email protected]

Marie BEHOUNKOVADepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Prof. David BERCOVICIDepartment of Geology and Geophysics, Yale Univer-sity, PO Box 208109, New Haven, CT 06520-8109, [email protected]

Prof. Craig BINADepartment of Geological Sciences, Northwestern Uni-versity, 1847 Sheridan Road, Evanston, IL 60208-2150,[email protected]

Dr. Doris BREUERInstitut fur Planetologie, Wilhelm-Klemm Str. 10,48149 Munster, [email protected]

Dr. Susanne BUITERGeodynamics Group, Dalhousie University, B3H 4J1Halifax (NS), [email protected]

Miroslav CADAInstitute of Geophysics, ETH Honggerberg, CH-8093Zurich, [email protected]

Dr. Ondrej CADEKDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Dr. Emanuele CASAROTTIINGV, Via di Vigna Murata, 605, 00143 ROMA, [email protected]

Dr. Gael CHOBLETUniversity of Nantes, UMR 6112 Planetologie,BP 92208, 44322 Nantes, [email protected]

Prof. Ulrich CHRISTENSENMax Planck Institute for Aeronomy, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, [email protected]

Dr. Spina CIANETTIINGV, Via di Vigna Murata, 605, 00143 ROMA, [email protected]

Dr. Hana CIZKOVADepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Dr. Nicolas COLTICEUniversite Claude Bernard Lyon 1, 43, bd du 11 Novem-bre 1918, 69622 Villeurbanne, [email protected]

Giulio DAL FORNODipartimento di Fisica, Universita di Bologna, VialeBerti-Pichat, 8, 40127 BOLOGNA, [email protected]

Dr. Anne DAVAILLEInstitut de Physique du globe de Paris, Departementde Sismologie, 4, Place Jussieu, 75252 Paris cedex 05,[email protected]

Roberta DE FRANCOFaculty of Earth Sciences, University of Utrecht, Bu-dapestlaan 4, 3584 CD UTRECHT, The [email protected]

Dr. Frederic DESCHAMPSFaculty of Earth Sciences, University of Utrecht, Bu-dapestlaan 4, 3584 CD UTRECHT, The [email protected]

Dr. Fabien DUBUFFETCNRS/ENS Lyon, 46 allee d’Italie, 69364 Lyoncedex 07, [email protected]

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Dr. Caroline DUMOULINUniversite de Nantes, UFR des Sciences et des Tech-niques, Laboratoire de Planetologie et Geodynamique,2 rue de la Houssinire, B.P. 92208, 44322 Nantescedex 3, [email protected]

Alwina ENNSInstitute of Meteorology and Geophysics, J.W. GoetheUniversity, Feldbergstr. 47, 60323 Frankfurt am Main,[email protected]

Prof. Claudio FACCENNADip. Scienze Geologiche, Universita ”Roma TRE”,Largo San Lorenzo Murialdo 1, Roma, [email protected]

Prof. Cinzia FARNETANIInstitut de Physique du globe de Paris, Departementde Sismologie, 4, Place Jussieu, 75252 Paris cedex 05,[email protected]

Dr. Luce FLEITOUTLaboratoire de geologie, Ecole normale superieure,24, rue Lhomond, 75005 Paris, [email protected]

Dr. Kevin FLEMINGGeoForschungsZentrum, Potsdam (GFZ), Telegrafen-berg, D-14473 Potsdam, [email protected]

Dr. Claude FROIDEVAUXLaboratoire de geologie, Ecole normale superieure,24, rue Lhomond, 75005 Paris, [email protected]

Dr. Francesca FUNICIELLODip. Scienze Geologiche, Universita ”Roma TRE”,Largo San Lorenzo Murialdo 1, Roma, [email protected]

Attila GALSADepartment of Geophysics, Eotvos University, Paz-many P. Str. 1/c, 1117 Budapest, [email protected]

Dr. Carlo GIUNCHIINGV, Via di Vigna Murata, 605, 00143 ROMA, [email protected]

Dr. Saskia GOESInstitute of Geophysics, ETH Honggerberg, CH-8093Zurich, [email protected]

Dr. Rob GOVERSFaculty of Earth Sciences, University of Utrecht, Bu-dapestlaan 4, 3584 CD UTRECHT, The [email protected]

Jan HAGEDOORNGeoForschungsZentrum, Potsdam (GFZ), Telegrafen-berg, D-14473 Potsdam, [email protected]

Prof. Ulli HANSENInstitute of Geophysics, University of Munster, Cor-rensstr. 24, D-48149 Munster, [email protected]

Dr. Vaclav HANUSInstitute of Geophysics, Academy of Sciencesof the Czech Republic, Bocnı II/1401, 141 31 Praha 4-Sporilov, Czech [email protected]

Dr. Ladislav HANYKDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

John W. HERNLUNDDepartment of Earth and Space Sciences, UCLA, 3806Geology Building, Box 951567, Los Angeles, CA 90095-1567, [email protected]

Dr. Satoru HONDAEarthquake Research Institute, University of Tokyo, 1-1-1, Yayoi, Bunkyou-ku, Tokyo 113-0032, [email protected]

Dr. John R. HOPPERGEOMAR, Research Center for Marine Geosciences,Wischhofstrasse 1-3, D-24148 Kiel, [email protected]

Dr. Ritske HUISMANSGeodynamics Group, Dalhousie University, B3H 4J1Halifax (NS), [email protected]

Prof. Gery T. JARVISDepartment of Earth and Atmospheric Science, YorkUniversity, 4700 Keele Street, Toronto, Ontario,M3J 1P3, [email protected]

Damien JURINELaboratoire de Dynamique des Systemes Geologiques,Institut de Physique du globe de Paris, 4, place JussieuT 14/15 Bte 89, 75252 PARIS Cedex 05, [email protected]

Dr. Edouard KAMINSKIInstitut de Physique du globe de Paris, 4, Place Jussieu,75252 Paris cedex 05, [email protected]

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Dr. Mikhail KARPYTCHEVCentre Littoral De Geophysique, Pole Sciences et Tech-nologie, Departement des Sciences de la Terre, Uni-versite de La Rochelle, Avenue Michel Crepeau, 17000La Rochelle, [email protected]

Boris KAUSGeologisches Institut, ETH Zurich, Sonnegstrasse 5,[email protected]

Yann KRIENLaboratoire de geologie, Ecole normale superieure, 24,rue Lhomond, 75005 Paris, [email protected]

Mgr. Martin KUKACKADepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Prof. Nick KUSZNIRDepartment of Earth Sciences, University of Liverpool,4 Brownlow Street, Liverpool, L69 3GP, United [email protected]

William LANDUYTDepartment of Geology and Geophysics, Yale Univer-sity, PO Box 208109, New Haven, CT 06520-8109, [email protected]

Garret Michael LEAHYDepartment of Geology and Geophysics, Yale Univer-sity, PO Box 208109, New Haven, CT 06520-8109, [email protected]

Dr. Laszlo LENKEYDepartment of Geophysics, Eotvos University,Pazmany P. Str. 1/c, 1117 Budapest, [email protected]

Tatiana LIOUBETSKAIADepartment of Geology and Geophysics, Yale Univer-sity, PO Box 208109, New Haven, CT 06520-8109, [email protected]

Frank Cord LOHMANGEOMAR, Research Center for Marine Geosciences,Wischhofstrasse 1-3, D-24148 Kiel, [email protected]

Dr. Gabriele MARQUARTFaculty of Earth Sciences, University of Utrecht, Bu-dapestlaan 4, 3584 CD UTRECHT, The [email protected]

Prof. Zdenek MARTINECDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Also at: GFZ Potsdam, [email protected]

Dr. Fred MARTONBayerisches Geoinstitut, Universitat Bayreuth, Univer-sitatsstrae 30, D-95447 Bayreuth, [email protected]

Dr. Ctirad MATYSKADepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Peter MIHALFFYInstitute of Meteorology and Geophysics, J. W. GoetheUniversity, Feldbergstr. 47, 60323 Frankfurt am Main,[email protected]

Dr. Marc MONNEREAUUMR5562/OMP, 14, av. E. Belin, 31400 Toulouse,[email protected]

Raffaella MONTELLIDepartment of Geosciences – Guyot Hall, PrincetonUniversity, Princeton, NJ 08540, [email protected]

Gabriele MORRAInstitute of Geophysics, ETH Honggerberg, CH-8093Zurich, [email protected]

Kristian MUELLERInstitute of Meteorology and Geophysics, J. W. GoetheUniversity, Feldbergstr. 47, 60323 Frankfurt am Main,[email protected]

Takashi NAKAGAWADepartment of Earth and Space Sciences, UCLA, 3806Geology Building, Box 951567, Los Angeles, CA 90095-1567, [email protected]

Karen NIEHUUSInstitute of Meteorology and Geophysics, J. W. GoetheUniversity, Feldbergstr. 47, 60323 Frankfurt am Main,[email protected]

Martin PAUERDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Gilles Nicolas PELFRENELaboratoire de geologie, Ecole normale superieure,24, rue Lhomond, 75005 Paris, [email protected]

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Claire PERRYInstitut de Physique du globe de Paris, Departementde Sismologie, 4, Place Jussieu, 75252 Paris cedex 05,[email protected]

Prof. Jason PHIPPS-MORGANGEOMAR, Research Center for Marine Geosciences,Wischhofstrasse 1-3, D-24148 Kiel, [email protected]

Dr. Claudia PIROMALLOINGV, Via di Vigna Murata, 605, 00143 ROMA, [email protected]

Prof. Klaus REGENAUER-LIEBCSIRO Perth, Exploration and Mining, Perth, [email protected]

Dr. Yanick RICARDENS Lyon, 46 allee d’Italie, 69364 Lyon cedex 07,[email protected]

Prof. Michael RIEDELUniversity of Potsdam, Institute of Geosciences, Karl-Liebknecht-Str. 24, D-14476 Golm, [email protected]@geo.uni-potsdam.de

Thomas RUEDASDansk Lithosfærecenter, Øster Voldgade 10, L, 1350København K, [email protected]

Helmuth RUEPKEGEOMAR, Research Center for Marine Geosciences,Wischhofstrasse 1-3, D-24148 Kiel, [email protected]

Prof. Harro SCHMELINGInstitute of Meteorology and Geophysics, J.W. GoetheUniversity, Feldbergstr. 47, 60323 Frankfurt am Main,[email protected]

Hugo SCHOTMANFaculty of Aerospace Engineering, Section Astrody-namics & Satellite systems, Kluyverweg 1, 2629 HSDelft, The [email protected]

Ondrej SOUCEKDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Prof. Giorgio SPADAUniversity of Urbino, Via Santa Chiara 27, I-61029Urbino, PU, [email protected]

Dr. Ales SPICAKInstitute of Geophysics, Academy of Sciencesof the Czech Republic, Bocnı II/1401, 141 31 Praha 4-Sporilov, Czech [email protected]

Prof. Tilman SPOHNInstitut fur Planetologie, Wilhelm-Klemm Str. 10,48149 Munster, [email protected]

Ondrej SRAMEKDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected] at: ENS Lyon, [email protected]

Claudia STEINInstitute of Geophysics, University of Munster, Cor-rensstr. 24, D-48149 Munster, [email protected]

Paolo STOCCHIUniversity of Urbino, Via Santa Chiara 27, I-61029Urbino, PU, [email protected]

Balint SULEGeodetic and Geophysical Research Institute of theHungarian Acad. Sci., Meredek u. 18, H-1112 Budapest,[email protected]

Prof. Paul TACKLEYDepartment of Earth and Space Sciences, Universityof California, Los Angeles, 595 Charles Young DriveEast, Box 951567, Los Angeles, CA 90095-1567, [email protected]

Eh TANCALTECH, Pasadena, CA 91125, [email protected]

Dr. Stano ULRICHInstitute of Geophysics, Academy of Sciencesof the Czech Republic, Bocnı II/1401, 141 31 Praha 4-Sporilov, Czech [email protected]

Marek VALASEKDepartment of Geophysics, Faculty of Mathematics andPhysics, Charles University, V Holesovickach 2, 180 00Prague, Czech [email protected]

Dr. Jirı VANEKInstitute of Geophysics, Academy of Sciencesof the Czech Republic, Bocnı II/1401, 141 31 Praha 4-Sporilov, Czech Republic

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Dr. Jeroen VAN HUNENUniversity of Colorado, Department of Physics, Boul-der CO 80309, [email protected]

Dr. Ludek VECSEYInstitute of Geophysics, Academy of Sciencesof the Czech Republic, Bocnı II/1401, 141 31 Praha 4-Sporilov, Czech [email protected]

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8th european workshop on numerical modeling of...

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