Acknowledgements:

work by author AP is being supported by a grant under the European Social Fund,

through resources of Region Friuli Venezia Giulia in the form of a PhD fellowship at

the University of Trieste. POR 2014-2020, HEaD UNITS. ID: FP1687011001

The contents expressed herein are those of the authors and do not necessarily

reflect the views of the funding entities.

*contact: alberto.pastorutti@phd.units.itTectonophysics & Geodynamics Research Group

Dept. of Mathematics and Geosciences, Univ. of Trieste

via Edoardo Weiss, 1 34128 Trieste (Italy)

30 40 50 60 70 80 90

mW/m2

Layered lithosphere definition

n-th LAYERA - radioactive heat production (law, parameters)k - thermal conductivity (law, parameters)depth map

(label, ID)

grid discretisation(rectilinear, var. step)

initial T guessto compute k(T)

to volume

Volume of thermal parameters

FD solver

Temperature volume

1.5

2

2.5

3

k

0.5

1

1.5

Aᶜ W/m3

W/(m∙K)

and derived functionals(e.g. heat flow across Moho)

(two xz slices are shown)0 1 2 3 4 5 6 7 8

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

10

15

20

25

30

35

40

45

50

UTM34N easting [105 m]

UT

M3

4N

no

rth

ing

[1

06 m

]

mW/m2

4 4.5 5 5.5 6 6.5 7 7.5 8

0

0.5

1

1.5

2

2.5

dist. along section [105 m]

de

pth

[10

5 m

]

GGMup to N=250(grav. dist.)

topo. eff.up to N=250

dV_ELL_RET2014 [4]

SEDS eff.of 0.25x0.25 deg

tesseroids- - -isost. eff.up to N=30

RWI_ISOS_2012 [5]

- --gravity disturbance [mGal] Moho depth [km]gravity disturbance, a�er reduction

reductions

global isostastic regional sedimentsglobal topography

reduction densities:

2670 kg/m3 topography

1030 kg/m3 oceans

reduction density

2150 kg/m3

28 30 32 34 36 38 40 42 4415

20

25

30

35

40

45

50

55

60

65

surf

ace

HF

- b

asa

l HF

[mW

/m2]

Moho depth [km]

modelledmeasured

a�er reduction for modelled sub-crustal heat flow (Qm)

subsequent substitutionof T in k(T)

fittedinitial

Qm

su

b-c

rust

al H

F [m

W/m

2]

LAB depth, from [0] [km]50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

0

distance along section [km]

de

pth

[k

m]

SED

UCC

LCC

SCLM

LAB(1300 °C)

3 mW/m2

100x hor. exagg.

3 μW/m3

0.3 μW/m3

2 μW/m3

30 40 50 60 70 80 90 10040

50

60

70

80

mo

de

lle

d Q

(0)

[mW

/m2]

measured Q(0) [mW/m2]

measured Q(0) vs modelled Q(0)

[mW/m2] [mW/m2][μW/m3]

3. Gravity processing

[1] Reguzzoni, M., & Sampietro, D. (2015). GEMMA: An Earth crustal model based on GOCE satellite data. International Journal of Applied Earth Observation and Geoinformation, 35, Part A, 31–43. doi:10.1016/j.jag.2014.04.002[2] Brockmann, J. M., Zehentner, N., Höck, E., Pail, R., Loth, I., Mayer-gürr, T., & Schuh, W. D. (2014). EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission. Geophysical Research Letters, 41(22), 8089–8099. doi:10.1002/2014GL061904[3] Szwillus, W., Ebbing, J., & Holzrichter, N. (2016). Importance of far-field topographic and isostatic corrections forregional density modelling. Geophysical Journal International, 207(1), 274–287. doi:10.1093/gji/ggw270[4] Rexer, M., Hirt, C., Claessens, S., & Tenzer, R. (2016). Layer-Based Modelling of the Earth’s Gravitational Potential up to 10-km Scale in Spherical Harmonics in Spherical and Ellipsoidal Approximation. Surveys in Geophysics, 37(6), 1035–1074.doi:10.1007/s10712-016-9382-2[5] Grombein, T., Luo, X., Seitz, K., & Heck, B. (2014). A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients. Surveys in Geophysics, 35(4), 959–982.doi:10.1007/s10712-014-9283-1[6] Pasyanos, M. E., Masters, T. G., Laske, G., & Ma, Z. (2014). LITHO1.0: An updated crust and lithospheric model of the Earth. Journal of Geophysical Research: Solid Earth, 119(3), 2153–2173. doi:10.1002/2013JB010626[7] Tesauro, M., Kaban, M. K., & Cloetingh, S. A. P. L. (2008). EuCRUST-07: A new reference model for the European crust. Geophysical Research Letters, 35(5), 1–5. doi:10.1029/2007GL032244

UC:LC ratio fixed,heat production of UCis fitted tosfc. heat flow

1. Introduction

2. Methods

5. Discussion

References

Surface heat flow measurements in central

Europe, as available in the global heat flow

database (heatflow.und.edu). Blank areas, wich rely on fill-in, are obtained with a grid of distance

to nearest measurement. 100% white = more than 40 km.

Gridded surface heat flow, by kriging and low-

pass filtering (330 km Gaussian).

Heat flow is a direct observable of the planetary thermal state, a complex superposition of contributions. Among those, the heterogeneity in crustal radiogenic heat hinders both the estimation of sub-crustal temperatures and the interpolation of surface measurements. These are irregularly sampled, as is o�en the case with terrestrial data. On the other hand, global gravity models provide uniform coverage, regardless of previous exploration, and satellite-only solutions including data from GOCE (ESA) have been proved suitable in retrieving the crustal geometry at regional scale [1].What if we tie a heat production estimate to a grav-Moho depth?

Processing of gravity data:- GOCE-only global model (GO_CONS_GCF2_TIM_R5) [2]- Reduction for far-field effects [3] of topography, isostasy and regional sediments. All effects 8 km over GRS80, S.A.

4. Thermal modelling We base our thermal modelling on a steady state, 3D conduction hypothesis, surface to thermal lithosphere-asthenosphere boundary (1300 °C), allowing for non uniform heat production and thermal conductivity and non flat upper and bottom boundaries.

The heat equation is solved with a finite difference scheme on a rectilinear domain, coarsely discretised at higher depths.Temperature dependence of k is accounted for through subsequent substitution, achieving sub-degree variations at the 4th iteration.

Processing of heat flow data: we filter out short wavelengths, attributing them to near surface heat transfer regimes (e.g. fluid circulation), and re-grid the measurements to a 20x20 km reticule of cell medians.

Thermal reference model: we set the sediments (topography to crystalline basement) and the sub-continental lithospheric mantle (SCLM, from Moho to LAB) to reference values of density, th. conductivity, heat production and their relationship to temperature and/or depth.

Integration with other data:- Lithosphere-Asthenosphere boundary from LITHO1.0 [6]- Sediments from EuCRUST07 [7]

SEDIMENTS

UPPER CRUST

LOWER CRUST

SCLMLAB, set at 1300 °C

}

topography, set at 20°C

first guess: reference values iterative fitting

residual misfit (meas. - mod.)gridded measurements modelled surface HF

35 97 -17 28

Residuals are attributed to variation in the heat production of the upper crust, unaccounted for in the initial guess. We fit it through iterative correction columns where surface measurements are available. A natural neighbor gridder fills in the others.At iteration 5, maximum surface HF misfit is less than 0.5 mW/m2.

fitted heat prod. of upper crust resulting surface HF

initialguess

Q0

misfit

do thermal fwd.

and compare

ΔAUC

guess

divide by

UC thickness

Effect of crustal contribution on sub-crustal heat flow

OUTCOME

- Successful integration of GGM and heat flow

measurements: straightforward work flow from gravity

functional to thermal parameters.

- Flexible, lightweight modelling enables fast testing of

lithospheric scale thermal behaviour.

- Non-linear superposition of crustal and sub-crustal

heat flow contributions hinders simple back-stripping

approach (no simple subtraction) - however iterative,

subsequent substitution converges fast.

OPEN ISSUES

- Attributing all the misfit of a first guess to one

parameter is useful, but a large simplification is

involved.

- Even without parameter uncertainty, separation of

crustal and sub-crustal component is ambiguous.

- External observables, independently modelled, can be

integrated to validate model.

(e.g. part of this test area shows a direct crust-lithosphere

thickness relationship: assigning lower crustal heat

production or lower SCLM conductivity results in similar

output - albeit with different surface footprints)

FURTHER DEVELOPMENT

- Evaluation of propagation of uncertainty and method

stability.

- Constrain on Qc/Qm partition: geothermal (estimated)

vs geodetic elastic thickness.

- Gravity segment: define a criterion for regional

reduction global functionals, adopt a more versatile

Moho inversion scheme.

this area

synth.example

Constraining the continental crustradiogenic heat productionwith a gravimetric MohoAlberto Pastorutti* and Carla BraitenbergDept. of Mathematics and Geosciences, Univ. of Trieste, Italy

G4.3 X2.445EGU2018-7739-1

global gravity model

regional anomaly crust-mantleboundary depth

correction for

• global topography

• far-field isostatic effects

• regional sediments inversion

availablesurface heat flow

measurements

fit for crustal heat productionconstrained,

modelled,surface heat flow

inversion

Olenburg-Parker, iterativedensity contrast -0.450 kg/m3

LP filtered at 140 km