Interpreting Seismic ObservablesGeoff Abers, Greg Hirth

Velocities: compositional effects vs P,TAttenuation at high P, T

Anisotropy (Hirth)

Upload from bSpace -> Seismic_Properties: Hacker&AbersMacro08Dec2010.xls & various papers

A random tomographic image

(Ferris et al., 2006 GJI)

Crustal tomography: Woodlark Rift, Papua New Guinea- Transition from continental to oceanic crust

Arc crust velocities

Arc Vp along-strike AleutiansVs. SiO2 in arc lavas[Shillington et al., 2004]

Arc lower crust predictions[Behn & Kelemen, 2006]

Velocity variations within subducting slab

WE

Green: relocated, same velocities. yellow: catalog hypocenters

CAFE Transect, Washington Cascades (Abers et al., Geology, 2009)

km from coast

dlnVs = 10-15%

dlnVs = 2-4%

Unusual low Vp/Vs in wedgeVp/Vs = 1.65-1.70

Alaska (Rossi et al. 2006)

Andes 31°S (Wagner et al. 2004)

“Normal” N HonshuZhang et al. (Geology 2004)

Vp/Vs = 1.8-1.9

Strange: no volcanics

* PREM: Vp = 8.04 km/s, Vp/Vs = 1.80

Velocities & H2O in metabasalts

• Crust Hydrated at:– low P, or – low T

eclogite

blueschist

amphibolitegr-sch

(Hacker et al., 2003a JGR;Hacker & Abers, 2004 Gcubed)

10092

87

95

8184

%Vp/VpHARZ

%Vp ~ 99-103 %(eclogite/peridotite)

%Vp ~ 85-95 %(hydrated/peridotite)

What else affects velocities? (b) temperature (c) fluids

k

k = bulk modulus = shear modulus Takei (2002) poroelastic theory

Temperature

Pore fluids

melts

H2O

Faul & Jackson (2005) anelasticity + anharmonicity

aspect ratio 0.1-0.5

Two Approaches• (1) Direct measurement of rock

velocities

V vs. composition…

Arc lower crustBehn & Kelemen 2006

Crustal rock variationsBrocher, 2005

Second Approach• (2) Measure/calculate mineral properties, and aggregate

Disaggregate rock into mineral modal abundances

For each mineral, look up K, G, V, … at STP &

derivatives

Extrapolate K(P,T), G(P,T), …

Aggregate to crystal mixture Calculate Vp, Vs

Eclogite: Abalos et al., GSABull 2011

Peridotites: Lee, 2003

Whole-rock vs. calculated velocities

(Oceanic gabbros, from Carlson et al., Gcubed 2009)

Measured vs predicted Vp

• Oceanic gabbros (data)

• Thick line: predictions

• What is going on?

Behn & Kelemen, 2003 Gcubed

Calculating seismic velocities from mineralogy, P,T(Hacker et al., 2003, JGR; Hacker & Abers 2004, Gcubed)

Thermodynamic parameters for 55 end-member minerals - 3rd order finite strain EOS - aggregated by solid mixing thy.

Track V, , H2O, major elem., T,P

Queensland Granulite Xenoliths: 1GPa 900C

1.70

1.72

1.74

1.76

1.78

1.80

1.82

1.84

1.86

6.00 6.50 7.00 7.50 8.00 8.50

Vp, km/s

Vp/Vs

felsic (60-70% SiO2)

metased (53-56%)

mafic granulite (46-53%SiO2)restite/cumulate (41-44%)Chudleigh maficcumulatesserp-hz (600C)m

iner

als

elastic parameters

Compiled Parameters

• o = (P=0 GPa,T=25 C) = density• KT0 = isothermal bulk modulus (STP)• G0 = shear modulus (STP)

• a0; da/dT or similar = coef. Thermal expansion• K’ = dKT/dP = pressure derivative• G = dlnG/dln = T derivative (G(T))• G’ = dG/dP = pressure derivative• gth = 1st (thermal) Grüneisen parameter• dT = 2nd (adiabatic) Grüneisen parameter (K(T))

Elastic Moduli vs. P, T

• Computational Strategy: – First increase T

• thermal expansion…– Second increase P

• 3rd order finite strain EoS

Integrate in T

Inte

grat

e in

P

STP

From Hacker et al. 2003a

Aggregating & Velocities• Mixture theories, simple: Voight-Reuss-Hill

– average K, 1/K, both• Complex Hashin-Shtrikman Mixtures

– sorted/weighted averages

€

Vp = KS + (4 /3)Gρ

€

Vs = Gρ

Finally, turn elastic parameters to seismic velocities using the usual…

Usage notes

“Raw” data table: elastic parameters & derivativesIntermediate calculation tableWork table: Enter compositions, P,T hereMineralinformation & stored compositions

“database” includes references & notes on source of values

Usage notes: rocks mins modes

Compositions fromHacker et al. 2003MetagabbrosMetaperidotites

Petrology for people who don’t know the secret codes

Usage Notes: you manipulate “rocks” sheet

Enter compositions here… (adds to 100%)

… and P,T here…(optional: d, f for anelastic correction)

…then click to run

(primary output)

More info below

The mineral database – how good?

Dry, major mantle minerals: OK

Hydrous, and/or highly anisotropic..???

Shear Modulus (& derivatives)???

Inside the macro…

Yellow: extrapolated, calculated from related parameters, orotherwise indirect

V a0 KT K’ G

€

G

∂G∂ρ P G’ g dth

Big problems w/ shear modulus

A couple of Apps…

Hydrated metabasalts

(after Hacker, 2008; Hacker and Abers, 2004)

use “Perple_X” to calculate phases, HAMacro to calculate velocities

Predict T(P) from model

(Abers et al., 2006, EPSL)

& Facies from petrology

(Hacker et al., 2003)

H2O

Vs

2D model predictions

Predictions from thermal/petrologic model

Serpentinization effect on Vp

[Hyndman and Peacock, 2003]

Are downgoing plates serpentinized? (Nicaragua forearc)

Result: low Vp/Vs in “deeper” wedge

Where slab is deep:Vp/Vs = 1.64-1.69 (consistent w/ tomography)

The Andes [Wagner et al., 2004, JGR]

31.1°SFlat Slab

32.6°S

Vp/Vs < 1.68-1.72

Vp/Vs and composition: need quartz

Andes

AKwedge

What is seismic attenuation?

Q = DE/E - loss of energy per cycle

DE

Amplitude ~ exp(-pftT/Q)

T

1/f

What Causes Attenuation?

Upper Crust: cracks, pores

Normal Mantle: thermally activated dissipation

Cold Slabs: ??

(scattering may dominate if 1/Qintrinsic is low)

Seismic Attenuation (1/Q) at high T

Faul & Jackson (2005), adjusted to 2.5 GPa

d=1 mm

10 mm

At High T, Q Has:

• strong T sensitivity

• some to H2O, grain size, melt

• weak compositional sensitivity•shear, not bulk 1/Q

High-Temperature Background (HTB)

Simple model (Jackson et al. 2002)

grainsize

period activationenergy

temperature

a = 0.2-0.3 (frequency dep.)m = a (grain size dep.)

Attenuating Signals

2 sDH1D = 0.92°RCK

D = 0.91° wedge

RCK DH1

updip

P wavesdepth 126 km(Stachnik et al., 2004, JGR)

Q Measurements

Fit P, S spectra:T/Q, M0, fc

0.5 – (10-20) Hz

Forearc Path Wedge Path

S waves, slab event, D ~ 100 km

u(f) = U0 Asource(f) e-pfT/Q Q and amplitude u(f):

Path-averaged Qs

assumes Q(f) from laboratory predictions

Invert these tomographically

Test of Q theory: Ratio of Bulk / Shear attenuation

high1/Qs

high1/Qk

Alaska cross-section

(Stachnik et al., 2004)

Test of HTB: Frequency DependenceQ = Q0 fa

Lab: Faul & Jackson 2005

Observations from Alaska

Forearcs: cold; subarc mantle: hotHeat flow in northern Cascadia: step 20-30 km from arc

(Wada and Wang, 2009; after Wang et al. 2005; Currie et al., 2004)

Results from Alaska (BEAAR): 1/QS

In wedge core:

QS ~ 100-140 @ 1 Hz 1200-1400°C (dry)

lo Q hi Q

(Stachnik et al., 2004 JGR)

Attenuation in Central America (TUCAN)

(Rychert et al., 2008 G-Cubed)

Anisotropy

EXTRAS

€

A(ω) = A0 exp −ωX /QV( )

Attenuation vs Velocity: Physical Dispersion

No attenuation

Attenuation + Causality = Delay in high-frequency energy

“Attenuation” without causality

Attenuation vs Velocity: Physical Dispersion

No attenuation

Attenuation + Causality

€

A(ω) = A0 exp −ωX /QV( )

This means: • Band-limited measurements of travel time are late• Band-limited measures give slower apparent velocities• As T increases, both V and Q decrease

Physical Dispersion: Faul/Jackson approx.

K

Ganharmonic

anharmonic + anelastic

Physical Dispersion: Karato approx.

Karato, 1993 GRL

Net effect: interpreting DT from DVs

Faul & Jackson, 2005 EPSL

Deep under the hood: adiabatic vs. isothermal

Important distinction between adiabatic (const. S) and isothermal (const. T) processes

Useful: Bina & Helffrich, 1992 Ann. Rev.; Hacker and Abers, 2004 GCubed

€

KT ≡ −V ∂P∂V ⎛ ⎝ ⎜

⎞ ⎠ ⎟T

Labs & petrologists usually measure this

€

KS ≡ −V ∂P∂V ⎛ ⎝ ⎜

⎞ ⎠ ⎟S

Seismic waves see this (not the same!)

Deep under the hood: 1st Grüneisen parameter relates elastic to thermal properties

€

g≡V ∂P∂E ⎛ ⎝ ⎜

⎞ ⎠ ⎟V

= − ∂lnT∂lnV ⎛ ⎝ ⎜

⎞ ⎠ ⎟S

E is the internal energy, related to temperatureS is entropy – e.g. defines the adiabat

A more useful relationship can be obtained with some definitions/algebra…

€

g=aKTVCV

= αKSVCP

a = coef. Thermal expansionKT, KS = (isothermal, isentropic) bulk modulusCV, CP = specific heat at const. (volume, P)

Useful: Bina & Helffrich, 1992 Ann. Rev.; Anderson et al., 1992 Rev. Geophys.

The “other” parameters & scalings

€

dT ≡ − 1α

∂lnKT

∂T ⎛ ⎝ ⎜

⎞ ⎠ ⎟P

- Relates thermal expansion (of volume) to thermal changes of bulk modulus

K’ = ∂K/∂P is usually around 4.0

see Anderson et al., 1992

€

G≡G

∂G∂ρ P

= −1α

∂lnG∂T

⎛ ⎝ ⎜

⎞ ⎠ ⎟P

dT ~ g + K’

In absence of any data…

€

G ~ δT

- Same for shear modulus

Related/useful: Adiabatic GradientSome monkeying around gives

Useful: Bina & Helffrich, 1992 Ann. Rev.; Hacker and Abers, 2004 GCubed

€

∂T∂P ⎛ ⎝ ⎜

⎞ ⎠ ⎟S

= TγKS

€

∂T∂z ⎛ ⎝ ⎜

⎞ ⎠ ⎟S

= ∂T∂P ⎛ ⎝ ⎜

⎞ ⎠ ⎟S

∂P∂z ⎛ ⎝ ⎜

⎞ ⎠ ⎟= ρgTγ

KS

So that the adiabatic gradient is

This is a useful formulism:g ~ 0.8 – 1.3 for most solid-earth materials (1.1 is good

average)g ~ 10 m s2 throughout upper mantleHOMEWORK: what is the geothermal gradient?