Interpreting Seismic Observables
Geoff Abers, Greg Hirth
Velocities: compositional effects vs P,T
Attenuation at high P, T
Anisotropy (Hirth)
Upload from bSpace -> Seismic_Properties:
Hacker&AbersMacro08Dec2010.xls
& various papers
A random tomographic image
Crustal tomography: Woodlark Rift, Papua New Guinea
- Transition from continental to oceanic crust
(Ferris et al., 2006 GJI)
Arc crust velocities
Arc Vp along-strike Aleutians
Vs. SiO2 in arc lavas
[Shillington et al., 2004]
Arc lower crust predictions
[Behn & Kelemen, 2006]
Velocity variations within subducting slab
dlnVs = 10-15%
E
W
km from coast
dlnVs = 2-4%
CAFE Transect, Washington Cascades (Abers et al., Geology, 2009)
Green: relocated, same velocities. yellow: catalog hypocenters
Unusual low Vp/Vs in wedge
* PREM: Vp = 8.04 km/s, Vp/Vs = 1.80
Vp/Vs = 1.65-1.70
Vp/Vs = 1.8-1.9
Alaska (Rossi et al. 2006)
Andes 31°S (Wagner et al. 2004)
“Normal” N Honshu
Zhang et al. (Geology 2004)
Strange: no volcanics
Velocities & H2O in metabasalts
• Crust Hydrated at:
%Vp/VpHARZ
– low P, or
– low T
100
92
%Vp ~ 99-103 %
(eclogite/peridotite)
%Vp ~ 85-95 %
(hydrated/peridotite)
(Hacker et al., 2003a JGR;
Hacker & Abers, 2004 Gcubed)
eclogite
87
blueschist
gr-sch
84
95
amphibolite
81
What else affects velocities? (b) temperature (c) fluids
k
Pore fluids
melts
Temperature

k = bulk modulus
 = shear modulus
H2O
Takei (2002) poroelastic theory
aspect ratio 0.1-0.5
Faul & Jackson (2005) anelasticity +
anharmonicity
Two Approaches
• (1) Direct measurement of rock
velocities
V vs. composition…
Crustal rock variations
Brocher, 2005
Arc lower crust
Behn & Kelemen 2006
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
Peridotites: Lee, 2003
Extrapolate K(P,T), G(P,T),
…
Aggregate to crystal mixture
Eclogite: Abalos et al., GSABull 2011
Calculate Vp, Vs
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)
elastic parameters
Thermodynamic parameters for 55
end-member minerals
- 3rd order finite strain EOS
- aggregated by solid mixing thy.
felsic (60-70% SiO2)
Queensland Granulite Xenoliths:
1GPa 900C
metased (53-56%)
mafic granulite (46-53%
SiO2)
restite/cumulate (4144%)
Chudleigh mafic
cumulates
serp-hz (600C)
1.86
1.84
1.82
1.80
Vp/Vs
minerals
Track V, , H2O, major elem., T,P
1.78
1.76
1.74
1.72
1.70
6.00
6.50
7.00
7.50
Vp, km/s
8.00
8.50
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…
Integrate in P
– Second increase P
• 3rd order finite strain
EoS
STP
Integrate in T
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
Finally, turn elastic parameters to seismic velocities using the usual…
Vp 
K S  (4 /3)G

Vs 
G

Usage notes
“Raw” data table: elastic parameters & derivatives
Intermediate calculation table
Work table: Enter compositions, P,T here
Mineralinformation & stored compositions
“database” includes references & notes on source of values
Usage notes: rocks mins modes
Petrology for people who don’t know the secret codes
Compositions from
Hacker et al. 2003
Metagabbros
Metaperidotites
Usage Notes: you manipulate “rocks” sheet
Enter compositions here… (adds to 100%)
… and P,T here…
(optional: d, f for anelastic correction)
(primary output)
…then click to run
More info below
The mineral database – how good?
Dry, major mantle minerals: OK
Hydrous, and/or highly anisotropic..???
Shear Modulus (& derivatives)???
Inside the macro…
V

a0
KT
K’ G

Yellow: extrapolated, calculated
from related parameters, or
otherwise indirect
Big problems w/ shear modulus
 G
G  P
G’ g dth
A couple of Apps…
use “Perple_X” to calculate phases, HAMacro to calculate velocities
Hydrated metabasalts
(after Hacker, 2008; Hacker and Abers, 2004)
Predict T(P) from
model
(Abers et al., 2006, EPSL)
& Facies from petrology
(Hacker et al., 2003)
Predictions from thermal/petrologic model
H2O
Vs
2D model predictions
Serpentinization effect on Vp
Are downgoing plates
serpentinized?
(Nicaragua forearc)
[Hyndman and Peacock, 2003]
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°S
Flat Slab
Vp/Vs < 1.68-1.72
32.6°S
Vp/Vs and composition: need quartz
Andes
AK
wedge
What is seismic attenuation?
Q = DE/E - loss of energy per cycle
DE
T
1/f
Amplitude ~ exp(-pftT/Q)
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
At High T, Q Has:
• strong T sensitivity
• some to H2O, grain size, melt
• weak compositional sensitivity
•shear, not bulk 1/Q
d=1 mm
10 mm
Faul & Jackson (2005), adjusted to 2.5 GPa
High-Temperature Background (HTB)
Simple model (Jackson et al. 2002)
grain period
size
activation temperature
energy
a = 0.2-0.3 (frequency dep.)
m = a (grain size dep.)
Attenuating Signals
RCK
D = 0.91°
wedge
DH1
D = 0.92°
updip
2s
RCK
(Stachnik et al., 2004, JGR)
DH1
P waves
depth 126 km
Q Measurements
Q and amplitude u(f):
u(f) = U0 Asource(f)
Forearc Path
Wedge Path
e-pfT/Q
Fit P, S spectra:
T/Q, M0, fc
0.5 – (10-20) Hz
S waves, slab event, D ~ 100 km
Path-averaged Qs
Invert these tomographically
assumes Q(f) from laboratory predictions
Test of Q theory:
Ratio of Bulk / Shear attenuation
high
1/Qs
Alaska cross-section
(Stachnik et al., 2004)
high
1/Qk
Test of HTB: Frequency Dependence
Q = Q 0 fa
Lab: Faul & Jackson 2005
Observations from Alaska
Forearcs: cold; subarc mantle: hot
Heat 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)
(Stachnik et al., 2004 JGR)
lo Q
hi Q
Attenuation in Central America
(TUCAN)
(Rychert et al., 2008 G-Cubed)
Anisotropy
EXTRAS
Attenuation vs Velocity: Physical Dispersion
A()  A0 expX /QV 

No attenuation
“Attenuation” without causality
Attenuation + Causality = Delay in high-frequency energy
Attenuation vs Velocity: Physical Dispersion
A()  A0 expX /QV 

No attenuation
Attenuation
+ Causality
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
G
anharmonic
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
P 
KT  V  
V T
Labs & petrologists usually measure this
P 
K S  V  
V S
Seismic waves see this (not the same!)
Useful: Bina & Helffrich, 1992 Ann. Rev.; Hacker and Abers, 2004 GCubed
Deep under the hood: 1st Grüneisen parameter
relates elastic to thermal properties
P 
lnT 
g  V    

E V
lnV S
E is the internal energy, related to temperature
S is entropy – e.g. defines the adiabat
A more useful relationship can be obtained with some definitions/algebra…
g

aKT V
CV

aK SV
CP
a = coef. Thermal expansion
KT, KS = (isothermal, isentropic) bulk modulus
CV, CP = specific heat at const. (volume, P)

Useful: Bina & Helffrich, 1992 Ann. Rev.; Anderson et al., 1992 Rev. Geophys.
The “other” parameters & scalings
1 lnKT 
dT   

a  T P
G

 G
1lnG 
 

G  P a  T P
- Relates thermal expansion (of volume) to
thermal changes of bulk modulus
- Same for shear modulus
In absence of any data…

K’ = ∂K/∂P is usually around 4.0
G ~ dT
dT ~ g + K’

see Anderson et al., 1992
Related/useful: Adiabatic Gradient
Some monkeying around gives
T  Tg
  
P S K S
So that the adiabatic gradient is
T  T  P  gTg
      

z S P S z  K S

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 mantle
HOMEWORK: what is the geothermal gradient?
Useful: Bina & Helffrich, 1992 Ann. Rev.; Hacker and Abers, 2004 GCubed