Multiscale Seismology:

the future of inversion

W. MENKELamont-Doherty Earth Observatory

Columbia University

E. CHESNOKOV and R.L. BROWNInstitute for Theoretical Geophysics

University of Oklahoma

Thesis

The past 15 years has seen a tremendous improvement in the fidelity of many types of seismic images.

This improvement was driven by, more and higher quality seismometers, faster computers, better data archiving and processing methodologies.

But our ability tointegrate knowledge from multiple data types

hasn’t kept up. Often different data types are telling us seemingly-contradictory things.

Example:

Surface Wave Tomography

e.g. of North America

Woodward and Snieder, 1993

275 seismograms

Zhang & Tanimoto, 1993

18,000 seismograms globally, about 324 prorated for area

685 seismograms

400,000 seismograms globally, about 7,200 prorated for area

note inversion includes transverse anisotropy

“Exponential”

growth

of

data !

Images better & better in evolutionary

way

But how do these impressive images

connect with

other things we know about the earth?

Connection 1

Continental Scale Body Wave Traveltimes

Surface wave models have big asthenospheric LVZ’s that imply very large

shadow zones

Are such shadows actually observed in continental-scale P or S waves?

Connection 2

SKS Shear Wave Splitting

From Gaherty

North America has large amount of transverse anisotropy

Predicts

Correctly predicts large Love-Rayleigh discrepancy along paths

parallel to MOMA Array

But inconsistent with SKS splitting results along MOMA array

Fouch’s splitting data as plotted by Gaherty

No plausible anisotropic material can have fast-axis parallel to array and have large Love-Rayleigh discrepancy parallel to the array, too

More overlap in parameters than length scale !

Hypothesis:

differentlength scales

strongly influence interpretation

EARTH OBSERVATION

INVERSION

StrongSpooky

Interactions

(seismic waves)

Length scale ofLength scale of

Length scale of

we understand this interactionpretty well

(but only in very idealized media)

strong spooky interactionsOBSERVATION

(seismic waves)EARTHLength scale of

Length scale of

WHAT IS THE STRUCURE OF THIS MEDIUM ?

,, ρμ

,, ρμ

bulk modulus 1

shear modulus 1,

density 1

thickness 1

bulk modulus 2

shear modulus 2

density 2

thickness 2

WHAT IS THE STRUCTURE OF THIS MEDIUM ?

Inhomogenous with various properties of

isotropic layers?

YES !when <<thickness

WHAT IS THE STRUCTURE OF THIS MEDIUM ?

Strongly Scattering?

YES !when ~thickness

WHAT IS THE STRUCURE OF THIS MEDIUM ?

Effectively homogeneous and anisotropic?

YES !when >>thickness

Theory for understanding this effectin 3-D media with random heterogeneitiesis well developed …

Elasticity and density written in terms of average and deviation from average

• Chesnokov et al. 2000

weird! effective density is a tensor ..

1. elasticity and density are frequency-dependent

2. integrals embody interaction of wavefield with scale length of heterogeneities …

3. … through correlation functions

“UPSCALING” ExampleReconciling Sonic Log with VSP

Collect Sonic Logs (500 Hz) of Vp, Vs1, Vs2, density

Infer all components of Cijkl(f=500 Hz)

Compute Correlation Functions

Predict Cijkl(f=50 Hz)

Compare with VSP (50 Hz) experiment

Is this Inversion?

Not quite …

Sonic Log

Result for C55

Predicted VSPVSP

theorycan be

extendedto include

more complicated

micro-physics

e.g.fluid/rock

interactions

There’s been some interesting efforts on this side of the triangle, too

stro

ng s

pook

y in

tera

ctio

ns

OBSERVATIONLength scale of

INVERSIONLength scale of

True Slip on Hypothetical Fault

ThreeInversionsThatFit the DataEquallyWell

Results of Slip Inversions Highly Dependent onScale of Model Representation

Courtesy of Morgan Page

A Challenge of the Future

Create

Earth knowledge

that

practitioners using

different techniques

AGREE UPON

!

EARTH

INVERSION

Joint Inversions thathandle multiple scales

in a Physics-Based way

OBSERVATION(seismic waves)

Length scale ofLength scale of

Length scale of

The Future ?

Scale1 Data

physics-based parameterization

1

Assessment of underlying physics

Scale2 Data

Business as Usual

Scale1 Data

Ad-hoc parameterization

1

Ad-hoc parameterization

2

Speculative attempts to integrate and reconcile results

Scale2 Data

feedback

confusion ?!Improved knowledge of earth