Multiscale Seismology:
the future of inversion
W. MENKE
Lamont-Doherty Earth Observatory
Columbia University
E. CHESNOKOV and R.L. BROWN
Institute 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 to
integrate 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
North America has large amount of
transverse anisotropy
From Gaherty
Correctly predicts large LoveRayleigh discrepancy along paths
parallel to MOMA Array
Predicts
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:
different
length scales
strongly influence interpretation
Length scale of
Length scale of
EARTH
OBSERVATION
(seismic waves)
Strong
Spooky
Interactions
Length scale of
INVERSION
Length scale of
Length scale of
EARTH
OBSERVATION
strong spooky interactions
(seismic waves)
we understand this interaction
pretty well
(but only in very idealized media)
WHAT IS THE STRUCURE OF
THIS MEDIUM ?
bulk modulus 1
μ, ρ,
shear modulus 1,
density 1
thickness 1
μ,
ρ,
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
l<<thickness
WHAT IS THE STRUCTURE OF THIS MEDIUM ?
Strongly Scattering?
YES !
when
l~thickness
WHAT IS THE STRUCURE OF THIS MEDIUM ?
Effectively homogeneous
and anisotropic?
YES !
when
l>>thickness
Theory for understanding this effect
in 3-D media with random heterogeneities
is well developed …
Elasticity and density written in terms of average and deviation from average
1. elasticity and density are
frequency-dependent
weird! effective
density is a tensor ..
•
Chesnokov et al. 2000
2. integrals embody
interaction of wavefield with
scale length of
heterogeneities …
3. … through correlation
functions
“UPSCALING” Example
Reconciling 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 …
Result for C55
Sonic Log
VSP
Predicted VSP
theory
can be
extended
to include
more
complicated
microphysics
e.g.
fluid/rock
interactions
There’s been some
interesting efforts on
this side of the
triangle, too
Length scale of
INVERSION
Length scale of
OBSERVATION
Results of Slip Inversions Highly Dependent on
Scale of Model Representation
True Slip on
Hypothetical Fault
Three
Inversions
That
Fit the
Data
Equally
Well
Courtesy
of Morgan
Page
A Challenge of the Future
Create
Earth knowledge
that
practitioners using
different techniques
AGREE UPON
!
Length scale of
Length scale of
EARTH
OBSERVATION
(seismic waves)
Joint Inversions that
handle multiple scales
in a Physics-Based way
Length scale of
INVERSION
Business as Usual
Scale1 Data
Ad-hoc
parameterization
2
Speculative attempts
to integrate and
reconcile results
Scale1 Data
Scale2 Data
physics-based
parameterization
1
feedback
Ad-hoc
parameterization
1
Scale2 Data
The Future ?
Assessment of
underlying physics
Improved knowledge of earth
confusion ?!