HR: 11:20h
AN: NG42A-05 INVITED [Abstracts]
TI: Toward Seismic Tomography based upon Adjoint Methods
AU: * Tromp, J
EM: jtromp@gps.caltech.edu
AF: Seismological Laboratory, California Institute of Technology, MS 252-21, Padena, CA 91106
United States
AU: Liu, Q
EM: lqy@gps.caltech.edu
AF: Seismological Laboratory, California Institute of Technology, MS 252-21, Padena, CA 91106
United States
AU: Tape, C
EM: carltape@gps.caltech.edu
AF: Seismological Laboratory, California Institute of Technology, MS 252-21, Padena, CA 91106
United States
AU: Maggi, A
EM: alessia@gps.caltech.edu
AF: Seismological Laboratory, California Institute of Technology, MS 252-21, Padena, CA 91106
United States
AU: Zhou, Y
EM: yingz@gps.caltech.edu
AF: Seismological Laboratory, California Institute of Technology, MS 252-21, Padena, CA 91106
United States
AB:
We demonstrate that Fréchet derivatives for tomographic inversions
may be obtained based upon just two calculations for each earthquake:
one calculation for the current 3D model and a second, `adjoint',
calculation that uses time-reversed signals at the receivers as
simultaneous, fictitious sources. For a given model~m,
we consider objective functions χ(m) that minimize
differences between frequency-dependent traveltime and amplitude anomalies.
We show that the Fréchet derivatives of such objective functions may
be written in the generic form
δχ=∫VKm(x) δln m(x) d3x,
where δ ln m=δ m/m denotes the relative model perturbation.
The volumetric kernel Km is defined throughout the model volume V
and is determined by time-integrated products between spatial and temporal
derivatives of the regular displacement field s and the adjoint
displacement field s† obtained by using time-reversed signals at the receivers as simultaneous sources.
For each event, the construction of the kernel Km requires
one forward calculation for the regular field s and one adjoint
calculation
involving the fields s and s†.
For multiple events the kernels are simply summed.
The final summed kernel is controlled by the
distribution of events and stations and thus determines image resolution.
The summed kernel is a weighted combination of
finite-frequency `banana-donut' kernels. We illustrate the characteristics
of these 3D finite-frequency kernels based upon adjoint simulations
for a variety of arrivals, e.g., P, S, PS, Pdiff, PKIKP, and SKS.
One particularly nice feature of an adjoint calculation of a finite-frequency
kernel is that one need not be able to identify the arrival; the adjoint
calculation will automatically reveal how this arrival `sees' the
compressional- and shear-wave speed of the Earth. For this reason, any
arrival in the data that is reasonably well fit by the current
synthetics becomes a set of measurements, which rapidly leads to
a large data base with a wide variety of arrivals and related kernels.
To facilitate the iterative non-linear inverse problem, we demonstrate
how to find basis functions for the model parameters
that are optimally concentrated
where the summed kernel is large. Specifically, we determine the
smallest-dimensional set of band-limited orthonormal
model parameter basis functions that result in the largest gradient of
a misfit function.
These optimal basis functions are used in a standard conjugate gradient
algorithm to determine the (local) minimum of the misfit function.
DE: 7260 Theory
DE: 7270 Tomography (6982, 8180)
DE: 7290 Computational seismology
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005