HR: 14:25h
AN: S33D-04 [Abstracts]
TI: Using Adjoint Methods to Construct 3-D global Banana-Doughnut Kernels
AU: * Liu, Q
EM: lqy@gps.caltech.edu
AF: Seismological Laboratory
California Institute of Technology, 1200 E California Blvd,
MC 252-21, Pasadena, CA 91125
United States
AU: Tromp, J
EM: jtromp@gps.caltech.edu
AF: Seismological Laboratory
California Institute of Technology, 1200 E California Blvd,
MC 252-21, Pasadena, CA 91125
United States
AB:
We derive the adjoint equations associated with
the calculation of the Fréchet derivatives for tomographic inversions
by the Lagrange multiplier method.
The Fréchet derivative of an objective function χ(m),
where m denotes the Earth model, may be written in the generic
form δχ=∫ Km(x) δ ln m(x) d3x,
where δln m=δ m/m denotes the relative model perturbation.
We construct the 3-D finite-frequency `banana-doughnut' kernel Km by
simultaneously computing the so-called `adjoint' wave field
s† forward in time and
reconstructing the regular wave field s backward in time.
The adjoint wave field is produced by using time-reversed signals
at the receivers as fictitious, simultaneous sources,
while the regular wave field is
reconstructed on the fly by propagating the last frame
of the wave field saved by a previous forward simulation backward in time.
The approach is based upon the spectral-element method,
and only two simulations are needed to produce density, shear-wave,
and compressional-wave sensitivity kernels.
This method is applied to both 1-D and 3-D global velocity models.
Various 3-D shear-wave and compressional-wave sensitivity kernels
are presented for different phases in the seismograms (P, S, SS,
Pdiff, PKP, etc).
These kernels illustrate the sensitivity of the observations to
the structural parameters, and form the basis for fully 3-D tomographic
inversions to update the structural model.
DE: 7200 SEISMOLOGY
DE: 7260 Theory
DE: 7270 Tomography (6982, 8180)
DE: 7290 Computational seismology
DE: 8180 Tomography (6982, 7270)
SC: Seismology [S]
MN: Fall Meeting 2005