HR: 0800h
AN: S31B-1042    [Abstracts]
TI: Using Adjoint Methods to Construct 3-D Banana-Doughnut Kernels
AU: * Liu, Q
EM: lqy@gps.caltech.edu
AF: California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125 United States
AU: Tromp, J
EM: jtromp@gps.caltech.edu
AF: California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125 United States
AB: We use adjoint methods popular in climate and ocean dynamics to calculate Fr\'{e}chet derivatives for tomographic inversions. The Fr\'{e}chet derivative of an objective function $\chi(m)$, where $m$ denotes the Earth model, may be written in the generic form $\delta\chi=\int K_m(\mathbf{x})\,\delta\ln m(\mathbf{x})\,d^3\mathbf{x}$, where $\delta\ln m=\delta m/m$ denotes the relative model perturbation. We construct the 3-D finite-frequency `banana-donut' kernel $K_m$ by simultaneously computing the so-called `adjoint' wave field $\mathbf{s}^\dagger$ forward in time and reconstructing the regular wave field $\mathbf{s}$ 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 speed, and compressional-wave speed sensitivity kernels. This method is applied to a complicated 3-D southern California model. Various density, shear-wave speed, and compressional-wave speed sensitivity kernels are presented for different phases in the seismograms. 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: 7260 Theory and modeling
DE: 7203 Body wave propagation
SC: Seismology [S]
MN: 2004 AGU Fall Meeting