HR: 10:35h
AN: S32A-02 INVITED    [Abstracts]
TI: An Efficient Approach to the Calculation and Storage of Fr{é}chet kernels for Finite-Frequency Tomography
AU: * Zhao, L
EM: zhaol@earth.sinica.deu.tw
AF: Institute of Earth Sciences, Academia Sinica, 128 Academia Road, Sec.2, Nankang District, Taipei, 11529, Taiwan
AU: Chevrot, S
EM: chevrot@dtp.obs-mip.fr
AF: Dynamique Terrestre et Plan{é}taire, UMR 5562, Observatoire Midi Pyr{é}n{é}es, Universit{é} Paul Sabatier, 14 Avenue Edouard Belin, Toulouse, 31400, France
AB: Numerical modeling experiments of wave propagation have shown that the traveltime and amplitude anomalies of a finite-frequency seismic wave are influenced by the heterogeneities in the first Fresnel zone of the wave, a region surrounding its ray path. This leads to the so-called 'banana-doughnut' sensitivity (Fr{é}chet) kernels for finite-frequency waves whose values vary in the first Fresnel zone, rather than concentrate only on the ray path. Therefore, if finite-frequency effect is not taken into account in seismic tomography, the unrealistic sensitivity kernels will limit the resolution to roughly the widths of the first Fresnel zones of the seismic waves, even if all the other aspects are perfect. For the same reason, to realize the full potential of finite-frequency approach in seismic tomography, the spatial sampling in computing the Fr{é}chet kernels and in discretizing the structural model must be sufficiently small so that there are enough sampling points within the width of the first Fresnel zone. This introduces a high demand in computational resources including memory, CPU time, disk storage and the input/output (I/O) operations. To facilitate the practice of finite-frequency high-resolution tomography, we develop an efficient algorithm for computing the Fr{é}chet kernels based on the normal-mode theory in spherically symmetric earth models. The strain Green tensors (SGTs) for a spherically symmetric reference model are computed by normal-mode summation on a dense depth-distance grid by normal-mode summation. This normal-mode SGT database can then be used to calculate all the wavefield quantities needed in seismic studies including synthetic seismograms, partial derivatives with respect to source parameters for the inversion of CMT solutions, and the Fr{é}chet kernels for various kinds of model parameters for the inversions of anelastic and anisotropic structures. The SGT database approach provides the necessary efficiency for calculating the Fr{é}chet kernels with sufficient spatial samples in the first Fresnel zones. To reduce the disk storage and the I/O demands, we also develop an algorithm for the compressions of the SGTs and the Fr{é}chet kernels based on wavelet decomposition. We will compare the orthogonal Haar wavelets with the bi-orthogonal Cohen-Daubechies-Feauveau (CDF) wavelets which are characterized by a higher regularity and thus ensure a higher compression rate.
DE: 7270 Tomography (6982, 8180)
DE: 7290 Computational seismology
SC: Seismology [S]
MN: 2007 Fall Meeting