HR: 11:05h
AN: S12A-03    [Abstracts]
TI: An Approximate 3D Elastodynamic Green's Function for an Inhomogeneous Elastic Medium
AU: * Sanchez-Sesma, F J
EM: sesma@servidor.unam.mx
AF: Instituto de Ingenieria, Universidad Nacional Autonoma de Mexico, Circuito Escolar, Cd. Universitaria, Coyoacan, Mexico, DF 04510 Mexico
AU: Ramirez-Guzman, L
EM: lramirez@andrew.cmu.edu
AF: Laboratory of Computational Mechanics, Civil and Environmental Engineering Department, Carnegie Mellon University, Forbes 5000, Pittsburgh, PA 15217 United States
AU: Luzon, F
EM: fluzon@ual.es
AF: Departamento de Fisica Aplicada, Universidad de Almeria, Canada de San Urbano s/n, Almeria, 04120 Spain
AB: The seismic rays from a given point source within a constant-gradient elastic isotropic medium (a medium with linear variation of wave velocities) are known to be circular. This feature comes along with the remarkable fact that the associated wave fronts are cylindrical or spherical in two or three-dimensions, respectively. The rays and wavefronts form a bipolar orthogonal system with well known properties. These unique circumstances allowed us to construct analytical approximations for the corresponding elastodynamic Green's functions. The derivation of our analytical approximations starts in 2D with the anti-plane SH line source making a generalization of the homogeneous medium Green's functions that relies on the asymptotic ray theory to establish both travel times and geometrical spreading factors. Our approximation accounts for both near-source effects and low frequencies. Moreover, the said correction is frequency-independent and this allows to obtain the Green's function in time domain. This remarkable result was heuristically extended to the in-plane P-SV line source vector case and was validated with the staggered stress-velocity pseudo spectral method with excellent results. Details are given in Sanchez-Sesma, Madariaga and Irikura (2001). In this paper our discovery is extended to 3D for a unit point force. Thus our approximation for the elastodynamic Green's function in a constant-gradient medium becomes the counterpart of the classical Stokes' problem for a homogeneous, isotropic elastic medium. The adequate behavior of our analytical expressions in 3D is tested by comparing them with results from a fourth order finite difference scheme. Acknowledgements This research have had the support of DGAPA-UNAM, Mexico, under grant IN121202 and CONACYT, Mexico, under project NC-204, by CICYT, Spain, under REN2002-04198-CO2-02/RIES, by the E.U. with FEDER, and the team RNM-194 of Junta de Andalucˇa, Spain. Reference Sanchez-Sesma, F. J., R. Madariaga and K. Irikura (2001), An approximate elastic 2D Green's functions for a constant gradient medium, Geophys. J. Int., 146, 237-248.
DE: 7260 Theory and modeling
DE: 7299 General or miscellaneous
DE: 7203 Body wave propagation
DE: 7209 Earthquake dynamics and mechanics
DE: 7218 Lithosphere and upper mantle
SC: Seismology [S]
MN: 2004 AGU Fall Meeting