SCATTERING OF ELASTIC WAVES FROM INHOMOGENEITIES EMBEDDED IN A LAYERED HALF-SPACE.

摘要

Integro-differential equations for the scattering of elastic waves in three dimensions and the scattering of horizontally polarized shear waves, SH waves, in two dimensions are developed for both the interior and the exterior problems. The vector integro-differential equations are written in terms of the total vector displacement within a three-dimensional inhomogeneity; the scalar integro-differential equations are written in terms of the total SH displacement within a two-dimensional inhomogeneity. The inhomogeneities may be embedded in any whole-space or half-space for which a Green's function is calculable. Radiation conditions, which are not readily available in the literature, are developed for the scattered vector displacement field in a layered half-space.; The scalar integro-differential equation for the interior problem is solved for the total SH displacement within a two-dimensional scattering inhomogeneity using the collocation or point matching formulation of the method of moments. The scattered displacement exterior to the inhomogeneity is obtained by integration over the inhomogeneity of the product of the Green's function and the total displacement as well as first and second order partial spatial derivatives of the total displacement in general.; The scalar integro-differential equation solution is favorably compared with analytic solutions for the scattering of plane harmonic SH waves by a circular cylinder in a whole-space and a semi-circular cylinder embedded in a half-space with its flat side flush with the free surface. The error in the numerical solution is dependent upon the discretization level and the material contrast ratio between the inhomogeneity and the surrounding medium. Convergence tests indicate that a discretization level of six cells per wavelength should produce results with errors on the order of 1-2% for shear modulus contrast ratios of up to ten with concurrent density contrast ratios of up to five.; The response of two earth models of geophysical interest to excitation by line sources of SH displacement is also calculated. The interaction of two adjacent inhomogeneities of square cross section is examined as a function of frequency and Q. The interaction decreases with an increase in frequency and/or a decrease in Q. Q structure and source receiver separation are found to effect the spectral ratio slope in the case of an inhomogeneous Q model of a geothermal field. Positive, zero, and negative slopes are obtained when the average Q of the media traversed by the source signal is higher, the same, and lower respectively, than the Q of the reference medium.