Boris Gurevich Ada P. Sadovnichaja Sergei L. Lopatnikov
VNII Geosystem, Moscow, Russia
Sergei A. Shapiro
Geophysical Institute, University of Karlsruhe, Hertzstr. 16, 76187 Karlsruhe, Germany
The problem of the scattering of an elastic wave by a small (compared to the wavelength of the fast compressional wave) elliptical porous inclusion placed in another fluid-saturated porous medium is studied using the Born approximation. The mechanical behavior of both host and inclusion materials is described by the low-frequency version of Biot's theory. Explicit formulas for the amplitudes of the scattered normal compressional and shear waves and of Biot's slow compressional wave are obtained. The effectiveness of Biot's slow wave generation depends essentially on the ratio of the wavelength of the slow compressional wave to the inhomogeneity size. For large values of this ratio the results agree with the earlier low-frequency results [J. G. Berryman, J. Math. Phys. 26, 1408--1419 (1985)] derived for a spherical inclusion. In the opposite case new results are obtained. They are used to estimate the effective velocity and attenuation of the normal compressional wave in a porous medium containing randomly distributed inclusions. The frequency dependence of the attenuation is consistent with the results for randomly layered porous materials.