THE BORN APPROXIMATION IN THE PROBLEM OF ELASTIC WAVE SCATTERING BY A SPHERICAL INHOMOGENEITY IN A FLUID-SATURATED POROUS-MEDIUM

The Born approximation is applied to the problem of scattering of elastic waves by a small (compared to the wavelength of the fast compressional wave) spherical porous inclusion placed in another porous medium described by the low-frequency version of Biot's theory. The results depend significantly on the ratio of the wavelength of slow compressional wave to the inhomogeneity size. For small values of this ratio results are in accordance with exact results of Berryman [J. Math. Phys. 26, 1408 (1985)]. In the opposite case new results are obtained and used to calculate compressional wave attenuation in a porous medium containing randomly distributed inclusions. The frequency dependence of attenuation is found to be in agreement with the results for randomly layered porous materials.