Volume scattering from random porous media

Abstract

The new volume scattering model, which enables us to treat the scattering of Biot’s slow compressional wave from random porous media, is derived applying the Born approximation to Biot’s equations of motion. Within the framework of the Biot theory it is assumed that the fluid-saturated unconsolidated sediment has low values of frame bulk and shear moduli relative to the other moduli of the medium and the shear wave is negligible. This enables us to treat the Biot theory easier. The equations of motion in inhomogeneous media are then simplified and coupled Helmholtz equations for compressional waves are derived applying the mode’s decoupling method to the simplified equations of motion. The Born approximation is applied to the coupled Helmholtz equations in random media. The derived equations can be treated as extended forms of fluid bottom models. In this model, the 3-D power spectrum is inferred from porosity and permeability fluctuations instead of velocity and density fluctuations generally used. The permeability fluctuation can be estimated from grain-size distribution. In the limit of low frequency or high porosity, the results coincide with the fluid bottom model [T. Yamamoto, J. Acoust. Soc. Am. 99, 866–879 (1996)]. The differences of this new model and others will be discussed.