A unified theory for elastic wave propagation through porous media containing cracks—An extension of Biot’s poroelastic wave theory

Abstract

Rocks in earth’s crust usually contain both pores and cracks. This phenomenon significantly affects the propagation of elastic waves in earth. This study describes a unified elastic wave theory for porous rock media containing cracks. The new theory extends the classic Biot’s poroelastic wave theory to include the effects of cracks. The effect of cracks on rock’s elastic property is introduced using a crack-dependent dry bulk modulus. Another important frequency-dependent effect is the “squirt flow” phenomenon in the cracked porous rock. The analytical results of the new theory demonstrate not only reduction of elastic moduli due to cracks but also significant elastic wave attenuation and dispersion due to squirt flow. The theory shows that the effects of cracks are controlled by two most important parameters of a cracked solid: crack density and aspect ratio. An appealing feature of the new theory is its maintenance of the main characteristics of Biot’s theory, predicting the characteristics of Biot’s slow wave and the effects of permeability on elastic wave propagation. As an application example, the theory correctly simulates the change of elastic wave velocity with gas saturation in a field data set. Compared to Biot theory, the new theory has a broader application scope in the measurement of rock properties of earth’s shallow crust using seismic/acoustic waves.