Acoustic properties of fluid filled porous rocks

Abstract

During 1941–62, Biot laid the foundation of a comprehensive theory concerning the mechanics of deformation and acoustic wave propagation in fluid-filled porous solids. The theory describes the motion of the solid matrix and the pore fluids by coupled differential equations and predicts the existence of three body waves: a single shear wave, a fast compressional wave and a slow compressional wave. The latter propagates in the manner of a diffusion process. In this paper we will review the fundamental aspects of Biot's theory and present some theoretical results for the attenuation and dispersion of seismic waves in a partially gas saturated porous rock. The importance of this problem for seismic exploration was first pointed out by White [Geophysics 40, 224–232 (1975)], and later reformulated by Odé and Dutta [Geophysics 44, 1777– 1788 (1979)]. Further we will illustrate the correspondence of the mathematical description of Biot's theory with the theory of heat conduction. Finally we will provide an explanation based on Biot's theory of a recently observed “slow” bulk compressional wave in fluid-filled porous solids at ultrasonic frequencies.