Acoustic properties of fluid filled porous rocks Free

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.