Dynamics of Saturated Rocks. III: Rayleigh Waves

Abstract

The propagation of plane harmonic Rayleigh waves in a half‐space elastic, fully saturated, rock medium characterized by two degrees of porosity—one due to the pores and the other due to the fissures—is studied analytically. With the aid of the Helmholtz method of decomposition of displacement and velocity vectors, the application of the boundary conditions, and the usual assumption of exponential attenuation of waves with depth, the governing equations of motion finally reduce to the secular equation for Rayleigh waves. The solution of this equation helps to determine both the phase velocity and attenuation coefficient of the Rayleigh waves as functions of frequency. A parametric numerical study reveals that, for certain ranges of frequencies, velocity and attenuation of the two‐porosity model show small and large differences, respectively, from their values for the single‐porosity model.