The unreasonable success of Gassmann's theory ... revisited

The poroelastic theory of Gassmann (1951) is widely used in fluid substitution problems of seismic monitoring in media considered as isotropic. Disagreements between experimental results and the predictions of this theory sometimes reported in the literature, at least in the laboratory, are often due to unsuitable experimental techniques. Here we focus on the importance of correct velocity measurements and demonstrate that only the careful phase velocity technique give consistent results with Gassmann's theory, in contrast with first break method or correlation technique. Using the phase velocity method we unambiguously show that Gassmann's theory, a quasi-static theory in principle, surprisingly explain experimental results outside its strict domain of applicability, for instance in the ultrasonic frequency band (0.1-1.0 MHz), which seems "unreasonable" (Rasolofosaon and Zinszner, 2002). This seems to be due to the negligible velocity dispersion due to purely poroelastic effects. From another point of view it is not commonly appreciated that Gassmann in his original paper also dealt with anisotropic Porous media, but of a special type. In his simplified theory the grain constituent is assumed isotropic, and only the rock skeleton is anisotropic. Besides the much greater simplicity of the formalism of the simplified theory, we note a substantial reduction of the number of characteristic elastic parameters to be estimated for the grain constituent, namely from 6 in the general theory to I in the simplified theory, which is quite convenient for practical applications. We a posteriori demonstrate the relevancy of this theory with numerical simulations and experimental ultrasonic measurements in the laboratory, which clearly provides additional credit to Gassmann's theory, emphasizing once again its "unreasonable success".