Can one hear the shape of a saturation patch ?

The theory of the acoustics of patchy-saturation in porous media is used to analyze experimental data on wave velocity and attenuation in partially water saturated limestones. It is demonstrated that the theory can be used to deduce the value of V /A, the ratio of the volume to area of the water patch, and l f , the Poisson size of the water patch. One can " hear " the shape of a patch if the properties of the rock and the measurement frequencies are such as to satisfy the specific requirements for the validity of the theory. The Biot theory [Biot, 1954] can be used to describe the acoustic properties of an elastic porous solid fully-saturated with a compressible Newtonian fluid. (For a review see [Johnson, 1986] and references therein.) The input parameters of the theory are directly measurable on a given sample by independent means. The success of the theory in predicting the dispersion and the attenuation of the fast compressional, slow compressional, and shear modes has been demonstrated in a number of relevant experiments ([Johnson, 1994] and references therein). Johnson [2001] has extended this theory to the case of an elastic porous frame containing two different fluids filling the entire frame in non-mixing " patches " (i.e. at every point of the sample, the