Inversion of seismic velocities for the pore aspect ratio spectrum of a rock

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Abstract
Laboratory measured seismic velocities of various rocks as a function of pressure and saturation are inverted to obtain their spectra of pore shapes. The inversion is based on the theory of closing of the pores as a function of pressure and the velocity changes that result. The rocks are modeled in terms of a matrix and spheroidal pores of different aspect ratios. To obtain the volume concentration of pores of each aspect ratio, two inversion schemes were formulated and examined. The linearized iterative inversion scheme gave a better result. The inversion was applied to both high‐porosity sedimentary rocks and low‐porosity igneous rocks. It worked well for all the rocks considered. The method has the power to resolve different aspect‐ratio cracks. It is predictive, i.e., using the pore aspect ratio spectrum from the inversion of velocity of a rock under one saturation condition, the velocities under a different saturation condition can be predicted via the direct problem. There are significant differences between the pore aspect ratio spectra of different rock types. For the Westerly granite, the pore aspect ratio spectrum obtained from velocity data is comparable to direct SEM observations.