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

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.

Thermal conductivity of fluid-saturated rocks

“…The idealization of a rock as being composed of a solid permeated with nonintersecting pores of spheroidal shape has been used with great success in modeling mechanical and acoustical properties (e.g., Cheng & Toks5z 1979;Zimmerman 1984).…”

Poisson's ratio structure of young oceanic crust

“…Decreasing porosity with depth is thought to be responsible for the rapid increase in both the P (compressional) and $ (shear) wave velocities (Vp •nd V• respectively) observed across seismic layer 2 [Whitmarsh, 1978]. Cracks (holes with an aspect ratio of less than 0.5) generally affect Vp and Vs disproportionately and thus change the Poisson's ratio (rr) of a material [Chen and Toksoz, 1979]. Theory predicts that rr is increased by the presence of thin cracks (aspect ratio less than 0.005) and is decreased by thick cracks (aspect ratio more than 0.05 [Shearer, 1988]).…”

Laboratory studies of the acoustic properties of samples from Salton Sea Scientific Drilling Project and their relation to microstructure and field measurements

“…The increase in seismic velocity associated with increasing confining and effective pressure in laboratory studies is well known (Toksoz et a!., 1976;Todd and Simmons, 1972;Nur and Simmons, 1969). Various theories can be used to relate such increases in velocity with pressure to the spectrum of pore shapes and microfractures within the rock fabric (Cheng and Toksoz, 1979;O'Connell and Budiansky, 1977). The experimental results obtained when subjecting individual rock samples to increasing pressures may be seen as a partial analog to increases of velocity with depth, as it is expected that fewer thin cracks remain open as presure increases.…”