Inversion of dry and saturated P- and S-wave velocities for the poreaspect-ratio spectrum using a cracked porous medium elastic wave theory

Subsurface rocks contain pores and cracks of various sizes. The cracked porous medium elastic wave theory that describes wave propagation characteristics due to the porecrack interaction is extended to include cracks of different aspect ratios. The extended theory is applied to model P- and S-wave velocity data of dry and fluid-saturated rock under pressure loading conditions, so as to determine the pore-aspect-ratio spectrum through an inversion procedure. The inversion result is consistent with that from the scanning electron microscope analysis, showing significant improvement versus previous inversion. The inverted pore-aspectratio spectrum is input into the wave theory to predict the velocity dispersion of the rock in the full frequency range. The predicted dispersion and its variation trend with pressure agree with the data measured in the (2-200, 106) Hz range at various differential pressures, whereas the modeling using a single-aspect-ratio theory has difficulty matching the data. This research work provides not only a method for analyzing the pore structure characteristics of rocks from the laboratory ultrasonic velocity data, but also a way to predict the seismic wave dispersion from the data.