Estimates of velocity dispersion between seismic and ultrasonic frequencies

Abstract

It is generally accepted that acoustic velocities in fluid‐saturated rocks vary with frequency. Evidence comes from experimental measurements and from theoretical causality arguments. We have developed a simple analysis technique that gives estimates of total velocity dispersion between zero frequency and any measurement frequency. The technique requires compressional (P) and shear (S) wave velocity measurements on dry and fully saturated rock. Assuming that the dry velocities are independent of frequency, the Biot‐Gassmann equations are used to calculate the zero‐frequency velocities in the fully saturated rock. Any difference between the measured velocities and the calculated zero‐frequency velocities is interpreted as evidence of dispersion. Application of this analysis technique to a variety c ultrasonic data sets gives consistent results. In many rocks, dispersion between zero frequency and ultrasonic frequencies is on the order of 10 percent at low effective stress, and it decreases to only a few percent at higher stresses. Dispersion varies with degree of saturation and with fluid viscosity in the same way as do low‐frequency attenuation measurements. The results are readily interpreted in terms of the same local‐flow absorption/dispersion mechanism that has been used to explain recent laboratory attenuation measurements. This apparent dispersion places upper bounds on seismic‐to‐sonic velocity differences. It also points out possible discrepancies between seismic velocities and ultrasonic laboratory measurements.