Scattering and Frequency Effects on Ultrasonic Velocities of Carbonates

Scattering of elastic waves causes velocity dispersion, which increases uncertainty in seismic analysis. Understanding the sources of scattering and the degree of velocity dispersion are critical to improve subsurface imaging in efforts to locate resources and study subsurface processes. In addition to scattering, other mechanisms, such as the wave-induced fluid flow in saturated rocks cause velocity dispersion. To study the effect of scattering on velocity dispersion, we conducted laboratory measurements of ultrasonic velocities on dry rock samples and performed wave-propagation simulations on CT-scanned 3D volumes of those samples. The set of samples consists of homogeneous and heterogeneous carbonate rocks with porosities between 3% and 26%. Ultrasonic velocities were measured at frequencies between 0.3 and 1 MHz, and numerical wave propagation simulations on the digital volumes were performed using an elastic approximation and a finite-difference method. The homogeneous sample and the corresponding numerical simulations exhibit negligible velocity dispersion. On the other hand, heterogeneous samples exhibit significant dispersion, and the corresponding numerical simulations accurately reproduce the observed dispersion in terms of magnitude and frequency shift. We conclude that scattering has a first-order effect on the velocities of the elastic waves in heterogeneous samples. This effect should be considered in conjunction with laboratory measurements in heterogeneous carbonates similar to those studied here. Furthermore, we illustrate a method to characterize frequency-dependent ultrasonic velocities (i.e., dispersion) and show that finite-difference modeling can reproduce the laboratory-observed dispersion.