Scattering and Frequency Effects on Ultrasonic Velocities of Carbonates

The scattering of elastic waves (scattering) causes velocity dispersion that increases uncertainties of seismic analyses and could be misinterpreted as the result of other phenomena. One of these phenomena is the wave-induced fluid flow in saturated rocks, which comprise most of the rocks in the crust of our planet. Therefore, understanding scattering sources and distinguishing among different sources of velocity dispersion is critical to improve subsurface imaging to locate resources and understand subsurface processes. Here, we present and discuss measurements and numerical modeling of ultrasonic wave velocities in 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 CT-scanned samples 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 large dispersion, and the corresponding numerical simulations reproduce well the observed dispersion. We conclude that scattering has a first-order effect on the velocities of the elastic waves and should be considered when applying rock physics models in heterogenous carbonates similar to those studied here. e illustrate a method to characterize frequency-dependent ultrasonic velocities (i.e., dispersion) and show that finite-difference modeling can reproduce the laboratory-observed dispersion, including the typical frequency shift produced by scatterers and dispersive media.