Frequency-dependent P-wave anelasticity due to multiscale (fractal) heterogeneities in rocks

Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different fre-quencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that estab-lishes a relation between the wave properties at different frequency bands considering a size range of hetero-geneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10-6, 10-1.5] m and [10-6, 10- 3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band.