Influence of microstructural homogeneity on saturated velocities estimation and wave dispersion

This study investigates the influence of microstructural homogeneity—characterized by crack-related parameters such as crack porosity, crack density, and crack aspect ratio—on the accuracy of models predicting saturated wave velocities, including those based on Gassmann, Biot, and Mavko-Jizba theories, as well as their effects on wave dispersion. We measured P- and S-wave velocities in eight limestone samples under dry and saturated conditions at various pressures. Utilizing the measured dry velocities, we calculated crack-related parameters by integrating the differential effective medium method with the David and Zimmerman approach (DEM-DZ model). Our findings reveal that the quantity and distribution of crack aspect ratios significantly affect model performance and dispersion. When total porosity and crack porosity are comparable, predictions of saturated velocities improve, with reduced wave dispersion observed in samples exhibiting fewer cracks and higher aspect ratios. Among the models predicting saturated velocities, Gassmann's model displayed the highest prediction error, while Mavko-Jizba's model showed the greatest accuracy. We introduce the microstructure homogeneity coefficient (MHC), a nonlinear combination of total porosity and crack-related parameters, as a measure of wave dispersion. Results indicate that lower porosities and crack densities, combined with higher aspect ratios, correspond to higher MHC values, suggesting greater microstructural homogeneity and reduced wave dispersion. MHC values ranged from 22.67 for the most homogeneous sample to 5.81 for the most heterogeneous sample. This trend correlates with P-wave dispersion values of 0.016 for the homogeneous sample and 0.092 for the heterogeneous sample, as well as S-wave dispersion values of 0.009 and 0.092, respectively.