A sphere-equivalency approach for calculating the elastic property of an isotropic solid containing aligned inclusions: Modeling and experiment data verification

Abstract

Accurate modeling of elastic properties of cracked rocks in the earth’s shallow crust has long been an important topic in the field of geophysics. A sphere-equivalency approach of elastic wave scattering was used to model the elastic moduli of an isotropic solid containing aligned cracks. The results were compared with those of the existing Eshelby-Cheng and Hudson’s theories for dry and fluid saturation conditions, showing remarkably improved stability and accuracy for high crack concentrations, especially for Hudson’s second-order model. The stability and accuracy of the new approach were determined for varying solid and crack parameters. Finally, the new and existing theories were applied to model the laboratory ultrasonic experimental data measured on artificially cracked samples with varying wave frequencies and crack concentrations. Compared to Hudson’s theory, the new model agrees significantly better with the data. Specifically, the root-mean-square errors of theoretical fitting to data from our model are generally smaller than those from the other two models. We have thus developed an effective tool for modeling elastic properties of cracked rocks.