Abstract
We develop an analytic model of a wedge-shaped crack connected with stiff pore space for wave dispersion and attenuation in isotropic porous rocks using the wave-induced fluid flow (WIFF) mechanism. This model addresses squirt flow, a significant factor influencing wave propagation behavior across seismic, sonic, and even ultrasonic frequencies. Our model bridges the gap between existing models, demonstrating consistency with Gassmann’s model at low frequencies and Mavko-Jizba’s model at high frequencies. Using a hybrid-dimensional approach, we derive a simple formula for the modified fluid modulus to enable the calculation of elastic moduli for saturated rocks. The model predicts dispersion and attenuation behaviors at low, intermediate, and high frequencies and accounts for differences in liquid- and gas-saturated rocks. Comparisons with existing disk-shaped models and laboratory measurements showcase the potential advantage of a wedge-shaped model for describing seismic dispersion. Validation is achieved through good agreement with the published measurements of four rock samples. This model can readily integrate with classic WIFF theories, such as Biot’s poroelasticity, extending its applicability across a broader frequency range.
Paper information
Fubin Chen; Zhaoyun Zong; Xingyao Yin. A squirt-flow model in isotropic porous rocks containing wedge-shaped cracks and its interpretation for laboratory measurements. Geophysics (2025) 90 (2): MR141–MR153.https://doi.org/10.1190/geo2024-0292.1
