The power-law characteristics in the microcrack system of a rock: inversion and analysis of laboratory velocity-pressure data

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2026
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Abstract
Summary The pore-crack network, characterized by the distribution of pore aspect ratios and porosity, controls the seismic properties of a rock. The increase in laboratory ultrasonic velocity with effective pressure reflects the closure of microcracks, thereby allowing the pore-aspect-ratio spectrum to be inverted through rock-physics modelling. Previous studies on sandstone samples have suggested that the pore-aspect-ratio spectrum (porosity distribution vs. pore-aspect-ratio distribution) follows a power-law distribution; however, its robustness across different lithologies, model dependence, and origin remain poorly understood. In this study, these questions are further investigated. We compile laboratory ultrasonic velocity-pressure data from 50 rock samples spanning a wide range of lithologies and porosities. Then we invert the power-law exponent (the slope of the power-law distribution) from these data by integrating the pore-aspect-ratio spectrum into two independent rock-physics models: the existing Kuster-Toksöz (KT) model and the multi-crack wave theory (MCWT) that incorporates the squirt-flow mechanism. The inversion results show that both models obtain power-law pore-aspect-ratio spectra across lithologies, with the MCWT showing improved modelling of the squirt-flow effect in saturated P-wave velocities, leading to smaller fitting errors. Theoretical modelling explains the differences between the two models in their fitting behavior and inverted power-law exponent values. Furthermore, we demonstrate that the power-law pore-aspect-ratio spectrum can be derived from widely observed power-law fracture length and aperture distributions of the crack system. The result also establishes a relationship between the power-law exponent and porosity that well explains the global data trend from inverting the velocity-pressure data of rock samples. The significance of the power-law exponent and the applicability of the E-porosity relationship are also discussed. Our findings support a robust power-law pore-aspect-ratio spectrum across different lithologies and highlight its simplicity and practical applicability for analyzing velocity-pressure data in cracked-porous rocks.
Reference Key
openalex_W7171724156 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors He‐Ming Wang, Wen-Hao Wang, Mai‐Linh Doan, Xiao-Ming Tang
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag302
URL
https://doi.org/10.1093/gji/ggag302
Keywords Keywords not found

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