Simultaneous seismic inversion of effective stress parameter, fluid bulk modulus, and fracture density in TTI media

Predictions of fluid distribution, stress field, and natural fracture are essential for exploiting unconventional shale gas reservoirs. Given the high likelihood of tilted fractures in subsurface formations, this study focuses on simultaneous seismic inversion to estimate fluid bulk modulus, effective stress parameter, and fracture density in the tilted transversely isotropic (TTI) medium. In this article, a novel PP-wave reflection coefficient approximation equation is first derived based on the constructed TTI stiffness matrix incorporating fracture density, effective stress parameter, and fluid bulk modulus. The high accuracy of the proposed equation has been demonstrated using an anisotropic two-layer model. Furthermore, a stepwise seismic inversion strategy with the L_P quasi-norm sparsity constraint is implemented to obtain the anisotropic and isotropic parameters. Three synthetic model tests with varying signal-to-noise ratios (SNRs) confirm the method's feasibility and noise robustness. Ultimately, the proposed method is applied to a 3D fractured shale gas reservoir in the Sichuan Basin, China. The results have effectively characterized shale gas distribution, stress fields, and tilted natural fractures, with validation from geological structures, well logs, and microseismic events. These findings can provide valuable guidance for hydraulic fracturing development, enabling more reliable predictions of reservoir heterogeneity and completion quality.