Centered T-matrix method for pressure-dependent effective elastic moduli of rocks

Summary Effective elastic moduli govern seismic wave velocities in porous rocks and are widely used to interpret laboratory and field measurements. Predicting these moduli from microstructure remains difficult for rocks with high porosity, strong elastic contrast, anisotropic mineral fabrics, and connected pore space. We revisit the T-matrix approach and propose a centered formulation that cleanly separates the response of a chosen reference medium from the additional effects of heterogeneity and interactions. This reorganization yields a single framework that recovers several widely used closures as special cases, including a one-pass (optical-potential) evaluation and self-consistent (coherent-potential) schemes, and it clarifies what microstructural information is required to improve predictions. We show that the self-consistent closure can be written as a Riccati-type fixed-point problem; in our tests this form is numerically convenient and gives similar effective moduli as the self-consistent scheme so-called coherent-potential approximation (CPA). Across the parameter ranges considered, the centered one-pass evaluation provides a particularly favorable accuracy-cost trade-off. The framework also supports non-ellipsoidal pore and grain shapes through inclusion-averaged one-body blocks and admits systematic higher-order corrections when needed. To demonstrate geophysical relevance, we introduce a pressure-dependent comparison medium based on contact-mechanics scalings and validate the resulting pressure-dependent moduli against laboratory measurements for a sandstone. Overall, the proposed formulation provides a practical route to pressure-dependent rock-physics modeling while making explicit the assumptions and limits behind commonly used T-matrix and effective-medium theory variants.