Nonlinear seismic inversion in triaxial stress-induced anisotropic media modelled by microcrack closure mechanism

Summary Subterranean rock masses are in true triaxial stress (TTS) fields, which can preferentially close internal microcracks, thereby inducing elastic anisotropy. However, the seismic response under TTS is poorly understood. Here, an analytical PP-wave reflection coefficient for triaxial stress-induced anisotropic media modelled by microcrack closure mechanism is proposed for seismic inversion. Considering a micromechanical model in which microcracks are represented by stress-dependent compliances, the stress magnitude and orientation are firstly incorporated to account for the elastic anisotropy resulting from triaxial stress-induced microcrack closure. A good agreement is obtained between the model predictions and the existing laboratory measurements. Based on weak anisotropy assumption, we then deduce the effective stiffness tensor of the triaxial stress-induced anisotropic media. Three sets of stress-related anisotropy indicators (SRAIs) are introduced to quantify the microcrack closure effect and anisotropy magnitude induced by triaxial stress. Furthermore, a linearized PP-wave reflection coefficient equation for triaxially stressed isotropic media is derived using the scattering theory. Numerical results validate the feasibility and accuracy of the proposed formula, and reveal the influence of TTS on the PP-wave amplitude variation with angle and azimuth (AVAz). Finally, due to the highly ill-conditioned AVAz inverse problem in triaxial stress-induced anisotropic media, a model and data driven inversion approach is proposed through building on a convolutional neural network. We stepwise estimate the isotropic elastic parameters and SRAIs based on azimuthal seismic amplitude difference inversion strategy. Tests on both synthetic and real seismic data indicate that the nonlinear AVAz inversion framework outperforms conventional approaches in terms of stability and accuracy. Our study allows the construction of elastic properties in triaxial stress-induced anisotropic media, and may provide new insights into determining in-situ stress from seismic data.