Calibration of Velocity-stress Relationships Under Hydrostatic Stress For Their Use Under Non-hydrostatic Stress Conditions

TLDR: In this paper, the authors computed stress sensitivity parameters for intrinsically transverse isotropic (TI) shales and sandstones under hydrostatic stress using literature data from Wang (2002b).

Abstract: We have computed stress sensitivity parameters for intrinsically transverse isotropic (TI) shales and sandstones under hydrostatic stress using literature data from Wang (2002b). We use the three-parameter non-linear model that relates the whole stiffness tensor and the whole stress tensor. We introduce physical and empirical constraints in the inversion of parameters c111, c112, c123 to compensate for the absence of non-hydrostatic stress data. The constraints c111 < c112 and c155 < c144 ensure respectively that P-waves are dominated by the stress in the polarization direction and S-waves by stresses in the polarization and propagation direction. We confirm the validation of the model for all 16 shale samples and 10 out of 20 sandstone samples (35 MPa stress range) when intrinsic anisotropy is present and greater than 4.5 %. Sand samples show higher stress sensitivity than shale samples. With this methodology, we suggest that velocity-stress relationships can be calibrated in the lab under hydrostatic stress and then used under non-hydrostatic stress conditions.