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Theoretical models for the description of stress dependencies for anisotropic rocks are important for building velocity models and the interpretation of seismic data with respect to stress, lithology, and pore content. Especially important is the accurate description of the change of anisotropy due to applied anisotropic stress by means of a quantitative model to aid the interpretation. The porosity-deformation approach (PDA; originally introduced as the piezosensitivity theory) describes stress-induced changes of elastic properties without any knowledge about the geometry and orientation of the microcracks. We have developed a formulation of the theory for a transverse isotropic rock, which was loaded parallel to the bedding plane, and we found that it can be described theoretically as an orthorhombic rock. We also found out how properties that described the velocity change due to hydrostatic loading can be used to predict elastic anisotropy under additional axial loading. The number of free parameters are reduced by using the PDA compared with phenomenological fitting of data. We have used literature data of ultrasonic-wave velocity obtained during the geomechanical multistage measurements on a water-saturated Norwegian Sea shale sample to test the adapted theory. In a first step, we found that the PDA well-described the hydrostatic velocity-stress dependency. The obtained stress sensitivity and compliant porosity values give reasonable results compared with the microstructure of shales. In a second step, the obtained parameters were used for predicting the obtained shear compliances under triaxial stress conditions. Our results help to give an interpretation of the components of the stress sensitivity that describes the S-wave velocities.

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