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Reliable analysis of time-lapse seismic data to detect movements of pore fluids requires consideration of variations in subsurface stress as well as fluid saturations. Achieving this goal requires reliable rock physics models that relate these stress changes to seismic velocity. Although there are many theories for the effective elastic properties of fractured media, only a small number directly include stress-dependence. Therefore, we have developed a new model that provides expressions that are comparatively easy to work with and requires estimation of only a small number of parameters. In this paper, we apply this model for the first time to the inversion of published laboratory measurements of pressure-dependent anisotropic seismic velocities. Specifically, we utilize measured velocities in two orthogonal directions to estimate the model parameters for a transversely isotropic medium. The model is then used to predict directional velocity variation in other directions at ambient pressure, and the errors in all cases are small. Synthetic shear wave seismograms computed for a hypothetical carbonate reservoir model show the changes in shear wave splitting and travel times that are predicted when seismic properties are computed using the theoretical model and help to illustrate the potential applications of the theoretical model to reservoir characterization.

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