Seismic azimuthal anisotropy is apparent when P-wave velocities vary with source-receiver azimuth and downward-propagating S-waves split into two quasi-S-waves, polarized in orthogonal directions. Not accounting for these effects can degrade seismic image quality and result in erroneous amplitude analysis and geologic interpretations. There are currently no physical models available to describe how azimuthal anisotropy induced by differential horizontal stress varies with sand-shale lithology and depth; we develop a model that does so, in unconsolidated sand-shale sequences offshore North West Australia. Our method naturally introduces two new concepts: “critical anisotropy” and “anisotropic depth limit.” Critical anisotropy is the maximum amount of azimuthal anisotropy expected to be observed at the shallowest sediment burial depth, where the confining pressure and sediment compaction are minimal. The anisotropic depth limit is the maximum depth where the stress-induced azimuthal anisotropy is expected to be observable, where the increasing effects of confining pressure, compaction, and cementation make the sediments insensitive to differential horizontal stress. We test our model on borehole log data acquired in the Stybarrow Field, offshore North West Australia, where significant differential horizontal stress and azimuthal anisotropy are present. We determine our model parameters by performing regressions using dipole shear log velocities, gamma-ray shale volume logs, and depth trend data. We perform a blind test using the model parameters derived from one well to accurately predict the azimuthal anisotropy values at two other wells in an adjacent area. We use our anisotropy predictions to improve the well-tie match of the modeled angle-dependent reflectivity amplitudes to the 3D seismic amplitude variation with offset data observed at the well locations. Future applications of our method may allow the possibility to estimate the sand-shale content over a wide exploration area using anisotropic parameters derived from surface 3D seismic data.