The Relation Between TTI/TOR Symmetry Angle, Geo-history and Stress

We explore the apparent orthorhombic symmetry of a stressed, tilted transversely isotropic (TTI) layer under a tri-axial state of stress using a stress-dependent excess compliance model where fractures/cracks are bedding normal and bedding parallel, and for fractures that are consistent with the principle stress directions which is not related to the layer dip (e.g., present day). We show that for bedding parallel and bedding normal fractures the symmetry axis at any state of stress is aligned with the structural framework (i.e. the layer dip and its normal) and the medium symmetry is exactly orthorhombic. However, for fractures that are aligned with the maximum horizontal stress such that their normal is not normal to the dipping layer, the symmetry is monoclinic. The nearest medium orthorhombic approximation shows that the symmetry axis changes with depth such that at high stresses the symmetry tends to be more aligned with the structure while at lower stresses and higher fracture compliance the rock symmetry will deviate towards the stress direction. This result provides an important constraint on anisotropic seismic velocity model building and orthorhombic AVAZ analysis.