Orientation-invariant wave equations for elastic media with TTI or TORT symmetries

SUMMARY

Seismic depth-imaging and inversion in complex geology often use wave-equation operators for TTI or TORT symmetries, but these still struggle with numerical instabilities due to incorrect adjoint operators and rapid tilt variations of symmetry axes of elastic tensors.

We propose a novel approach using frame bundles to describe heterogeneous anisotropic velocity models, aligning local coordinate frames with the elastic stiffness tensor’s tilt. This creates a curved manifold, allowing us to derive wave-equations invariant to symmetry orientation changes of elastic tensors describing the velocity model.

Our method provides true adjoint operators, supports various parameterizations of symmetry axes orientations, and interprets tilt variations as additional forces related to the manifold’s curvature.