TTI Reflection waveform inversion based on the modified gradient sampling algorithm

Summary Reflection waveform inversion (RWI) is an effective method for reconstructing subsurface parameters with low-to-moderate wavenumbers. As the influence of anisotropy on seismic data becomes increasingly significant, RWI should be extended to tilted transversely isotropic (TTI) media (TTI-RWI) to improve inversion accuracy. Unlike conventional isotropy or vertical transverse isotropy (VTI) assumptions, the TTI model provides a more realistic representation of geological structures with intense tectonic activity. Nevertheless, the practical implementation of TTI-RWI faces two challenges. First, as it relies on waveform matching, an inaccurate initial model can cause cycle-skipping and convergence to local minima. Second, the inherent coupling between velocity and anisotropic parameters leads to significant parameter crosstalk. These issues often coexist when prior information is limited. To address the first challenge, we propose a modified gradient sampling algorithm (GSA) that incorporates global optimization information to mitigate cycle-skipping without increasing computational cost. For the second challenge, we design a two-stage inversion strategy where the vertical P-wave velocity vp0 is first inverted using GSA, followed by joint inversion of vp0 and the anisotropic parameter ε via Gauss-Newton optimization. The effectiveness of the proposed TTI-RWI approach is validated through numerical experiments on the Overthrust model and applications to field marine towed-streamer data.