Elastic full-waveform inversion in tilted transverse isotropy media using Gauss Newton optimization

Abstract

In anisotropic full waveform inversion (FWI), the underground medium is commonly assumed to be vertical transverse isotropy (VTI). However, in reality, the presence of stress and tectonic movements often leads to a nonzero tilt angle θt of the strata's symmetry axis. This introduces variations in the direction of the fast axis during the propagation of seismic waves. Therefore, it is more practical and beneficial to consider tilted transverse isotropy (TTI) media when dealing with complex geological structures, as it enhances the accuracy of imaging and inversion. However, the consideration of TTI media also introduces a significant challenge of parameter coupling, commonly known as crosstalk or trade-off. This refers to the situation where the update of one parameter affects and projects onto other parameters. To address this issue and improve the inversion accuracy, we incorporate the Hessian within the inversion process. The off-diagonal elements of the Hessian matrix specifically provide important information about the correlations between different parameters, which aids in their decoupling and mitigates the effect of crosstalk. In numerical experiments, we applied the Gauss-Newton (GN) method to TTI elastic FWI and compared the results with those obtained using the preconditioned conjugate gradient (P-CG) method.The inversion results indicate that the GN method can better alleviate the parameter coupling, making simultaneous inversion of multiple parameters possible. θt