An Anisotropic Waveform Inversion Using an Optimal Transport Matching Filter Objective: An Application to an Offshore Field Dataset

Considering the conventional seismic wavelength and the nature of the Earth's layering, seismic waves experience, in many parts of the subsurface, considerable anisotropy, and with the effect of gravity on sedimentation, the anisotropy tends to be transversely isotropic with a vertical axis of symmetry [vertical transverse isotropy (VTI)] nature. Inverting to such a model of the Earth using waveforms, we face considerable nonlinearity and parameter tradeoff. A recently introduced optimal transport of the matching filter (OTMF) provided us with a robust misfit function for reducing cycle skipping in full-waveform inversion (FWI). We apply a VTI FWI using the OTMF misfit on a field dataset from offshore Australia, comparing its performance to that of conventional FWI using the L2-norm misfit in a variety of circumstances. Due to strong anisotropy in this region, an isotropic inversion can fit the record, leading to common image gathers (CIGs) with sizable linear moveouts. Thus, in an anisotropic VTI setup, starting the inversion from 3 Hz, both the L2-norm and the OTMF misfit functions can generate a geologically meaningful model and recover similar anisotropy anomalies. We demonstrate that the OTMF misfit, in some sense, can address the nonlinearity of FWI due to its intrinsic global updating features. Compared to the results from isotropic FWI, the improvements in the RTM image and the CIGs further demonstrate the benefits of including anisotropy in the FWI inversion engine and the good performance of the OTMF in mitigating cycle skipping.