Full waveform inversion (FWI) develops a subsurface model that best explains the observed seismic data through iteratively minimizing the misfit between modelled and observed data.

This is inherently a nonlinear optimization problem and thus often suffers from local-minima and cycle-skipping issues. To attack these issues, TGS FWI starts from low frequency, small offset data, then gradually extends to higher frequency and longer offset data; using a dynamic warping technique to resolve long wavelength components.  The process then turns to an L2 norm to obtain a high-resolution solution; inverts the transmitted waves first for the shallow part, and then changes to reflection mode for the deep part. TGS FWI provides a spatial correlation map, phase residual map and other tools to QC the convergence and possible cycle-skipping. 

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Kirchhoff PSDM: FWI Velocity
Kirchhoff PSDM: Initial Velocity