Elastic full waveform inversion (FWI) is most commonly solved as an elastodynamic problem, based on modeling and processing of vector displacement. It can alternately be framed as a simultaneous inversion of PP/PS/SP/SS data, taking as input the measured field after decomposition into P- and S-wave components. Advantages include: (1.) Interpretability: FWI quantities involve 2x2 matrices whose off-diagonal elements are classical converted-wave processes; (2.) Computational efficiencies: simple wave equations are invoked in simulation and gradient construction; (3.) Flexibility: the ability to selectively incorporate or neglect PP, PS, SP and/or SS data as desired; and (4.) Leverage: existing 3C/9C concepts and technology readily apply. By “conceptual leverage” we mean that: the close relationship between Gauss-Newton FWI updates derived from pre-critical reflection data and standard linearized multicomponent AVO inversion is evident in this formulation; also, the same ease with which we move from one AVO parameterization to another (e.g., VP-VS-rho, Poisson’s ratio, Goodway’s lambda- and mu-impedances, Russell and Gray’s poroelastic/fluid terms, etc.) is available to “P-S space” FWI workflows. How all of these apparent advantages of P-S FWI stack up against those of “displacement space” FWI is not certain. One possibility is to use a P-S FWI workflow at early iterations, when the model is relatively homogeneous, but to transition to a displacement-type FWI workflow at later iterations, as the model gains greater levels of heterogeneity.
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