Elastic full waveform inversion in the P- and S-wave domain

Kris Innanen
University of Calgary

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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