Multiparameter seismic full waveform inversion in fractured media: anisotropic parameter estimation and cross-talk suppression

Abstract:

We consider the estimation, through multiparameter full waveform inversion (FWI), of the elastic constants in naturally fractured geological volumes, treating them as equivalent anisotropic media. Some multiparameter FWI success stories have been reported, a range of challenges remain, one being the parameter cross-talk, i.e., the confusion associated with the overlap of one parameter’s Fréchet derivative wavefield with another’s. Parameter cross-talk is largely decided by the scattering pattern produced by each parameter, i.e., the relative strength of incoming to outgoing waves from a volume scattering element as a function of opening angle. We have derived the 3D scattering patterns associated with the elastic constants of general anisotropic media, and applied them, in the specific case of HTI media, in an analysis of anisotropic parameter cross-talk and the ability of a FWI update to suppress it. This involves the inverse Hessian operator and its various approximations, in their capacity to adjust and weight bare gradients. Gradients alone exhibit cross-talk, as well as artifacts caused by doubly-scattered energy in the data residuals. We determine with numerical examples that the approximate inverse Hessian associated with a Gauss-Newton update contains the mechanism necessary to suppress a significant fraction of parameter cross-talk in the gradient; and, that the residual-dependent portion of the inverse Hessian, constructed using the adjoint-state method, contains the mechanisms for suppression of multi-parameter second-order scattering artifacts in the gradient.