Bayesian full waveform inversion in anisotropic elastic media using the iterated extended Kalman filter

Abstract

Uncertainty quantification in the context of seismic imaging is important for interpretinginverted subsurface models and updating reservoir models. The limited illumination, noisydata and poor initial model in the seismic full waveform inversion (FWI) lead to inversionuncertainties. This is particularly true for anisotropic elastic FWI, which suffers from extra parameter trade-off problems. In this work, we address the uncertainty quantificationof anisotropic elastic FWI problem in the framework of Bayesian inference. Specially, weestimate the uncertainties of the subsurface elastic parameters in the Bayesian anisotropicelastic FWI by combining the iterated extended Kalman filter with an explicit representation of the sensitivity matrix with Green’s functions. The sensitivity matrix is based onthe integral equation approach, which is also within the context of nonlinear inverse scattering theory. We give the results of numerical tests with examples for anisotropic elasticmedia. They show that the proposed Bayesian inversion method can provide reasonablereconstructed results for the elastic coefficients of the stiffness tensor and the framework issuitable for accessing the uncertainties.