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

Uncertainty quantification in the context of seismic imaging is important for interpreting inverted subsurface models and updating reservoir models. The limited illumination, noisy data, and poor initial models in the seismic full-waveform inversion (FWI) lead to inversion uncertainties. This is particularly true for anisotropic elastic FWI, which suffers from extra parameter trade-off challenges. We have addressed the uncertainty quantification of the anisotropic elastic FWI problem in the framework of Bayesian inference. In particular, we estimate the uncertainties of the subsurface elastic parameters in Bayesian anisotropic elastic 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 on the integral equation approach, which is also within the context of the nonlinear inverse scattering theory. We determine the results of numerical tests with examples for anisotropic elastic media. They show that the adopted Bayesian inversion method can provide reasonable reconstructed results for the elastic coefficients of the stiffness tensor and the framework is suitable for accessing the uncertainties.