Multiparameter Bayesian full-waveform inversion with uncertainty quantification based on regularized inverse scattering theory for elastic transversely isotropic media

Complex subsurface structures exhibit significant anisotropic characteristics, making multi-parameter imaging techniques important for achieving a more comprehensive geological interpretation. Full-waveform inversion (FWI) as a state-of-the-art method for reconstructing subsurface properties based on seismic wavefield modeling and data misfit minimization, has been widely applied to isotropic media in both synthetic and field datasets. However, challenges such as crosstalk correlation and inaccuracy of the initial model indicate that further advancements are required to enhance resolution and computational efficiency. We propose an elastic FWI in the frequency domain for two-dimensional (2D) TI media to characterize their physical properties appropriately, as they are common in sedimentary basin environments. Different from traditional inversion schemes, our approach is formulated based on Bayesian inference, which automatically facilitates uncertainty analysis of the inversion results. Seismic data are acquired via the integral equation (IE) method grounded in scattering theory, where the sensitivity kernel is explicitly constructed using Green’s functions, hence facilitating the calculation of gradient and Hessian. A Krylov subspace iterative method provides the approximated solution of the Lippmann-Schwinger (L-S) equation without sacrificing the accuracy. Furthermore, we incorporate the minimum support (MS) stabilizing functional as a model misfit term to regularize the objective function. A randomized singular value decomposition (SVD) approach is used to approximate and decompose the prior preconditioned Hessian. Both the model and covariance are updated through the iterative extended Kalman filter (IEKF) that implemented in the form of the Levenberg–Marquardt (LM) algorithm, thereby enabling a practical uncertainty quantification. Numerical tests are conducted on two synthetic TI models with vertical and tilted symmetry axes, respectively, illustrating the precision and robustness of our method.