Probabilistic amplitude-versus-angle inversion via annealed Stein variational gradient descent, automatic differentiation, and model-space compression

Amplitude-versus-angle (AVA) inversion is a widely used geophysical technique for estimating subsurface elastic properties from seismic reflection data. However, its ill-posed nature necessitates robust and efficient methods for uncertainty quantification. This work presents a novel Bayesian AVA inversion framework that integrates annealed Stein variational gradient descent (A-SVGD) with discrete cosine transform (DCT) compression of the model space. A-SVGD introduces an annealing schedule to enhance posterior exploration, while DCT significantly reduces problem dimensionality, improving stability and convergence. The inversion employs full Zoeppritz equations as the forward model and leverages automatic differentiation for efficient and accurate gradient computation. Synthetic tests demonstrate that A-SVGD outperforms standard SVGD in convergence speed and uncertainty quantification. The DCT-based model-space compression achieves performance comparable to full-domain inversion, but at a fraction of the computational cost. Further tests under realistic conditions (e.g. where errors are introduced in both the estimated source wavelet and noise statistics) highlight the robustness of the proposed approach. Additionally, replacing the Jacobian with a DCT-projected analytical approximation shows promise for accelerating computation, though its applicability is model-dependent. Overall, this study demonstrates that A-SVGD in a DCT-compressed domain provides a powerful and efficient solution for probabilistic AVA inversion and achieves final predictions comparable with those obtained with a gradient-based Markov chain Monte Carlo method.