AGU24 - Nonlinear Geophysics (NG)Mon, Dec 09, 2024, Washington DC & OnlineSession NG01-01: Bayesian posterior sampling in non-linear seismic inverse problem using deep generative priorAn inverse problem involves deducing the causes from observed effects within a system, often requiring the solution of partial differential equations that describe the system underlying physics. In geophysical seismic imaging, the goal is to reconstruct subsurface structures (typically velocity and density fields) by analyzing seismic waveforms recorded at the Earth's surface. This involves solving the non-linear wave equation to model the propagation of seismic waves through the Earth. Full Waveform Inversion (FWI) is a deterministic technique using gradient methods. However, FWI faces challenges such as non-uniqueness and computational complexity, emphasizing the need for advanced methods to accurately quantify uncertainties in inferred subsurface properties.Bayesian inference offers a robust framework for solving inverse problems and quantifying uncertainties by applying Bayes' theorem. This approach constructs a posterior probability density function of model parameters given the observed data. In this work, we introduce the approach that parameterizes the unknowns by training Wasserstein Generative Adversarial Networks (WGAN), to learn the prior distribution in the latent space capable of generating realistic subsurface images. Once trained, the GAN remains fixed, providing a powerful generative prior for Bayesian posterior sampling.In this work, we experiment and compare various posterior sampling methods, including Markov chain Monte Carlo (McMC) sampling, variational Bayesian inference methods using normalizing flow (NF), inference neural network (INN), Stein Variational Gradient Descent (SVGD). We evaluate their performance in terms of computational efficiency and accuracy in capturing the posterior distribution. The integration of deep generative priors with various Bayesian sampling techniques demonstrates significant improvements in handling the high-dimensionality of non-linear geophysical inverse problems, offering a direction for future research in uncertainty quantification.