geotechnical engineering firms

Abstract: Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism from the diffusion prior. Numerical experiments demonstrate that the diffusion-regularized ASVGD-FWI produces more geologically consistent mean models, suppresses nonphysical artifacts, and yields uncertainty estimates that are more concentrated around structurally complex and poorly constrained regions. These results suggest that learned diffusion priors can effectively enhance Bayesian FWI by improving both inversion stability and the interpretability of posterior uncertainty.

Abstract: Three-dimensional (3D) velocity model building (VMB) remains computationally challenging with conventional approaches and native 3D neural networks, largely due to the prohibitive memory and training cost of full 3D formulations. Therefore, we introduce a depth-progressive framework that achieves 3D VMB using 2D generative diffusion models through a depth-as-channel formulation, in which the depth dimension of each 3D velocity patch is mapped to the channel dimension of a 2D U-Net. This allows the model to synthesize overlapping depth patches sequentially from shallow to deep while conditioning the prediction of the deeper patch on the shallower one, as well as on any available geophysical constraints, including well logs and structural attributes. During training, paired shallow-deep patch pairs with randomized overlaps are used to teach the network how deeper velocity structures relate to shallower information, and a classifier-free guidance strategy enables the model to handle missing constraints gracefully. At inference, starting from a shallow velocity prior, the model recursively generates deeper patches in a top-down manner, and a depth-attenuated Gaussian blending scheme merges overlapping predictions into spatially coherent 3D volumes while accounting for the progressive accumulation of uncertainty at greater depths. Numerical experiments on both in-distribution benchmark models, including Overthrust, SEAM Arid, and SEG/EAGE, and the out-of-distribution Marmousi model demonstrate that the method effectively propagates shallow velocity priors downward and produces high-quality 3D velocity volumes across a range of geological settings and conditioning scenarios. Compared to a 3D benchmark of equivalent architecture, the proposed method significantly reduces parameter count, training cost, and inference cost, while maintaining superior VMB accuracy.