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We introduce a probabilistic technique for full-waveform inversion, using variational inference and conditional normalizing flows to quantify uncertainty in migration-velocity models and its impact on imaging. Our approach integrates generative artificial intelligence with physics-informed common-image gathers, reducing reliance on accurate initial velocity models. Considered case studies demonstrate its efficacy producing realizations of migration-velocity models conditioned by the data. These models are used to quantify amplitude and positioning effects during subsequent imaging. 

We present the Seismic Laboratory for Imaging and Modeling/Monitoring open-source software framework for computational geophysics and, more generally, inverse problems involving the wave equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, the software is designed to be both readable and scalable, allowing researchers to easily formulate problems in an abstract fashion while exploiting the latest developments in high-performance computing. The design principles and their benefits are illustrated and demonstrated by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which, aside from coupling of wave physics and multiphase flow, involves machine learning. 

Abstract. Many applications in science require that computational models and data becombined. In a Bayesian framework, this is usually done by defininglikelihoods based on the mismatch of model outputs and data. However,matching model outputs and data in this way can be unnecessary or impossible.For example, using large amounts of steady state data is unnecessary becausethese data are redundant. It is numerically difficult to assimilate data inchaotic systems. It is often impossible to assimilate data of a complexsystem into a low-dimensional model. As a specific example, consider alow-dimensional stochastic model for the dipole of the Earth's magneticfield, while other field components are ignored in the model. The aboveissues can be addressed by selecting features of the data, and defininglikelihoods based on the features, rather than by the usual mismatch of modeloutput and data. Our goal is to contribute to a fundamental understanding ofsuch a feature-based approach that allows us to assimilate selected aspectsof data into models. We also explain how the feature-based approach can beinterpreted as a method for reducing an effective dimension and derive newnoise models, based on perturbed observations, that lead to computationallyefficient solutions. Numerical implementations of our ideas are illustratedin four examples.