# Stochastic seismic waveform inversion using generative adversarial networks as a geological prior

arXiv: https://arxiv.org/abs/1806.03720 · HTML: https://mlsanity.com/paper/1806.03720/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2018.

## Built on by (most cited first, 30 of 48)

- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Controllable seismic velocity synthesis using generative diffusion models](https://mlsanity.com/paper/2402.06277/) (2024)
- [Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems](https://mlsanity.com/paper/2102.03169/) (2021)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Learning by example: fast reliability-aware seismic imaging with normalizing flows](https://mlsanity.com/paper/2104.06255/) (2021)
- [Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning](https://mlsanity.com/paper/2108.10163/) (2021)
- [Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models](https://mlsanity.com/paper/2112.03860/) (2021)
- [Mining the manifolds of deep generative models for multiple data-consistent solutions of ill-posed tomographic imaging problems](https://mlsanity.com/paper/2202.05311/) (2022)
- [Learning 4DVAR inversion directly from observations](https://mlsanity.com/paper/2211.09741/) (2022)
- [Robust Physics-Guided Diffusion for Full-Waveform Inversion](https://mlsanity.com/paper/2603.16393/) (2026)
- [Data-driven Full-waveform Inversion Surrogate using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2105.00100/) (2021)
- [Direct multi-modal inversion of geophysical logs using deep learning](https://mlsanity.com/paper/2201.01871/) (2021)
- [Generating unrepresented proportions of geological facies using Generative Adversarial Networks](https://mlsanity.com/paper/2203.09639/) (2022)
- [A Frequency-Velocity CNN for Developing Near-Surface 2D Vs Images from Linear-Array, Active-Source Wavefield Measurements](https://mlsanity.com/paper/2207.09580/) (2022)
- [A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network](https://mlsanity.com/paper/2312.04752/) (2023)
- [Stochastic full waveform inversion with deep generative prior for uncertainty quantification](https://mlsanity.com/paper/2406.04859/) (2024)
- [Diffusion prior as a direct regularization term for FWI](https://mlsanity.com/paper/2506.10141/) (2025)
- [DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network](https://mlsanity.com/paper/2104.04704/) (2021)
- [Wave-Informed Matrix Factorization with Global Optimality Guarantees](https://mlsanity.com/paper/2107.09144/) (2021)
- [Regularized Training of Intermediate Layers for Generative Models for Inverse Problems](https://mlsanity.com/paper/2203.04382/) (2022)
- [Signal Recovery with Non-Expansive Generative Network Priors](https://mlsanity.com/paper/2204.13599/) (2022)
- [Integrating Physics of the Problem into Data-Driven Methods to Enhance Elastic Full-Waveform Inversion with Uncertainty Quantification](https://mlsanity.com/paper/2406.05153/) (2024)
- [Geological and Well prior assisted full waveform inversion using conditional diffusion models](https://mlsanity.com/paper/2412.06959/) (2024)

## Abstract (arXiv)

We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate MALA sampling allows efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.