# Data-driven Seismic Waveform Inversion: A Study on the Robustness and Generalization

arXiv: https://arxiv.org/abs/1809.10262 · HTML: https://mlsanity.com/paper/1809.10262/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2018.

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

- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [An Empirical Study of Large-Scale Data-Driven Full Waveform Inversion](https://mlsanity.com/paper/2307.15388/) (2023)
- [An Intriguing Property of Geophysics Inversion](https://mlsanity.com/paper/2204.13731/) (2022)
- [RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion](https://mlsanity.com/paper/2509.21659/) (2025)
- [Making Invisible Visible: Data-Driven Seismic Inversion with Spatio-temporally Constrained Data Augmentation](https://mlsanity.com/paper/2106.11892/) (2021)
- [mathbfmathbbEFWI: Multi-parameter Benchmark Datasets for Elastic Full Waveform Inversion of Geophysical Properties](https://mlsanity.com/paper/2306.12386/) (2023)
- [Revisit Geophysical Imaging in A New View of Physics-informed Generative Adversarial Learning](https://mlsanity.com/paper/2109.11452/) (2021)
- [Edge-InversionNet: Enabling Efficient Inference of InversionNet on Edge Devices](https://mlsanity.com/paper/2310.09667/) (2023)
- [Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion](https://mlsanity.com/paper/2606.14139/) (2026)
- [DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network](https://mlsanity.com/paper/2104.04704/) (2021)
- [Enhanced prediction accuracy with uncertainty quantification in monitoring CO2 sequestration using convolutional neural networks](https://mlsanity.com/paper/2212.04567/) (2022)
- [PreAdaptFWI: Pretrained-Based Adaptive Residual Learning for Full-Waveform Inversion Without Dataset Dependency](https://mlsanity.com/paper/2502.11913/) (2025)
- [Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)](https://mlsanity.com/paper/2504.10720/) (2025)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [NuSPAN: A Proximal Average Network for Nonuniform Sparse Model -- Application to Seismic Reflectivity Inversion](https://mlsanity.com/paper/2105.00003/) (2021)
- [SVInvNet: A Densely Connected Encoder-Decoder Architecture for Seismic Velocity Inversion](https://mlsanity.com/paper/2312.08194/) (2023)
- [Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging](https://mlsanity.com/paper/2410.08329/) (2024)
- [Acoustic Waveform Inversion with Image-to-Image Schr"odinger Bridges](https://mlsanity.com/paper/2506.15346/) (2025)
- [SA-EMO: Structure-Aligned Encoder Mixture of Operators for Generalizable Full-waveform Inversion](https://mlsanity.com/paper/2511.11627/) (2025)
- [Inverse Problems Conditioned on Observation Ensembles: Applications and Methods](https://mlsanity.com/paper/2601.22029/) (2026)
- [DiffSOS: Acoustic Conditional Diffusion Model for Speed-of-Sound Reconstruction in Ultrasound Computed Tomography](https://mlsanity.com/paper/2603.00382/) (2026)
- [Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture](https://mlsanity.com/paper/2606.01110/) (2026)
- [Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity](https://mlsanity.com/paper/2606.22867/) (2026)
- [ScoreField: Neural Inverse Scattering with Score-Based Generative Priors](https://mlsanity.com/paper/2608.02937/) (2026)
- [ROMNet: a hybrid reduced order modeling and machine learning approach to waveform inversion](https://mlsanity.com/paper/2608.25160/) (2026)
- [Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion](https://mlsanity.com/paper/2609.12899/) (2026)
- [Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent](https://mlsanity.com/paper/2610.19187/) (2026)

## Abstract (arXiv)

Acoustic- and elastic-waveform inversion is an important and widely used method to reconstruct subsurface velocity image. Waveform inversion is a typical non-linear and ill-posed inverse problem. Existing physics-driven computational methods for solving waveform inversion suffer from the cycle skipping and local minima issues, and not to mention solving waveform inversion is computationally expensive. In recent years, data-driven methods become a promising way to solve the waveform inversion problem. However, most deep learning frameworks suffer from generalization and over-fitting issue. In this paper, we developed a real-time data-driven technique and we call it VelocityGAN, to accurately reconstruct subsurface velocities. Our VelocityGAN is built on a generative adversarial network (GAN) and trained end-to-end to learn a mapping function from the raw seismic waveform data to the velocity image. Different from other encoder-decoder based data-driven seismic waveform inversion approaches, our VelocityGAN learns regularization from data and further impose the regularization to the generator so that inversion accuracy is improved. We further develop a transfer learning strategy based on VelocityGAN to alleviate the generalization issue. A series of experiments are conducted on the synthetic seismic reflection data to evaluate the effectiveness, efficiency, and generalization of VelocityGAN. We not only compare it with existing physics-driven approaches and data-driven frameworks but also conduct several transfer learning experiments. The experiment results show that VelocityGAN achieves state-of-the-art performance among the baselines and can improve the generalization results to some extent.