# Intro - Paragraph 1 @article{virieux2009overview, title={An overview of full-waveform inversion in exploration geophysics}, author={Virieux, Jean and Operto, St{\'e}phane}, journal={Geophysics}, volume={74}, number={6}, pages={WCC1--WCC26}, year={2009}, publisher={Society of Exploration Geophysicists} } @article{gahlot_twin, title={An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring}, author={Gahlot, Abhinav Prakash and Orozco, Rafael and Yin, Ziyi and Herrmann, Felix J}, journal={arXiv preprint arXiv:2410.01218}, year={2024} } @article{gahlot_li_injectivity, title={A digital twin for geological carbon storage with controlled injectivity}, author={Gahlot, Abhinav Prakash and Li, Haoyun and Yin, Ziyi and Orozco, Rafael and Herrmann, Felix J}, journal={arXiv preprint arXiv:2403.19819}, year={2024} } @misc{park_defino, title={A reduced-order derivative-informed neural operator for subsurface fluid-flow}, author={Jeongjin Park and Grant Bruer and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Felix J. Herrmann}, year={2026}, eprint={2509.13620}, archivePrefix={arXiv}, primaryClass={physics.comp-ph}, url={https://arxiv.org/abs/2509.13620}, } @misc{deng_pjrm, title={Probabilistic Joint Recovery Method for CO$_2$ Plume Monitoring}, author={Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}, year={2025}, eprint={2501.18761}, archivePrefix={arXiv}, primaryClass={cs.LG}, url={https://arxiv.org/abs/2501.18761}, } # Intro - Paragraph 2 @ARTICLE{seismicfwi, author={Jia, Anqi and Sun, Jian and Du, Bo and Lin, Yuzhao}, journal={IEEE Transactions on Geoscience and Remote Sensing}, title={Seismic Full Waveform Inversion With Uncertainty Analysis Using Unsupervised Variational Deep Learning}, year={2025}, volume={63}, number={}, pages={1-16}, keywords={Uncertainty;Data models;Computational modeling;Probabilistic logic;Bayes methods;Mathematical models;Training;Computational efficiency;Optimization;Deep learning;Deep learning;full waveform inversion (FWI);uncertainty analysis;variational autoencoder (VAE)}, doi={10.1109/TGRS.2025.3564647} } @misc{orozco2024velocitymodel, title={Machine learning-enabled velocity model building with uncertainty quantification}, author={Rafael Orozco and Huseyin Tuna Erdinc and Yunlin Zeng and Mathias Louboutin and Felix J. Herrmann}, year={2024}, eprint={2411.06651}, archivePrefix={arXiv}, primaryClass={cs.LG}, url={https://arxiv.org/abs/2411.06651}, } @article{erdinc2025power, author = {Huseyin Tuna Erdinc and Yunlin Zeng and Abhinav Prakash Gahlot and Felix J. Herrmann}, title = {Power-scaled Bayesian inference with score-based generative models}, volume = {Fifth International Meeting for Applied Geoscience & Energy}, series = {SEG Technical Program Expanded Abstracts}, pages = {21-25}, year = {2025}, month = {08}, eprint={2504.10807}, archivePrefix={arXiv}, note = {Also available at: https://arxiv.org/abs/2504.10807} } @article{taufik2026accelerating, author = {Taufik, Mohammad H and Alkhalifah, Tariq}, title = {Accelerating Bayesian full waveform inversion using reconstruction-guided diffusion sampling}, journal = {Geophysical Journal International}, volume = {245}, number = {2}, pages = {ggag066}, year = {2026}, month = {02}, abstract = {Full waveform inversion (FWI) is a powerful tool in seismic imaging, capable of producing high-resolution models of the subsurface. However, the method remains computationally intensive and sensitive to initial models due to its nonlinearity and ill-posed nature. To quantify uncertainty in FWI results, variational inference (VI) methods, such as Stein Variational Gradient Descent (SVGD), have been increasingly explored. These approaches approximate the posterior distribution by evolving a set of particles using gradient information from the log-posterior. Despite their promise, their effectiveness heavily depends on the quality of the prior used for initialization. In this work, we propose a hybrid framework that improves the efficiency and robustness of VI-based FWI by initializing SVGD with samples drawn from a reconstruction-guided diffusion model. Rather than replacing SVGD with a generative sampler, our approach preserves the theoretical foundations of VI while leveraging the expressive capacity of deep generative models. The diffusion model is trained to generate geologically plausible models conditioned on seismic images, thereby guiding the SVGD initialization toward regions of high posterior support. This initialization significantly reduces the number of required SVGD updates and improves convergence, while keeping the core VI formulation intact. Our results show enhanced posterior approximation and more geologically consistent solutions, with an order of magnitude lower computational cost compared to naïvely initialized SVGD. However, challenges remain, such as the computational demands of likelihood evaluations, the formation of a training set that encompasses all plausible realizations and sensitivity to reconstruction-guidance weights during sampling. Overall, this method provides a principled and efficient approach to uncertainty-aware FWI, integrating physics-informed inference with data-driven generative modelling for practical applications in full waveform inversion.}, issn = {1365-246X}, doi = {10.1093/gji/ggag066}, url = {https://doi.org/10.1093/gji/ggag066}, eprint = {https://academic.oup.com/gji/article-pdf/245/2/ggag066/66936482/ggag066.pdf}, } @misc{hu2025, title={Bayesian full waveform inversion with learned prior using deep convolutional autoencoder}, author={Shuhua Hu and Mrinal K Sen and Zeyu Zhao and Abdelrahman Elmeliegy and Shuo Zhang}, year={2025}, eprint={2511.02737}, archivePrefix={arXiv}, primaryClass={physics.geo-ph}, url={https://arxiv.org/abs/2511.02737}, } @article{zeng2026full, author = {Zeng, Yunlin and Tuna Erdinc, Huseyin and Orozco, Rafael and Herrmann, Felix J.}, title = {Full-waveform variational inference with full common-image gathers and diffusion network}, volume = {Fifth International Meeting for Applied Geoscience & Energy}, series = {SEG Technical Program Expanded Abstracts}, pages = {1159-1163}, year = {2025}, month = {08}, abstract = {Accurate seismic imaging and velocity estimation are essential for subsurface characterization. Conventional inversion techniques, such as full-waveform inversion, remain computationally expensive and sensitive to initial velocity models. To address these challenges, we propose a simulation-based inference framework with conditional elucidated diffusion models for posterior velocity-model sampling. Our approach incorporates both horizontal and vertical subsurface offset commonimage gathers to capture a broader range of reflector geometries, including gently dipping structures and steep dipping layers. Additionally, we introduce the background-velocity model as an input condition to enhance generalization across varying geological settings. We evaluate our method on the SEAM dataset, which features complex salt geometries, using a patchbased training approach. Experimental results demonstrate that adding the background-velocity model as an additional conditioning variable significantly enhances performance, improving SSIM from 0. 717 to 0. 733 and reducing RMSE from 0. 381km/s to 0. 274km/s. Furthermore, uncertainty quantification analysis shows that our proposed approach yields bettercalibrated uncertainty estimates, reducing uncertainty calibration error from 6. 68km/s to 3. 91km/s. These results show robust amortized seismic inversion with uncertainty quantification.}, doi = {10.1190/image2025-4316892.1}, url = {https://doi.org/10.1190/image2025-4316892.1}, eprint = {https://pubs.geoscienceworld.org/segeab/proceedings-pdf/SEGEAB.44/1/1159/7752249/image2025-4316892.1.pdf}, } @misc{brandolin2026vmb, title={Velocity Model Building and Editing with Guided Denoising Diffusion Implicit Models}, author={Francesco Brandolin and Tariq Alkhalifah}, year={2026}, eprint={2603.01231}, archivePrefix={arXiv}, primaryClass={physics.geo-ph}, url={https://arxiv.org/abs/2603.01231}, } @article{geofwi, author = {Li, Chao and Shen, Yiran and Fomel, Sergey and Waheed, Umair Bin and Savvaidis, Alexandros and Chen, Yangkang}, title = {GeoFWI: A Large Velocity Model Data Set for Benchmarking Full Waveform Inversion Using Deep Learning}, journal = {Journal of Geophysical Research: Machine Learning and Computation}, volume = {3}, number = {2}, pages = {e2025JH001037}, keywords = {deep learning, FWI, benchmark data set, diffusion model}, doi = {https://doi.org/10.1029/2025JH001037}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2025JH001037}, eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2025JH001037}, note = {e2025JH001037 2025JH001037}, abstract = {Abstract Full waveform inversion (FWI) plays an increasingly important role in the field of seismic imaging due to its strong ability to estimate subsurface properties. Specifically, data-driven FWI (DDFWI) establishes a straightforward mapping relationship between seismic data and the corresponding velocity model, yielding promising results. However, DDFWI requires abundant velocity models for network training to improve generality. Consequently, we present an open-source, large-scale velocity model data set, namely GeoFWI, to facilitate the test and validation of different DDFWI methods. The data set consists of various geologically meaningful velocity models with different structures (e.g., undulating structures, folding layers, faults, and salt bodies). In this study, we exploit the GeoFWI data set as a foundation to conduct benchmarking over different FWI methods, including classic FWI, DDFWI, deep learning (DL) matching-based FWI, diffusion-model-based FWI, and so on. We hope that this new GeoFWI velocity model data set can facilitate a fair and transparent evaluation of FWI and stimulate the development of DL-based FWI in the geophysics community. The GeoFWI data set and related information can be found in the Open Research Section.}, year = {2026} } # Intro - Paragraph 3 @misc{self_supervised_learning, title={Self-Supervised Learning from Noisy and Incomplete Data}, author={Julián Tachella and Mike Davies}, year={2026}, eprint={2601.03244}, archivePrefix={arXiv}, primaryClass={stat.ML}, url={https://arxiv.org/abs/2601.03244}, } @article{daras2023ambient, title={Ambient diffusion: Learning clean distributions from corrupted data}, author={Daras, Giannis and Shah, Kulin and Dagan, Yuval and Gollakota, Aravind and Dimakis, Alex and Klivans, Adam}, journal={Advances in Neural Information Processing Systems}, volume={36}, pages={288--313}, year={2023} } @article{aali2025ambient, title={Ambient diffusion posterior sampling: Solving inverse problems with diffusion models trained on corrupted data}, author={Aali, Aryan and Daras, Giannis and Levac, Bojan and Kumar, Sai Manas and Dimakis, Alex and Tamir, Jonathan}, journal={The Thirteenth International Conference on Learning Representations}, year={2025}, url={https://openreview.net/forum?id=qeXcMutEZY} } # Theory and Methodology - Seismic imaging and Bayesian inference with summary statistics @article{tarantola1984inversion, title={Inversion of seismic reflection data in the acoustic approximation}, author={Tarantola, Albert}, journal={Geophysics}, volume={49}, number={8}, pages={1259--1266}, year={1984}, publisher={Society of Exploration Geophysicists} } @inproceedings{orozco2023adjoint, title={Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification}, author={Orozco, Rafael and Siahkoohi, Ali and Rizzuti, Gabrio and van Leeuwen, Tristan and Herrmann, Felix J}, booktitle={Medical Imaging 2023: Image Processing}, volume={12464}, pages={365--375}, year={2023}, organization={SPIE} } # Theory and Methodology - Simulation-based inference with conditional score-based networks @article{sbi, author = {Kyle Cranmer and Johann Brehmer and Gilles Louppe }, title = {The frontier of simulation-based inference}, journal = {Proceedings of the National Academy of Sciences}, volume = {117}, number = {48}, pages = {30055-30062}, year = {2020}, doi = {10.1073/pnas.1912789117}, URL = {https://www.pnas.org/doi/abs/10.1073/pnas.1912789117}, eprint = {https://www.pnas.org/doi/pdf/10.1073/pnas.1912789117}} @article{arruda2025diffusion, title={Diffusion Models in Simulation-Based Inference: A Tutorial Review}, author={Arruda, Jonas and Bracher, Niels and K{\"o}the, Ullrich and Hasenauer, Jan and Radev, Stefan T}, journal={arXiv preprint arXiv:2512.20685}, year={2025}, url={https://arxiv.org/abs/2512.20685}, } @article{song2020score, title={Score-based generative modeling through stochastic differential equations}, author={Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P and Kumar, Abhishek and Ermon, Stefano and Poole, Ben}, journal={arXiv preprint arXiv:2011.13456}, year={2020} } @article{karras2022elucidating, title={Elucidating the design space of diffusion-based generative models}, author={Karras, Tero and Aittala, Miika and Aila, Timo and Laine, Samuli}, journal={Advances in neural information processing systems}, volume={35}, pages={26565--26577}, year={2022} } @article{erdinc2024geostat, title={Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations with Diffusion Models}, author={Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}, journal={arXiv preprint arXiv:2406.05136}, year={2024}, url={https://arxiv.org/abs/2406.05136}, } # Numerical Study @article{BG, author = "E. Jones, C. and A. Edgar, J. and I. Selvage, J. and Crook, H.", title = "Building Complex Synthetic Models to Evaluate Acquisition Geometries and Velocity Inversion Technologies", journal= "In 74th EAGE Conference and Exhibition Incorporating EUROPEC 2012", year = "2012", volume = "", number = "", pages = "cp–293", doi = "https://doi.org/10.3997/2214-4609.20148575", url = "https://www.earthdoc.org/content/papers/10.3997/2214-4609.20148575", publisher = "European Association of Geoscientists \& Engineers", issn = "2214-4609", type = "", eid = "cp-293-00580", } @software{judi, author = {Mathias Louboutin and Philipp Witte and Ziyi Yin and Henryk Modzelewski and Kerim and Carlos da Costa and Peterson Nogueira}, title = {slimgroup/JUDI.jl: v3.2.3}, month = mar, year = 2023, publisher = {Zenodo}, version = {v3.2.3}, doi = {10.5281/zenodo.7785440}, url = {https://doi.org/10.5281/zenodo.7785440} } @article{yin2024wise, title={WISE: Full-waveform variational inference via subsurface extensions}, author={Yin, Ziyi and Orozco, Rafael and Louboutin, Mathias and Herrmann, Felix J}, journal={Geophysics}, volume={89}, number={4}, pages={A23--A28}, year={2024}, publisher={Society of Exploration Geophysicists} } @misc{ukndr, author = {{North Sea Transition Authority}}, title = {UK National Data Repository}, year = {2026}, howpublished = {https://www.nstauthority.co.uk/data-and-insights/data/uk-national-data-repository/}, note = {Contains information provided by the North Sea Transition Authority and/or other third parties} } @article{hou2016accelerating, title={Accelerating extended least-squares migration with weighted conjugate gradient iteration}, author={Hou, Jie and Symes, William W}, journal={Geophysics}, volume={81}, number={4}, pages={S165--S179}, year={2016}, publisher={Society of Exploration Geophysicists} } @misc{bhar2025sagewise, author = {Bhar, Ipsita and Erdinc, Huseyin Tuna and Souza, Thales and Orozco, Rafael and Herrmann, Felix J.}, title = {Seismic Dataset Curation from UK National Data Repository to Validate SAGE and WISE}, year = {2025}, howpublished = {ML4SEISMIC Partners Meeting}, note = {Available at: https://slim.gatech.edu/content/seismic-dataset-curation-uk-national-data-repository-validate-sage-and-wise}, }