@unpublished {zeng2026IMAGEbjv,
	title = {Bayesian Joint Velocity and Impedance Inversion via Diffusion Models Conditioned on Common Image Gathers},
	year = {2026},
	month = {3},
	abstract = {We present a multi-parameter simulation-based inference framework for joint Bayesian recovery of subsurface velocity and acoustic impedance from seismic data. A score-based diffusion model is conditioned on two complementary Common Image Gathers (CIGs): an inverse-scattering CIG encoding reflectivity amplitude and an anti-ISIC CIG encoding kinematic velocity errors. The model simultaneously samples the posterior distributions of both parameters. Training labels are deliberately decoupled to prevent the model from exploiting the Gardner relationship: velocity targets are lightly smoothed to match the long-wavelength content of the anti-ISIC CIG, while impedance targets retain the unsmoothed ground truth. On the Compass benchmark the model achieves velocity SSIM of 0.967 (RMSE 0.050 km/s) and impedance SSIM 0.867 (RMSE 0.279 km/s{\textperiodcentered}g/cm{\textthreesuperior}), with velocity quality confirmed by CIG focusing.},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEbjv/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEbjv/IMAGE_Yunlin.pdf},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@unpublished {deng2026IMAGEbag,
	title = {Bridging the Acoustic-Elastic Gap in Seismic Inversion via Robust Summary Statistics},
	year = {2026},
	month = {3},
	abstract = {Simulation-based seismic inversion provides a principled framework for uncertainty quantification, but its performance degrades when the physics used in simulation differ from those of observed data. In practice, seismic inversion is often misspecified because the true physics are only partially known or too costly to model at scale, making field observations out of distribution relative to the simulations used for training; here, we study this issue through the acoustic-elastic gap. We introduce ElasNet, a misspecification-robust probabilistic inversion framework that bridges acoustic simulations and elastic observations through physics-informed summary statistics. We use acoustically imaged common-image gathers (CIGs) as structured summaries of seismic data, compress them with an attention-based summary network, and use maximum mean discrepancy (MMD) to align acoustic and elastic feature distributions during training while learning a conditional normalizing flow for posterior estimation with only acoustic data. Experiments on 2D Compass models show that the proposed approach reduces acoustic-elastic discrepancies in inferred velocity models and improves structural consistency and uncertainty calibration. These results demonstrate that robust summary statistics and distribution matching provide a scalable pathway for simulation-based seismic inversion under realistic physics mismatch.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, IMAGE, Imaging, Inverse problems, mmd, SEG, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/deng2026IMAGEbag/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/deng2026IMAGEbag/IMAGE_Venice.pdf},
	author = {Zijun Deng and Abhinav Prakash Gahlot and Shiqin Zeng and Felix J. Herrmann}
}
@unpublished {li2026IMAGEsca,
	title = {JUDIAgent: a scientific coding agent for JUDI workflows in wave-equation imaging},
	year = {2026},
	month = {3},
	abstract = {We present JUDIAgent, a scientific coding assistant for JUDI.jl, an open-source Julia framework for wave-equation-based seismic modeling, imaging, and inversion. In seismic experimentation, the practical difficulty is not only writing executable code, but assembling a complete seismic workflow with the required physical model, acquisition geometry, modeling or migration operator, and saved outputs needed for inspection. JUDIAgent addresses this problem by retrieving JUDI examples, generating Julia code, running the code in the target environment, and checking whether the generated script contains the requested workflow pieces and outputs, such as acquisition geometry and saved figures. We demonstrate the system with validated 2D forward-modeling and reverse-time migration (RTM) examples. These case studies show that, for JUDI-based seismic scripts, domain-aware validation can turn a lightweight user request into a more complete experimental workflow by detecting missing workflow steps that are not captured by runtime correctness alone and by making the resulting scripts easier to inspect and revise.},
	keywords = {Agentic AI, devito, FWI, IMAGE, Imaging, JUDI, RTM, scientific coding agent, SEG},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/li2026IMAGEsca/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/li2026IMAGEsca/IMAGE_Haoyun.pdf},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@unpublished {zeng2026IMAGEssn,
	title = {Self-attention summary networks for subsurface velocity-model building from common-image gathers},
	year = {2026},
	month = {3},
	abstract = {Common-image gathers (CIGs) contain physically meaningful information about velocity-model errors through reflector focusing and residual moveout, but in conventional imaging workflows they are typically used only as diagnostic tools. In this work, we propose a multiscale self-attention summary network that maps high-dimensional 3D CIG volumes into compact conditioning embeddings for probabilistic subsurface velocity inversion. These learned embeddings preserve offset-dependent kinematic structure and spatial coherence while reducing variability caused by background-velocity mismatch. Conditioned on these summary embeddings, a flow-matching model learns a transport from a Gaussian source distribution to the posterior distribution of plausible velocity fields. Numerical experiments show that, compared with direct conditioning on raw CIGs, the proposed summary network improves posterior velocity inference. In particular, the multiscale attention design provides greater robustness to background-model mismatch, yielding more accurate posterior reconstructions and lower predictive uncertainty.},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEssn/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEssn/IMAGE_Shiqin.pdf},
	author = {Shiqin Zeng and Yunlin Zeng and Abhinav Prakash Gahlot and Zijun Deng and Felix J. Herrmann}
}
@unpublished {gahlot2025EAGEagc,
	title = {Advancing Geological Carbon Storage Monitoring with 3D Digital Shadow Technology},
	year = {2025},
	month = {6},
	keywords = {3D digital shadow, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, FWI, GCS, Imaging, Inverse problems, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/gahlot2025EAGEagc/abstract.html},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2025IMSIafi,
	title = {Amortized Full-Waveform Inference w/ Learned Summary Statistics},
	booktitle = {Reduced Order and Surrogate Modeling for Digital Twins, IMSI, Chicago},
	year = {2025},
	month = {11},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IMSI/2025/herrmann2025IMSIafi},
	author = {Rafael Orozco and Ziyi Yin and Shiqin Zeng and Felix J. Herrmann}
}
@conference {herrmann20205IMAGEapg,
	title = {Attention Please: Getting the Most from CIGs with Learned Summary Statistics},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/herrmann20205IMAGEapg},
	author = {Shiqin Zeng and Rafael Orozco and Yunlin Zeng and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {zeng2025ML4SEISMICbde,
	title = {Background-Conditioned Diffusion Inversion for Seismic Velocity Models},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Accurate seismic imaging and velocity estimation are important for subsurface characterization, yet conventional full-waveform inversion remains computationally expensive and highly sensitive to initial velocity models. To address these challenges, we propose a simulation-based inference framework using conditional elucidated diffusion models for posterior velocity-model sampling. Our approach integrates both horizontal and vertical subsurface-offset common-image gathers to capture a wider range of reflector geometries, from gently dipping to steeply inclined layers. We further condition the model on the background-velocity field to improve generalization across diverse geological settings. Evaluations on the SEAM dataset, which includes complex salt geometries, demonstrate that this conditioning substantially improves performance, increasing SSIM from 0.717 to 0.733 and reducing RMSE from 0.381 km/s to 0.274 km/s. Uncertainty analysis further shows enhanced calibration, lowering uncertainty calibration error from 6.68 km/s to 3.91 km/s. These results confirm that our diffusion-based simulation framework enables robust seismic inversion with reliable uncertainty quantification.},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, MVA, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/zeng2025ML4SEISMICbde},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@conference {deng2025ML4SEISMICbag,
	title = {Bridging the Acoustic{\textendash}Elastic Gap in Seismic Inversion via Robust Summary Statistics},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Simulation-based Bayesian inference (SBI) enables uncertainty quantification in seismic inversion but typically assumes that simulated and observed data follow the same physics. In reality, this assumption does not hold. The Earth is elastic, yet large-scale simulations are often acoustic due to the prohibitive cost of elastic modeling. This acoustic{\textendash}elastic mismatch introduces model misspecification, leading to biased posterior estimates and reduced interpretability. We propose a robust conditional generative framework that mitigates this mismatch by learning a shared representation between acoustic and elastic domains. The approach integrates a robust summary network within a conditional normalizing flow, trained primarily on acoustic simulations and guided by limited elastic supervision. It enables elastic-consistent posterior inference from inexpensive acoustic simulations, balancing computational efficiency with physical realism. This framework offers a scalable path toward uncertainty-aware subsurface characterization under model misspecification, bridging the gap between fast acoustic modeling and physically accurate elastic data.},
	keywords = {Amortized Variational Inference, attention, Bayesian inference, CIG, deep learning, FWI, generative model, Imaging, Inverse problems, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/deng2025ML4SEISMICbag},
	author = {Zijun Deng and Abhinav Prakash Gahlot and Shiqin Zeng and Felix J. Herrmann}
}
@conference {li2025IMAGEceo,
	title = {CO2 Enhanced Oil Recovery Through Digital Shadow Modeling},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, IMAGE, Imaging, Inverse problems, permeability, reservoir simulation, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/li2025IMAGEceo},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/li2025IMAGEceo/IMAGE_Haoyun.pdf},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {li2025ML4SEISMICdsc,
	title = {Digital Shadow for CO2-based Enhanced Oil Recovery (CO2-EOR)},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We present a Digital Shadow for CO2-based Enhanced Oil Recovery (CO2-EOR), a data-driven surrogate model that predicts reservoir dynamics by conditioning on time-lapse seismic observations. Built upon conditional normalizing flows, the Digital Shadow learns the posterior distribution of subsurface states{\textemdash}CO2 and oil saturation{\textemdash}conditioned on seismic data generated through coupled multiphase flow and rock-physics modeling. The framework integrates high-fidelity simulations with JutulDarcy.jl, nonlinear seismic forward modeling and imaging with JUDI.jl, and nonlinear rock-physics mappings to relate saturation changes to changes in the acoustic properties. Trained on 128 stochastic realizations derived from a North Sea permeability distribution, the model achieves accurate posterior samples for the saturation fields with high structural similarity to the ground truth. This work demonstrates how integrating differentiable physics with generative modeling enables seismic-informed monitoring of CO2 plume evolution and oil recovery, laying the foundation for a Digital Twin of CO2-based EOR operations.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/li2025ML4SEISMICdsc},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Olav Moyner and Felix J. Herrmann}
}
@unpublished {gahlot2025EAGEerd,
	title = {Enhancing robustness of Digital Shadow for CO 2  Storage Monitoring with Augmented Rock Physics Modeling},
	year = {2025},
	month = {6},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, GCS, Imaging, Inverse problems, rock physics, RTM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/gahlot2025EAGEerd/abstract.html},
	author = {Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {zeng2025IMAGEfwi,
	title = {Full-waveform variational inference with common-image gathers},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/zeng2025IMAGEfwi/IMAGE_Yunlin.pdf},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@conference {orozco2025SIAMisu,
	title = {Industry-Scale Uncertainty-Aware Full Waveform Inference with Generative Models},
	booktitle = {SIAM Conference on Computational Science and Engineering (CSE25)},
	year = {2025},
	note = {(SIAM CSE25, Dallas)},
	month = {03},
	abstract = {In this talk, we address the challenge of Bayesian sampling for ill-posed inverse problems involving expensive PDE forward operators. To tackle this, we propose the use of generative models and discuss three key challenges along with our solutions. First, we address the constraints of GPU memory by introducing patch-based training and memory-efficient invertible networks, enabling the handling of large-scale data. Second, we demonstrate that these models can be effectively trained using only prior data available from acoustic observations and borehole well data, making the approach practical for real-world applications. Third, we explore various strategies to enhance the reliability of posterior samples by incorporating physics-based constraints through the wave operator. We conclude by presenting experiments that showcase the capabilities of these methods in field-data Full Waveform Inversion (FWI) workflows, scaling up to industry-scale problems with large 2D (512x7000 degrees of freedom) and 3D models.},
	keywords = {Bayesian sampling, FWI, Generative models, Inverse problems, Normalizing flows, SIAM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2025/orozco2025SIAMisu},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Mathias Louboutin and Felix J. Herrmann}
}
@unpublished {deng2025EAGEpjrm,
	title = {Probabilistic Joint Recovery Method for CO2 Plume Monitoring},
	year = {2025},
	month = {6},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, image generative model, Imaging, Inverse problems, JRM, Summary Statistics, Uncertainty quantification},
	doi = {10.48550/arXiv.2501.18761},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/deng2025EAGEpjrm/EAGE_Venice.pdf},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {li2025ML4SEISMICric,
	title = {Risk-Aware Injectivity Control for Energy Storage},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We introduce a digital-twin{\textendash}driven framework for real-time injectivity control that maximizes injected CO2 while enforcing reservoir safety. The forward model is a multiphase flow simulator evolving reservoir states under injectivity controls q; time-lapse seismic acts as the observation operator to reduce uncertainty of the the state (reservoir{\textquoteright}s saturation/pressure). Risk is handled via two complementary metrics: the Probability of Failure (POF) for exceedance likelihood and the less conservative CVaR (superquantile) for tail severity. For the optimization, we employ smooth surrogates{\textemdash}a logistic exceedance rate for POF and the Rockafellar{\textendash}Uryasev formulation for CVaR{\textemdash}enabling gradient-based control with constraints. Within a finite-horizon Model Predictive Control (MPC) loop, we optimize a trajectory per posterior sample and aggregate the ensemble of optimal rates into an empirical (KDE-kernel) Cumulative Density Function (CDF) with binomial confidence bands; the final controlled injectivity q is chosen as the largest rate whose upper confidence bound satisfies the target risk level. Case studies demonstrate that POF-constrained optimization is more conservative than CVaR-based optimization, In addition, sensitivity of the policy to the CVaR tail level, α, is reduced compared to POF{\textquoteright}s parameter sensitivity, allowing for adaptive, uncertainty-aware control that balances injectivity and fracture risk. The proposed framework also unifies time-lapse seismic-informed inference, risk metrics, and MPC into a practical approach for safe high-throughput underground energy storage.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/li2025ML4SEISMICric},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {deng2025IMAGEtfi,
	title = {Time-lapse full-waveform inversion with uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, IMAGE, image generative model, Imaging, Inverse problems, JRM, SEG, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/deng2025IMAGEtfi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/deng2025IMAGEtfi/IMAGE_Venice.pdf},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {deng2025ML4SEISMICtfi,
	title = {Time-lapse full-waveform inversion with uncertainty quantification},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Reliable management of underground energy storage systems, such as underground compressed Hydrogene or Air storage, rely on semi-continuous monitoring and rigorous quantification of subsurface uncertainty. Time-lapse seismic imaging provides valuable insights into fluid migration and storage integrity. However, traditional inversion techniques{\textemdash}particularly full-waveform inversion (FWI){\textemdash}are inherently ill-posed and deterministic, limiting their applicability for uncertainty-aware decision-making. The Joint Recovery Method (JRM) improves consistency across multiple surveys by jointly reconstructing shared structures, but does not capture uncertainty. We introduce the Probabilistic Joint Recovery Method (πJRM), which embeds uncertainty estimation within a joint inversion framework. πJRM leverages a shared generative model to infer wave-equation{\textendash}based posterior distributions for each monitoring survey, enabling probabilistic interpretation of time-lapse changes. Synthetic experiments demonstrate that πJRM accurately recovers dynamic reservoir evolution and provides uncertainty-aware reconstructions, offering a principled foundation for safe, efficient management of subsurface energy storage operations.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, image generative model, Imaging, Inverse problems, jrm pjrm, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/deng2025ML4SEISMICtfi},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {herrmann2025HPCuam,
	title = {Uncertainty-aware machine-learning enabled velocity-model building with Devito},
	booktitle = {18th Annual Energy High Performance Computing Conference 2025, RICE},
	year = {2025},
	note = {18th Annual High Performance Computing Conference 2025},
	month = {02},
	pages = {4th Annual Devito User and Developer Workshop},
	keywords = {devito, FWI, HPC, inversion, JUDI, machine learning, RICE, software, Uncertainty quantification, velocity model},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/RHPC/2025/herrmann2025HPCuam},
	author = {Felix J. Herrmann}
}
@article {yin2024wiser,
	title = {WISER: multimodal variational inference for full-waveform inversion without dimensionality reduction},
	journal = {Geophysics},
	volume = {90},
	year = {2025},
	note = {(GEOPHYSICS)},
	month = {03},
	abstract = {We present a semi-amortized variational inference framework designed for computationally feasible uncertainty quantification in 2D full-waveform inversion to explore the multimodal posterior distribution without dimensionality reduction. The framework is called WISER, short for full-Waveform variational Inference via Subsurface Extensions with Refinements. WISER leverages the power of generative artificial intelligence to perform approximate amortized inference that is low-cost albeit showing an amortization gap. This gap is closed through non-amortized refinements that make frugal use of acoustic wave physics. Case studies illustrate that WISER is capable of full-resolution, computationally feasible, and reliable uncertainty estimates of velocity models and imaged reflectivities.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, Summary Statistics, Uncertainty quantification, WISE, WISER},
	doi = {10.1190/geo2024-0483.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2024/yin2024wiser/WISER.html},
	author = {Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {herrmann2024ML4SEISMICdtg,
	title = {A Digital Twin for Geological Carbon Storage with Controlled Injectivity},
	year = {2024},
	month = {11},
	abstract = {We present an uncertainty-aware Digital Twin (DT) for geologic carbon storage (GCS), capable of handling multimodal time-lapse data and controlling CO 2  injectivity to mitigate reservoir fracturing risks. In GCS, DT represents virtual replicas of subsurface systems that incorporate real-time data and advanced generative Artificial Intelligence (genAI) techniques, including neural posterior density estimation via simulation-based inference and sequential Bayesian inference. These methods enable the effective monitoring and control of CO 2  storage projects, addressing challenges such as subsurface complexity, operational optimization, and risk mitigation. By integrating diverse monitoring data, e.g., geophysical well observations and imaged seismic, DT can bridge the gaps between seemingly distinct fields like geophysics and reservoir engineering. In addition, the recent advancements in genAI also facilitate DT with principled uncertainty quantification. Through recursive training and inference, DT utilizes simulated current state samples, e.g., CO 2  saturation, paired with corresponding geophysical field observations to train its neural networks and enable posterior sampling upon receiving new field data. However, it lacks decision-making and control capabilities, which is necessary for full DT functionality. This study aims to demonstrate how DT can inform decision-making processes to prevent risks such as cap rock fracturing during CO 2  storage operations.},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, Imaging, Inverse problems, ML4SEISMIC, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/herrmann2024ML4SEISMICdtg},
	author = {Abhinav Prakash Gahlot and Haoyun Li and Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {gahlot2024ICLdtg,
	title = {Digital Twins in the era of generative AI - Application to Geological CO2 Storage},
	year = {2024},
	month = {6},
	abstract = {Our industry is experiencing significant changes due to AI and the challenges of the energy transition. While some view these changes as threats, recent advances in AI offer unique opportunities, especially in the context of Digital Twins for subsurface monitoring and control. IBM defines "A digital twin is a virtual representation of an object or system that spans its lifecycle, is updated from real-time data, and uses simulation, machine learning and reasoning to help decision-making." During this talk, I will explore these concepts and their significance in addressing the challenges of monitoring \& control of geological CO2 storage projects. This talk also aims to illustrate how Digital Twins can serve as a platform to integrate the seemingly disparate and siloed fields of geophysics and reservoir engineering.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, control, data assimilation, deep learning, digital twin, FWI, GCS, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICL/2024/gahlot2024ICLdtg},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Haoyun Li and Huseyin Tuna Erdinc and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {zeng2024ML4SEISMICefv,
	title = {Enhancing Full-Waveform Variational Inference through Stochastic Resampling},
	year = {2024},
	month = {11},
	abstract = {Recent developments in simulation-based inference, like the full-waveform variational inference via subsurface extensions (WISE), enable rapid online estimation of subsurface velocities by leveraging pre-trained models. To achieve this, WISE employs subsurface-offset common image gathers to convert shot data into physics-informed summary statistics. While common image gathers effectively retain critical information even when initial velocity estimates are inaccurate, WISE{\textquoteright}s performance still depends on the assumption that the initial migration-velocity model is a single 1D velocity model. In this work, we present experiments using both 1D and 2D velocity models and develop a stochastic resampling method to generate variations of initial migration-velocity models. This technique allows us to systematically infer alternative velocity models that are consistent with the observed data, while enhancing the posterior sample quality and reducing dependency on the initial velocity model compared to the standard WISE approach.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/zeng2024ML4SEISMICefv},
	author = {Yunlin Zeng and Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {zeng2024IMAGEefw,
	title = {Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slimgroup.github.io/IMAGE2024/Yunlin_Zeng2024SEG/paper.html},
	author = {Yunlin Zeng and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@presentation {yin2024GTwise,
	title = {Generative AI for full-waveform variational inference},
	year = {2024},
	month = {1},
	abstract = {We introduce a probabilistic technique for full-waveform inversion, employing 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.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, FWI, generative AI, GT, inversion, machine learning, Normalizing flows, SLIM, Summary Statistics, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/GTseminar/2024/yin2024GTwise},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@mastersthesis {orozco2024THgmf,
	title = {GENERATIVE MODELS FOR UNCERTAINTY QUANTIFICATION OF MEDICAL AND SEISMIC IMAGING},
	year = {2024},
	note = {(PhD)},
	month = {12},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {This thesis investigates the intersection of machine learning-based generative models with physics-based methods to address imaging problems, with an emphasis on accelerat- ing computations while incorporating uncertainty quantification. Throughout the chapters, a key conclusion emerges: machine learning methods, though powerful, are insufficient when used in isolation. They must be combined with the trusted domain knowledge con- tained in numerical physics simulations to achieve robust results. The methods presented bridge two of the most impactful areas in modern computer science: numerical simula- tions methods rooted in linear algebra and the transformative potential of deep learning, particularly as exemplified by recent advancements in generative modeling. The focus of this work is on scenarios where the underlying physics is computation- ally expensive, requiring frugal use of simulations. This is particularly relevant in high- dimensional, ill-posed inverse problems, such as those encountered in the applications shown in this thesis: medical imaging and seismic exploration, where the forward oper- ator is governed by complex partial differential equations (PDEs). To address these challenges, this thesis introduces techniques that blend practical ma- chine learning approaches with theoretical insights, particularly through the use of physics- based summary statistics. These statistics enable efficient extraction of meaningful in- formation from physics simulations, reducing computational overhead while preserving the critical elements of the physical model. Theoretical foundations underpin the design choices, ensuring that the methods are both efficient and ameliorate the potential bias that would arise from using physics-based summary statistics instead of raw observations. As an engineering-focused work, the thesis places a strong emphasis on practicality and robustness. The proposed methods are stress-tested through validation experiments, on increasingly complex scenarios with a clear pathway toward deployment in the real-world. This applied perspective reflects the ultimate goal of leveraging these methods to create tangible, impactful changes in domains such as healthcare and geophysics. By bridging the gap between advanced machine learning and trusted physics-based methods, this work contributes to the development of innovative tools that balance computational efficiency, uncertainty quantification, and practical applicability.},
	keywords = {Bayesian inference, CCS, CIG, conditional normalizing flows, FWI, GCS, Generative models, Inverse problems, medical imaging, monitoring, Normalizing flows, PhD, RTM, scientific machine learning, time-lapse, Uncertainty quantification, Variational Inference, WISE, WISER},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/Thesis_Orozco_pdf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/defense-real},
	author = {Rafael Orozco}
}
@presentation {orozco2024ML4SEISMICmev,
	title = {Machine-learning enabled velocity-model building with uncertainty quantification},
	year = {2024},
	month = {11},
	abstract = {Accurately characterizing subsurface properties is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional characterization methods such as Full-Waveform Inversion (FWI) represent powerful tools but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth and aperture of data, limited azimuth and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling with physics-informed summary statistics, making it suitable for complicated imaging problems potentially including field datasets. Our approach leverages the power of conditional diffusion networks, and methodologically incorporates physics in the form of summary statistics, allowing for the computationally efficient generation of Bayesian posterior samples that offer an useful assessment of uncertainty of the inferred migration-velocity models. To validate our approach, we introduce a battery of tests that measure the quality of the image estimates as well as the quality of the inferred uncertainties. With modern synthetic datasets, we maximally leverage the advantages of using subsurface-offset Common Image Gathers (CIGs) as the conditioning observable. Next, we tackle the challenging SEAM salt model that requires incorporating salt flooding into our approach based on the iterative refinements of ASPIRE {\textemdash} Amortized posteriors with Summaries that are Physics-based and Iteratively REfined.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/orozco2024ML4SEISMICmev},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Thales Souza and Yunlin Zeng and Ziyi Yin and Felix J. Herrmann}
}
@conference {orozco2024IPMSnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	booktitle = {Inverse Problems: Modelling and Simulation},
	year = {2024},
	month = {5},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, IPMS, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi/herrmann2024.pdf},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {orozco2024ICLnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	year = {2024},
	month = {6},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICL/2024/orozco2024ICLnwi},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {gahlot2024ML4SEISMICosm,
	title = {Optimizing CO2 Storage Monitoring with Enhanced Rock Physics Modeling},
	year = {2024},
	month = {11},
	abstract = {Based on the latest data-assimilation and machine-learning techniques, Digital Twins (DTs) have shown promise for high-fidelity monitoring and control of underground CO2​ storage. While the use of these techniques have important advantages, they do rely on certain assumptions. If these assumptions are not met, the DT{\textquoteright}s neural networks may no longer infer the state of the CO2 plume (pressure/saturation) accurately. By augmenting the forecast ensemble, we address this issue.},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, Imaging, Inverse problems, ML4SEISMIC, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/gahlot2024ML4SEISMICosm},
	author = {Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {deng2024ML4SEISMICpjr,
	title = {Probabilistic Joint Recovery Method for CO2 plume monitoring},
	year = {2024},
	month = {11},
	abstract = {Accurately predicting fluid flow patterns in Carbon Capture and Storage (CCS) is a challenging task, particularly due to uncertainties in CO 2  plume dynamics and reservoir properties. While previous deterministic methods such as the Joint Recovery Method (JRM) have provided valuable insights, their effectiveness is limited as tools for decision-making since they do not communicate uncertainty. To address this, we propose a Probabilistic Joint Recovery Method (PJRM) that computes the posterior distribution at each monitoring survey while leveraging the shared structure among surveys through a common generative model. By efficiently computing posterior distributions for each monitoring survey, this method aims to provide valuable uncertainty information to decision-makers in CCS projects, augmenting their workflow with principled risk minimization.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, igm, image generative model, Imaging, Inverse problems, JRM, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/deng2024ML4SEISMICpjr},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {erdinc2024ML4SEISMICsfm,
	title = {SAGE {\textendash} Subsurface foundational model with AI-driven Geostatical Extraction},
	year = {2024},
	month = {11},
	abstract = {In this study, we present a novel approach for synthesizing diverse subsurface velocity models using diffusion-based generative models. Traditional methods often depend on large, high-quality datasets of 2D velocity models, which can be difficult to obtain in subsurface applications. In contrast, our method leverages incomplete well and seismic data to generate high-fidelity velocity samples without requiring fully sampled training datasets.The results demonstrate that the generative model accurately captures long-range geological structures and aligns well with unseen ground-truth velocity models. Furthermore, it is shown that the diversity of generated velocity models can be increased through prior guidance in the training phase, and model uncertainties can be reduced with well conditioning during inference.Experiments conducted with multiple datasets (BG, Synthoseis, and North Sea data) and velocity models featuring various geological structures (e.g., faults, salt bodies) suggest that our approach facilitates realistic subsurface velocity synthesis, providing valuable inputs for full-waveform inversion and enhancing seismic-based subsurface modeling.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/erdinc2024ML4SEISMICsfm},
	author = {Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@presentation {bruer2024ML4SEISMICsmp,
	title = {Seismic monitoring of CO2 plume dynamics using ensemble Kalman filtering},
	year = {2024},
	month = {11},
	abstract = {Monitoring CO 2  injected and stored in subsurface reservoirs is critical for avoiding failure scenarios and enables real-time optimization of CO 2  injection rates. Sequential Bayesian data assimilation (DA) is a statistical method for combining information over time from multiple sources to estimate a hidden state, such as the spread of the subsurface CO 2  plume. An example of scalable and efficient sequential Bayesian DA is the ensemble Kalman filter (EnKF). We improve upon existing DA literature in the seismic-CO 2  monitoring domain by applying this scalable DA algorithm to a high-dimensional CO 2  reservoir using two-phase flow dynamics and time-lapse full waveform seismic data with a realistic surface-seismic survey design. We show more accurate estimates of the CO 2  saturation field using the EnKF compared to using either the seismic data or the fluid physics alone. Furthermore, we test a range of values for the EnKF hyperparameters and give guidance on their selection for seismic CO 2  reservoir monitoring.},
	keywords = {Bayesian inference, data assimilation, ensemble Kalman filter, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, two-phase flow, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/bruer2024ML4SEISMICsmp},
	author = {Grant Bruer and Abhinav Prakash Gahlot and Edmond Chow and Felix J. Herrmann}
}
@presentation {bhar2024ML4SEISMICshs,
	title = {Sensitivity of Horizontal shear waves on Geological Carbon Storage},
	year = {2024},
	month = {11},
	abstract = {With the growing focus on Carbon Capture and Storage (CCS) activities, the significance of shear wave velocity (Vs) in monitoring CO2 is becoming increasingly important. Shear waves are instrumental in detecting CO2 leakage, evaluating CCS-induced seismicity, and identifying caprock failure. According to Biot-Gassmann rock physics models, changes in seismic velocity are expected during CO2 injection. This work specifically focuses on the horizontal component of shear wave velocity (Vsh). Shear (Sh) waves are more sensitive to density variations than P-wave or Sv wave velocities, leading us to anticipate changes in Sh velocity as CO2 saturation increases. While P-wave velocity tends to decrease with supercritical CO2 injection, the investigation of its effects on Sh waves presents a particularly compelling area of study. Therefore, we simulated the wave equation incorporating both P-wave and Sh wave velocities to better understand their impacts on imaging and CO2 injection processes.},
	keywords = {FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SH wave, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/bhar2024ML4SEISMICshs},
	author = {Ipsita Bhar and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@mastersthesis {yin2024THsgi,
	title = {Solving geophysical inverse problems with scientific machine learning},
	year = {2024},
	note = {(PhD)},
	month = {06},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Solving inverse problems involves estimating unknown parameters of interest from indirect measurements. Specifically, geophysical inverse problems seek to determine various Earth properties critical for geophysical exploration, carbon control, monitoring, and earthquake detection. These problems pose unique challenges: the parameters of interest are often high-dimensional, and the mapping from parameters to observables is computationally demanding. Moreover, these problems are typically non-convex and ill-posed, meaning that multiple sets of model parameters can adequately fit the observations, and inversion algorithms depend on accurate initial model parameters. This thesis introduces several innovative methods to tackle these challenges using scientific machine learning techniques. It discusses algorithms and software frameworks that utilize surrogate and generative models to achieve scalable and reliable inversion. It also examines the integration of conditional generative models with physics for Bayesian variational inference and uncertainty quantification. These methods have been applied to two critical inverse problems in geophysical applications: monitoring geological carbon storage and full-waveform inversion, both of which are plagued by the aforementioned computational challenges. The thesis consists of six papers. The first two papers present a scalable, interoperable, and differentiable programming framework for learned multiphysics inversion, showcased through realistic synthetic case studies in geological carbon storage monitoring. The third paper introduces a computationally efficient and reliable algorithm that employs surrogate models, particularly Fourier neural operators, to accelerate inversion. The reliability of this algorithm is ensured by using normalizing flows as learned constraints to safeguard the accuracy of the surrogate models throughout the inversion process. The subsequent paper explores a joint inversion approach and an explainable deep neural classifier for time-lapse seismic imaging and carbon dioxide leakage detection during geological carbon storage. The final two papers introduce amortized and semi-amortized variational inference approaches that employ information-preserving physics-informed summary statistics and refinements to provide computationally feasible and reliable uncertainty quantification in high-dimensional full-waveform inversion problems. They also assess the impact of the inherent uncertainty in these ill-posed inversion problems on subsequent imaging tasks.},
	keywords = {Bayesian inference, CCS, CIG, conditional normalizing flows, end-to-end, Fourier neural operators, FWI, GCS, Generative models, Inverse problems, JRM, monitoring, Normalizing flows, PhD, RTM, scientific machine learning, time-lapse, Uncertainty quantification, Variational Inference, WISE, WISER},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi_pres.pdf},
	author = {Ziyi Yin}
}
@article {yin2023wise,
	title = {WISE: full-Waveform variational Inference via Subsurface Extensions},
	journal = {Geophysics},
	volume = {89},
	year = {2024},
	note = {(GEOPHYSICS)},
	month = {04},
	abstract = {We introduce a probabilistic technique for full-waveform inversion, employing 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.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Geophysics, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	doi = {10.1190/geo2023-0744.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2024/yin2023wise/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {yin2024IMAGEwiser,
	title = {WISER: full-Waveform variational Inference via Subsurface Extensions with Refinements},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	abstract = {We introduce a cost-effective Bayesian inference method for full-waveform inversion (FWI) to quantify uncertainty in migration-velocity models and its impact on imaging. Our method targets inverse uncertainty due to null-space of the wave modeling operators and observational noise, and forward uncertainty where the uncertainty in velocity models is propagated to uncertainty in amplitude and positioning of imaged reflectivities. This is achieved by integrating generative artificial intelligence (genAI) with physics-informed common-image gathers (CIGs), which greatly reduces reliance on accurate initial FWI-velocity models. In addition, we illustrate the capability of fine-tuning the generative AI networks with frugal physics-based refinements to improve the inference accuracy.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE, WISER},
	url = {https://slimgroup.github.io/IMAGE2024/yin2024SEG/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2023IMAGEabf,
	title = {Amortized Bayesian Full Waveform Inversion and Experimental Design with Normalizing Flows},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE, Houston)},
	month = {08},
	abstract = {Probabilistic approaches to Full-Waveform Inversion (FWI), such as Bayesian ones, traditionally require expensive computations involving many wave-equation solves. To reduce the computational burden at test time, we propose to amortize the computational cost with offline training. After training, we aim to efficiently generate probabilistic FWI solutions with uncertainty. This aim is achieved by exploiting the ability of networks (i.e Normalizing Flows) to learn distributions, such as the Bayesian posterior. The posterior uncertainty is used during training to optimize the receiver sampling.},
	keywords = {bayesian, experimental design, FWI, Normalizing flows, SEG, Uncertainty quantification},
	url = {https://slimgroup.github.io/IMAGE2023/BayesianFWI/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/orozco2023IMAGEabf},
	author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2023IMAGEWSfnf,
	title = {Fast neural FWI with amortized uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE workshop, Houston)},
	month = {08},
	keywords = {bayesian, experimental design, FWI, Normalizing flows, SEG, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/herrmann2023IMAGEWSfnf},
	author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {orozco2023ML4SEISMICuqs,
	title = {Uncertainty quantification so what? Leveraging probabilistic seismic inversion for experimental design},
	year = {2023},
	month = {11},
	abstract = {Combining physics with recent developments of generative machine learning enables a scalable probabilistic framework for tackling seismic inversion problems including Full-Waveform Inversion. These probabilistic results can be proven to be from the Bayesian posterior but how exactly can we use them for practical downstream tasks? In this talk, we answer the question with a practical application of the probabilistic framework towards designing ocean bottom node placement of seismic imaging. With a simple adjustment to the original training objective, we show that jointly optimizing for an experimental design corresponds to maximizing the expected information gain used by the Bayesian community. After verifying this novel joint optimization with a stylized problem, we demonstrate its application for optimizing the placement of ocean bottom nodes in a synthetic seismic imaging experiment.},
	keywords = {bayesian, experimental design, FWI, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/orozco2023ML4SEISMICuqs},
	author = {Rafael Orozco and Mathias Louboutin and Peng Chen and Felix J. Herrmann}
}
@article {louboutin2023rte,
	title = {Wave-based inversion at scale on GPUs with randomized trace estimation},
	journal = {Geophysical Prospecting},
	year = {2023},
	note = {(Geophysical Prospecting)},
	month = {07},
	abstract = {Thanks to continued performance improvements in software and hardware, wave-equation based imaging technologies, such full-waveform inversion and reverse-time migration, are becoming more common place. However, wide-spread adaptation of these advanced imaging modalities has not yet materialized because current implementations are not able to reap the full benefits from accelerators, in particular those offered by memory-scarce graphics processing units. Through the use of randomized trace estimation, we overcome the memory bottleneck of this type of hardware. At the cost of limited computational overhead and controllable incoherent errors in the gradient, the memory footprint of adjoint-state methods is reduced drastically. Thanks to this relatively simple to implement memory reduction via an approximate imaging condition, we are able to benefit from graphics processing units without memory offloading. We demonstrate the performance of the proposed algorithm on acoustic 2- and 3-D full-waveform inversion examples and on the formation of image gathers in transverse tilted isotropic media.},
	keywords = {3D, CIG, FWI, GPUs, Random trace, stochastic},
	doi = {10.1111/1365-2478.13405},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2023/louboutin2023rte/paper.html},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@presentation {yin2023ML4SEISMICwise,
	title = {WISE: Full-waveform Inference with Subsurface Extensions},
	year = {2023},
	month = {11},
	abstract = {Quantifying uncertainty in full-waveform inversion is complex given the large sizes of both the model and data. A previous approach employed a variational inference framework, leveraging reverse-time migration to summarize observed data and approximate the posterior distribution through conditional normalizing flows. While reverse-time migration effectively summarizes the data when the background model is close to the true one, its accuracy diminishes with a less accurate background model. In our study, we suggest utilizing subsurface offset gathers as the summary statistics for the variational inference of full-waveform inversion. These gathers retain all the information in seismic data, even when the background model is cycle-skipped or fails to flatten the gathers. Through a case study on Compass model, we confirm our framework{\textquoteright}s effectiveness and show that subsurface offset gathers offer a better summary statistic than just reverse-time migration.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, FWI, inversion, machine learning, ML4SEISMIC, Normalizing flows, SLIM, Summary Statistics, uncertain quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/yin2023ML4SEISMICwise},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {louboutin2022SEGWSaaa,
	title = {Abstractions and algorithms for efficient seismic inversion on accelerators},
	booktitle = {IMAGE Workshop on What{\textquoteright}s Next for FWI and its Derived Products},
	year = {2022},
	note = {(IMAGE Workshop, Houston)},
	month = {09},
	abstract = {We present the SLIM open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics (e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.},
	keywords = {algorithms, deep learning, devito, FWI, Imaging, JUDI, LSRTM, SEG, software, workshop},
	url = {https://www.imageevent.org/Workshop/next-fwi-derived-products},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/louboutin2022SEGWSaaa/index.html},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@conference {louboutin2022RHPCafa,
	title = {Abstractions for at-scale seismic inversion},
	booktitle = {Rice Oil and Gas High Performance Computing Conference 2022},
	year = {2022},
	note = {Rice Oil and Gas High Performance Computing Conference 2022},
	month = {03},
	pages = {Thursday Workshop: Devito Training and Hackathon},
	abstract = {We present the SLIM open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics (e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.},
	keywords = {CCS, devito, FWI, HPC, inversion, JUDI, machine learning, RHPC, software, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/RHPC/2022/louboutin2022RHPCafa/RiceHPC22.pdf},
	url2 = {https://youtu.be/scRTbP8w6Wk?t=4542},
	author = {Mathias Louboutin and Ali Siahkoohi and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Yijun Zhang and Philipp A. Witte and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {louboutin2022SEGais,
	title = {Accelerating innovation with software abstractions for scalable computational geophysics},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {We present the SLIM open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics(e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.},
	keywords = {CCS, devito, FWI, HPC, inversion, JUDI, machine learning, SEG, software, Uncertainty quantification},
	doi = {10.1190/image2022-3750561.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/louboutin2022SEGais/louboutin_seg22.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/louboutin2022SEGais/index.html},
	author = {Mathias Louboutin and Philipp A. Witte and Ali Siahkoohi and Gabrio Rizzuti and Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {rizzuti2021ML4SEISMICdfw,
	title = {A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion},
	year = {2021},
	month = {11},
	abstract = {Many of the seismic inversion techniques currently proposed that focus on robustness with respect to the background model choice are not apt to large-scale 3D applications, and the methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously limited by convergence stagnation and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting models or inaccurate parameters (such as anisotropy) that are typically kept fixed during inversion. It is based on a dual reformulation of the classical wavefield reconstruction inversion, whose empirical robustness with respect to these issues is well documented in the literature. While the classical version is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation, our proposal allows the deployment of state-of-the-art time-domain finite-difference methods, and is potentially mature for industrial-scale problems.},
	keywords = {FWI, ML4SEISMIC, SLIM, wave-equation, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/rizzuti2021ML4SEISMICdfw/Tue-10-55-Rizzuti.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@presentation {louboutin2021ML4SEISMICrla,
	title = {Randomized linear algebra for inversion},
	year = {2021},
	month = {11},
	abstract = {Inverse problems in exploration geophysics or machine learning heavily relies on linear algebra and large matrices manipulations. To tackle the growing cost of storing these matrices, randomized algorithms have been developed to obtain information from these matrices via randomized sketching. Inspired by previous work on extended image volumes, we will first show in this talk how the seismic imaging condition can be expressed in a randomized linear algebra framework leading to drastic memory savings. In a second part, we will extend this idea to convolutional neural networks to reduce the memory cost of training by orders of magnitude. We will demonstrate the practicality of these methods on representative examples.},
	keywords = {FWI, HPC, inversion, ML4SEISMIC, randomized linear algebra, SLIM, software},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/louboutin2021ML4SEISMICrla/Tue-10-20-Louboutin.pdf},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@conference {rizzuti2021SIAMGSwrid,
	title = {Time-domain Wavefield Reconstruction Inversion for large-scale seismic inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2021},
	note = {(SIAM GS, virtual)},
	month = {06},
	abstract = {Data fitting based on a wave equation model has driven the modern development in seismic imaging, and it is now relevant for large scale inversion. A wider adoption is currently being limited by available computational resources and the classical limitations of non-linear optimization, which often produces suboptimal local minima. A class of methods based on the inexact solution of the wave equation, known as wavefield reconstruction inversion, have shown remarkable robustness towards local minima, however the solvers required for the inexact wave equation scale badly to 3D problems. We propose a reformulation of wavefield reconstruction inversion which involves the solution of the classical time-domain wave equation, and it is practical for large-scale problems. Applications to tilted-transverse isotropy synthetic datasets clearly demonstrate the advantage over traditional full-waveform inversion.},
	keywords = {FWI, SIAM, time domain, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMGS/2021/rizzuti2021SIAMGSwrid/rizzuti2021SIAMGSwrid.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@conference {louboutin2021SEGulm,
	title = {Ultra-low memory seismic inversion with randomized trace estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {787-791},
	abstract = {Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques from randomized linear algebra. By means of a carefully selected realistic synthetic example, we demonstrate that we are capable of achieving competitive inversion results at a fraction of the memory cost of conventional full-waveform inversion with limited computational overhead. By exchanging memory for negligible computational overhead, we open with the presented technology the door towards the use of low-memory accelerators such as GPUs.},
	keywords = {FWI, HPC, inversion, randomized linear algebra, SEG},
	doi = {10.1190/segam2021-3584072.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/louboutin2021SEGulm/louboutinp.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/louboutin2021SEGulm/louboutin2021SEGulm.mp4},
	software = {https://github.com/slimgroup/TimeProbeSeismic.jl},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@mastersthesis {louboutin2020THmfi,
	title = {Modeling for inversion in exploration geophysics},
	year = {2020},
	note = {(PhD)},
	month = {03},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic inversion, and more generally geophysical exploration, aims at better understanding the earth{\textquoteright}s subsurface, which is one of today{\textquoteright}s most important challenges. Firstly, it contains natural resources that are critical to our technologies such as water, minerals and oil and gas. Secondly, monitoring the subsurface in the context of CO2 sequestration, earthquake detection and global seismology are of major interests with regard to safety and the environment hazards. However, the technologies to monitor the subsurface or find resources are scientifically extremely challenging. Seismic inversion can be formulated as a mathematical optimization problem that minimizes the difference between field recorded data and numerically modeled synthetic data. The process of solving this optimization problem then requires to numerically model, thousands of times, wave-propagation in large three-dimensional representations of part of the earth subsurface. The mathematical and computational complexity of this problem, therefore, calls for software design that abstracts these requirements and facilitates algorithm and software development. My thesis addresses some of the challenges that arise from these problems; mainly the computational cost and access to the right software for research and development. In the first part, I will discuss a performance metric that improves the current runtime-only benchmarks in exploration geophysics. This metric, the roofline model, first provides insight at the hardware level of the performance of a given implementation relative to the maximum achievable performance. Second, this study demonstrates that the choice of numerical discretization has a major impact on the achievable performance depending on the hardware at hand and shows that a flexible framework with respect to the discretization parameters is necessary. In the second part, I will introduce and describe Devito, a symbolic finite-difference DSL that provides a high-level interface to the definition of partial differential equations (PDE) such as the wave equation. Devito, from the symbolic definition of PDEs, then generates and compiles highly optimized C code on-the-fly to compute the solution of the PDE. The combination of the high-level abstractions and the just-in-time compiler enable research for geophysical exploration and PDE-constrainted optimization based on the paradigm of separation of concerns. This allows researchers to concentrate on their respective field of study while having access to computationally performant solvers with a flexible and easy to use interface to successfully implement complex representations of the physics. The second part of my thesis will be split into two sub-parts; first describing the symbolic application programming interface (API), before describing and benchmarking the just-in-time compiler. I will end my thesis with concluding remarks, the latest developments and a brief description of projects that were enabled by Devito.},
	keywords = {finite-differences, FWI, HPC, Imaging, inversion, Modeling, performance, PhD, RTM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi_pres.pdf},
	author = {Mathias Louboutin}
}
@mastersthesis {witte2020THsal,
	title = {Software and algorithms for large-scale seismic inverse problems},
	year = {2020},
	note = {(PhD)},
	month = {02},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic imaging and parameter estimation are an import class of inverse problems with practical relevance in resource exploration, carbon control and monitoring systems for geohazards. The goal of seismic inverse problems is to image subsurface geological structures and estimate physical rock properties such as wave speed or density. Mathematically, this can be achieved by solving an optimization problem in which we minimize the mismatch between numerically modeled data and observed data from a seismic survey. As wave propagation through a medium is described by wave equations, seismic inverse problems involve solving a large number of partial differential equations (PDEs) during numerical optimization using finite difference modeling, making them computationally expensive. Additionally, seismic inverse problems are typically ill-posed, non-convex or ill-conditioned, thus making them challenging from a mathematical standpoint as well. Similar to the field of deep learning, this calls for software that is not only optimized for performance, but also enables geophysical domain specialists to experiment with algorithms in high-level programming languages and using different computing environments, such as high-performance computing (HPC) clusters or the cloud. Furthermore, they call for the adaption of dimensionality reduction techniques and stochastic algorithms to address computational cost from the algorithmic side. This thesis makes three distinct contributions to address computational challenges encountered in seismic inverse problems and to facilitate algorithmic development in this field. Part one introduces a large-scale framework for seismic modeling and inversion based on the paradigm of separation of concerns, which combines a user interface based on domain specific abstractions with a Python package for automatic code generation to solve the underlying PDEs. The modular code structure makes it possible to manage the complexity of a seismic inversion code, while matrix-free linear operators and data containers enable the implementation of algorithms in a fashion that closely resembles the underlying mathematical notation. The second contribution of this thesis is an algorithm for seismic imaging, that addresses its high computational cost and large memory imprint through a combination of on-the-fly Fourier transforms, stochastic sampling techniques and sparsity-promoting optimization. The algorithm combines the best of both time- and frequency-domain inversion, as the memory imprint is independent of the number of modeled time steps, while time-to-frequency conversions avoid the need to solve Helmholtz equations, which involve inverting ill-conditioned matrices. Part three of this thesis introduces a novel approach for adapting the cloud for high-performance computing applications like seismic imaging, which does not rely on a fixed cluster of permanently running virtual machines. Instead, computational resources are automatically started and terminated by the cloud environment during runtime and the workflow takes advantage of cloud-native technologies such as event-driven computations and containerized batch processing. The performance and cost analysis shows that this approach is able to address current shortcomings of the cloud such as inferior resilience, while at the same time reducing operating cost up to an order of magnitude. As such, the workflow provides a strategy for cost effectively running large-scale seismic imaging problems in the cloud and is a viable alternative to conventional HPC clusters.},
	keywords = {algorithms, AWS, FWI, Imaging, PhD, RTM, seismic, software},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal_pres.pdf},
	author = {Philipp A. Witte}
}
@techreport {louboutin2020SEGtwri,
	title = {Time-domain Wavefield Reconstruction Inversion in a TTI medium},
	number = {TR-CSE-2020-1},
	year = {2020},
	month = {4},
	institution = {Georgia Institute of Technology},
	abstract = {We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping. The original method was formulated in the frequency domain with acoustic isotropic physics. However, frequency-domain modeling requires sophisticated iterative solvers that are difficult to scale to industrial-size problems and more realistic physical assumptions, such as tilted transverse isotropy, object of this study. The work presented here is based on a recently proposed dual formulation of wavefield reconstruction inversion, which allows time-domain propagator that are suitable to both large scales and more accurate physics.},
	keywords = {anisotropy, FWI, TTI, WRI},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/louboutin2020SEGtwri/louboutin2020SEGtwri.html},
	url2 = {https://arxiv.org/pdf/2004.07355.pdf},
	author = {Mathias Louboutin and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {louboutin2020SIAMTXLAtdw,
	title = {Time-Domain Wavefield Reconstruction Inversion In Tilted Transverse Isostropic Media},
	booktitle = {SIAM Texas-Louisiana},
	year = {2020},
	note = {SIAMTXLA},
	month = {10},
	abstract = {We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping. The original method was formulated in the frequency domain with acoustic isotropic physics. However, frequency-domain modeling requires sophisticated iterative solvers that are difficult to scale to industrial-size problems and more realistic physical assumptions, such as tilted transverse isotropy, object of this study. The work presented here is based on a recently proposed dual formulation of wavefield reconstruction inversion, which allows time-domain propagator that are suitable to both large scales and more accurate physics.},
	keywords = {FWI, Time-domain, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMTXLA/2020/louboutin2020SIAMTXLAtdw/louboutin2020SIAMTXLAtdw_pres.pdf},
	author = {Mathias Louboutin and Gabrio Rizzuti and Felix J. Herrmann}
}
@mastersthesis {peters2019THiso,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	year = {2019},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Inverse problems in the imaging sciences encompass a variety of applications. The primary problem of interest is the identification of physical parameters from observed data that come from experiments governed by partial-differential-equations. The secondary type of imaging problems attempts to reconstruct images and video that are corrupted by, for example, noise, subsampling, blur, or saturation. The quality of the solution of an inverse problem is sensitive to issues such as noise and missing entries in the data. The non-convex seismic full-waveform inversion problem suffers from parasitic local minima that lead to wrong solutions that may look realistic even for noiseless data. To meet some of these challenges, I propose solution strategies that constrain the model parameters at every iteration to help guide the inversion. To arrive at this goal, I present new practical workflows, algorithms, and software, that avoid manual tuning-parameters and that allow us to incorporate multiple pieces of prior knowledge. Opposed to penalty methods, I avoid balancing the influence of multiple pieces of prior knowledge by working with intersections of constraint sets. I explore and present advantages of constraints for imaging. Because the resulting problems are often non-trivial to solve, especially on large 3D grids, I introduce faster algorithms, dedicated to computing projections onto intersections of multiple sets. To connect prior knowledge more directly to problem formulations, I also combine ideas from additive models, such as cartoon-texture decomposition and robust principal component analysis, with intersections of multiple constraint sets for the regularization of inverse problems. The result is an extension of the concept of a Minkowski set. Examples from non-unique physical parameter estimation problems show that constraints in combination with projection methods provide control over the model properties at every iteration. This can lead to improved results when the constraints are carefully relaxed.},
	keywords = {FWI, Optimization, PhD, regularization, Sets},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso_pres.pdf},
	author = {Bas Peters}
}
@article {witte2018alf,
	title = {A large-scale framework for symbolic implementations of seismic inversion algorithms in Julia},
	journal = {Geophysics},
	volume = {84},
	number = {3},
	year = {2019},
	note = {(Geophysics)},
	month = {03},
	pages = {F57-F71},
	abstract = {Writing software packages for seismic inversion is a very challenging task, since problems such as full-waveform inversion or least-squares imaging are both algorithmically and computationally demanding due to the large number of unknown parameters and the fact that we are propagating waves over many wavelengths. Software frameworks therefore need to combine both versatility and performance to provide geophysicists with the means and flexibility to implement complex algorithms that scale to exceedingly large 3D problems. Following these principles, we introduce the Julia Devito Inversion framework, an open-source software package in Julia for large-scale seismic modeling and inversion based on Devito, a domain-specific language compiler for automatic code generation. The framework consists of matrix-free linear operators for implementing seismic inversion algorithms that closely resembles the mathematical notation, a flexible resilient parallelization and an interface to Devito for generating optimized stencil code to solve the underlying wave equations. In comparison to many manually optimized industry codes written in low-level languages, our software is built on the idea of independent layers of abstractions and user interfaces with symbolic operators, making it possible to manage both the complexity of algorithms and performance optimizations, while preserving modularity, which allows for a level of expressiveness needed to formulate a broad range of wave-equation-based inversion problems. Through a series of numerical examples, we demonstrate that this allows users to implement algorithms for waveform inversion and imaging as simple Julia scripts that scale to large-scale 3D problems; thus providing a truly performant research and production framework.},
	keywords = {FWI, inversion, LSRTM, Modeling, software},
	doi = {10.1190/geo2018-0174.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/witte2018alf/witte2018alf.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Navjot Kukreja and Fabio Luporini and Michael Lange and Gerard J. Gorman and Felix J. Herrmann}
}
@article {louboutin2017fwip2,
	title = {Full-Waveform Inversion - Part 2: adjoint modeling},
	journal = {The Leading Edge},
	volume = {37},
	number = {1},
	year = {2018},
	note = {(The Leading Edge)},
	month = {1},
	pages = {69-72},
	abstract = {This tutorial is the second part of a three part tutorial series on full-waveform inversion (FWI), in which we provide a step by step walk through of setting up forward and adjoint wave equation solvers and an optimization framework for inversion. In part 1 (Louboutin et al., 2017), we demonstrated how to discretize the acoustic wave equation and how to set up a basic forward modeling scheme using Devito, a domain-specific language (DSL) in Python for automated finite-difference (FD) computations (Lange et al., 2016). Devito allows us to define wave equations as symbolic Python expressions (Meurer et al., 2017), from which optimized FD stencil code is automatically generated at run time. In part 1, we show how we can use Devito to set up and solve acoustic wave equations with (impulsive) seismic sources and sample wavefields at the receiver locations to model shot records.},
	keywords = {acoustic, devito, finite-difference, FWI, tutorial},
	doi = {10.1190/tle37010069.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2018/louboutin2017fwip2/louboutin2017fwip2.html},
	author = {Mathias Louboutin and Philipp A. Witte and Michael Lange and Navjot Kukreja and Fabio Luporini and Gerard Gorman and Felix J. Herrmann}
}
@article {witte2018fwip3,
	title = {Full-Waveform Inversion - Part 3: optimization},
	journal = {The Leading Edge},
	volume = {37},
	number = {2},
	year = {2018},
	note = {(The Leading Edge)},
	month = {1},
	pages = {142-145},
	abstract = {This tutorial is the third part of a full-waveform inversion (FWI) tutorial series with a step-by-step walkthrough of setting up forward and adjoint wave equations and building a basic FWI inversion framework. For discretizing and solving wave equations, we use Devito, a Python-based domain-specific language for automated generation of finite-difference code (Lange et al., 2016). The first two parts of this tutorial (Louboutin et al., 2017, 2018) demonstrated how to solve the acoustic wave equation for modeling seismic shot records and how to compute the gradient of the FWI objective function using the adjoint-state method. With these two key ingredients, we will now build an inversion framework that can be used to minimize the FWI least-squares objective function.},
	keywords = {devito, finite-differences, FWI, inversion, Modeling, tutorial},
	doi = {10.1190/tle37020142.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2018/witte2018fwip3/witte2018fwip3.html},
	author = {Philipp A. Witte and Mathias Louboutin and Keegan Lensink and Michael Lange and Navjot Kukreja and Fabio Luporini and Gerard Gorman and Felix J. Herrmann}
}
@conference {kadu2018SEGMSFWI,
	title = {Full-waveform inversion with Mumford-Shah regularization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {1258-1262},
	abstract = {Full-waveform inversion (FWI) is a non-linear procedure to es- timate subsurface rock parameters from surface measurements of induced seismic waves. This procedure is ill-posed in nature and hence, requires regularization to enhance some structure depending on the prior information. Recently, Total-variation (TV) regularization has gained popularity due to its ability to produce blocky structures. Contrary to this, the earth behave more like a piecewise smooth function. TV regularization fails to enforce this prior information into FWI. We propose a Mumford-Shah functional to incorporate the piecewise smooth spatial structure in the FWI procedure. The resulting opti- mization problem is solved by a splitting method. We show the improvement in results against TV regularization on two synthetic camembert examples.},
	keywords = {FWI, Mumford-Shah, regularization, SEG},
	doi = {10.1190/segam2018-2997224.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/kadu2018SEGMSFWI/kadu2018SEGMSFWI.pdf},
	author = {Ajinkya Kadu and Rajiv Kumar and Tristan van Leeuwen}
}
@mastersthesis {zhang2018THlss,
	title = {Large-scale seismic data compression: application to full waveform inversion and extended image volume},
	year = {2018},
	note = {(MSc)},
	month = {04},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Conventional oil and gas fields are increasingly difficult to explore and im- age, resulting in a call for more complex wave-equation based inversion al- gorithms that require dense long-o↵set samplings. Consequently, there is an exponential growth in the size of data volumes and prohibitive demands on computational resources. In this work, we propose a method to com- press and process seismic data directly in a low-rank tensor format, which drastically reduces the amount of storage required to represent the data. We first outline how seismic data exhibits low-rank structure in a particular transform-domain, which can be exploited to compress the dense data in one extremely storage-efficient tensor format when the data is fully sampled. In the more realistic case of missing data, we can use interpolation techniques based on the same tensor format to recover fully sampled data volume in compressed form. In either case, once we have our data represented in its compressed tensor form, we design an algorithm to extract source or receiver gathers directly from the compressed parameters. This extraction process can be done on-the-fly directly on the compressed data, in the full wave- form inversion context, and does not require scanning through the entire dataset in order to form shot gathers. To the best of our knowledge, this work is one of the first major contributions to working with seismic data applications directly in the compressed domain without reconstructing the entire data volume. We use a stochastic inversion approach, which works with small subsets of source experiments at each iteration, further to reduce the computational and memory costs of full waveform inversion. We also demonstrate how this data compression and extraction technique can be ap- plied to forming full subsurface image gathers through probing techniques.},
	keywords = {compression, extended image volume, FWI, hierarchical tucker, MSc, multilinear algebra, on-the-fly, thesis},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2018/zhang2018THlss/zhang2018THlss.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2018/zhang2018THlss/zhang2018THlss_pres.pdf},
	author = {Yiming Zhang}
}
@conference {alfaraj2018SEGswi,
	title = {Seismic waveform inversion using decomposed one-way wavefields},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {1379-1383},
	abstract = {Conventional seismic full waveform inversion (FWI) estimates a velocity model by matching the two-way predicted data with the observed data. The non-linearity of the problem and the complexity of the Earth{\textquoteright}s subsurface, which results in complex wave propagation may lead to unsatisfactory inversion results. Moreover, having inaccurate overburden models, i.e water velocity model in the ocean bottom acquisition setting, may lead to erroneous velocity models. In order to obtain better velocity models, we simplify the FWI problem by decomposing the total two-way observed and predicted wavefields into one-way wavefields at the receiver locations using acoustic wavefield decomposition. We then propose to fit the less-complex one-way wavefield to obtain a velocity model that contains valuable information about the overburden. We use this inverted velocity model as a better initial model for the inversion using the other more-complex one-way wavefield. We demonstrate our proposed algorithm on acoustic non-inverse crime synthetic data produced from the Marmousi2 model. The proposed method provides improved inversion results compared with conventional FWI due to properly accounting for separate model updates from the up- and down-going wavefields.},
	keywords = {decomposition, FWI, one-way, SEG},
	doi = {10.1190/segam2018-2998162.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/alfaraj2018SEGswi/alfaraj2018SEGswi.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/alfaraj2018SEGswi/alfaraj2018SEGswi_pres.pdf},
	author = {Ali M. Alfaraj and Rajiv Kumar and Felix J. Herrmann}
}
@mastersthesis {fang2018THsea,
	title = {Source estimation and uncertainty quantification for wave-equation based seismic imaging and inversion},
	year = {2018},
	note = {(PhD)},
	month = {04},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {In modern seismic exploration, wave-equation-based inversion and imaging approaches are widely employed for their potential of creating high-resolution subsurface images from seismic data by using the wave equation to describe the underlying physical model of wave propagation. Despite their successful practical applications, some key issues remain unsolved, including local minima, unknown sources, and the largely missing uncertainty analyses for the inversion. This thesis aims to address the following two aspects: to perform the inversion without prior knowledge of sources, and to quantify uncertainties in the inversion. The unknown source can hinder the success of wave-equation-based ap- proaches. A simple time shift in the source can lead to misplaced reflectors in linearized inversions or large disturbances in nonlinear problems. Unfortunately, accurate sources are typically unknown in real problems. The first major contribution of this thesis is, given the fact that the wave equation linearly depends on the sources, I have proposed on-the-fly source estimation techniques for the following wave-equation-based approaches: (1) time-domain sparsity-promoting least-squares reverse-time migration; and (2) wavefield-reconstruction inversion. Considering the linear dependence of the wave equation on the sources, I project out the sources by solving a linear least-squares problem, which enables us to conduct successful wave- equation-based inversions without prior knowledge of the sources. Wave-equation-based approaches also produce uncertainties in the resulting velocity model due to the noisy data, which would influence the subsequent exploration and financial decisions. The difficulties related to practical uncertainty quantification lie in: (1) expensive computation related to wave-equation solves, and (2) the nonlinear parameter-to-data map. The second major contribution of this thesis is the proposal of a computationally feasible Bayesian framework to analyze uncertainties in the resulting velocity models. Through relaxing the wave-equation constraints, I obtain a less nonlinear parameter-to-data map and a posterior distribution that can be adequately approximated by a Gaussian distribution. I derive an implicit formulation to construct the covariance matrix of the Gaussian distribution, which allows us to sample the Gaussian distribution in a computationally efficient manner. I demonstrate that the proposed Bayesian framework can provide adequately accurate uncertainty analyses for intermediate to large- scale problems with an acceptable computational cost.},
	keywords = {FWI, LS-RTM, PhD, source estimation, UQ, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea_pres.pdf},
	author = {Zhilong Fang}
}
@article {fang2017sewri,
	title = {Source estimation for wavefield-reconstruction inversion},
	journal = {Geophysics},
	volume = {83},
	number = {4},
	year = {2018},
	note = {(Geophysics)},
	pages = {R345-R359},
	abstract = {Source estimation is essential to all the wave-equation-based seismic inversions, including full-waveform inversion and the recently proposed wavefield-reconstruction inversion. When the source estimation is inaccurate, errors will propagate into the predicted data and introduce additional data misfit. As a consequence, inversion results that minimize this data misfit may become erroneous. To mitigate the errors introduced by the incorrect and pre-estimated sources, an embedded procedure that updates sources along with medium parameters is necessary for the inversion. So far, such a procedure is still missing in the context of wavefield-reconstruction inversion, a method that is, in many situations, less prone to local minima related to the so-called cycle skipping, compared to full-waveform inversion through exact data-fitting. While wavefield-reconstruction inversion indeed helps to mitigate issues related to cycle skipping by extending the search space with wavefields as auxiliary variables, it relies on having access to the correct source functions. In this paper, we remove the requirement of having the accurate source functions by proposing a source estimation technique specifically designed for wavefield-reconstruction inversion. To achieve this task, we consider the source functions as unknown variables and arrive at an objective function that depends on the medium parameters, wavefields, and source functions. During each iteration, we apply the so-called variable projection method to simultaneously project out the source functions and wavefields. After the projection, we obtain a reduced objective function that only depends on the medium parameters and invert for the unknown medium parameters by minimizing this reduced objective. Numerical experiments illustrate that this approach can produce accurate estimates of the unknown medium parameters without any prior information of the source functions.},
	keywords = {estimation, FWI, source, variable projection, WRI},
	doi = {10.1190/geo2017-0700.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/fang2017sewri/fang2017sewri.html},
	author = {Zhilong Fang and Rongrong Wang and Felix J. Herrmann}
}
@article {fang2017uqfip,
	title = {Uncertainty quantification for inverse problems with weak partial-differential-equation constraints},
	journal = {Geophysics},
	volume = {83},
	number = {6},
	year = {2018},
	note = {(Geophysics)},
	pages = {R629-R647},
	abstract = {In a statistical inverse problem, the objective is a complete statistical description of unknown parameters from noisy observations in order to quantify uncertainties of the parameters of interest. We consider inverse problems with partial-differential-equation-constraints, which are applicable to a variety of seismic problems. Bayesian inference is one of the most widely-used approaches to precisely quantify statistics through a posterior distribution, incorporating uncertainties in observed data, modeling kernel, and prior knowledge of the parameters. Typically when formulating the posterior distribution, the partial-differential-equation-constraints are required to be exactly satisfied, resulting in a highly nonlinear forward map and a posterior distribution with many local maxima. These drawbacks make it difficult to find an appropriate approximation for the posterior distribution. Another complicating factor is that traditional Markov chain Monte Carlo methods are known to converge slowly for realistically sized problems. In this work, we relax the partial-differential-equation-constraints by introducing an auxiliary variable, which allows for Gaussian deviations in the partial-differential-equations. Thus, we obtain a new bilinear posterior distribution consisting of both data and partial-differential-equation misfit terms. We illustrate that for a particular range of variance choices for the partial-differential-equation misfit term, the new posterior distribution has fewer modes and can be well-approximated by a Gaussian distribution, which can then be sampled in a straightforward manner. Since it is prohibitively expensive to explicitly construct the dense covariance matrix of the Gaussian approximation for intermediate to large-scale problems, we present a method to implicitly construct it, which enables efficient sampling. We apply this framework to two-dimensional seismic inverse problems with 1,800 and 92,455 unknown parameters. The results illustrate that our framework can produce comparable statistical quantities to those produced by conventional Markov chain Monte Carlo type methods while requiring far fewer partial-differential-equation solves, which are the main computational bottlenecks in these problems.},
	keywords = {acoustic, FWI, UQ, weak-constraint},
	doi = {10.1190/geo2017-0824.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/fang2017uqfip/fang2017uqfip.html},
	author = {Zhilong Fang and Curt Da Silva and Rachel Kuske and Felix J. Herrmann}
}
@conference {louboutin2017EAGEdns,
	title = {Data normalization strategies for full-waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
	note = {(EAGE, Paris)},
	month = {06},
	abstract = {Amplitude mismatch is an inherent problem in seismic inversion. Most of the source estimation techniques are associated with amplitude uncertainty due to incomplete representation of the physics or estimation method parameters. Rewriting the inversion problem in an amplitude free formulation allows to mitigate the amplitude ambiguity and help the inversion process to converge. We present in this work two different strategies to lessen amplitude effects in seismic inversion, derive the corresponding update directions and show how we handle scaling error correctly in both the objective function and the gradient.},
	keywords = {EAGE, FWI, inversion, nonlinear, normalization},
	doi = {10.3997/2214-4609.201700720},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/louboutin2017EAGEdns/louboutin2017EAGEdns.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/louboutin2017EAGEdns/louboutin2017EAGEdns_poster.pdf},
	author = {Mathias Louboutin and Llu{\'\i}s Guasch and Felix J. Herrmann}
}
@conference {wang2017SEGdff,
	title = {A denoising formulation of full-waveform inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {1594-1598},
	abstract = {We propose a wave-equation-based subsurface inversion method that in many cases is more robust than the conventional Full-Waveform Inversion. The new formulation is written in a denoising form that allows the synthetic data to match the observed ones up to a small error. Compared to the Full-Waveform Inversion, our method treats the noise arising from the data measuring/recording process and that from the synthetic modelling process separately. Comparing to the Wavefields Reconstruction Inversion, the new formulation mitigates the difficulty of choosing the penalty parameter λ. To solve the proposed optimization problem, we develop an efficient frequency domain algorithm that alternatively updates the model and the data. Numerical experiments confirm strong stability of the proposed method by comparisons between the results of our algorithm with that from both plain FWI and a weighted formulation of the FWI.},
	keywords = {denoising, FWI, SEG},
	doi = {10.1190/segam2017-17794690.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/wang2017SEGdff/wang2017SEGdff.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/wang2017SEGdff/wang2017SEGdff_pres.pdf},
	author = {Rongrong Wang and Felix J. Herrmann}
}
@conference {herrmann2017SIAMdsa,
	title = {Domain-specific abstractions for full-waveform inversion},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	keywords = {FWI, Inverse problems, SIAM, software},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/herrmann2017SIAMdsa/herrmann2017SIAMdsa_pres.pdf},
	author = {Felix J. Herrmann and Curt Da Silva}
}
@conference {louboutin2017EAGEess,
	title = {Extending the search space of time-domain adjoint-state FWI with randomized implicit time shifts},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
	note = {(EAGE, Paris)},
	month = {06},
	abstract = {Adjoint-state full-waveform inversion aims to obtain subsurface properties such as velocity, density or anisotropy parameters, from surface recorded data. As with any (non-stochastic) gradient based optimization procedure, the solution of this inversion procedure is to a large extend determined by the quality of the starting model. If this starting model is too far from the true model, these derivative-based optimizations will likely end up in local minima and erroneous inversion results. In certain cases, extension of the search space, e.g. by making the wavefields or focused matched sources additional unknowns, has removed some of these non-uniqueness issues but these rely on time-harmonic formulations. Here, we follow a different approach by combining an implicit extension of the velocity model, time compression techniques and recent results on stochastic sampling in non-smooth/non-convex optimization},
	keywords = {cycle skipping, EAGE, FWI, inversion, nonconvex, time domain},
	doi = {10.3997/2214-4609.201700831},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/louboutin2017EAGEess/louboutin2017EAGEess.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/louboutin2017EAGEess/louboutin2017EAGEess_pres.pdf},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@article {louboutin2017fwi,
	title = {Full-Waveform Inversion - Part 1: forward modeling},
	journal = {The Leading Edge},
	volume = {36},
	number = {12},
	year = {2017},
	note = {(The Leading Edge)},
	month = {12},
	pages = {1033-1036},
	abstract = {Since its re-introduction by Pratt (1999), full-waveform inversion (FWI) has gained a lot of attention in geophysical exploration because of its ability to build high resolution velocity models more or less automatically in areas of complex geology. While there is an extensive and growing literature on the topic, publications focus mostly on technical aspects, making this topic inaccessible for a broader audience due to the lack of simple introductory resources for newcomers to geophysics. We will accomplish this by providing a hands-on walkthrough of FWI using Devito (Lange et al. 2016), a system based on domain-specific languages that automatically generates code for time-domainfinite-differences.},
	keywords = {devito, finite-differences, FWI, Modeling, tutorial},
	doi = {10.1190/tle36121033.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2017/louboutin2017fwi/louboutin2017fwi.html},
	author = {Mathias Louboutin and Philipp A. Witte and Michael Lange and Navjot Kukreja and Fabio Luporini and Gerard Gorman and Felix J. Herrmann}
}
@conference {zhang2017SEGmsd,
	title = {Massive 3D seismic data compression and inversion with hierarchical Tucker},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {1347-1352},
	abstract = {Modern-day oil and gas exploration, especially in areas of complex geology such as fault belts and sub-salt areas, is an increasingly expensive and risky endeavour. Typically long-offset and dense sampling seismic data are required for subsequent shot based processing procedures, e.g. wave-equation based inversion (WEI) and surface-related multiple elimination (SRME). However, these strict requirements result in an exponential growth in data volume size and prohibitive demands on computational resources, given the multidimensional nature of the data volumes. Moreover the physical constraints and cost limitations impose restrictions on acquiring fully sampled data. In this work, we propose to invert our large-scale data from a set of subsampled measurements, resulting in an estimate of the true volume in a compressed low-rank tensor format. Rather than expanding the data to its fully-sampled form for later downstream processes, we demonstrate how to use this compressed data directly via on-the-fly common shot or receiver gathers extraction. The combination of massive compression and fast on demand data reconstruction of 3D shot or receiver gathers leads to a substantial reduction in memory costs but with minimal effects on results in the subsequent processing procedures. We demonstrate the effective implementation of our proposed framework on full-waveform inversion on a 3D seismic synthetic data set generated from a Overthrust model.},
	keywords = {3D, FWI, SEG, tensor algebra},
	doi = {10.1190/segam2017-17742951.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/zhang2017SEGmsd/zhang2017SEGmsd.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/zhang2017SEGmsd/zhang2017SEGmsd_pres.pdf},
	author = {Yiming Zhang and Curt Da Silva and Rajiv Kumar and Felix J. Herrmann}
}
@article {esser2016TLEcwi,
	title = {Constrained waveform inversion for automatic salt flooding},
	journal = {The Leading Edge},
	volume = {35},
	number = {3},
	year = {2016},
	note = {(The Leading Edge)},
	month = {03},
	pages = {235-239},
	abstract = {Given appropriate data acquisition, processing to remove nonprimary arrivals, and use of an accurate migration algorithm, it is the quality of the subsurface velocity model that typically controls the quality of imaging that can be obtained from salt-affected seismic data. Full-waveform inversion has the potential to improve the accuracy, resolution, repeatability, and speed with which such velocity models can be generated, but, in the absence of an accurate starting model, that potential is difficult to realize in practice. Presented are successful inversion results, obtained from synthetic subsalt models, using a robust full-waveform inversion code that includes constraints upon the set of allowable earth models. These constraints include limitations on the total variation of the velocity of the model and, most significantly, on the asymmetric variation of velocity with depth such that negative velocity excursions are limited. During the iteration, these constraints are relaxed progressively so that the final model is driven principally by the seismic data, but the constraints act to steer the inversion path away from local minima in its early stages. This methodology is applied to portions of the 2004 BP benchmark and Phase I SEAM salt models, recovering an accurate model of the salt body, including its base and flanks, and an accurate model of the subsalt velocity structure, starting from one-dimensional velocity models that are severely cycle skipped. This approach removes entirely the requirement to pick salt boundaries from migrated seismic data, and acts as a form of automatic salt and sediment flooding during full-waveform inversion.},
	keywords = {FWI, high-contrast and high velocity, salt, total-variation minimization, velocity-model building},
	doi = {10.1190/tle35030235.1},
	url = {http://dx.doi.org/10.1190/tle35030235.1},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Felix J. Herrmann and Mike Warner}
}
@conference {wang2016SEGfde,
	title = {Frequency down-extrapolation with TV norm minimization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {1380-1384},
	abstract = {In this work, we present a total-variation (TV)-norm minimization method to perform model-free low-frequency data extrapolation for the purpose of assisting full-waveform inversion. Low-frequency extrapolation is the process of extending reliable frequency bands of the raw data towards the lower end of the spectrum. To this end, we propose to solve a TV-norm based convex optimization problem that has a global minimum and is equipped with a fast solver. The approach takes into account both the sparsity of the reflectivity series associated with a single trace, as well as the inter-trace correlations. A favorable byproduct of this approach is that it allows one to work with coarsely sampled trace along time (as coarse as 0.02s per sample), hence substantially reduces the size of the proposed optimization problem. Last, we show the effectiveness of the method for frequency-domain FWI on the Marmousi model.},
	keywords = {extrapolation, FWI, SEG, sparse},
	doi = {10.1190/segam2016-13879674.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/wang2016SEGfde/wang2016SEGfde.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/wang2016SEGfde/wang2016SEGfde_pres.pdf},
	author = {Rongrong Wang and Felix J. Herrmann}
}
@conference {peters2016SEGprs,
	title = {Parallel reformulation of the sequential adjoint-state method},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {1411-1415},
	abstract = {This abstract is about reducing the total computation time to solve full-waveform inversion problems. A common problem formulation is a nonlinear least-squares problem where the gradient is computed using the adjoint-state algorithm. This formulation offers parallelism for the computation of gradients for different sources and frequencies. The adjoint-state algorithm itself is sequential however and this is a limiting factor when a lot of compute nodes are available and only a few wavefields need to be computed. This situation occurs when stochastic optimization strategies are used to minimize the objective function. We present a parallel reformulation of the sequential adjoint-state algorithm, which allows the forward- and adjoint wavefields to be computed in parallel. Both algorithms are mathematically equivalent but the parallel version is twice as fast in run time. An important characteristic of the proposed algorithm is that one wavefield needs to be computed per source and one per receiver. These fields can be used to apply the (inverse) Gauss-Newton Hessian to a vector without recomputing wavefields. A 2D example shows that good full-waveform inversion results are obtained, even when a small number of sources and receivers is used.},
	keywords = {FWI, numerical linear algebra, parallel computing, PDE-constrained optimization, SEG},
	doi = {10.1190/segam2016-13966771.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/peters2016SEGprs/peters2016SEGprs.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/peters2016SEGprs/peters2016SEGprs_pres.pdf},
	author = {Bas Peters and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2015SIAMpcf,
	title = {Pros and cons of full- and reduced-space methods for Wavefield Reconstruction Inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2015},
	note = {(SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, California)},
	month = {06-07},
	abstract = {By insisting on fitting observed data, Wavefield Reconstruction Inversion (WRI) is no longer cycle skipped and therefore less reliant on the accuracy of starting models. While extending the search space mitigates local minima, there are challenges scaling to 3D seismic when using reduced-space methods that require accurate solves. Conversely, full-space methods allow for inaccurate solves but require storage of all wavefields. We weigh pros and cons of these two approaches in the seismic context.},
	keywords = {FWI, SIAM, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/herrmann2015SIAMpcf/herrmann2015SIAMpcf_pres.pdf},
	author = {Felix J. Herrmann and Bas Peters}
}
@conference {herrmann2015ASEGrae,
	title = {Randomized algorithms in exploration seismology},
	booktitle = {ASEG Annual Conference Proceedings},
	year = {2015},
	note = {(ASEG, Perth)},
	month = {02},
	abstract = {As in several other industries, progress in exploration seismology relies on the collection and processing of massive data volumes that grow exponentially in size as the survey area and desired resolution increase. This exponential growth {\textendash}- in combination with the increased complexity of the next-generation of iterative wave-equation based inversion algorithms {\textendash}- puts strains on our acquisition systems and computational back ends impeding progress in our field. During this talk, I will review how recent randomized algorithms from Compressive Sensing and Machine learning can be used to overcome some of these challenges by fundamentally rethinking how we sample and process seismic data. The key idea here is to reduce acquisition and computational costs by deliberately working on small randomized subsets of the data at a desired accuracy. I will illustrate these concepts using a variety of compelling examples on realistic synthetics and field data.},
	keywords = {Acquisition, ASEG, compressed sensing, FWI, Imaging, seismology},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ASEG/2015/herrmann2015ASEGrae/herrmann2015ASEGrae.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIras,
	title = {Randomized algorithms in seismic imaging},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {As in several other industries, progress in exploration seismology relies on the collection and processing of massive data volumes that grow exponentially in size as the survey area and desired resolution increase. This exponential growth {\textendash} in combination with the increased complexity of the next-generation of iterative wave-equation based inversion algorithms {\textendash} puts strains on our acquisition systems and computational back ends impeding progress in our field. During this talk, I will review how recent randomized algorithms from Compressive Sensing and Machine learning can be used to overcome some of these challenges by fundamentally rethinking how we sample and process seismic data. The key idea here is to reduce acquisition and computational costs by deliberately working on small randomized subsets of the data at a desired accuracy. I will illustrate these concepts using a variety of compelling examples on realistic synthetics and field data.},
	keywords = {FWI, Imaging, randomization, seismic},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIras/herrmann2015IIPFWIras_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {kumar2015IIPFWIrmb,
	title = {Rank minimization based seismic data processing and inversion},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present the low-rank extensions of full-waveform inversion to mitigate the local-minima issues. The purpose formulation is computationally tractable and does not involve any extra computational cost compared to the adjoint-state method.},
	keywords = {FWI, inversion, Processing, rank minimization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/kumar2015IIPFWIrmb/kumar2015IIPFWIrmb_pres.pdf},
	author = {Rajiv Kumar and Curt Da Silva and Oscar Lopez and Aleksandr Y. Aravkin and Hassan Mansour and Haneet Wason and Ernie Esser and Felix J. Herrmann}
}
@conference {louboutin2015IIPFWIrwi,
	title = {Regularizing waveform inversion by projections onto convex sets},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing. This is joint work with Bas Peters.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/louboutin2015IIPFWIrwi/louboutin2015IIPFWIrwi_pres.pdf},
	author = {Mathias Louboutin and Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {lin2015IIPFWIsws,
	title = {Software and workflows at SLIM/SINBAD},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	keywords = {FWI, SLIM, software},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/lin2015IIPFWIsws/lin2015IIPFWIsws_pres.pdf},
	author = {Tim T.Y. Lin and Curt Da Silva and Felix J. Herrmann}
}
@conference {witte2015IIPFWIspl,
	title = {Sparsity-promoting least-square migration with linearized Bregman and compressive sensing},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present a novel adaptation of a recently developed relatively simple iterative algorithm to solve large-scale sparsity-promoting optimization problems. Our algorithm is particularly suitable to large-scale geophysical inversion problems, such as sparse least-squares reverse-time migration or Kirchoff migration since it allows for a tradeoff between parallel computations, memory allocation, and turnaround times, by working on subsets of the data with different sizes. Comparison of the proposed method for sparse least-squares imaging shows a performance that rivals and even exceeds the performance of state-of-the art one-norm solvers that are able to carry out least-squares migration at the cost of a single migration with all data.},
	keywords = {Bregman, compressed sensing, FWI, migration, sparsity promotion, time domain},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/witte2015IIPFWIspl/witte2015IIPFWIspl_pres.pdf},
	author = {Philipp A. Witte and Ning Tu and Ernie Esser and Mengmeng Yang and Mathias Louboutin and Felix J. Herrmann}
}
@conference {fang2015IIPFWIsoa,
	title = {Stochastic optimization and its application to seismic inversion},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	keywords = {FWI, inversion, Optimization, stochastic},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/fang2015IIPFWIsoa/fang2015IIPFWIsoa_pres.pdf},
	author = {Zhilong Fang and Tim Burgess and Felix J. Herrmann}
}
@conference {lin2015IIPFWIsdh,
	title = {The student-driven HPC environment at SLIM},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {A major role of academic environments is to provide learning experiences for students to critically analyze and develop methods, both at a high-level of mathematical rigour, and at a low-enough level of implementation in order to yield experimental results on real datasets. Often these two goals are in conflict with each other, in terms of both learning time and attention. At SLIM, we strive to strike a balance between the two by abstracting away many of the low-level aspects of distributed HPC under a framework that matches syntactically with the mathematics of our field, while exposing enough control parameters for tuning performance characteristics. This talk will touch on the history of our efforts at SLIM, and culminate in an overview of our current method of interacting with the in-house compute cluster.},
	keywords = {FWI, HPC},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/lin2015IIPFWIsdh/lin2015IIPFWIsdh_pres.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {witte2015IIPFWItdf,
	title = {Time-domain FWI in TTI media},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We develop an inversion workflow for tilted transverse isotropic (TTI) media using a purely acoustic formulation of the wave equation. The anisotropic modeling kernel is used for the forward modeling operator, as well as for the adjoint Jacobian to back propagate the data residual, thus providing the true gradient of the FWI objective function.},
	keywords = {FWI, time domain, TTI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/witte2015IIPFWItdf/witte2015IIPFWItdf_pres.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@conference {oghenekohwo2015IIPFWItlf,
	title = {Time-lapse FWI with distributed compressed sensing},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {In this talk, I will discuss our most recent application of full-waveform inversion (FWI) to time-lapse seismic data inversion. Specifically, I will illustrate how a joint recovery model (JRM) can be used in a joint inversion framework, leveraging ideas from distributed compressed sensing (DCS). The key idea involves exploiting the common information in the baseline and monitor gradients during the inversion.},
	keywords = {distributed compressed sensing, FWI, time lapse},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/oghenekohwo2015IIPFWItlf/oghenekohwo2015IIPFWItlf_pres.pdf},
	author = {Felix Oghenekohwo and Rajiv Kumar and Ernie Esser and Felix J. Herrmann}
}
@conference {fang2015EAGEuqw,
	title = {Uncertainty quantification for Wavefield Reconstruction Inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {In this work, we propose a method to quantify the uncertainty of wavefield reconstruction inversion under the framework of Bayesian inference. Unlike the conventional method using the wave equation as the forward mapping, we involve the wave equation misfit in the posterior distribution and propose a new posterior distribution. The negative log-likelihood of the new distribution is less oscillatory than that of the conventional posterior distribution, and its Gauss-Newton Hessian is a diagonal matrix that can be generated without any additional computational cost. We use the diagonal Gauss-Newton Hessian to derive an approximate Gaussian distribution at the maximum likelihood point to quantify the uncertainty. This method makes the uncertainty quantification for WRI computationally tractable and is able to provide reasonable uncertainty analysis based on our numerical results.},
	keywords = {EAGE, FWI, UQ, WRI},
	doi = {10.3997/2214-4609.201413198},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/fang2015EAGEuqw/fang2015EAGEuqw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/fang2015EAGEuqw/fang2015EAGEuqw_pres.pdf},
	author = {Zhilong Fang and Chia Ying Lee and Curt Da Silva and Felix J. Herrmann and Rachel Kuske}
}
@conference {fang2015IIPFWIuqw,
	title = {Uncertainty quantification for Wavefield Reconstruction Inversion},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {In this work, we propose a method to quantify the uncertainty of wavefield reconstruction inversion under the framework of Bayesian inference. Unlike the conventional method using the wave equation as the forward mapping, we involve the wave equation misfit in the posterior distribution and propose a new posterior distribution. The negative log-likelihood of the new distribution is less oscillatory than that of the conventional posterior distribution, and its Gauss-Newton Hessian is a diagonal matrix that can be generated without any additional computational cost. We use the diagonal Gauss-Newton Hessian to derive an approximate Gaussian distribution at the maximum likelihood point to quantify the uncertainty. This method makes the uncertainty quantification for WRI computationally tractable and is able to provide reasonable uncertainty analysis based on our numerical results.},
	keywords = {FWI, uncertainty, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/fang2015IIPFWIuqw/fang2015IIPFWIuqw_pres.pdf},
	author = {Zhilong Fang and Chia Ying Lee and Curt Da Silva and Felix J. Herrmann and Rachel Kuske}
}
@conference {oghenekohwo2015EAGEuci,
	title = {Using common information in compressive time-lapse full-waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {The use of time-lapse seismic data to monitor changes in the subsurface has become standard practice in industry. In addition, full-waveform inversion has also been extended to time-lapse seismic to obtain useful time-lapse information. The computational cost of this method are becoming more pronounced as the volume of data increases. Therefore, it is necessary to develop fast inversion algorithms that can also give improved time-lapse results. Rather than following existing joint inversion algorithms, we are motivated by a joint recovery model which exploits the common information among the baseline and monitor data. We propose a joint inversion framework, leveraging ideas from distributed compressive sensing and the modified Gauss-Newton method for full-waveform inversion, by using the shared information in the time-lapse data. Our results on a realistic synthetic example highlight the benefits of our joint inversion approach over a parallel inversion method that does not exploit the shared information. Preliminary results also indicate that our formulation can address time-lapse data with inconsistent acquisition geometries.},
	keywords = {EAGE, FWI, time-lapse},
	doi = {10.3997/2214-4609.201413086},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/oghenekohwo2015EAGEuci/oghenekohwo2015EAGEuci.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/oghenekohwo2015EAGEuci/oghenekohwo2015EAGEuci_poster.pdf},
	author = {Felix Oghenekohwo and Rajiv Kumar and Ernie Esser and Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIwcc,
	title = {Wavefield Reconstruction Inversion with convex constraints},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {During this talk, we discuss how to exploit the special structure of Wavefield Reconstruction Inversion (WRI) to include convex bound and total-variation constraints in a computationally feasible manner. The resulting method shows promising results on challenging models that include high-velocity high-contrast inclusions such as salt or basalt. This is joint work with Ernie Esser who passed away and who is dearly missed.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIwcc/herrmann2015IIPFWIwcc_pres.pdf},
	author = {Felix J. Herrmann and Ernie Esser and Llu{\'\i}s Guasch}
}
@conference {fang2015IIPFWIwri,
	title = {Wavefield Reconstruction Inversion with source estimation and its application to 2014 Chevron synthetic blind test dataset},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present a robust wavefield reconstruction inversion with source estimation. The source wavelet is estimated with the reconstruction of wavefield simultaneously by solving an extended data augmentation problem. We apply this method to the 2014 Chevron synthetic blind test dataset and show the robustness of our method.},
	keywords = {FWI, source estimation, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/fang2015IIPFWIwri/fang2015IIPFWIwri_pres.pdf},
	author = {Zhilong Fang and Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIwri,
	title = {Wavefield-Reconstruction Inversion {\textemdash} WRI},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI {\textemdash} which attempts to minimize the error between observed and predicted data obtained by solving a wave equation {\textendash} WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.},
	keywords = {FWI, inversion, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIwri/herrmann2015IIPFWIwri_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {lago2014EAGEfst,
	title = {Fast solution of time-harmonic wave-equation for full-waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {For many full-waveform inversion techniques, the most computationally intensive step is the computation of a numerical solution for the wave equation on every iteration. In the frequency domain approach, this requires the solution of very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we bring out attention specifically to CGMN method for solving PDEs, known for being flexible (i.e. it is able to treat equally acoustic data as well as visco-elastic or more complex scenarios) efficient with respect both to memory and computation time, and controllable accuracy of the final approximation. We propose an improvement for the known CGMN method by imposing a minimal residual condition, which incurs in one extra model vector storage. The resulting algorithm called CRMN enjoys several interesting properties as monotonically nonincreasing behaviour of the norm of the residual and minimal residual, guaranteeing optimal convergence for the relative residual criterion. We discuss numerical experiments both in an isolated PDE solve and also within the inversion procedure, showing that in a realistic scenario we can expect a speedup around 25\% when using CRMN rather than CGMN.},
	keywords = {CGMN, CRMN, EAGE, FWI, Time-Harmonic Wave Equation},
	doi = {10.3997/2214-4609.20140812},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lago2014EAGEfst/lago2014EAGEfst.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lago2014EAGEfst/lago2014EAGEfst_pres.pdf},
	author = {Rafael Lago and Art Petrenko and Zhilong Fang and Felix J. Herrmann}
}
@conference {fang2014EAGEfuq,
	title = {Fast uncertainty quantification for 2D full-waveform inversion with randomized source subsampling},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {Uncertainties arise in every area of seismic exploration, especially in full-waveform inversion, which is highly non-linear. In the framework of Bayesian inference, uncertainties can be analyzed by sampling the posterior probability density distribution with a Markov chain Monte-Carlo (McMC) method. We reduce the cost of computing the posterior distribution by working with randomized subsets of sources. These approximations, together with the Gaussian assumption and approximation of the Hessian, leads to a computational tractable uncertainty quantification. Application of this approach to a synthetic leads to standard deviations and confidence intervals that are qualitatively consistent with our expectations.},
	keywords = {EAGE, FWI, Markov chain Monte Carlo, randomized sources subsampling, Uncertainty quantification},
	doi = {10.3997/2214-4609.20140715},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/fang2014EAGEfuq/fang2014EAGEfuq.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/fang2014EAGEfuq/fang2014EAGEfuq_pres.pdf},
	author = {Zhilong Fang and Curt Da Silva and Felix J. Herrmann}
}
@techreport {wang2014SEGfwi,
	title = {Full waveform inversion with interferometric measurements},
	number = {TR-EOAS-2014-5},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {In this note, we design new misfit functions for full-waveform inversion by using interferometric measurements to reduce sensitivity to phase errors. Though established within a completely different setting from the linear case, we obtain a similar observation: the interferometry can improve robustness under certain modeling errors. Moreover, in order to deal with errors on both source and receiver sides, we propose a higher order interferometry, which, as a generalization of the usual definition, involves the cross correlation of four traces. A proof of principle simulations is included on a stylized example.},
	keywords = {FWI},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/wang2014SEGfwi/wang2014SEGfwi.html},
	author = {Rongrong Wang and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {herrmann2014ROSErpe,
	title = {Relax the physics and expand the search space {\textendash} FWI via Wavefield Reconstruction Inversion},
	booktitle = {ROSE Consortium; Norway},
	year = {2014},
	note = {(ROSE Consortium)},
	month = {05},
	keywords = {Consortium, FWI, ROSE, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ROSE/2014/herrmann2014ROSErpe.pdf},
	author = {Felix J. Herrmann}
}
@techreport {zfang2014SEGsqn,
	title = {A stochastic quasi-Newton McMC method for uncertainty quantification of full-waveform inversion},
	number = {TR-EOAS-2014-6},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {In this work we propose a stochastic quasi-Newton Markov chain Monte Carlo (McMC) method to quantify the uncertainty of full-waveform inversion (FWI). We formulate the uncertainty quantification problem in the framework of the Bayesian inference, which formulates the posterior probability as the conditional probability of the model given the observed data. The Metropolis-Hasting algorithm is used to generate samples satisfying the posterior probability density function (pdf) to quantify the uncertainty. However it suffers from the challenge to construct a proposal distribution that simultaneously provides a good representation of the true posterior pdf and is easy to manipulate. To address this challenge, we propose a stochastic quasi-Newton McMC method, which relies on the fact that the Hessian of the deterministic problem is equivalent to the inverse of the covariance matrix of the posterior pdf. The l-BFGS (limited-memory Broyden{\textendash}Fletcher{\textendash}Goldfarb{\textendash}Shanno) Hessian is used to approximate the inverse of the covariance matrix efficiently, and the randomized source sub-sampling strategy is used to reduce the computational cost of evaluating the posterior pdf and constructing the l-BFGS Hessian. Numerical experiments show the capability of this stochastic quasi-Newton McMC method to quantify the uncertainty of FWI with a considerable low cost.},
	keywords = {FWI, McMC, quasi-Newton, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/zfang2014SEGsqn/zfang2014SEGsqn.html},
	author = {Zhilong Fang and Felix J. Herrmann}
}
@conference {herrmann2014SEGWS,
	title = {Wavefield Reconstruction Inversion (WRI) {\textendash} a new take on wave-equation based inversion},
	booktitle = {SEG Workshop on Full Waveform Inversion - Elastic Approaches and Issues with Anisotropy, Nonshallow Inversion, Poor Starting Model; Denver},
	year = {2014},
	note = {(SEG Workshop, Denver)},
	month = {10},
	keywords = {FWI, SEG, workshop, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/herrmann2014SEGWSwri/herrmann2014SEGWSwri_pres.pdf},
	author = {Felix J. Herrmann and Ernie Esser and Tristan van Leeuwen and Bas Peters}
}
@conference {herrmann2013SIAMdrfwi,
	title = {Dimensionality reduction in FWI},
	booktitle = {SIAM},
	year = {2013},
	month = {02},
	keywords = {dimensionality reduction, FWI, SIAM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2013/herrmann2013SIAMdrfwi/herrmann2013SIAMdrfwi_pres.pdf},
	author = {Felix J. Herrmann}
}
@article {VanLeeuwen11TRfwiwse,
	title = {Fast waveform inversion without source encoding},
	journal = {Geophysical Prospecting},
	volume = {61},
	year = {2013},
	note = {Article first published online: 10 JULY 2012},
	month = {06},
	pages = {10-19},
	abstract = {Randomized source encoding has recently been proposed as a way to dramatically reduce the costs of full waveform inversion. The main idea is to replace all sequential sources by a small number of simultaneous sources. This introduces random crosstalk in the model updates and special stochastic optimization strategies are required to deal with this. Two problems arise with this approach: i) source encoding can only be applied to fixed-spread acquisition setups, and ii) stochastic optimization methods tend to converge very slowly, relying on averaging to get rid of the cross-talk. Although the slow convergence is partly offset by the low iteration cost, we show that conventional optimization strategies are bound to outperform stochastic methods in the long run. In this paper we argue that we don{\textlnot}{\o}t need randomized source encoding to reap the benefits of stochastic optimization and we review an optimization strategy that combines the benefits of both conventional and stochastic optimization. The method uses a gradually increasing batch of sources. Thus, iterations are very cheap initially and this allows the method to make fast progress in the beginning. As the batch size grows, the method behaves like conventional optimization, allowing for fast convergence. Numerical examples suggest that the stochastic and hybrid method perform equally well with and without source encoding and that the hybrid method outperforms both conventional and stochastic optimization. The method does not rely on source encoding techniques and can thus be applied to non fixed-spread data.},
	keywords = {FWI, Optimization, SLIM},
	doi = {10.1111/j.1365-2478.2012.01096.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01096.x/abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2013/VanLeeuwen11TRfwiwse/VanLeeuwen11TRfwiwse.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@article {moghaddam2013GEOPnoa,
	title = {A new optimization approach for source-encoding full-waveform inversion},
	journal = {Geophysics},
	volume = {78},
	number = {3},
	year = {2013},
	month = {05},
	pages = {R125-R132},
	abstract = {Waveform inversion is the method of choice for determining highly heterogeneous subsurface structure. However, conventional waveform inversion requires that the wavefield for each source is computed separately. This makes it very expensive for realistic 3D seismic surveys. Source-encoding waveform inversion, in which the sources are modelled simultaneously, is considerably faster than conventional waveform inversion but suffers from artifacts. These artifacts can partly be removed by assigning random weights to the source wavefields. We found that the misfit function, and therefore also its gradient, for source-encoding waveform inversion is an unbiased random estimation of the misfit function used in conventional waveform inversion. We found a new method of source-encoding waveform inversion which takes into account the random nature of the gradients used in the optimization. In this new method, the gradient at each iteration is a weighted average of past gradients such that the most recent gradients have the largest weights with exponential decay. This way we damped the random fluctuations of the gradient by incorporating information from the previous iterations. We compare this new method with existing source-encoding waveform inversion methods as well as conventional waveform inversion and found that the model misfit reduction is faster and smoother than those of existing source-encoding waveform inversion methods, and it approaches the model misfit reduction obtained in conventional waveform inversion.},
	keywords = {FWI, Geophysics, Optimization, source encoding},
	doi = {10.1190/GEO2012-0090.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/moghaddam2013GEOPnoa/moghaddam2013GEOPnoa.pdf},
	author = {Peyman P. Moghaddam and Henk Keers and Felix J. Herrmann and Wim A. Mulder}
}
@conference {herrmann2013SEGOMANrdw,
	title = {Recent developments in wave-equation based inversion technology},
	booktitle = {SEG Workshop on FWI; Oman},
	year = {2013},
	month = {04},
	keywords = {3D, Exploration seismology, FWI, randomized sampling, SEG, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/herrmann2013SEGOMANrdw/herrmann2013SEGOMANrdw_pres.pdf},
	author = {Felix J. Herrmann}
}
@article {haber10TRemp,
	title = {An effective method for parameter estimation with PDE constraints with multiple right hand sides},
	journal = {SIAM Journal on Optimization},
	volume = {22},
	number = {3},
	year = {2012},
	month = {07},
	abstract = {Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right-hand sides can be reformulated as stochastic programming problems by combining the right-hand sides into a few {\quotedblbase}simultaneous{\textquotedblright} sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.},
	keywords = {FWI, Optimization, SLIM},
	url = {http://dx.doi.org/10.1137/11081126X},
	author = {Eldad Haber and Matthias Chung and Felix J. Herrmann}
}
@article {Li11TRfrfwi,
	title = {Fast randomized full-waveform inversion with compressive sensing},
	journal = {Geophysics},
	volume = {77},
	number = {3},
	year = {2012},
	month = {05},
	pages = {A13-A17},
	abstract = {Wave-equation based seismic inversion can be formulated as a nonlinear inverse problem where the medium properties are obtained via minimization of a least- squares misfit functional. The demand for higher resolution models in more geologically complex areas drives the need to develop techniques that explore the special structure of full-waveform inversion to reduce the computational burden and to regularize the inverse problem. We meet these goals by using ideas from compressive sensing and stochastic optimization to design a novel Gauss-Newton method, where the updates are computed from random subsets of the data via curvelet-domain sparsity promotion. Application of this idea to a realistic synthetic shows improved results compared to quasi-Newton methods, which require passes through all data. Two different subset sampling strategies are considered: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs.},
	keywords = {Compressive Sensing, FWI, Optimization, SLIM},
	doi = {10.1190/geo2011-0410.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2012/Li11TRfrfwi/Li11TRfrfwi.pdf},
	author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2012SEGfwi,
	title = {FWI from the West Coasts: lessons learned from "Gulf of Mexico Imaging Challenges: What Can Full Waveform Inversion Achieve?"},
	booktitle = {SEG Workshop on FWI; Las Vegas},
	year = {2012},
	publisher = {SEG},
	organization = {SEG},
	keywords = {FWI, SEG, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/herrmann2012SEGfwi/herrmann2012SEGfwi_pres.pdf},
	author = {Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason and Felix J. Herrmann}
}
@article {Aravkin11TRridr,
	title = {Robust inversion, dimensionality reduction, and randomized sampling},
	journal = {Mathematical Programming},
	volume = {134},
	number = {1},
	year = {2012},
	month = {08},
	pages = {101-125},
	abstract = {We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student{\textquoteright}s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 \% corrupted data.},
	keywords = {FWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization},
	doi = {10.1007/s10107-012-0571-6},
	url = {http://www.springerlink.com/content/35rwr101h5736340/},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/MathematicalProgramming/aravkin2012MPrid/aravkin2012MPrid.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Felix J. Herrmann and Tristan van Leeuwen}
}
@article {vanLeeuwen2010IJGswi,
	title = {Seismic waveform inversion by stochastic optimization},
	journal = {International Journal of Geophysics},
	volume = {2011},
	year = {2011},
	note = {Article ID: 689041, 18pages},
	month = {12},
	abstract = {We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.},
	keywords = {FWI, Optimization, SLIM},
	doi = {10.1155/2011/689041},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InternationJournalOfGeophysics/2011/vanLeeuwen10IJGswi/vanLeeuwen10IJGswi.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
