@article {yin2022TLEdgc,
	title = {Derisking geological carbon storage from high-resolution time-lapse seismic to explainable leakage detection},
	journal = {The Leading Edge},
	volume = {42},
	number = {1},
	year = {2023},
	note = {(The Leading Edge)},
	month = {01},
	pages = {69-76},
	abstract = {Geological carbon storage represents one of the few truly scalable technologies capable of reducing the CO$_2$ concentration in the atmosphere. While this technology has the potential to scale, its success hinges on our ability to mitigate its risks. An important aspect of risk mitigation concerns assurances that the injected CO$_2$ remains within the storage complex. Amongst the different monitoring modalities, seismic imaging stands out with its ability to attain high resolution and high fidelity images. However, these superior features come, unfortunately, at prohibitive costs and time-intensive efforts potentially rendering extensive seismic monitoring undesirable. To overcome this shortcoming, we present a methodology where time-lapse images are created by inverting non-replicated time-lapse monitoring data jointly. By no longer insisting on replication of the surveys to obtain high fidelity time-lapse images and differences, extreme costs and time-consuming labor are averted. To demonstrate our approach, hundreds of noisy time-lapse seismic datasets are simulated that contain imprints of regular CO$_2$ plumes and irregular plumes that leak. These time-lapse datasets are subsequently inverted to produce time-lapse difference images used to train a deep neural classifier. The testing results show that the classifier is capable of detecting CO$_2$ leakage automatically on unseen data and with a reasonable accuracy.},
	keywords = {CAM, CCS, classification, explainability, JRM, resolution, seismic imaging, time-lapse},
	doi = {10.1190/tle42010069.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2022/yin2022TLEdgc/paper.html},
	software = {https://github.com/slimgroup/GCS-CAM},
	author = {Ziyi Yin and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2023CCUSdgs,
	title = {Derisking geological storage with simulation-based seismic monitoring design and machine learning},
	booktitle = {Carbon, Capture, Utilization, and Storage},
	year = {2023},
	note = {(CCUS, Houston)},
	month = {04},
	keywords = {CAM, CCS, CCUS, classification, explainability, JRM, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CCUS/2023/herrmann2023CCUSdgs/CCUS2023.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/CCUS/2023/herrmann2023CCUSdgs},
	author = {Felix J. Herrmann and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Ziyi Yin and Mathias Louboutin}
}
@article {siahkoohi2022ravi,
	title = {Reliable amortized variational inference with physics-based latent distribution correction},
	journal = {Geophysics},
	volume = {88},
	number = {3},
	year = {2023},
	note = {(Geophysics)},
	month = {05},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs of the forward operator and the selection of an appropriate prior distribution. Amortized variational inference addresses these challenges where a neural network is trained to approximate the posterior distribution over existing pairs of model and data. When fed previously unseen data and normally distributed latent samples as input, the pretrained deep neural network{\textendash}-in our case a conditional normalizing flow{\textendash}-provides posterior samples with virtually no cost. However, the accuracy of this approach relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the highly heterogeneous structure of the Earth. In addition, accurate amortized variational inference requires the observed data to be drawn from the training data distribution. As such, we offer a solution that increases the resilience of amortized variational inference when faced with data distribution shifts, e.g., changes in the forward model or prior distribution. Our method involves a physics-based correction to the conditional normalizing flow latent distribution to provide a more accurate approximation to the posterior distribution for the observed data at hand. To accomplish this, instead of a standard Gaussian latent distribution, we parameterize the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance. These unknown quantities are then estimated by minimizing the Kullback-Leibler divergence between the corrected and true posterior distributions. While generic and applicable to other inverse problems, by means of a seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty with approximately the same cost as five reverse-time migrations.},
	keywords = {Inverse problems, Normalizing flows, seismic imaging, Uncertainty quantification, Variational Inference},
	doi = {10.1190/geo2022-0472.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/siahkoohi2022ravi/paper.html},
	software = {https://github.com/slimgroup/ReliableAVI.jl},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2022EAGEcvm,
	title = {Capturing velocity-model uncertainty and two-phase flow with Fourier Neural Operators},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {AI in Geoscience and Geophysics: Current Trends and Future Prospects (Dedicated Session)},
	keywords = {CCS, EAGE, Fourier neural operators, JRM, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/herrmann2022EAGEcvm/index.html},
	author = {Ali Siahkoohi and Thomas J. Grady II and Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@article {siahkoohi2021dbif,
	title = {Deep Bayesian inference for seismic imaging with tasks},
	journal = {Geophysics},
	volume = {87},
	number = {5},
	year = {2022},
	note = {(Geophysics)},
	month = {07},
	pages = {281-302},
	abstract = {We propose to use techniques from Bayesian inference and deep neural networks to translate uncertainty in seismic imaging to uncertainty in tasks performed on the image, such as horizon tracking. Seismic imaging is an ill-posed inverse problem because of unavoidable bandwidth and aperture limitations, which that is hampered by the presence of noise and linearization errors. Many regularization methods, such as transform-domain sparsity promotion, have been designed to deal with the adverse effects of these errors, however, these methods run the risk of biasing the solution and do not provide information on uncertainty in the image space and how this uncertainty impacts certain tasks on the image. A systematic approach is proposed to translate uncertainty due to noise in the data to confidence intervals of automatically tracked horizons in the image. The uncertainty is characterized by a convolutional neural network (CNN) and to assess these uncertainties, samples are drawn from the posterior distribution of the CNN weights, used to parameterize the image. Compared to traditional priors, in the literature it is argued that these CNNs introduce a flexible inductive bias that is a surprisingly good fit for many diverse domains in imaging. The method of stochastic gradient Langevin dynamics is employed to sample from the posterior distribution. This method is designed to handle large scale Bayesian inference problems with computationally expensive forward operators as in seismic imaging. Aside from offering a robust alternative to maximum a posteriori estimate that is prone to overfitting, access to these samples allow us to translate uncertainty in the image, due to noise in the data, to uncertainty on the tracked horizons. For instance, it admits estimates for the pointwise standard deviation on the image and for confidence intervals on its automatically tracked horizons.},
	keywords = {deep priors, horizon tracking, seismic imaging, Uncertainty quantification},
	doi = {10.1190/geo2021-0666.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2022/siahkoohi2021dbif/paper.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {erdinc2022AAAIdcc,
	title = {De-risking Carbon Capture and Sequestration with Explainable CO$_2$ Leakage Detection in Time-lapse Seismic Monitoring Images},
	booktitle = {AAAI 2022 Fall Symposium: The Role of AI in Responding to Climate Challenges},
	year = {2022},
	note = {(AAAI 2022 Fall Symposium: The Role of AI in Responding to Climate Challenges, Arlington)},
	month = {11},
	abstract = {With the growing global deployment of carbon capture and sequestration technology to combat climate change, monitoring and detection of potential CO$_2$ leakage through existing or storage induced faults are critical to the safe and long-term viability of the technology. Recent work on time-lapse seismic monitoring of CO$_2$ storage has shown promising results in its ability to monitor the growth of the CO$_2$ plume from surface recorded seismic data. However, due to the low sensitivity of seismic imaging to CO$_2$ concentration, additional developments are required to efficiently interpret the seismic images for leakage. In this work, we introduce a binary classification of time-lapse seismic images to delineate CO$_2$ plumes (leakage) using state-of-the-art deep learning models. Additionally, we localize the leakage region of CO$_2$ plumes by leveraging Class Activation Mapping (CAM) methods.},
	keywords = {AAAI, CAM, CCS, classification, explainability, JRM, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AAAI/2022/erdinc2022AAAIdcc/erdinc2022AAAIdcc.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AAAI/2022/erdinc2022AAAIdcc/index.html},
	author = {Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {siahkoohi2022ML4SEISMICluq,
	title = {Low-cost uncertainty quantification for large-scale inverse problems},
	year = {2022},
	month = {11},
	abstract = {Bayesian inference for large-scale inverse problems is challenged by the computationally costly forward operator evaluations during posterior distribution sampling. Recent advances in variational inference and deep learning reduce these costs by pretraining a neural network capable of sampling the posterior distribution for previously unseen observed data. In geophysical applications, however, the accuracy of these methods depends on sufficiently capturing subsurface variability through a training dataset, which is challenging given the heterogeneity of the Earth{\textquoteright}s subsurface and our lack of access to it. Moreover, these methods may be unreliable in the presence of data distribution shifts, e.g., a change in the number of source experiments, noise distribution, or geological features to be imaged. As such, we present a solution that increases the robustness of deep-learning-based Bayesian inference approaches when faced with changes in data distribution. Our proposed method involves a physics-based adaptation to the latent distribution of a conditional normalizing flow that is pretrained to approximate the posterior distribution for previously unseen data. Instead of feeding standard Gaussian latent samples to the conditional normalizing flow, this method parameterizes the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, estimated by minimizing the Kullback-Leibler divergence between predicted and true posterior distributions. This method is applicable to a wide range of inverse problems and has the potential to significantly reduce the costs of Bayesian variational inference. By means of a realistic seismic imaging example we demonstrate that the proposed latent distribution adaptation method mitigates the Bayesian inference errors induced by data distribution shifts, including shifts in the forward model and prior distribution.},
	keywords = {Inverse problems, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/siahkoohi2022ML4SEISMICluq/siahkoohi2022ML4SEISMICluq_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {siahkoohi2022EAGEweb,
	title = {Wave-equation based inversion with amortized variational Bayesian inference},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {Session 2: Velocity model building and imaging (different domains)},
	abstract = {Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth{\textquoteright}s highly heterogeneous structure is unknown, present a challenge in encoding prior knowledge through analytical expressions. Our main contribution is a generative-model-based regularization approach, robust to out-of-distribution data, which exploits the prior knowledge embedded in existing data and model pairs. Utilizing an amortized variational inference objective, a conditional normalizing flow (NF) is pretrained on pairs of low- and high-fidelity migrated images in order to achieve a low-fidelity approximation to the seismic imaging posterior distribution for previously unseen data. The NF is used after pretraining to reparameterize the unknown seismic image in an inversion scheme involving physics-guided data misfit and a Gaussian prior on the NF latent variable. Solving this optimization problem with respect to the latent variable enables us to leverage the benefits of data-driven conditional priors whilst being informed by physics and data. The numerical experiments demonstrate that the proposed inversion scheme produces seismic images with limited artifacts when dealing with noisy and out-of-distribution data.},
	keywords = {conditional priors, EAGE, Normalizing flows, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/Mon-Herrmann.pdf},
	software = {https://github.com/slimgroup/ConditionalNFs4Imaging.jl},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {herrmann2021KAUSTdbi,
	title = {Deep Bayesian Inference for Task-based Seismic Imaging},
	booktitle = {KAUST},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {03},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.},
	keywords = {Bayesian inference, Inverse problems, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/herrmann2021KAUSTdbi/Kaust.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {siahkoohi2021EarthMLfar,
	title = {Fast and reliability-aware seismic imaging with conditional normalizing flows},
	booktitle = {Intelligent illumination of the Earth},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {09},
	abstract = {The posterior probability distribution provides a comprehensive description of the solution in ill-posed inverse problems. Sampling from the posterior distribution in the context of seismic imaging is challenged by the high-dimensionality of the unknown and the expensive-to-evaluate forward operator. These challenges limit the applicability of Markov Chain sampling methods due to the costs associated with the forward operator. Moreover, explicitly choosing a prior distribution that captures the true heterogeneity exhibited by the Earth{\textquoteright}s subsurface further complicates casting seismic imaging into a Bayesian framework. To handle this situation and to assess uncertainty, we propose a data-driven variational inference approach based on conditional normalizing flows (NFs). The proposed scheme leverages existing data, which are in the form of low- and high-fidelity migrated image pairs, to train a conditional NF capable of characterizing the posterior distribution. After training, the NF can be used to sample from the posterior distribution associated with a previously unseen seismic survey, which is in some sense close, e.g., data from a neighboring survey area. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding band-limited noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image{\textquoteright}s reliability.},
	keywords = {Normalizing flows, seismic imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/siahkoohi2021EarthMLfar/siahkoohi2021EarthMLfar.pdf},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2021Delftlwi,
	title = {Learned wave-based imaging - variational inference at scale},
	booktitle = {Delft},
	year = {2021},
	note = {(Delft, virtual)},
	month = {06},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth rank medical ultrasound and seismic imaging amongst the most challenging problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks. During this talk, I will show how recent developments in Normalizing Flows, a new type of invertible neural networks, can be used to cast wave-based imaging into a scalable Bayesian framework. Contrary to conventional methods, where sample images are drawn from the posterior distribution during inversion, our approach trains Normalizing Flows capable of generating samples from the posterior. Aside from greatly reducing the computational cost, this approach gives us access to the image itself (via Maximum a posteriori or mean estimation) and its multidimensional statistical distribution including its pointwise variance.},
	keywords = {medical imaging, Normalizing flows, seismic imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/Delft/2021/herrmann2021Delftlwi/herrmann2021Delftlwi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/Delft/2021/herrmann2021Delftlwi/herrmann2021Delftlwi.mp4},
	author = {Felix J. Herrmann and Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin}
}
@conference {siahkoohi2021SEGlbe,
	title = {Learning by example: fast reliability-aware seismic imaging with normalizing flows},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {1580-1585},
	abstract = {Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low- and high-fidelity migrated images. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image{\textquoteright}s reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current and assess its reliability.},
	keywords = {deep learning, Normalizing flows, SEG, seismic imaging, Variational Inference},
	doi = {10.1190/segam2021-3581836.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.mp4},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Ali Siahkoohi and Felix J. Herrmann}
}
@presentation {siahkoohi2021ML4SEISMICmcn,
	title = {Multifidelity conditional normalizing flows for physics-guided Bayesian inference},
	year = {2021},
	month = {11},
	abstract = {We introduce a scalable Bayesian inference approach that combines techniques from deep learning with a physic-based variational inference formulation. Bayesian inference for ill-posed inverse problems is challenged by the high-dimensionality of the unknown, computationally expensive forward operator, and choosing a prior distribution that accurately encodes prior knowledge on the unknown. To handle this situation and to assess uncertainty, we propose to approximate the posterior distribution using a pretrained conditional normalizing flow, which is trained on existing low- and high-fidelity estimations of the unknown. To further improve the accuracy of this approximation, we use transfer learning and finetune this normalizing flow by minimizing the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density. This amounts to minimizing a physic-based variational inference objective with respect to the network weights, which we believe might scale better than Bayesian inference with Markov Chain sampling methods. We apply the proposed Bayesian inference approach to seismic imaging where we use quasi-real data obtained from the Parihaka dataset.},
	keywords = {deep learning, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/siahkoohi2021ML4SEISMICmcn/Mon-11-45-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {siahkoohi2020SEGCHAPTERGTdlbuq,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	year = {2020},
	note = {(SEG Student Chapter)},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are more difficult to image.},
	keywords = {deep learning, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/SEGCHAPTERGT/2020/siahkoohi2020SEGCHAPTERGTdlbuq/siahkoohi2020SEGCHAPTERGTdlbuq.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {siahkoohi2020EAGEdlb,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2020},
	note = {Accepted in EAGE},
	month = {1},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are difficult to image.},
	keywords = {deep learning, EAGE, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2020/siahkoohi2020EAGEdlb/siahkoohi2020EAGEdlb.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {yin2020SEGesi,
	title = {Extended source imaging {\textendash}- a unifying framework for seismic and medical imaging},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {3502-3506},
	abstract = {We present three imaging modalities that live on the crossroads of seismic and medical imaging. Through the lens of extended source imaging, we can draw deep connections among the fields of wave-equation based seismic and medical imaging, despite first appearances. From the seismic perspective, we underline the importance to work with the correct physics and spatially varying velocity fields. Medical imaging, on the other hand, opens the possibility for new imaging modalities where outside stimuli, such as laser or radar pulses, can not only be used to identify endogenous optical or thermal contrasts but that these sources can also be used to insonify the medium so that images of the whole specimen can in principle be created.},
	keywords = {medical imaging, SEG, seismic imaging, variable projection},
	doi = {10.1190/segam2020-3426999.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/yin2020SEGesi/yin2020SEGesi.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/yin2020SEGesi/yin2020SEGesi_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/yin2020SEGesi/yin2020SEGesi_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Ziyi Yin and Rafael Orozco and Philipp A. Witte and Mathias Louboutin and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {siahkoohi2020SEGwdp,
	title = {Weak deep priors for seismic imaging},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {2998-3002},
	abstract = {Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in a convenient and analytical way. Parameterizing the unknowns with a convolutional neural network (CNN), and assuming an uninformative Gaussian prior on its weights, leads to a variational prior on the output space that favors "natural" images and excludes noisy artifacts, as long as overfitting is prevented. This is the so-called deep-prior approach. In seismic imaging, however, evaluating the forward operator is computationally expensive, and training a randomly initialized CNN becomes infeasible. We propose, instead, a weak version of deep priors, which consists of relaxing the requirement that reflectivity models must lie in the network range, and letting the unknowns deviate from the network output according to a Gaussian distribution. Finally, we jointly solve for the reflectivity model and CNN weights. The chief advantage of this approach is that the updates for the CNN weights do not involve the modeling operator, and become relatively cheap. Our synthetic numerical experiments demonstrate that the weak deep prior is more robust with respect to noise than conventional least-squares imaging approaches, with roughly twice the computational cost of reverse-time migration, which is the affordable computational budget in large-scale imaging problems.},
	keywords = {deep prior, machine learning, SEG, seismic imaging},
	doi = {10.1190/segam2020-3417568.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@article {tu2015GJIsem,
	title = {Source estimation with surface-related multiples{\textendash}-fast ambiguity-resolved seismic imaging},
	journal = {Geophysical Journal International},
	volume = {205},
	year = {2016},
	note = {(published online in Geophysical Journal International)},
	month = {03},
	pages = {1492-1511},
	abstract = {We address the problem of obtaining a reliable seismic image without prior knowledge of the source wavelet, especially from data that contain strong surface-related multiples. Conventional reverse-time migration requires prior knowledge of the source wavelet, which is either technically or computationally challenging to accurately determine; inaccurate estimates of the source wavelet can result in seriously degraded reverse-time migrated images, and therefore wrong geological interpretations. To solve this problem, we present a "wavelet-free" imaging procedure that simultaneously inverts for the source wavelet and the seismic image, by tightly integrating source estimation into a fast least-squares imaging framework, namely compressive imaging, given a reasonably accurate background velocity model. However, this joint inversion problem is difficult to solve as it is plagued with local minima and the ambiguity with respect to amplitude scalings because of the multiplicative, and therefore nonlinear, appearance of the source wavelet in the otherwise linear formalism. We have found a way to solve this nonlinear joint-inversion problem using a technique called variable projection, and a way to overcome the scaling ambiguity by including surface-related multiples in our imaging procedure following recent developments in surface-related multiple prediction by sparse inversion. As a result, we obtain without prior knowledge of the source wavelet high-resolution seismic images, comparable in quality to images obtained assuming the true source wavelet is known. By leveraging the computationally efficient compressive-imaging methodology, these results are obtained at affordable computational costs compared with conventional processing work flows that include surface-related multiple removal and reverse-time migration.},
	keywords = {computational seismology, free surface, Inverse theory, multiples, seismic imaging, time series analysis, wave propagation},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2016/tu2015GJIsem/tu2015GJIsem.pdf},
	url2 = {http://gji.oxfordjournals.org/content/205/3/1492.full.pdf?keytype=ref\&ijkey=zFydRGQpiJzeCS9},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}
@mastersthesis {tu2015THfis,
	title = {Fast imaging with surface-related multiples},
	year = {2015},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Surface-related multiples, which are waves that bounce more than once between the water surface and the subsurface reflectors, constitute a significant part of the data acquired in marine seismic surveys. If left untreated, they can lead to misplaced phantom reflectors in the image, and result in erroneous interpretations of the subsurface structure. As a result, these multiples are removed before the imaging procedure in conventional seismic data processing. However, because they interact more with the subsurface medium, they may carry extra information that is not present in the primaries. Therefore instead of removing these multiples, a more desirable alternative is to make active use of them. We derive from the well-established "Surface-Related Multiple Elimination" relation, and arrive at a linearized expression of the wave-equation based modelling that incorporates the surface- related multiples. We then present a computationally efficient approach to iteratively invert this expression to obtain an image of the subsurface from data that contain multiples. We achieve the computational efficiency inside each iteration by (i) using the wave-equation solver to implicitly carry out the expensive multiple prediction; and (ii) reducing the number of wave-equation solves during data simulation by subsampling the monochromatic source experiments. We show that, compared with directly applying the cross-correlation/deconvolutional imaging conditions, the presented approach can suppress the coherent imaging artifacts from multiples more effectively. We also show that, by curvelet-domain sparsity promoting and occasionally drawing new data samples during the inversion, the proposed inversion method gains improved robustness to velocity errors in the background model, as well as modelling errors incurred during linearization of the wave-equation. To combine the information encoded in both the primaries and the multiples, we then propose a highly accurate source estimation method to jointly invert the total upgoing wavefield. We show with field data examples that we can reap benefits from both the relative noise-free primaries and the extra illumination coverage of the multiples. We also demonstrate that the inclusion of multiples help mitigate the amplitude ambiguity during source estimation. We conclude the thesis with an outlook for future research directions, as well as potential extensions of the proposed work.},
	keywords = {inversion, least-squares, multiples, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis_pres.pdf},
	author = {Ning Tu}
}
@conference {tu2015PIMSsls,
	title = {Sparse least-squares seismic imaging with source estimation utilizing multiples},
	booktitle = {PIMS Workshop on Advances in Seismic Imaging and Inversion},
	year = {2015},
	note = {(PIMS Workshop on Advances in Seismic Imaging and Inversion, University of Alberta, Edmonton)},
	month = {05},
	abstract = {We present an least-squares seismic imaging method that (1) is efficient by subsampling the monochromatic source experiments; (2) does not require the prior knowledge of the source wavelet, by inverting for the seismic image and the source wavelet simultaneously using variable projection; and (3) makes active use of surface-related multiples to increase the illumination and to resolve the scaling ambiguity in source estimation, by tightly integrating the well-established surface-related-multiple-prediction into the wave-equation based modelling. As a result, we are able to obtain ambiguity-resolved, high-fidelity least-squares inverted seismic images with computational costs that are comparable to conventional reverse-time migrations with all the data. We demonstrate the efficacy of the proposed method using synthetic examples.},
	keywords = {inversion, least-squares migration, multiples, PIMS, seismic imaging, source estimation, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/PIMS/2015/tu2015PIMSsls/tu2015PIMSsls_pres.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@mastersthesis {li2015THsps,
	title = {Sparsity promoting seismic imaging and full-waveform inversion},
	year = {2015},
	note = {(PhD)},
	month = {07},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis will address the large computational costs of solving least-squares migration and full-waveform inversion problems. Least-squares seismic imaging and full-waveform inversion are seismic inversion techniques that require iterative minimizations of large least-squares misfit functions. Each iteration requires an evaluation of the Jacobian operator and its adjoint, both of which require two wave-equation solves for all sources, creating prohibitive computational costs. In order to reduce costs, we utilize randomized dimensionality reduction techniques, reducing the number of sources used during inversion. The randomized dimensionality reduction techniques create subsampling related artifacts, which we mitigate by using curvelet-domain sparsity-promoting inversion techniques. Our method conducts least-squares imaging at the approximate cost of one reverse-time migration with all sources, and computes the Gauss-Newton full-waveform inversion update at roughly the cost of one gradient update with all sources. Finally, during our research of the full-waveform inversion problem, we discovered that we can utilize our method as an alternative approach to add sparse constraints on the entire velocity model by imposing sparsity constraints on each model update separately, rather than regularizing the total velocity model as typically practiced. We also observed this alternative approach yields a faster decay of the residual and model error as a function of iterations. We provided empirical arguments why and when imposing sparsity on the updates can lead to improved full-waveform inversion results.},
	keywords = {Full-waveform inversion, Gauss-Newton method, least-squares imaging, seismic imaging, sparsity promoting},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps_pres.pdf},
	author = {Xiang Li}
}
@conference {herrmann2012SSPamp,
	title = {Approximate message passing meets exploration seismology},
	booktitle = {2012 IEEE Statistical Signal Processing Workshop (SSP) (SSP{\textquoteright}12)},
	year = {2012},
	month = {03},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Ann Arbor, Michigan, USA},
	abstract = {Data collection, data processing, and imaging in exploration seismology increasingly hinge on large-scale sparsity promoting solvers to remove artifacts caused by efforts to reduce costs. We show how the inclusion of a {\textquoteright}message term{\textquoteright} in the calculation of the residuals improves the convergence of these iterative solvers by breaking correlations that develop between the model iterate and the linear system that needs to be inverted. We compare this message-passing scheme to state-of-the-art solvers for problems in missing-trace interpolation and in dimensionality-reduced imaging with phase en- coding.},
	keywords = {Compressive Sensing, Exploration seismology, seismic imaging, transform-domain sparsity promotion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SSP/2012/herrmann2012SSPamp/herrmann2012SSPamp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SSP/2012/herrmann2012SSPamp/herrmann2012SSPamp_pres.pdf},
	author = {Felix J. Herrmann}
}
@techreport {vanleeuwen2012smii,
	title = {A parallel matrix-free framework for frequency-domain seismic modelling, imaging and inversion in Matlab},
	number = {TR-EOAS-2012-5},
	year = {2012},
	month = {07},
	abstract = {I present a parallel matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The framework provides basic building blocks for designing and testing optimization-based formulations of both linear and non-linear seismic in- verse problems. By overloading standard linear-algebra operations, such as matrix-vector multiplications, standard optimization packages can be used to work with the code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. I present some numerical examples on both linear and non-linear seismic inverse problems.},
	keywords = {Matlab, object-oriented programming, Optimization, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012smii/vanleeuwen2012smii.pdf},
	author = {Tristan van Leeuwen}
}
