@article {orozco2024IPaspire,
	title = {ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems},
	journal = {Inverse Problems},
	volume = {41},
	year = {2025},
	note = {(Inverse Problems)},
	month = {3},
	abstract = {Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances in machine learning and variational inference (VI) have lowered the computational barrier by learning from examples. Two VI paradigms have emerged that represent different tradeoffs: amortized and non-amortized. Amortized VI can produce fast results but due to generalizing to many observed datasets it produces suboptimal inference results. Non-amortized VI is slower at inference but finds better posterior approximations since it is specialized towards a single observed dataset. Current amortized VI techniques run into a sub-optimality wall that can not be improved without more expressive neural networks or extra training data. We present a solution that enables iterative improvement of amortized posteriors that uses the same networks architectures and training data. The benefits of our method requires extra computations but these remain frugal since they are based on physics-hybrid methods and summary statistics. Importantly, these computations remain mostly offline thus our method maintains cheap and reusable online evaluation while bridging the approximation gap these two paradigms. We denote our proposed method ASPIRE - Amortized posteriors with Summaries that are Physics-based and Iteratively REfined. We first validate our method on a stylized problem with a known posterior then demonstrate its practical use on a high-dimensional and nonlinear transcranial medical imaging problem with ultrasound. Compared with the baseline and previous methods from the literature our method stands out as an computationally efficient and high-fidelity method for posterior inference.},
	keywords = {Amortization Gap, Amortized Variational Inference, Bayesian inference, medical imaging, Normalizing flows, simulation-based inference},
	doi = {10.1088/1361-6420/adba3d},
	url = {https://doi.org/10.1088/1361-6420/adba3d},
	author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@article {orozco2023invnet,
	title = {InvertibleNetworks.jl: A Julia package for scalable normalizing flows},
	journal = {Journal of Open Source Software},
	volume = {9},
	year = {2024},
	month = {7},
	abstract = {InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging the inherent invertibility of normalizing flows, which significantly reduces memory requirements during backpropagation compared to existing normalizing flow packages that rely on automatic differentiation frameworks. InvertibleNetworks.jl has been adapted for diverse applications, including seismic imaging, medical imaging, and CO2 monitoring, demonstrating its effectiveness in learning high-dimensional distributions.},
	keywords = {Bayesian inference, computing, conditional normalizing flows, deep learning, HPC, Inverse problems, memory, Normalizing flows, software, Uncertainty quantification},
	doi = {10.21105/joss.06554},
	url = {https://doi.org/10.21105/joss.06554},
	author = {Rafael Orozco and Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@article {yin2024tfp,
	title = {Time-lapse full-waveform permeability inversion: a feasibility study},
	journal = {The Leading Edge},
	volume = {43},
	year = {2024},
	note = {(The Leading Edge)},
	month = {8},
	abstract = {Time-lapse seismic monitoring necessitates integrated workflows that combine seismic and reservoir modeling to enhance reservoir property estimation. We present a feasibility study of an end-to-end inversion framework that directly inverts for permeability from prestack time-lapse seismic data. To assess the method{\textquoteright}s robustness, we design experiments focusing on its sensitivity to initial models and potential errors in modeling. Our study leverages the Compass model to simulate CO2 storage in saline aquifers, which is derived from well and seismic data from the North Sea, a candidate site for geological carbon storage.},
	keywords = {4D, CCS, coupled inversion, end-to-end, fluid-flow, GCS, inversion, monitoring, time-lapse},
	doi = {10.1190/tle43080544.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2024/yin2024tfp/paper.html},
	author = {Ziyi Yin and Mathias Louboutin and Olav M{\o}yner and Felix J. Herrmann}
}
@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}
}
@article {yin2022TLEdgc,
	title = {Derisking geologic 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}
}
@article {louboutin2023lmi,
	title = {Learned multiphysics inversion with differentiable programming and machine learning},
	journal = {The Leading Edge},
	volume = {42},
	year = {2023},
	note = {(The Leading Edge)},
	month = {07},
	pages = {452-516},
	abstract = {We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Imaging, inversion, invertible networks, machine learning, monitoring, multiphysics, Normalizing flows, SLIM, software, time-lapse},
	url = {https://library.seg.org/doi/10.1190/tle42070474.1},
	presentation = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.html},
	author = {Mathias Louboutin and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Olav M{\o}yner and Gerard J. Gorman and Felix J. Herrmann}
}
@article {grady2022SCtll,
	title = {Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs},
	journal = {Computers \& Geosciences},
	volume = {178},
	year = {2023},
	note = {(Computers and Geosciences)},
	month = {07},
	pages = {105402},
	abstract = {Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. We demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO2 dynamics in the Earth{\textquoteright}s subsurface.},
	keywords = {CCS, Computers and Geosciences, deep learning, Fourier neural operators, HPC, large-scale, Model Parallelism, Multiphase Flow, Operator Learning},
	doi = {10.1016/j.cageo.2023.105402},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ComputersAndGeosciences/2023/grady2022SCtll/grady2022SCtll.pdf},
	software = {https://github.com/slimgroup/dfno},
	author = {Thomas J. Grady II and Rishi Khan and Mathias Louboutin and Ziyi Yin and Philipp A. Witte and Ranveer Chandra and Russell J. Hewett and Felix J. Herrmann}
}
@article {zhang2023otl,
	title = {Optimized time-lapse acquisition design via spectral gap ratio minimization},
	journal = {Geophysics},
	volume = {88},
	number = {4},
	year = {2023},
	note = {(Geophysics)},
	month = {07},
	pages = {A19-A23},
	abstract = {Modern-day reservoir management and monitoring of geological carbon storage increasingly call for costly time-lapse seismic data collection. In this letter, we show how techniques from graph theory can be used to optimize acquisition geometries for low-cost sparse 4D seismic. Based on midpoint-offset domain connectivity arguments, the proposed algorithm automatically produces sparse non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
	keywords = {Acquisition, JRM, matrix factorization, spectral gap, survey design, time-lapse, wavefield reconstruction},
	doi = {10.1190/geo2023-0024.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/zhang2023otl/Spectral_Gap_Paper.html},
	author = {Yijun Zhang and Ziyi Yin and Oscar Lopez and Ali Siahkoohi and Mathias Louboutin and Rajiv Kumar and Felix J. Herrmann}
}
@article {yin2023smi,
	title = {Solving multiphysics-based inverse problems with learned surrogates and constraints},
	journal = {Advanced Modeling and Simulation in Engineering Sciences},
	volume = {10},
	year = {2023},
	note = {(Advanced Modeling and Simulation in Engineering Sciences)},
	month = {10},
	abstract = {Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.},
	keywords = {AMSES, deep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows},
	doi = {10.1186/s40323-023-00252-0},
	url = {https://doi.org/10.1186/s40323-023-00252-0},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/AMSES/2023/yin2023smi/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@article {lopez2020gsb,
	title = {Spectral Gap-Based Seismic Survey Design},
	journal = {IEEE Transactions on Geoscience and Remote Sensing},
	year = {2023},
	month = {1},
	abstract = {Seismic imaging in challenging sedimentary basins and reservoirs requires acquiring, processing, and imaging very large volumes of data (tens of terabytes). To reduce the cost of acquisition and the time from acquiring the data to producing a subsurface image, novel acquisition systems based on compressive sensing, low-rank matrix recovery, and randomized sampling have been developed and implemented. These approaches allow practitioners to achieve dense wavefield reconstruction from a substantially reduced number of field samples. However, designing acquisition surveys suited for this new sampling paradigm remains a critical and challenging role in oil, gas, and geothermal exploration. Typical random designs studied in the low-rank matrix recovery and compressive sensing literature are difficult to achieve by standard industry hardware. For practical purposes, a compromise between stochastic and realizable samples is needed. In this paper, we propose a deterministic and computationally cheap tool to alleviate randomized acquisition design, prior to survey deployment and large-scale optimization. We consider universal and deterministic matrix completion results in the context of seismology, where a bipartite graph representation of the source-receiver layout allows for the respective spectral gap to act as a quality metric for wavefield reconstruction. We provide realistic scenarios to demonstrate the utility of the spectral gap as a flexible tool that can be incorporated into existing survey design workflows for successful seismic data acquisition via low-rank and sparse signal recovery.},
	keywords = {biadjacency matrix, bipartite graph, Compressive Sensing, IEEE, low rank matrix completion, nuclear norm minimization, seismic data, seismic trace interpolation, spectral gap},
	doi = {10.1109/TGRS.2023.3237464},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETGRS/2023/lopez2020gsb/lopez2020gsb.pdf},
	author = {Oscar Lopez and Rajiv Kumar and Nick Moldoveanu 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}
}
@article {kukreja2020lcc,
	title = {Lossy Checkpoint Compression in Full Waveform Inversion},
	journal = {Geoscientific Model Development},
	volume = {15},
	number = {9},
	year = {2022},
	note = {(Geoscientific Model Development)},
	month = {5},
	pages = {3815-3829},
	abstract = {This paper proposes a new method that combines check-pointing methods with error-controlled lossy compression for large-scale high-performance Full-Waveform Inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the Exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory footprint during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.},
	keywords = {checkpointing, full waveform inversion, GMD, Lossy compression, memory},
	doi = {10.5194/gmd-15-3815-2022},
	url = {https://arxiv.org/pdf/2009.12623.pdf},
	author = {Navjot Kukreja and Jan Hueckelheim and Mathias Louboutin and John Washbourne and Paul H. J. Kelly and Gerard J. Gorman}
}
@article {rizzuti2020dfw,
	title = {A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion},
	journal = {Geophysics},
	volume = {86},
	number = {6},
	year = {2021},
	note = {(Geophysics)},
	month = {10},
	pages = {1ND-Z3},
	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 = {3D, finite-difference, Full-waveform inversion, wave equation},
	doi = {10.1190/geo2020-0743.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2021/rizzuti2020dfw/rizzuti2020dfw.html},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@article {luporini2018aap,
	title = {Architecture and performance of Devito, a system for automated stencil computation},
	journal = {ACM Trans. Math. Softw.},
	volume = {46},
	number = {1},
	year = {2020},
	note = {(ACM Trans. Math. Softw.)},
	month = {04},
	abstract = {Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of generating highly-optimized code given symbolic equations expressed in Python, specialized in, but not limited to, affine (stencil) codes. The lowering process {\textendash} from mathematical equations down to C++ code {\textendash} is performed by the Devito compiler through a series of intermediate representations. Several performance optimizations are introduced, including advanced common sub-expressions elimination, tiling and parallelization. Some of these are obtained through well-established stencil optimizers, integrated in the back-end of the Devito compiler. The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented. The effectiveness of such performance optimizations is demonstrated using operators drawn from seismic imaging applications.},
	keywords = {compiler, finite difference method, performance optimization, stencil, structured grid, symbolic processing},
	doi = {10.1145/3374916},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ACMTOMS/2020/luporini2018aap/luporini2018aap.pdf},
	author = {Fabio Luporini and Mathias Louboutin and Michael Lange and Navjot Kukreja and Philipp A. Witte and Jan H{\"u}ckelheim and Charles Yount and Paul H. J. Kelly and Felix J. Herrmann and Gerard J. Gorman}
}
@article {witte2019TPDedas,
	title = {An Event-Driven Approach to Serverless Seismic Imaging in the Cloud},
	journal = {IEEE Transactions on Parallel and Distributed Systems},
	volume = {31},
	number = {9},
	year = {2020},
	note = {(IEEE Transactions on Parallel and Distributed Systems)},
	month = {03},
	pages = {2032-2049},
	abstract = {Adapting the cloud for high-performance computing (HPC) is a challenging task, as software for HPC applications hinges on fast network connections and is sensitive to hardware failures. Using cloud infrastructure to recreate conventional HPC clusters is therefore in many cases an infeasible solution for migrating HPC applications to the cloud. As an alternative to the generic lift and shift approach, we consider the specific application of seismic imaging and demonstrate a serverless and event-driven pproach for running large-scale instances of this problem in the cloud. Instead of permanently running compute instances, our workflow is based on a serverless architecture with high throughput batch computing and event-driven computations, in which computational resources are only running as long as they are utilized. We demonstrate that this approach is very flexible and allows for resilient and nested levels of parallelization, including domain decomposition for solving the underlying partial differential equations. While the event-driven approach introduces some overhead as computational resources are repeatedly restarted, it inherently provides resilience to instance shut-downs and allows a significant reduction of cost by avoiding idle instances, thus making the cloud a viable alternative to on-premise clusters for large-scale seismic imaging.},
	keywords = {cloud, event-driven, Imaging, LSRTM, serverless},
	doi = {10.1109/TPDS.2020.2982626},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETPDS/2020/witte2019TPDedas/witte2019TPDedas.html},
	author = {Philipp A. Witte and Mathias Louboutin and Henryk Modzelewski and Charles Jones and James Selvage and Felix J. Herrmann}
}
@article {kukreja2019PASCccd,
	title = {Combining checkpointing and data compression to accelerate adjoint-based optimization problems},
	journal = {Euro-Par 2019: Parallel Processing},
	year = {2019},
	note = {(Euro-Par 2019: Parallel Processing)},
	pages = {87-100},
	publisher = {Springer International Publishing},
	abstract = {Seismic inversion and imaging are adjoint-based optimization problems that processes up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory requirement by a certain factor, particularly if some loss in accuracy is acceptable. A popular alternative is checkpointing, where data is stored at selected points in time, and values at other times are recomputed as needed from the last stored state. This allows arbitrarily large adjoint computations with limited memory, at the cost of additional recomputations. In this paper we combine compression and checkpointing for the first time to compute a realistic seismic inversion. The combination of checkpointing and compression allows larger adjoint computations compared to using only compression, and reduces the recomputation overhead significantly compared to using only checkpointing.},
	keywords = {Adjoint-state, checkpointing, compression, FD, HPC, Inverse problems},
	doi = {10.1007/978-3-030-29400-7_7},
	url = {https://slim.gatech.edu/Publications/Public/Journals/PASC/2019/kukreja2019PASCccd/kukreja2019PASCccd.pdf},
	author = {Navjot Kukreja and Jan H{\"u}ckelheim and Mathias Louboutin and Paul Hovland and Gerard Gorman}
}
@article {witte2018cls,
	title = {Compressive least-squares migration with on-the-fly Fourier transforms},
	journal = {Geophysics},
	volume = {84},
	number = {5},
	year = {2019},
	note = {(Geophysics)},
	month = {08},
	pages = {R655-R672},
	abstract = {Least-squares reverse-time migration is a powerful approach for true amplitude seismic imaging of complex geological structures, but the successful application of this method is currently hindered by its enormous computational cost, as well as high memory requirements for computing the gradient of the objective function. We tackle these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration using on-the-fly Fourier transforms. We formulate the least-squares migration objective function in the frequency domain and compute gradients for randomized subsets of shot records and frequencies, thus significantly reducing data movement and the number of overall wave equations solves. By using on-the-fly Fourier transforms, we can compute an arbitrary number of monochromatic frequency-domain wavefields with a time-domain modeling code, instead of having to solve individual Helmholtz equations for each frequency, which quickly becomes computationally infeasible when moving to high frequencies. Our numerical examples demonstrate that compressive imaging with on-the-fly Fourier transforms provides a fast and memory-efficient alternative to time-domain imaging with optimal checkpointing, whose memory requirements for a fixed background model and source wavelet is independent of the number of time steps. Instead, memory and additional computational cost grow with the number of frequencies and determine the amount of subsampling artifacts and crosstalk. In contrast to optimal checkpointing, this offers the possibility to trade both memory and computational cost for image quality or a larger number of iterations and is advantageous in new computing environments such as the cloud, where compute is often cheaper than memory and data movement.},
	keywords = {Fourier, least squares migration, sparsity-promotion},
	doi = {10.1190/geo2018-0490.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/witte2018cls/witte2018cls.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Fabio Luporini and Gerard J. Gorman and Felix J. Herrmann}
}
@article {louboutin2018dae,
	title = {Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration},
	journal = {Geoscientific Model Development},
	year = {2019},
	note = {(Geoscientific Model Development)},
	abstract = {We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform Inversion and Reverse-Time Migration are used to invert terabytes of seismic data to create images of the earth{\textquoteright}s subsurface. Even using modern supercomputers, it can take weeks to process a single seismic survey and create a useful subsurface image. The computational cost is dominated by the numerical solution of wave equations and their corresponding adjoints. Therefore, a great deal of effort is invested in aggressively optimizing the performance of these wave-equation propagators for different computer architectures. Additionally, the actual set of partial differential equations being solved and their numerical discretization is under constant innovation as increasingly realistic representations of the physics are developed, further ratcheting up the cost of practical solvers. By embedding a domain-specific language within Python and making heavy use of SymPy, a symbolic mathematics library, we make it possible to develop finite difference simulators quickly using a syntax that strongly resembles the mathematics. The Devito compiler reads this code and applies a wide range of analysis to generate highly optimized and parallel code. This approach can reduce the development time of a verified and optimized solver from months to days.},
	keywords = {finite-differences, HPC, Modeling, wave-equation},
	doi = {10.5194/gmd-12-1165-2019},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GMD/2019/louboutin2018dae/louboutin2018dae.pdf},
	author = {Mathias Louboutin and Michael Lange and Fabio Luporini and Navjot Kukreja and Philipp A. Witte and Felix J. Herrmann and Paulius Velesko and Gerard J. Gorman}
}
@article {witte2019ecl,
	title = {Geophysics Bright Spots: Efficient coding of large-scale seismic inversion algorithms},
	journal = {The Leading Edge},
	volume = {38},
	number = {6},
	year = {2019},
	note = {(The Leading Edge)},
	pages = {482-484},
	abstract = {In {\textquotedblleft}A large-scale framework for symbolic implementations of seismic inversion algorithms in Julia,{\textquotedblright} Witte et al. describe new developments in how to code complex geophysical algorithms in a concise way. Subsurface seismic imaging and parameter estimation are among the most computationally challenging problems in the scientific community. Codes for solving seismic inverse problems, such as FWI or least-squares reverse time migration (LS-RTM), need to be highly optimized, but at the same time, facilitate the implementation of complex optimization algorithms. Traditionally, production-level codes in the oil and gas industry were exclusively written in low-level languages, such as C or Fortran, with extensive amounts of manual performance optimizations, thus making code maintenance, debugging, and adoption of new algorithms prohibitively challenging. Witte et al. present a paradigm of software engineering for seismic inverse problems based on symbolic user interfaces and code generation with automated performance optimization. Inspired by recent deep learning frameworks, the Julia Devito inversion framework (JUDI; an open-source software package) combines high-level abstractions for expressing seismic inversion algorithms with a domain-specific language compiler called Devito for solving the underlying wave equations. Devito{\textquoteright}s generated code is compiled just in time and outperforms codes with manual performance optimizations. JUDI utilizes Julia{\textquoteright}s high-level parallelization, making the software easily adaptable to a variety of computing environments such as densely connected HPC clusters or the cloud. The numerical examples (Figure 3) demonstrate the ability to implement a variety of complex algorithms for FWI and LS-RTM in a few lines of Julia code and run it on large-scale 3D models. The paper concludes that abstractions and performance are not mutually exclusive, and use of symbolic user interfaces can facilitate the implementation of new and innovative seismic inversion algorithms.},
	keywords = {bright spots, inversion, Julia, large-scale},
	doi = {10.1190/tle38060482.1},
	url = {https://library.seg.org/doi/10.1190/tle38060482.1},
	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 {siahkoohi2019itl,
	title = {The importance of transfer learning in seismic modeling and imaging},
	journal = {Geophysics},
	year = {2019},
	note = {(GEOPHYSICS)},
	abstract = {Accurate forward modeling is essential for solving inverse problems in exploration seismology. Unfortunately, it is often not possible to afford being physically or numerically accurate. To overcome this conundrum, we make use of raw and processed data from nearby surveys. We propose to use this data, consisting of shot records or velocity models, to pre-train a neural network to correct for the effects of, for instance, the free surface or numerical dispersion, both of which can be considered as proxies for incomplete or inaccurate physics. Given this pre-trained neural network, we apply transfer learning to finetune this pre-trained neural network so it performs well on its task of mapping low-cost, but low-fidelity, solutions to high-fidelity solutions for the current survey. As long as we can limit ourselves during finetuning to using only a small fraction of high-fidelity data, we gain processing the current survey while using information from nearby surveys. We demonstrate this principle by removing surface-related multiples and ghosts from shot records and the effects of numerical dispersion from migrated images and wave simulations},
	keywords = {deep learning, Imaging, Modeling, SRME, transfer learning},
	doi = {10.1190/geo2019-0056.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/siahkoohi2019itl/siahkoohi2019itl.html},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@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}
}
@article {liu2018ssi,
	title = {Simultaneous-shot inversion for PDE-constrained optimization problems with missing data},
	journal = {Inverse Problems},
	volume = {35},
	number = {2},
	year = {2018},
	note = {(Inverse Problems)},
	pages = {025003},
	abstract = {Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using {\textquoteleft}simultaneous shots{\textquoteright}, or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach.},
	keywords = {Full-waveform inversion, low-rank interpolation, Optimization},
	doi = {10.1088/1361-6420/aaf317},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2018/liu2018ssi/liu2018ssi.pdf},
	author = {Michelle Liu and Rajiv Kumar and Eldad Haber and Aleksandr Y. Aravkin}
}
@article {kumar2016bls,
	title = {Beating level-set methods for 5D seismic data interpolation: a primal-dual alternating approach},
	journal = {IEEE Transactions on Computational Imaging},
	year = {2017},
	note = {(published online in IEEE Transactions on Computational Imaging)},
	month = {04},
	abstract = {Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to {\textquoteright}fill in{\textquoteright} data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques. Residual-constrained formulations require less parameter tuning when the target noise floor is known. We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume in a compressed manner using low-rank matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The develop optimization framework works on the whole seismic temporal frequency slices and does not require windowing or non-trivial sorting of seismic data. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5D seismic data volume (upto 1010 data-points), generated from the geologically complex synthetic 3D Compass velocity model, where 80\% of the data has been removed. We also develop a robust extension of the primal-dual approach to deal with the outliers (or noise) in the data.},
	keywords = {alternating minimization, matrix completion, primal-dual splitting, seismic data, seismic trace interpolation},
	doi = {10.1109/TCI.2017.2693966},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransComputationalImaging/2017/kumar2016bls/kumar2016bls.pdf},
	author = {Rajiv Kumar and Oscar Lopez and Damek Davis and Aleksandr Y. Aravkin 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}
}
@article {louboutin2016ppf,
	title = {Performance prediction of finite-difference solvers for different computer architectures},
	journal = {Computers \& Geosciences},
	volume = {105},
	year = {2017},
	note = {(Computers \& Geosciences)},
	month = {08},
	pages = {148-157},
	abstract = {The life-cycle of a partial differential equation (PDE) solver is often characterized by three development phases: the development of a stable numerical discretization; development of a correct (verified) implementation; and the optimization of the implementation for different computer architectures. Often it is only after significant time and effort has been invested that the performance bottlenecks of a PDE solver are fully understood, and the precise details varies between different computer architectures. One way to mitigate this issue is to establish a reliable performance model that allows a numerical analyst to make reliable predictions of how well a numerical method would perform on a given computer architecture, before embarking upon potentially long and expensive implementation and optimization phases. The availability of a reliable performance model also saves developer effort as it both informs the developer on what kind of optimisations are beneficial, and when the maximum expected performance has been reached and optimisation work should stop. We show how discretization of a wave-equation can be theoretically studied to understand the performance limitations of the method on modern computer architectures. We focus on the roofline model, now broadly used in the high-performance computing community, which considers the achievable performance in terms of the peak memory bandwidth and peak floating point performance of a computer with respect to algorithmic choices. A first principles analysis of operational intensity for key time-stepping finite-difference algorithms is presented. With this information available at the time of algorithm design, the expected performance on target computer systems can be used as a driver for algorithm design.},
	keywords = {finite differences, HPC, Modeling, performance},
	doi = {https://doi.org/10.1016/j.cageo.2017.04.014},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ComputersAndGeosciences/2016/louboutin2016ppf/louboutin2016ppf.pdf},
	author = {Mathias Louboutin and Michael Lange and Felix J. Herrmann and Navjot Kukreja and Gerard Gorman}
}
@article {lin2015scatterEPSI,
	title = {Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps},
	journal = {Geophysics},
	volume = {81},
	number = {3},
	year = {2016},
	note = {(Geophysics)},
	month = {05},
	pages = {V183-V197},
	abstract = {We propose to solve the Estimation of Primaries by Sparse Inversion problem without any explicit data reconstruction, from a seismic record with missing near-offsets and large holes in the acquisition grid which does not produce aliasing but otherwise causes large errors in the multiple prediction. Exclusion of the unknown data as an inversion variable from the process is desirable, since it sidesteps possible issues arising from fitting observations that are also unknowns in the same inversion problem. Instead, we simulate their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the confines of the unobserved trace locations. Each term in this scattering series simply involves convolution of the predicted wavefield once more with the current estimated surface-free Green{\textquoteright}s function at these unobserved locations. We investigate the necessary modifications to the primary estimation algorithm to account for the resulting nonlinearity in the modeling operator, and also demonstrate that just a few scattering terms are enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data show that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps. This is achieved with a similar computational cost and better memory efficiency compared to explicit data reconstruction. We also show on real data that our scheme outperforms pre-interpolation of the near-offset gap.},
	keywords = {EPSI, multiples, Optimization, REPSI, scattering, sparsity},
	doi = {10.1190/geo2015-0263.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2016/lin2015scatterEPSI/lin2015scatterEPSI.html},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@article {li2015GEOPmgn,
	title = {Modified Gauss-Newton full-waveform inversion explained{\textendash}-why sparsity-promoting updates do matter},
	journal = {Geophysics},
	volume = {81},
	number = {3},
	year = {2016},
	note = {(Geophysics)},
	month = {05},
	pages = {R125-R138},
	abstract = {Full-waveform inversion can be formulated as a nonlinear least-squares optimization problem. This non-convex problem can be extremely computationally expensive because it requires repeatedly solving large linear systems that correspond to discretized partial differential equations. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling weakens subsurface illumination and introduces subsampling related incoherent artifacts. These subsampling-related artifacts{\textendash}-in conjunction with local minima that are known to plague full-waveform inversion{\textendash}-motivate us to come up with a technique to "regularize" this problem. Following earlier work, we take advantage of the fact that curvelets represent subsurface models and perturbations parsimoniously. At first impulse promoting sparsity on the model directly seems the most natural way to proceed, but we will demonstrate that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. While constraining the one-norm of the descent directions does not change not change the underlying full-waveform inversion objective, the constrained model updates remain descent directions, remove subsampling-related artifacts and improve the overall inversion result. We empirically observe this phenomenon in situations where the different model updates occur at roughly the same locations in the curvelet domain. We further investigate and analyze this phenomenon, where nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including phase retrieval and full-waveform inversion. In all cases, we observe a faster decay of the residual and model error as a function of the number of iterations.},
	keywords = {Full-waveform inversion, Gauss-Newton method, sparsity promotion},
	doi = {10.1190/geo2015-0266.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2016/li2015GEOPmgn/li2015GEOPmgn.pdf},
	author = {Xiang Li and Ernie Esser and Felix J. Herrmann}
}
@article {lopez2015IEEEogl,
	title = {Off-the-grid low-rank matrix recovery and seismic data reconstruction},
	journal = {IEEE Journal of Selected Topics in Signal Processing},
	volume = {10},
	number = {4},
	year = {2016},
	note = {(IEEE Journal of Selected Topics in Signal Processing)},
	month = {06},
	pages = {658-671},
	abstract = {Matrix sensing problems capitalize on the knowledge that a data matrix of interest exhibits low rank properties. This low dimensional structure often arises because the data matrix is obtained by sampling a smooth function on a regular (or structured) grid. However, in many practical situations the measurements are taken on an irregular grid (that is accurately known). This results in an "unstructured data matrix" that is less fit for the low rank model in comparison to its regular counterpart and therefore subject to degraded reconstruction via rank penalization techniques. In this paper, we propose and analyze a modified low-rank matrix recovery work-flow that admits unstructured observations. By incorporating a regularization operator which accurately maps structured data to unstructured data, into the nuclear-norm minimization problem, we are able to compensate for data irregularity. Furthermore, by construction our formulation yields output that is supported on a structured grid. We establish recovery error bounds for our methodology and offer matrix sensing and matrix completion numerical experiments including applications to seismic trace interpolation to demonstrate the potential of the approach.},
	keywords = {data regularization, matrix completion, matrix sensing, nonuniform discrete Fourier transform, nuclear-norm relaxation, seismic data, seismic trace interpolation},
	doi = {10.1109/JSTSP.2016.2555482},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEESignalProcessingMagazine/2016/lopez2015IEEEogl/lopez2015IEEEogl.pdf},
	url2 = {http://ieeexplore.ieee.org/xpl/login.jsp?tp=\&arnumber=7454674},
	author = {Oscar Lopez and Rajiv Kumar and Ozgur Yilmaz 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}
}
@article {herrmann2013TLEffwi,
	title = {Frugal full-waveform inversion: from theory to a practical algorithm},
	journal = {The Leading Edge},
	volume = {32},
	number = {9},
	year = {2013},
	month = {09},
	pages = {1082-1092},
	abstract = {As conventional oil and gas fields are maturing, our profession is challenged to come up with the next-generation of more and more sophisticated exploration tools. In exploration seismology this trend has led to the emergence of wave-equation based inversion technologies such as reverse-time migration and full-waveform inversion. While significant progress has been made in wave-equation based inversion, major challenges remain in the development of robust and computationally feasible workflows that give reliable results in geophysically challenging areas that may include ultra-low shear velocity zones or high-velocity salt. Moreover, sub-salt production carries risks that needs mitigation, which raises the bar from creating sub-salt images to inverting for sub-salt overpressure.},
	keywords = {Optimization, waveform inversion},
	doi = {10.1190/tle32091082.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2013/herrmann2013ffwi/herrmann2013ffwi.html},
	author = {Felix J. Herrmann and 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}
}
@article {lin2013GEOPrepsi,
	title = {Robust estimation of primaries by sparse inversion via one-norm minimization},
	journal = {Geophysics},
	volume = {78},
	number = {3},
	year = {2013},
	month = {05},
	pages = {R133-R150},
	abstract = {A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm.},
	keywords = {algorithm, biconvex, EPSI, multiples, Optimization, Pareto, sparsity, waveform inversion},
	doi = {10.1190/geo2012-0097.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/lin2013GEOPrepsi/lin2013GEOPrepsi.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@article {herrmann11GPelsqIm,
	title = {Efficient least-squares imaging with sparsity promotion and compressive sensing},
	journal = {Geophysical Prospecting},
	volume = {60},
	number = {4},
	year = {2012},
	month = {07},
	pages = {696-712},
	address = {University of British Columbia, Vancouver},
	abstract = {Seismic imaging is a linearized inversion problem relying on the minimization of a least-squares misfit functional as a function of the medium perturbation. The success of this procedure hinges on our ability to handle large systems of equations{\textendash}-whose size grows exponentially with the demand for higher resolution images in more and more complicated areas{\textendash}-and our ability to invert these systems given a limited amount of computational resources. To overcome this "curse of dimensionality" in problem size and computational complexity, we propose a combination of randomized dimensionality-reduction and divide-and-conquer techniques. This approach allows us to take advantage of sophisticated sparsity-promoting solvers that work on a series of smaller subproblems each involving a small randomized subset of data. These subsets correspond to artificial simultaneous-source experiments made of random superpositions of sequential-source experiments. By changing these subsets after each subproblem is solved, we are able to attain an inversion quality that is competitive while requiring fewer computational, and possibly, fewer acquisition resources. Application of this concept to a controlled series of experiments showed the validity of our approach and the relationship between its efficiency{\textendash}-by reducing the number of sources and hence the number of wave-equation solves{\textendash}-and the image quality. Application of our dimensionality-reduction methodology with sparsity promotion to a complicated synthetic with well-log constrained structure also yields excellent results underlining the importance of sparsity promotion.},
	keywords = {Compressive Sensing, Imaging, Optimization, SLIM},
	doi = {10.1111/j.1365-2478.2011.01041.x},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2012/herrmann11GPelsqIm/herrmann11GPelsqIm.pdf},
	url2 = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2011.01041.x/full},
	author = {Felix J. Herrmann and Xiang Li}
}
@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}
}
@article {Mansour11TRssma,
	title = {Randomized marine acquisition with compressive sampling matrices},
	journal = {Geophysical Prospecting},
	volume = {60},
	number = {4},
	year = {2012},
	month = {07},
	pages = {648-662},
	abstract = {Seismic data acquisition in marine environments is a costly process that calls for the adoption of simultaneous-source or randomized acquisition - an emerging technology that is stimulating both geophysical research and commercial efforts. Simultaneous marine acquisition calls for the development of a new set of design principles and post-processing tools. In this paper, we discuss the properties of a specific class of randomized simultaneous acquisition matrices and demonstrate that sparsity-promoting recovery improves the quality of reconstructed seismic data volumes. We propose a practical randomized marine acquisition scheme where the sequential sources fire airguns at only randomly time-dithered instances. We demonstrate that the recovery using sparse approximation from random time-dithering with a single source approaches the recovery from simultaneous-source acquisition with multiple sources. Established findings from the field of compressive sensing indicate that the choice of the sparsifying transform that is incoherent with the compressive sampling matrix can significantly impact the reconstruction quality. Leveraging these findings, we then demonstrate that the compressive sampling matrix resulting from our proposed sampling scheme is incoherent with the curvelet transform. The combined measurement matrix exhibits better isometry properties than other transform bases such as a non-localized multidimensional Fourier transform. We illustrate our results with simulations of "ideal" simultaneous-source marine acquisition, which dithers both in time and space, compared with periodic and randomized time-dithering.},
	keywords = {curvelet transform, Fourier, Marine acquisition},
	doi = {10.1111/j.1365-2478.2012.01075.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01075.x/abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2012/Mansour11TRssma/Mansour11TRssma.pdf},
	author = {Hassan Mansour and Haneet Wason and Tim T.Y. Lin and Felix J. Herrmann}
}
@article {herrmann2011RECORDERcsse1,
	title = {Compressive sensing in seismic exploration: an outlook on a new paradigm},
	journal = {CSEG Recorder},
	volume = {36},
	number = {4},
	year = {2011},
	note = {Part 1 was published in April and Part 2 was published in June},
	month = {04},
	pages = {19-33},
	abstract = {Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. While this approach has been extremely successful in the past, current efforts toward higher resolution images in increasingly complicated regions of the Earth continue to reveal fundamental shortcomings in our workflows. Chiefly amongst these is the so-called "curse of dimensionality" exemplified by Nyquist{\textquoteright}s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing towards seismic acquisition and processing for data that, from a traditional point of view, are considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are decoupled the stringent Nyquist sampling criterion. At the heart of our approach lies randomized incoherent sampling that breaks subsampling-related interferences by turning them into harmless noise, which we subsequently remove by promoting sparsity in a transform-domain. Acquisition schemes designed to fit into this regime no longer grow significantly in cost with increasing resolution and dimensionality of the survey area, but instead its cost ideally only depends on transform-domain sparsity of the expected data. Our contribution is split into two part.},
	url = {http://csegrecorder.com/articles/view/compressive-sensing-in-seismic-exploration-outlook-on-a-new-paradigm},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/CSEGRecorder/2011/herrmann2011RECORDERcsse/herrmann2011RECORDERcsse.pdf},
	author = {Felix J. Herrmann and Haneet Wason and Tim T.Y. Lin}
}
@article {herrmann2011RECORDERcsse2,
	title = {Compressive sensing in seismic exploration: an outlook on a new paradigm},
	journal = {CSEG Recorder},
	volume = {36},
	number = {6},
	year = {2011},
	note = {Part 1 was published in April and Part 2 was published in June},
	month = {06},
	pages = {34-39},
	abstract = {Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. While this approach has been extremely successful in the past, current efforts toward higher resolution images in increasingly complicated regions of the Earth continue to reveal fundamental shortcomings in our workflows. Chiefly amongst these is the so-called "curse of dimensionality" exemplified by Nyquist{\textquoteright}s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing towards seismic acquisition and processing for data that, from a traditional point of view, are considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are decoupled the stringent Nyquist sampling criterion. At the heart of our approach lies randomized incoherent sampling that breaks subsampling-related interferences by turning them into harmless noise, which we subsequently remove by promoting sparsity in a transform-domain. Acquisition schemes designed to fit into this regime no longer grow significantly in cost with increasing resolution and dimensionality of the survey area, but instead its cost ideally only depends on transform-domain sparsity of the expected data. Our contribution is twofold. First, we demonstrate by means of carefully designed numerical experiments that ideas from compressive sensing can be adapted to seismic acquisition. Second, we leverage the property that seismic data volumes are well approximated by a small percentage of curvelet coefficients. Thus curvelet-domain sparsity allows us to recover conventionally-sampled seismic data volumes from compressively-sampled data volumes whose size exceeds this percentage by only a small factor. Because compressive sensing combines transformation and encoding by a single linear encoding step, this technology is directly applicable to seismic acquisition and therefore constitutes a new paradigm where acquisitions costs scale with transform-domain sparsity instead of the gridsize. We illustrate this principle by showcasing recovery of a real seismic line from simulated compressively sampled acquisitions.},
	url = {http://csegrecorder.com/articles/view/compressive-sensing-in-seismic-exploration-an-outlook-on-a-new-paradigm},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/CSEGRecorder/2011/herrmann2011RECORDERcsse/herrmann2011RECORDERcsse.pdf},
	author = {Felix J. Herrmann and Haneet Wason and Tim T.Y. Lin}
}
@article {herrmann2009GEOPcsf,
	title = {Compressive simultaneous full-waveform simulation},
	journal = {Geophysics},
	volume = {74},
	number = {4},
	year = {2009},
	month = {07-08},
	pages = {A35-A40},
	abstract = {The fact that computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem{\textendash}-where simulated data is recovered from a relatively small number of independent simultaneous sources{\textendash}-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield{\textquoteright}s sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.},
	keywords = {Compressive Sensing, full-waveform, Modelling, SLIM},
	doi = {10.1190/1.3115122},
	url = {http://library.seg.org/doi/abs/10.1190/1.3115122},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcsf/herrmann2009GEOPcsf.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@article {lin2007GEOPcwe,
	title = {Compressed wavefield extrapolation},
	journal = {Geophysics},
	volume = {72},
	number = {5},
	year = {2007},
	month = {08},
	pages = {SM77-SM93},
	publisher = {SEG},
	abstract = {An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Modelling, SLIM, wave propagation},
	doi = {10.1190/1.2750716},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2007/lin07cwe/lin07cwe.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
