@conference {rizzuti2020SEGuqavp,
	title = {Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {1541-1545},
	abstract = {Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This analysis allows to assess the confidence in the candidate solution and how it is reflected in the tasks that are typically performed after imaging (e.g., stratigraphic segmentation following reservoir characterization). Classically, uncertainty comes in the form of a probability distribution formulated from Bayesian principles, from which we seek to obtain samples. A popular solution involves Monte Carlo sampling. Here, we propose instead an approach characterized by training a deep network that "pushes forward" Gaussian random inputs into the model space (representing, for example, density or velocity) as if they were sampled from the actual posterior distribution. Such network is designed to solve a variational optimization problem based on the Kullback-Leibler divergence between the posterior and the network output distributions. This work is fundamentally rooted in recent developments for invertible networks. Special invertible architectures, besides being computational advantageous with respect to traditional networks, do also enable analytic computation of the output density function. Therefore, after training, these networks can be readily used as a new prior for a related inversion problem. This stands in stark contrast with Monte-Carlo methods, which only produce samples. We validate these ideas with an application to angle-versus-ray parameter analysis for reservoir characterization.},
	keywords = {Full-waveform inversion, SEG, Uncertainty quantification},
	doi = {10.1190/segam2020-3428150.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Gabrio Rizzuti and Ali Siahkoohi and Philipp A. Witte and Felix J. Herrmann}
}
@conference {sharan2018SEGada,
	title = {A debiasing approach to microseismic},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {2942-2946},
	abstract = {Microseismic data is often used to locate fracture locations and their origin in time created by fracking. Although surface microseismic data can have large apertures and is easier to acquire than the borehole data, it often suffers from poor signal to noise ratio (S/R). Poor S/R poses a challenge in terms of estimating the correct location and source-time function of a microseismic source. In this work, we propose a denoising step in combination with a computationally cheap debiasing based approach to locate microseismic sources and to estimate their source-time functions with correct amplitude from extremely noisy data. Through numerical experiments, we demonstrate that our method can work with closely spaced microseismic sources with source-time functions of different peak amplitudes and frequencies. We have also shown the ability of our method with the smooth velocity model.},
	keywords = {Full-waveform inversion, Imaging, microseismic, noise, SEG, wave equation},
	doi = {10.1190/segam2018-2997252.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/sharan2018SEGada/sharan2018SEGada.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/sharan2018SEGada/sharan2018SEGada_pres.pdf},
	author = {Shashin Sharan and Rajiv Kumar and Rongrong Wang and Felix J. Herrmann}
}
@article {peters2018pmf,
	title = {Projection methods and applications for seismic nonlinear inverse problems with multiple constraints},
	journal = {Geophysics},
	volume = {84},
	number = {2},
	year = {2018},
	note = {(Geophysics)},
	month = {02},
	pages = {R251-R269},
	abstract = {Nonlinear inverse problems are often hampered by non-uniqueness and local minima because of missing low frequencies and far offsets in the data, lack of access to good starting models, noise, and modeling errors. A well-known approach to counter these deficiencies is to include prior information on the unknown model, which regularizes the inverse problem. While conventional regularization methods have resulted in enormous progress in ill-posed (geophysical) inverse problems, challenges remain when the prior information consists of multiple pieces. To handle this situation, we propose an optimization framework that allows us to add multiple pieces of prior information in the form of constraints. Compared to additive regularization penalties, constraints have a number of advantages making them more suitable for inverse problems such as full-waveform inversion. The proposed framework is rigorous because it offers assurances that multiple constraints are imposed uniquely at each iteration, irrespective of the order in which they are invoked. To project onto the intersection of multiple sets uniquely, we employ Dykstra{\textquoteright}s algorithm that scales to large problems and does not rely on trade-off parameters. In that sense, our approach differs substantially from approaches such as Tikhonov regularization, penalty methods, and gradient filtering. None of these offer assurances, which makes them less suitable to full-waveform inversion where unrealistic intermediate results effectively derail the iterative inversion process. By working with intersections of sets, we keep expensive objective and gradient calculations unaltered, separate from projections, and we also avoid trade-off parameters. These features allow for easy integration into existing code bases. In addition to more predictable behavior, working with constraints also allows for heuristics where we built up the complexity of the model gradually by relaxing the constraints. This strategy helps to avoid convergence to local minima that represent unrealistic models. We illustrate this unique feature with examples of varying complexity.},
	keywords = {constraints, Full-waveform inversion, intersection, Optimization, projection, regularization},
	doi = {10.1190/geo2018-0192.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/peters2018pmf/peters2018pmf.html},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {sharan2017SEGhrf,
	title = {High resolution fast microseismic source collocation and source time function estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {2778-2783},
	abstract = {Sparsity promotion based joint microseismic source collocation and source time function estimation, using Linearized Bregman algorithm, although simple to implement, suffers from slow convergence. This is due to the fact that Linearized Bregman algorithm has only first order of convergence. In this work, we propose to accelerate the existing Linearized Bregman algorithm using the L-BFGS algorithm. Without any initial guess for the source location or source time function, our method is able to estimate the source location and source time function for kinematically correct smooth velocity model. We demonstrate the effectiveness of our method for multiple sources spaced within half a wavelength. We also compare our results with Linearized Bregman based method in {\textquoteleft}{\textquoteleft}2.5{\textquoteleft}{\textquoteleft}D instead of {\textquoteleft}{\textquoteleft}2{\textquoteleft}{\textquoteleft}D.},
	keywords = {algorithm, Full-waveform inversion, microseismic, passive imaging, SEG, wave equation},
	doi = {10.1190/segam2017-17787749.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/sharan2017SEGhrf/sharan2017SEGhrf.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/sharan2017SEGhrf/sharan2017SEGhrf_pres.pdf},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@techreport {smithyman2014SEGjfw,
	title = {Joint full-waveform inversion of on-land surface and VSP data from the Permian Basin},
	number = {TR-EOAS-2014-4},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {Full-waveform Inversion is applied to generate a high-resolution model of P-wave velocity for a site in the Permian Basin, Texas, USA. This investigation jointly inverts seismic waveforms from a surface 3-D vibroseis surface seismic survey and a co-located 3-D Vertical Seismic Profiling (VSP) survey, which shared common source Vibration Points (VPs). The resulting velocity model captures features that were not resolvable by conventional migration velocity analysis.},
	keywords = {downhole receivers, Full-waveform inversion, land, seismic, vibroseis},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/smithyman2014SEGjfw/smithyman2014SEGjfw.html},
	author = {Brendan R. Smithyman and Bas Peters and Bryan DeVault and Felix J. Herrmann}
}
@conference {vanleeuwen2011EAGEhsdomwi,
	title = {A hybrid stochastic-deterministic optimization method for waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Present-day high quality 3D acquisition can give us lower frequencies and longer offsets with which to invert. However, the computational costs involved in handling this data explosion are tremendous. Therefore, recent developments in full-waveform inversion have been geared towards reducing the computational costs involved. A key aspect of several approaches that have been proposed is a dramatic reduction in the number of sources used in each iteration. A reduction in the number of sources directly translates to less PDE-solves and hence a lower computational cost. Recent attention has been drawn towards reducing the sources by randomly combining the sources in to a few supershots, but other strategies are also possible. In all cases, the full data misfit, which involves all the sequential sources, is replaced by a reduced misfit that is much cheaper to evaluate because it involves only a small number of sources (batchsize). The batchsize controls the accuracy with which the reduced misfit approximates the full misfit. The optimization of such an inaccurate, or noisy, misfit is the topic of stochastic optimization. In this paper, we propose an optimization strategy that borrows ideas from the field of stochastic optimization. The main idea is that in the early stage of the optimization, far from the true model, we do not need a very accurate misfit. The strategy consists of gradually increasing the batchsize as the iterations proceed. We test the proposed strategy on a synthetic dataset. We achieve a very reasonable inversion result at the cost of roughly 13 evaluations of the full misfit. We observe a speed-up of roughly a factor 20.},
	keywords = {EAGE, Full-waveform inversion, Optimization, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50341},
	author = {Tristan van Leeuwen and Felix J. Herrmann and Mark Schmidt and Michael P. Friedlander}
}
