@article {yin2023wise,
	title = {WISE: full-Waveform variational Inference via Subsurface Extensions},
	journal = {Geophysics},
	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 {moghaddam2013GEOPnoa,
	title = {A new optimization approach for source-encoding full-waveform inversion},
	journal = {Geophysics},
	volume = {78},
	number = {3},
	year = {2013},
	month = {05},
	pages = {R125-R132},
	abstract = {Waveform inversion is the method of choice for determining highly heterogeneous subsurface structure. However, conventional waveform inversion requires that the wavefield for each source is computed separately. This makes it very expensive for realistic 3D seismic surveys. Source-encoding waveform inversion, in which the sources are modelled simultaneously, is considerably faster than conventional waveform inversion but suffers from artifacts. These artifacts can partly be removed by assigning random weights to the source wavefields. We found that the misfit function, and therefore also its gradient, for source-encoding waveform inversion is an unbiased random estimation of the misfit function used in conventional waveform inversion. We found a new method of source-encoding waveform inversion which takes into account the random nature of the gradients used in the optimization. In this new method, the gradient at each iteration is a weighted average of past gradients such that the most recent gradients have the largest weights with exponential decay. This way we damped the random fluctuations of the gradient by incorporating information from the previous iterations. We compare this new method with existing source-encoding waveform inversion methods as well as conventional waveform inversion and found that the model misfit reduction is faster and smoother than those of existing source-encoding waveform inversion methods, and it approaches the model misfit reduction obtained in conventional waveform inversion.},
	keywords = {FWI, Geophysics, Optimization, source encoding},
	doi = {10.1190/GEO2012-0090.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/moghaddam2013GEOPnoa/moghaddam2013GEOPnoa.pdf},
	author = {Peyman P. Moghaddam and Henk Keers and Felix J. Herrmann and Wim A. Mulder}
}
@article {herrmann2008GEOPacd,
	title = {Adaptive curvelet-domain primary-multiple separation},
	journal = {Geophysics},
	volume = {73},
	number = {3},
	year = {2008},
	month = {08},
	pages = {A17-A21},
	publisher = {SEG},
	abstract = {In many exploration areas, successful separation of primaries and multiples greatly determines the quality of seismic imaging. Despite major advances made by surface-related multiple elimination (SRME), amplitude errors in the predicted multiples remain a problem. When these errors vary for each type of multiple in different ways (as a function of offset, time, and dip), they pose a serious challenge for conventional least-squares matching and for the recently introduced separation by curvelet-domain thresholding. We propose a data-adaptive method that corrects amplitude errors, which vary smoothly as a function of location, scale (frequency band), and angle. With this method, the amplitudes can be corrected by an elementwise curvelet-domain scaling of the predicted multiples. We show that this scaling leads to successful estimation of primaries, despite amplitude, sign, timing, and phase errors in the predicted multiples. Our results on synthetic and real data show distinct improvements over conventional least-squares matching in terms of better suppression of multiple energy and high-frequency clutter and better recovery of estimated primaries. \copyright2008 Society of Exploration Geophysicists},
	keywords = {Geophysics, Processing, SLIM},
	doi = {10.1190/1.2904986},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/herrmann08GEOacd/herrmann08GEOacd.pdf},
	author = {Felix J. Herrmann and Deli Wang and D. J. Verschuur}
}
@article {wang2008GEOPbws,
	title = {Bayesian wavefield separation by transform-domain sparsity promotion},
	journal = {Geophysics},
	volume = {73},
	number = {5},
	year = {2008},
	month = {07},
	pages = {1-6},
	abstract = {Successful removal of coherent noise sources greatly determines the quality of seismic imaging. Major advances were made in this direction, e.g., Surface-Related Multiple Elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors and clutter in the predicted signal components can be detrimental. Adopting a Bayesian approach along with the assumption of approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes the predictions produced by for example SRME as input and separates these components in a robust fashion. In addition, the proposed algorithm controls the energy mismatch between the separated and predicted components. Such a control, which was lacking in earlier curvelet-domain formulations, produces improved results for primary-multiple separation on both synthetic and real data.},
	keywords = {curvelet transform, Geophysics, Optimization, Processing, SLIM},
	doi = {10.1190/1.2952571},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/wang08GEObws/wang08GEObws.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/2008/wang08TRbss/paper_html/paper.html},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {hennenfent2008GEOPnii,
	title = {New insights into one-norm solvers from the Pareto curve},
	journal = {Geophysics},
	volume = {73},
	number = {4},
	year = {2008},
	month = {07},
	pages = {A23-A26},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. We show how these curves lead to new insights in one-norm regularization. First, we confirm the theoretical properties of smoothness and convexity of these curves from a stylized and a geophysical example. Second, we exploit these crucial properties to approximate the Pareto curve for a large-scale problem. Third, we show how Pareto curves provide an objective criterion to gauge how different one-norm solvers advance towards the solution.},
	keywords = {Acquisition, Geophysics, Optimization, Pareto, Processing, SLIM},
	doi = {10.1190/1.2944169},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf},
	author = {Gilles Hennenfent and Ewout van den Berg and Michael P. Friedlander and Felix J. Herrmann}
}
@article {hennenfent2008GEOPsdw,
	title = {Simply denoise: wavefield reconstruction via jittered undersampling},
	journal = {Geophysics},
	volume = {73},
	number = {3},
	year = {2008},
	month = {05},
	pages = {V19-V28},
	publisher = {SEG},
	abstract = {In this paper, we present a new discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements that are localized in the Fourier domain. Our work is motivated by empirical observations in the seismic community, corroborated by recent results from compressive sampling, which indicate favorable (wavefield) reconstructions from random as opposed to regular undersampling. As predicted by theory, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control and the main purpose of this paper is to introduce a sampling scheme, coined jittered undersampling, that shares the benefits of random sampling, while offering control on the maximum gap size. Our contribution of jittered sub-Nyquist sampling proves to be key in the formulation of a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After studying the behavior of the jittered undersampling scheme in the Fourier domain, its performance is studied for curvelet recovery by sparsity-promoting inversion (CRSI). Our findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly-undersampled data for the same amount of data collected.},
	keywords = {Acquisition, Compressive Sensing, Geophysics, Optimization, Processing, sampling, SLIM},
	doi = {10.1190/1.2841038},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/hennenfent08GEOsdw.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/paper_html/paper.html},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
