@article {peters2016cvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	journal = {The Leading Edge},
	volume = {36},
	number = {1},
	year = {2017},
	note = {(The Leading Edge)},
	month = {01},
	pages = {94-100},
	abstract = {Full-waveform inversion is challenging in complex geologic areas. Even when provided with an accurate starting model, the inversion algorithms often struggle to update the velocity model. Compared with other areas in applied geophysics, including prior information in full-waveform inversion is still in its relative infancy. In part, this is due to the fact that it is difficult to incorporate prior information that relates to geologic settings where strong discontinuities in the velocity model dominate, because these settings call for nonsmooth regularizations. We tackle this problem by including constraints on the spatial variations and value ranges of the inverted velocities, as opposed to adding penalties to the objective, which is more customary in mainstream geophysical inversion. By demonstrating the lack of predictability of edge-preserving inversion when the regularization is in the form of an added penalty term, we advocate the inclusion of constraints instead. Our examples show that the latter leads to more predictable results and to significant improvements in the delineation of salt bodies when these constraints are relaxed gradually in combination with extending the search space to approximately fit the observed data but not the noise.},
	keywords = {algorithm, full waveform inversion, noise, Optimization, penalty methods, salt dome, total variation},
	doi = {10.1190/tle36010094.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2016/peters2016cvp/peters2016cvp.html},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2016SEGWScvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	booktitle = {SEG Workshop on Where are we heading with FWI; Dallas},
	year = {2016},
	note = {(SEG Workshop, Dallas)},
	month = {10},
	abstract = {Full-waveform inversion is arguably one of the most challenging inverse problems out there. For this reason, it is remarkable that so much progress has been made over the years. While we can look back with confidence at an increasing number of success stories, the application of full-waveform technologies to deeper targets and complex geologies remains challenging making it an expensive proposition. So far, efforts to overcome some of these challenges have mainly been directed towards extended formulations such as Symes{\textquoteright}s and Biondi{\textquoteright}s subsurface offset/rau-parameters, Mike Warner/Lluis Guasch{\textquoteright}s Wiener filters in their adaptive full-waveform inversion, and van Leeuwen/Herrmann{\textquoteright}s Wavefield Reconstruction Inversion, where the wave-equation appears as a least-squares term in the objective. While this recent work {\textendash}- including other approaches such as different data-misfit objective functions {\textendash}- has removed some of FWI cycle-skip issues it does, with the exception perhaps of box constraints, not incorporate rudimentary information on the geology on the unknown model. Following recent work by Ernie Esser, we present a general framework how to incorporate this type of information in the form of constraints. Contrary to Tikhonov-like regularization or gradient filtering, imposing constraints has several key advantages, namely (i) they can be expressed in simple human understandable terms such as lower and upper limits for the velocity without the necessity to introduce additional parameters and assumptions on the probability distribution of the model; (ii) they can consist of several constraints, e.g. box and smoothness constraints, as long as their intersection in non-empty; and (iii) they can be imposed in a separate inner loop, which does not affect gradients and Hessians of full-waveform inversion itself. By means of examples, we will demonstrate the advocacy of constrained formulations as they apply to full-waveform inversion. This is joint work with Bas Peters.},
	keywords = {Full-waveform inversion, SEG, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/herrmann2016SEGWScvp/herrmann2016SEGWScvp_pres.pdf},
	author = {Felix J. Herrmann and Bas Peters}
}
@presentation {herrmann2016SINBADFcvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Full-waveform inversion is challenging in complex geological areas. Even when provided with an accurate starting model, the inversion algorithms often struggle to update the velocity model. Contrary to other areas in applied geophysics, including prior information in full-waveform inversion is still relatively in its infancy. In part this is due to the fact that incorporating prior information that relates to geological settings where strong discontinuities in the velocity model dominate is difficult, because these settings call for non-smooth regularizations. We tackle this problem by including constraints on the spatial variations and value ranges of the inverted velocities, as opposed to adding penalties to the objective as is more customary in main stream geophysical inversion. By demonstrating the lack of predictability of edge-preserving inversion when the regularization is in the form of an added penalty term, we advocate the inclusion of constraints instead. Our examples show that the latter lead to more predictable results and to significant improvements in the delineation of Salt bodies. This is joint work with Bas Peters.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/herrmann2016SINBADFcvp/herrmann2016SINBADFcvp.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/herrmann2016SINBADFcvp/herrmann2016SINBADFcvp.mov},
	author = {Felix J. Herrmann and Bas Peters}
}
@presentation {peters2016SINBADFcnc,
	title = {Convex \& non-convex constraint sets for full-waveform inversion},
	year = {2016},
	publisher = {SINBAD},
	abstract = {We extend some of our previous work on constrained formulations of full-waveform inversion. Some motivating examples illustrate why solving constrained problems directly is a simpler approach for solving non-linear inverse problems than penalized problem formulations. So far we used constraints which can be represented as convex sets, for which most optimization theory is developed. Some non-convex counterparts of convex sets are introduced and examples show that the algorithms developed for convex sets also work well with non-convex sets. The motivation to also explore non-convex sets, is that they sometimes translate prior geological knowledge into mathematical constraints in a more direct way. All presented material is available as a user-friendly toolbox. The toolbox works with any code which can provide a data-misfit function value and a gradient direction.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/peters2016SINBADFcnc/peters2016SINBADFcnc.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/peters2016SINBADFcnc/peters2016SINBADFcnc.mov},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {smithyman2015EAGEcwi,
	title = {Constrained waveform inversion of colocated VSP and surface seismic data},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Constrained Full-Waveform Inversion (FWI) is applied to produce a high-resolution velocity model from both Vertical Seismic Profiling (VSP) and surface seismic data. The case study comes from the Permian Basin in Texas, USA. This dataset motivates and tests several new developments in methodology that enable recovery of model results that sit within multiple a priori constraint sets. These constraints are imposed through a Projected Quasi-Newton (PQN) approach, wherein the projection set is the intersection of physical property bounds and anisotropic wavenumber filtering. This enables the method to recover geologically-reasonable models while preserving the fast model convergence offered by a quasi-Newton optimization scheme like l-BFGS. In the Permian Basin example, low-frequency data from both arrays are inverted together and regularized by this projection approach. Careful choice of the constraint sets is possible without requiring tradeoff parameters as in a quadratic penalty approach to regularization. Multiple 2D FWI results are combined to produce an interpolated 3D model that is consistent with the models from migration velocity analysis and VSP processing, while offering improved resolution and illumination of features from both datasets.},
	keywords = {EAGE, VSP, waveform inversion},
	doi = {10.3997/2214-4609.201412906},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi_pres.pdf},
	author = {Brendan R. Smithyman and Bas Peters and Felix J. Herrmann}
}
@presentation {peters2014SINBADcda,
	title = {Challenges and developments arising from 2D FWI of a land VSP dataset in the Permian Basin},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Full-waveform inversion was carried out to map 3D velocity structures for a site in the Permian Basin of Texas, USA. The data come from co-located surface and 3D VSP seismic surveys that share common source vibration points. This challenging on-land setting has been used as a testbed to evaluate our FWI algorithms and their effectiveness when applied to real-data problems. We discuss the challenges posed by this case study, and several new techniques and methodological refinements that have been developed and tested as a result. These include: regularization and incorporation of multiple datasets in an on-land FWI workflow; restrictions on the types of models allowed (viz., smoothness regularization) by quadratic penalty and by Projected Quasi-Newton (PQN) inversion; corrections to enable 2D FWI and recovery of 3D models; the state of ongoing work in WRI ({\textquoteleft}{\textquoteleft}Penalty Method{\textquoteright}{\textquoteright} inversion) and the handling of anisotropy.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/peters2014SINBADcda/peters2014SINBADcda.pdf},
	author = {Brendan R. Smithyman and Bas Peters and Felix J. Herrmann}
}
