@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}
}
@techreport {peters2015EAGErwi,
	title = {Regularizing waveform inversion by projection onto intersections of convex sets},
	number = {TR-EOAS-2015-4},
	year = {2015},
	month = {01},
	institution = {UBC},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function, several gradient and quasi-Newton based solvers and does not require significant additional computation. The method is demonstrated on the inversion of very noisy synthetic data and vertical seismic profiling field data.},
	keywords = {convex sets, regularization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/peters2015EAGErwi/peters2015EAGErwi.html},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@techreport {peters2015SEGrwi,
	title = {Regularizing waveform inversion by projections onto convex sets {\textendash}- application to the 2D Chevron 2014 synthetic blind-test dataset},
	number = {TR-EOAS-2015-7},
	year = {2015},
	month = {06},
	institution = {UBC},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing.},
	keywords = {blind-test, projection, regularization, SEG, Wavefield Reconstruction Inversion, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/peters2015SEGrwi/peters2015SEGrwi.html},
	author = {Bas Peters and Zhilong Fang and Brendan R. Smithyman 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}
}
