@article{Akcelik2002, author = {Akcelik, Volkan and Biros, George and Ghattas, Omar}, file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/ghattas\_TV.pdf:pdf}, isbn = {076951524X}, journal = {Supercomputing, ACM/IEEE}, number = {c}, pages = {1--15}, title = {{Parallel multiscale Gauss-Newton-Krylov methods for inverse wave propagation}}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1592877}, volume = {00}, year = {2002} } @article{Aravkin2012, abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. The structure of these problems allows efficient optimization strategies—a well-known example is variable projection , where nonlinear least-squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood and maximum a posteriori likelihood problems with nuisance parameters, such as variance or degrees of freedom (d.o.f.). As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, d.o.f. parameter estimation in the context of robust inverse problems, and automatic calibration. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large-scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.}, archivePrefix = {arXiv}, arxivId = {1206.6532}, author = {Aravkin, Aleksandr Y and van Leeuwen, Tristan}, eprint = {1206.6532}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/nuisance\_param.pdf:pdf}, journal = {Inverse Problems}, month = jun, number = {11}, pages = {115016}, title = {{Estimating nuisance parameters in inverse problems}}, url = {http://arxiv.org/abs/1206.6532}, volume = {28}, year = {2012} } @article{Aravkin2011, abstract = {We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such problems motivates dimensionality reduction techniques based on randomly mixing experiments. These techniques break down, however, when robust data-fitting formulations are used, which are essential in cases of missing data, unusually large errors, and systematic features in the data unexplained by the forward model. We survey robust methods within a statistical framework, and propose a semistochastic optimization approach that allows dimensionality reduction. The efficacy of the methods are demonstrated for a large-scale seismic inverse problem using the robust Student's t-distribution, where a useful synthetic velocity model is recovered in the extreme scenario of 60\% data missing at random. The semistochastic approach achieves this recovery using 20\% of the effort required by a direct robust approach.}, archivePrefix = {arXiv}, arxivId = {1110.0895}, author = {Aravkin, Aleksandr and Friedlander, Michael P. and van Leeuwen, Tristan}, doi = {10.1007/s10107-012-0571-6}, eprint = {1110.0895}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/robust\_inversion.pdf:pdf}, journal = {Mathematical \ldots}, keywords = {inverse problems,robust,seismic inversion,stochastic optimization}, month = oct, title = {{Robust inversion via semistochastic dimensionality reduction}}, url = {http://link.springer.com/article/10.1007/s10107-012-0571-6 http://arxiv.org/abs/1110.0895}, year = {2011} } @book{Bertsekas1999, author = {Bertsekas, Dimitri P.}, isbn = {1886529000}, pages = {780}, publisher = {Athena Scientific; 2nd edition}, title = {{Nonlinear Programming}}, url = {http://www.amazon.com/Nonlinear-Programming-Dimitri-P-Bertsekas/dp/1886529000/ref=sr\_1\_2?ie=UTF8\&qid=1395180760\&sr=8-2\&keywords=nonlinear+programming}, year = {1999} } @article{Chambolle2011, author = {Chambolle, Antonin and Pock, Thomas}, file = {:D$\backslash$:/Dropbox/docs/math/slim/amp/pd\_alg\_final.pdf:pdf}, journal = {Journal of Mathematical Imaging and Vision}, title = {{A first-order primal-dual algorithm for convex problems with applications to imaging}}, url = {http://link.springer.com/article/10.1007/s10851-010-0251-1}, year = {2011} } @article{Chung2005, author = {Chung, Eric T. and Chan, Tony F. and Tai, Xue-Cheng}, doi = {10.1016/j.jcp.2004.11.022}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/Chung-Chan-Tai-jcp-04.pdf:pdf}, issn = {00219991}, journal = {Journal of Computational Physics}, month = may, number = {1}, pages = {357--372}, title = {{Electrical impedance tomography using level set representation and total variational regularization}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999104004711}, volume = {205}, year = {2005} } @article{Esser2013, author = {Esser, Ernie and Lou, Yifei and Xin, Jack}, doi = {10.1137/13090540X}, file = {:D$\backslash$:/Dropbox/docs/math/slim/ernweb/90540.pdf:pdf}, issn = {1936-4954}, journal = {SIAM Journal on Imaging Sciences}, keywords = {basis pursuit,difference of convex programming,differential optical absorption spec-,hyperspectral imaging,nonnegative least squares,scaled gradient projec-,structured sparsity,tion,unmixing}, month = jan, number = {4}, pages = {2010--2046}, title = {{A Method for Finding Structured Sparse Solutions to Nonnegative Least Squares Problems with Applications}}, url = {http://epubs.siam.org/doi/abs/10.1137/13090540X}, volume = {6}, year = {2013} } @article{Esser2010, author = {Esser, Ernie and Zhang, Xiaoqun and Chan, Tony F.}, doi = {10.1137/09076934X}, file = {:D$\backslash$:/Dropbox/docs/math/slim/ernweb/76934.pdf:pdf}, issn = {1936-4954}, journal = {SIAM Journal on Imaging Sciences}, keywords = {convex optimization,l 1,operator splitting,primal-dual methods,total variation minimization}, month = jan, number = {4}, pages = {1015--1046}, title = {{A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science}}, url = {http://epubs.siam.org/doi/abs/10.1137/09076934X}, volume = {3}, year = {2010} } @article{He2012, author = {He, Bingsheng and Yuan, X}, file = {:D$\backslash$:/Dropbox/docs/math/slim/amp/HeYuan-SIIMS-2nd.pdf:pdf}, journal = {SIAM Journal on Imaging Sciences}, keywords = {contraction method,dual method,image restoration,primal-,proximal point algorithm,saddle-point problem,total variation}, pages = {1--35}, title = {{Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective}}, url = {http://epubs.siam.org/doi/abs/10.1137/100814494}, year = {2012} } @article{Herrmann2013, author = {Herrmann, Felix J. and Hanlon, Ian and Kumar, Rajiv and van Leeuwen, Tristan and Li, Xiang and Smithyman, Brendan and Wason, Haneet and Calvert, Andrew J. and Javanmehri, Mostafa and Takougang, Eric Takam}, doi = {10.1190/tle32091082.1}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/frugal\_fwi.pdf:pdf}, issn = {1070-485X}, journal = {The Leading Edge}, month = sep, number = {9}, pages = {1082--1092}, title = {{Frugal full-waveform inversion: From theory to a practical algorithm}}, url = {http://library.seg.org/doi/abs/10.1190/tle32091082.1}, volume = {32}, year = {2013} } @book{Nocedal1999, abstract = {Despite application of cryogen spray (CS) precooling, customary treatment of port wine stain (PWS) birthmarks with a single laser pulse does not result in complete lesion blanching for a majority of patients. One obvious reason is nonselective absorption by epidermal melanin, which limits the maximal safe radiant exposure. Another possible reason for treatment failure is screening of laser light within large PWS vessels, which prevents uniform heating of the entire vessel lumen. Our aim is to identify the parameters of sequential CS cooling and laser irradiation that will allow optimal photocoagulation of various PWS blood vessels with minimal risk of epidermal thermal damage.}, author = {Nocedal, J and Wright, S J}, booktitle = {Analysis}, chapter = {5}, doi = {10.1002/lsm.21040}, editor = {Glynn, Peter and Robinson, Stephen M}, isbn = {0387987932}, issn = {10969101}, number = {2}, pages = {164--75}, pmid = {21384397}, publisher = {Springer}, series = {Springer Series in Operations Research}, title = {{Numerical Optimization}}, url = {http://www.ncbi.nlm.nih.gov/pubmed/21643320}, volume = {43}, year = {1999} } @article{Rudin1992, author = {Rudin, LI and Osher, S and Fatemi, E}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/PhysicaRudinOsher.pdf:pdf}, journal = {Physica D: Nonlinear Phenomena}, pages = {259--268}, title = {{Nonlinear total variation based noise removal algorithms}}, url = {http://www.sciencedirect.com/science/article/pii/016727899290242F}, volume = {60}, year = {1992} } @article{Tarantola1984, author = {Tarantola, Albert}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/InversionOfSeismic.pdf:pdf}, journal = {Geophysics}, number = {8}, pages = {1259--1266}, title = {{Inversion of seismic reflection data in the acoustic approximation}}, url = {http://link.springer.com/article/10.1007/s10107-012-0571-6 http://arxiv.org/abs/1110.0895 http://library.seg.org/doi/abs/10.1190/1.1441754}, volume = {49}, year = {1984} } @article{VandenBerg2011, author = {van den Berg, Ewout and Friedlander, Michael P.}, doi = {10.1137/100785028}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/2011BergFriedlander.pdf:pdf}, issn = {1052-6234}, journal = {SIAM Journal on Optimization}, keywords = {10,100785028,1137,49m29,65k05,90c06,90c25,ams subject classifications,basis pursuit,completion,compressed sensing,convex program,doi,duality,group sparsity,matrix,newton,root-finding,s method,sparse solutions}, month = oct, number = {4}, pages = {1201--1229}, title = {{Sparse Optimization with Least-Squares Constraints}}, url = {http://epubs.siam.org/doi/abs/10.1137/100785028}, volume = {21}, year = {2011} } @article{VanLeeuwen2013, abstract = {Wave-equation based inversions, such as full-waveform inversion, are challenging because of their computational costs, memory requirements, and reliance on accurate initial models. To confront these issues, we propose a novel formulation of full-waveform inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term which measures how accurately the wavefields satisfy the wave-equation. Because we carry out the inversion over a larger search space, including both the model and synthetic wavefields, our approach suffers less from local minima. Our main contribution is the development of an efficient optimization scheme that avoids having to store and update the wavefields by explicit elimination. Compared to existing optimization strategies for full-waveform inversion, our method differers in two main aspects; i) The wavefields are solved from an augmented wave-equation, where the solution is forced to solve the wave-equation and fit the observed data, ii) no adjoint wavefields are required to update the model, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.}, author = {van Leeuwen, T. and Herrmann, F. J.}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/vanLeeuwen2013Penalty1.pdf:pdf}, journal = {Geophysical Journal International}, keywords = {computa-,controlled source seismology,inverse theory,seismic tomography}, number = {1}, pages = {661--667}, title = {{Mitigating local minima in full-waveform inversion by expanding the search space}}, url = {http://gji.oxfordjournals.org/cgi/doi/10.1093/gji/ggt258}, volume = {195}, year = {2013} } @techreport {Leeuwen, title = {A penalty method for {PDE}-constrained optimization}, year = {2013}, month = {04}, publisher = {UBC}, abstract = {We present a method for solving PDE constrained optimization problems based on a penalty formulation. This method aims to combine advantages of both full-space and reduced methods by exploiting a large search-space (consisting of both control and state variables) while allowing for an efficient implementation that avoids storing and updating the state-variables. This leads to a method that has roughly the same per-iteration complexity as conventional reduced approaches while dening an objective that is less non-linear in the control variable by implicitly relaxing the constraint. We apply the method to a seismic inverse problem where it leads to a particularly ecient implementation when compared to a conventional reduced approach as it avoids the use of adjoint state-variables. Numerical examples illustrate the approach and suggest that the proposed formulation can indeed mitigate some of the well-known problems with local minima in the seismic inverse problem.}, keywords = {Optimization, private, waveform inversion}, url = {https://www.slim.eos.ubc.ca/Publications/Private/Tech\%20Report/2013/vanLeeuwen2013Penalty2/vanLeeuwen2013Penalty2.pdf}, author = {Tristan van Leeuwen and Felix J. Herrmann} } @article{VanLeeuwen2013a, author = {van Leeuwen, Tristan and Herrmann, Felix J.}, doi = {10.1111/j.1365-2478.2012.01096.x}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/fastFWI.pdf:pdf}, issn = {00168025}, journal = {Geophysical Prospecting}, keywords = {full-waveform inversion,source-encoding,stochastic optimization}, month = jun, number = {2010}, pages = {10--19}, title = {{Fast waveform inversion without source-encoding}}, url = {http://doi.wiley.com/10.1111/j.1365-2478.2012.01096.x}, volume = {61}, year = {2013} } @article{Virieux2009, author = {Virieux, J. and Operto, S.}, doi = {10.1190/1.3238367}, file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/GPY\_2009\_VIRIEUX.pdf:pdf}, issn = {0016-8033}, journal = {Geophysics}, month = nov, number = {6}, pages = {WCC1--WCC26}, title = {{An overview of full-waveform inversion in exploration geophysics}}, url = {http://library.seg.org/doi/abs/10.1190/1.3238367}, volume = {74}, year = {2009} } @article{Zhang2010a, author = {Zhang, Xiaoqun and Burger, Martin and Osher, Stanley}, doi = {10.1007/s10915-010-9408-8}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/cam09-99.pdf:pdf}, issn = {0885-7474}, journal = {Journal of Scientific Computing}, keywords = {1 minimization,49k35,49m37,49n15,65k10,90c25,ams subjects,bregman iteration,inexact,proximal point iteration,saddle point,uzawa methods}, month = aug, number = {1}, pages = {20--46}, title = {{A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration}}, url = {http://link.springer.com/10.1007/s10915-010-9408-8}, volume = {46}, year = {2010} } @article{Zhu2008, author = {Zhu, Mingqiang and Chan, Tony}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/AMP/cam08-34.pdf:pdf}, journal = {UCLA CAM Report [08-34]}, number = {1}, pages = {1--29}, title = {{An Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration}}, year = {2008} } @techreport {esser2014SEGsgp, title = {A scaled gradient projection method for total variation regularized full waveform inversion}, year = {2014}, month = {04}, publisher = {UBC}, abstract = {We propose an extended full waveform inversion formulation that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model.}, keywords = {convex constraints, full waveform inversion, total variation regularization}, url = {https://www.slim.eos.ubc.ca/Publications/Public/TechReport/2014/esser2014SEGsgp/esser2014SEGsgp.html}, author = {Ernie Esser and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann} } @article{Haber2001, author = {Haber, E and Ascher, U M}, doi = {10.1088/0266-5611/17/6/319}, issn = {0266-5611}, journal = {Inverse Problems}, optmonth =dec, number = {6}, pages = {1847--1864}, title = {{Preconditioned all-at-once methods for large, sparse parameter estimation problems}}, url = {http://stacks.iop.org/0266-5611/17/i=6/a=319?key=crossref.8ad3fa0df4ae626ba0731b2d4158cdb6}, volume = {17}, year = {2001} } @inbook{Biondi2013, author = {Biondo Biondi and Ali Almomin}, title = {Tomographic full waveform inversion (TFWI) by extending the velocity model along the time-lag axis}, booktitle = {SEG Technical Program Expanded Abstracts}, year = {2013}, chapter = {200}, pages = {1031-1036}, doi = {10.1190/segam2013-1255.1}, URL = {http://library.seg.org/doi/abs/10.1190/segam2013-1255.1}, eprint = {http://library.seg.org/doi/pdf/10.1190/segam2013-1255.1} } @article {Symes2008mva, author = {Symes, William W.}, title = {Migration velocity analysis and waveform inversion}, journal = {Geophysical Prospecting}, volume = {56}, number = {6}, publisher = {Blackwell Publishing Ltd}, issn = {1365-2478}, url = {http://dx.doi.org/10.1111/j.1365-2478.2008.00698.x}, doi = {10.1111/j.1365-2478.2008.00698.x}, pages = {765--790}, year = {2008}, } @article {Li11TRfrfwi, title = {Fast randomized full-waveform inversion with compressive sensing}, journal = {Geophysics}, volume = {77}, number = {3}, year = {2012}, optmonth ={05}, pages = {A13-A17}, address = {University of British Columbia, Vancouver}, 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://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2012/Li11TRfrfwi/Li11TRfrfwi.pdf}, author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann} } @inbook{Warner2014, author = {Mike Warner and Lluís Guasch}, title = {Adaptive waveform inversion: Theory}, booktitle = {SEG Technical Program Expanded Abstracts}, year = {2014}, chapter = {207}, pages = {1089-1093}, doi = {10.1190/segam2014-0371.1}, URL = {http://library.seg.org/doi/abs/10.1190/segam2014-0371.1}, eprint = {http://library.seg.org/doi/pdf/10.1190/segam2014-0371.1} } @conference {leeuwen2014EAGEntf, title = {A new take on {FWI}: wavefield reconstruction inversion}, booktitle = {EAGE}, year = {2014}, month = {06}, abstract = {We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI {\textendash} which attempts to minimize the error between observed and predicted data obtained by solving a wave equation {\textendash} WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.}, keywords = {EAGE, Full-waveform inversion, Optimization, penalty method, Wavefield Reconstruction Inversion}, doi = {10.3997/2214-4609.20140703}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf.pdf}, presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf_pres.pdf}, author = {Tristan van Leeuwen and Felix J. Herrmann and Bas Peters} } @article {vanLeeuwen2010IJGswi, title = {Seismic waveform inversion by stochastic optimization}, journal = {International Journal of Geophysics}, volume = {2011}, year = {2011}, note = {Article ID: 689041, 18pages}, optmonth ={12}, abstract = {We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.}, keywords = {FWI, Optimization, SLIM}, doi = {10.1155/2011/689041}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/InternationJournalOfGeophysics/2011/vanLeeuwen10IJGswi/vanLeeuwen10IJGswi.pdf}, author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann} } @article{Krebs09, author = {Krebs, Jerome R. and Anderson, John E. and Hinkley, David and Neelamani, Ramesh and Lee, Sunwoong and Baumstein, Anatoly and Lacasse, Martin-Daniel}, title = {Fast full-wavefield seismic inversion using encoded sources}, volume = {74}, number = {6}, pages = {WCC177-WCC188}, year = {2009}, doi = {10.1190/1.3230502}, abstract = {Full-wavefield seismic inversion (FWI) estimates a subsurface elastic model by iteratively minimizing the difference between observed and simulated data. This process is extremely computationally intensive, with a cost comparable to at least hundreds of prestack reverse-time depth migrations. When FWI is applied using explicit time-domain or frequency-domain iterative-solver-based methods, the seismic simulations are performed for each seismic-source configuration individually. Therefore, the cost of FWI is proportional to the number of sources. We have found that the cost of FWI for fixed-spread data can be significantly reduced by applying it to data formed by encoding and summing data from individual sources. The encoding step forms a single gather from many input source gathers. This gather represents data that would have been acquired from a spatially distributed set of sources operating simultaneously with different source signatures. The computational cost of FWI using encoded simultaneous-source gathers is reduced by a factor roughly equal to the number of sources. Further, this efficiency is gained without significantly reducing the accuracy of the final inverted model. The efficiency gain depends on subsurface complexity and seismic-acquisition parameters. There is potential for even larger improvements of processing speed.}, URL = {http://geophysics.geoscienceworld.org/content/74/6/WCC177.abstract}, eprint = {http://geophysics.geoscienceworld.org/content/74/6/WCC177.full.pdf+html}, journal = {Geophysics} } @article{Haber2012EMP, author = {Haber, Eldad and Chung, Matthias and Herrmann, Felix}, doi = {10.1137/11081126X}, file = {:Users/tristanvanleeuwen/Documents/Mendeley Desktop//Haber, Chung, Herrmann - 2012 - An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides.pdf:pdf}, issn = {1052-6234}, journal = {SIAM Journal on Optimization}, optmonth =jul, number = {3}, pages = {739--757}, title = {{An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides}}, url = {http://epubs.siam.org/doi/abs/10.1137/11081126X}, volume = {22}, year = {2012} } @conference {peters2014EAGEweb, title = {Wave-equation based inversion with the penalty method: adjoint-state versus wavefield-reconstruction inversion}, booktitle = {EAGE}, year = {2014}, month = {06}, abstract = {In this paper we make a comparison between wave-equation based inversions based on the adjoint-state and penalty methods. While the adjoint-state method involves the minimization of a data-misfit and exact solutions of the wave-equation for the current velocity model, the penalty-method aims to first find a wavefield that jointly fits the data and honours the physics, in a least-squares sense. Given this reconstructed wavefield, which is a proxy for the true wavefield in the true model, we calculate updates for the velocity model. Aside from being less nonlinear{\textendash}the acoustic wave equation is linear in the wavefield and model parameters but not in both{\textendash}the inversion is carried out over a solution space that includes both the model and the wavefield. This larger search space allows the algortihm to circumnavigate local minima, very much in the same way as recently proposed model extentions try to acomplish. We include examples for low frequencies, where we compare full-waveform inversion results for both methods, for good and bad starting models, and for high frequencies where we compare reverse-time migration with linearized imaging based on wavefield-reconstruction inversion. The examples confirm the expected benefits of the proposed method.}, keywords = {EAGE, Full-waveform inversion, Imaging, Optimization, penalty method}, doi = {10.3997/2214-4609.20140704}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb.pdf}, presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb_pres.pdf}, author = {Bas Peters and Felix J. Herrmann and Tristan van Leeuwen} } @article{Billette2005, author = {Billette, FJ and Brandsberg-Dahl, S}, file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/BP2004.pdf:pdf}, journal = {67th EAGE Conference \& Exhibition}, number = {June}, pages = {13--16}, title = {{The 2004 BP velocity benchmark}}, url = {http://www.earthdoc.org/publication/publicationdetails/?publication=1404}, year = {2005} } @article{guo2013shape, title={Shape optimization and level set method in full waveform inversion with 3D body reconstruction}, author={Guo, Zhaohui and de Hoop, Maarten V and others}, journal={2013 SEG Annual Meeting}, year={2013}, publisher={Society of Exploration Geophysicists} }