@inproceedings{brougois1990marmousi,
 title={Marmousi, model and data},
 author={Brougois, A and Bourget, Marielle and Lailly, Patriek and Poulet, Michel and Ricarte, Patrice and Versteeg, Roelof},
 booktitle={EAEG Workshop-Practical Aspects of Seismic Data Inversion},
 year={1990}
}

@conference {wang2017SEGdff,
	title = {A denoising formulation of full-waveform inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {1594-1598},
	abstract = {We propose a wave-equation-based subsurface inversion method that in many cases is more robust than the conventional Full-Waveform Inversion. The new formulation is written in a denoising form that allows the synthetic data to match the observed ones up to a small error. Compared to the Full-Waveform Inversion, our method treats the noise arising from the data measuring/recording process and that from the synthetic modelling process separately. Comparing to the Wavefields Reconstruction Inversion, the new formulation mitigates the difficulty of choosing the penalty parameter ${\l}ambda$. To solve the proposed optimization problem, we develop an efficient frequency domain algorithm that alternatively updates the model and the data. Numerical experiments confirm strong stability of the proposed method by comparisons between the results of our algorithm with that from both plain FWI and a weighted formulation of the FWI.},
	keywords = {denoising, FWI, SEG},
	doi = {10.1190/segam2017-17794690.1},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2017/wang2017SEGdff/wang2017SEGdff.pdf},
	presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2017/wang2017SEGdff/wang2017SEGdff_pres.pdf},
	author = {Rongrong Wang and Felix J. Herrmann}
}

@techreport{candes2000curvelets,
 title={Curvelets: A surprisingly effective nonadaptive representation for objects with edges},
 author={Candes, Emmanuel J and Donoho, David L},
 year={2000},
 institution={DTIC Document}
}

@article {neelmani2008GTLECohere,
    title = {Coherent and random noise attenuation using the curvelet transform},
    journal = {The Leading Edge},
    volume = {27},
    number = {2},
    year = {2008},
    pages = {240-248},
    doi = {10.1190/1.2840373},
    url = {https://doi.org/10.1190/1.2840373},
    author = {Ramesh Neelamani and Anatoly I. Baumstein and Dominique G. Gillard and Mohamed T. Hadidi and William L. Soroka}
}


@article {lin2013GEOPrepsi,
    title = {Robust estimation of primaries by sparse inversion via one-norm minimization},
    journal = {Geophysics},
    volume = {78},
    number = {3},
    year = {2013},
    month = {05},
    pages = {R133-R150},
    abstract = {A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm.},
    keywords = {algorithm, biconvex, EPSI, multiples, Optimization, Pareto, sparsity, waveform inversion},
    doi = {10.1190/geo2012-0097.1},
    url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2013/lin2013GEOPrepsi/lin2013GEOPrepsi.pdf},
    author = {Tim T.Y. Lin and Felix J. Herrmann}
}

@article {herrmann2008GJInps,
	title = {Non-parametric seismic data recovery with curvelet frames},
	journal = {Geophysical Journal International},
	volume = {173},
	year = {2008},
	month = {04},
	pages = {233-248},
	keywords = {Acquisition, curvelet transform, reconstruction, SLIM},
	doi = {10.1111/j.1365-246X.2007.03698.x},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/GeophysicalJournalInternational/2008/herrmann2008GJInps.pdf},
	author = {Herrmann, Felix J. and Hennenfent, Gilles}
}

@article {candes2006stable,
	title = {Stable signal recovery from incomplete and inaccurate measurements},
	journal = {Communications on Pure and Applied Mathematics},
	volume = {59},
	number = {8},
	year = {2006},
	pages = {1207-1223},
        doi = {10.1002/cpa.20124},
	url = {http://dx.doi.org/10.1002/cpa.20124},
	author = {Candés, Emmanuel J. and Romberg, Justin K. and Tao, Terence}
}

@article {chen1998atomic,
	title = {Atomic Decomposition by Basis Pursuit},
	journal = {SIAM Journal on Scientific Computing},
	volume = {20},
	number = {1},
	year = {1998},
	pages = {33-61},
        doi = {10.1137/S1064827596304010},
	url = {https://doi.org/10.1137/S1064827596304010},
	author = {Chen, Scott Shaobing and Donoho, David L. and Saunders, Michael A.}
}

@article {fornasier2008recovery,
	title = {Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {46},
	number = {2},
	year = {2008},
	pages = {577-613},
        doi = {10.1137/0606668909},
	url = {https://doi.org/10.1137/0606668909},
	author = {Massimo Fornasier and Holger Rauhut}
}


@article {Li2012fast,
	title = {Fast randomized full-waveform inversion with compressive sensing},
	journal = {Geophysics},
	volume = {77},
	number = {3},
	year = {2012},
	month = {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}
}

@article {louboutin2017fwi,
	title = {Full-Waveform Inversion - Part 1: forward modeling},
	journal = {The Leading Edge},
	volume = {36},
	number = {12},
	year = {2017},
	note = {(The Leading Edge)},
	month = {12},
	pages = {1033-1036},
	abstract = {Since its re-introduction by Pratt (1999), full-waveform inversion (FWI) has gained a lot of attention in geophysical exploration because of its ability to build high resolution velocity models more or less automatically in areas of complex geology. While there is an extensive and growing literature on the topic, publications focus mostly on technical aspects, making this topic inaccessible for a broader audience due to the lack of simple introductory resources for newcomers to geophysics. We will accomplish this by providing a hands-on walkthrough of FWI using Devito (Lange et al. 2016), a system based on domain-specific languages that automatically generates code for time-domainfinite-differences.},
	keywords = {devito, finite-differences, FWI, Modeling, tutorial},
	doi = {10.1190/tle36121033.1},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/TheLeadingEdge/2017/louboutin2017fwi/louboutin2017fwi.html},
	author = {Mathias Louboutin and Philipp A. Witte and Michael Lange and Navjot Kukreja and Fabio Luporini and Gerard Gorman and Felix J. Herrmann}
}

@article{peter2010reservoir,
  title={Reservoir characterization using surface microseismic monitoring},
  author={Duncan, Peter M. and Eisner, Leo},
  journal={GEOPHYSICS},
  volume={75},
  number={5},
  pages={A139–A146},
  year={2010},
  url={http://dx.doi.org/10.1190/1.3467760}
}

@article {schmidt1986multiple,
	title = {Multiple emitter location and signal parameter estimation},
	journal = {IEEE Transactions on Antennas and Propagation},
	volume = {AP-34},
	number = {3},
	year = {1986},
	pages = {276-280},
        doi = {10.1109/TAP.1986.1143830},
	url = {http://dx.doi.org/10.1109/TAP.1986.1143830},
	author = {Schmidt, R}
}

@conference{gao2017EAGEmicroseismic,
	title = {Microseismic Event Localization via Least-squares Full Waveform Inversion with Group Sparsity Constraints},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
        month = {06},
	publisher = {EAGE},
	organization = {EAGE},
	abstract = {Microseismic source localization is posed as a linear inverse problem. A finite difference code that solves the acoustic wave equation in heterogeneous media is utilized to define a forward operator that maps subsurface sources to pressure measurements acquired on the surface of the earth. The inversion process entail inverting the aforementioned operator with the assistance of a group sparsity regularization term that promotes source focusing. By adopting group sparsity, we guarantee the retrieval of a sparse spatial distribution of sources with smooth temporal signatures.},
        keywords = {EAGE},
	doi = {10.3997/2214-4609.201701261},
	author = {W. Gao and M.D. Sacchi}
}

@conference{rubner1998IEEEmetric,
	title = {A metric for distributions with applications to image databases},
	booktitle = {Sixth {I}nternational {C}onference on {C}omputer {V}ision ({I}EEE Cat. No.98CH36271)},
	year = {1998},
        month = {01},
	 pages = {59-66},
        keywords = {image colour analysis;image texture;visual databases;color;distributions;easy-to-compute lower bounds;image databases;linear optimization;multi-dimensional scaling displays;partial matching;texture;transportation problem;Application software;Computer displays;Computer science;Frequency;Geoscience;Histograms;Image databases;Image retrieval;Navigation;Psychology},
	doi = {10.1109/ICCV.1998.710701},
	author = {Y. Rubner and C. Tomasi and L. J. Guibas}
}

@conference{arani2012SEGanalysis,
	title = {Analysis of passive surface‐wave noise in surface microseismic data and its implications},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2012},
        pages = {1493-1498},
	publisher = {SEG},
	organization = {SEG},
        keywords = {SEG},
	doi = {10.1190/1.3627485},
	url = {https://library.seg.org/doi/abs/10.1190/1.3627485},
	author = {Farnoush Forghani‐Arani and Mark Willis and Seth Haines and Mike Batzle and Michael Davidson}
}

@article {tu2015GJIsem,
	title = {Source estimation with surface-related multiples{\textendash}-fast ambiguity-resolved seismic imaging},
	journal = {Geophysical Journal International},
	volume = {205},
	year = {2016},
	note = {(published online in Geophysical Journal International)},
	month = {03},
	pages = {1492-1511},
	abstract = {We address the problem of obtaining a reliable seismic image without prior knowledge of the source wavelet, especially from data that contain strong surface-related multiples. Conventional reverse-time migration requires prior knowledge of the source wavelet, which is either technically or computationally challenging to accurately determine; inaccurate estimates of the source wavelet can result in seriously degraded reverse-time migrated images, and therefore wrong geological interpretations. To solve this problem, we present a "wavelet-free" imaging procedure that simultaneously inverts for the source wavelet and the seismic image, by tightly integrating source estimation into a fast least-squares imaging framework, namely compressive imaging, given a reasonably accurate background velocity model. However, this joint inversion problem is difficult to solve as it is plagued with local minima and the ambiguity with respect to amplitude scalings because of the multiplicative, and therefore nonlinear, appearance of the source wavelet in the otherwise linear formalism. We have found a way to solve this nonlinear joint-inversion problem using a technique called variable projection, and a way to overcome the scaling ambiguity by including surface-related multiples in our imaging procedure following recent developments in surface-related multiple prediction by sparse inversion. As a result, we obtain without prior knowledge of the source wavelet high-resolution seismic images, comparable in quality to images obtained assuming the true source wavelet is known. By leveraging the computationally efficient compressive-imaging methodology, these results are obtained at affordable computational costs compared with conventional processing work flows that include surface-related multiple removal and reverse-time migration.},
	keywords = {computational seismology, free surface, Inverse theory, multiples, seismic imaging, time series analysis, wave propagation},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/GeophysicalJournalInternational/2016/tu2015GJIsem/tu2015GJIsem.pdf},
	url2 = {http://gji.oxfordjournals.org/content/205/3/1492.full.pdf?keytype=ref\&ijkey=zFydRGQpiJzeCS9},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}

@conference {sun2016SEGfwi,
	title = {Full waveform inversion of passive seismic data for sources and velocities},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {1405-1410},
	abstract = {From the seismic imaging point of view, the difficulty in locating passive seismic sources lies in their unknown start times. In other words, the source model has an additional dimension of time, which leads to an extended model space. Without proper preconditioning, the computational cost of directly inverting for the source functions can be intractable. Using the recently proposed cross-correlation time-reversal imaging condition, we formulate the imaging task as an inverse problem, and use a sparse weighting function calculated from the cross-correlation of back-propagated events to constrain the model space. We demonstrate that the proposed approach can effectively reduce the number of model parameters, leading to a rapid convergence rate using preconditioned conjugate-gradient iterations. The least-squares imaging of passive seismic sources can be further incorporated into full waveform inversion for Earth properties using the variable projection method. Synthetic examples verify the proposed method.},
	doi = {10.1190/segam2016-13959115.1},
	author = {Junzhe Sun and Zhiguang Xue and Sergey Fomel and Tieyuan Zhu and Nori Nakata}
}


@article {wapennar1990decomposition,
	title = {Decomposition of multicomponent seismic data into primary {P}- and {S}-Wave responses},
	journal = {Geophysical Prospecting},
	volume = {38},
	number = {6},
	year = {1990},
	pages = {633-661},
        doi = {10.1111/j.1365-2478.1990.tb01867.x},
	url = {http://dx.doi.org/10.1111/j.1365-2478.1990.tb01867.x},
	author = {WAPENAAR, C. P. A. and HERRMANN, P. and VERSCHUUR, D. J. and BERKHOUT, A. J.}
}


@conference {kumar2016SEGtjm,
	title = {Time-jittered marine acquisition{\textendash}-a rank-minimization approach for {5D} source separation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {119-123},
	abstract = {Simultaneous source marine acquisition has been recognized as an economic way of improving spatial sampling and speedup acquisition time, where a single- (or multiple-) source vessel fires at jittered source locations and time instances. Consequently, the acquired simultaneous data volume is processed to separate the overlapping shot records resulting in densely sampled data volume. It has been shown in the past that the simultaneous source acquisition design and source separation process can be setup as a compressed sensing problem, where conventional seismic data is reconstructed from simultaneous data via a sparsity-promoting optimization formulation. While the recovery quality of separated data is reasonably well, the recovery process can be computationally expensive due to transform-domain redundancy. In this paper, we present a computationally tractable rank-minimization algorithm to separate simultaneous data volumes. The proposed algorithm is suitable for large-scale seismic data, since it avoids singular-value decompositions and uses a low-rank based factorized formulation instead. Results are illustrated for simulations of simultaneous time-jittered continuous recording for a 3D ocean-bottom cable survey.},
	keywords = {5D, marine, SEG, source separation, time-jittered acquisition},
	doi = {10.1190/segam2016-13878249.1},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2016/kumar2016SEGtjm/kumar2016SEGtjm.html},
	presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2016/kumar2016SEGtjm/kumar2016SEGtjm_pres.pdf},
	author = {Rajiv Kumar and Shashin Sharan and Haneet Wason and Felix J. Herrmann}
}


@book{devaney2012mathematical,
  place={Cambridge},
  author={Devaney, Anthony J.},
  title={Mathematical Foundations of Imaging, Tomography and Wavefield Inversion},
  DOI={10.1017/CBO9781139047838},
  publisher={Cambridge University Press},
  year={2012}
}


@article {devaney1998method,
	title = {A method for specifying non-radiating, monochromatic, scalar sources and their fields},
	journal = {Pure and Applied Optics: Journal of the European Optical Society Part A},
	volume = {7},
	number = {5},
	year = {1998},
	pages = {1213-1220},
	url = {http://stacks.iop.org/0963-9659/7/i=5/a=026},
	author = {Anthony J Devaney and Edwin A Marengo}
}


@Presentation {louboutin2016SINBADFhps,
	title = {High-performance seismic applications of {OPESCI}},
	journal = {SINBAD Fall consortium talks},
	year = {2016},
	publisher = {SINBAD},
	abstract = {We present our latest geophysical applications built on OPESCI. By using a high-level symbolic API, we allow for fast development and easy implementation of various (acoustic, VT, TTI) wave propagators relevant to exploration geophysics. We start by highlighting possibilities in an acoustic setting including classical operators such as forward modelling and linearised forward (Born) modelling as well as more advanced operators deriving from wave equations with double dipoles and the application of the PDE to a wavefield instead of applying its inverse. We will also show that the performance (time to solution) of this code is on par with industrial software libraries (10\% faster on the full SEAM model). We finally present our implementation of 3D TTI modelling and its adjoint including out comprehensive testing framework. This is joint work with Gerard Gorman},
	keywords = {Presentation, private, SINBAD, SINBADFALL2016, SLIM},
	url = {https://www.slim.eos.ubc.ca/Publications/Private/Conferences/SINBAD/2016/Fall/louboutin2016SINBADFhps/louboutin2016SINBADFhps.pdf},
	url2 = {https://www.slim.eos.ubc.ca/Publications/Private/Conferences/SINBAD/2016/Fall/louboutin2016SINBADFhps/louboutin2016SINBADFhps.mov},
	author = {Mathias Louboutin and Felix J. Herrmann}
}

@book{rockafellar1970convex,
  author={Rockafellar, R.T.},
  title={Convex Analysis},
  publisher={Princeton University Press},
  year={1970}
}


@book{boyd2009convex,
  author={Boyd, Stephen and Vandenberghe, Lieven},
  title={Convex Optimization},
  isbn={978-0-521-83378-3},
  publisher={Cambridge University Press},
  year={2009}
}

@conference{cosse2015SEGshort,
	title = {A short note on rank-2 relaxation for waveform inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2015},
        pages = {1344-1350},
	publisher = {SEG},
	organization = {SEG},
        keywords = {SEG},
	doi = {10.1190/segam2015-5925071.1},
	url = {http://dx.doi.org/10.1190/segam2015-5925071.1},
	author = {Augustin Cosse and Stephen D. Shank and Laurent Demanet}
}

@article {alkhalifah2000acoustic,
	title = {An acoustic wave equation for anisotropic media},
	journal = {GEOPHYSICS},
	volume = {65},
	number = {4},
	year = {2000},
	pages = {1239-1250},
        doi = {10.1190/1.1444815},
	url = {https://doi.org/10.1190/1.1444815},
	author = {Tariq Alkhalifah}
}

@article {etgen2009depth,
	title = {An overview of depth imaging in exploration geophysics},
	journal = {GEOPHYSICS},
	volume = {74},
	number = {6},
	year = {2009},
	pages = {WCA5-WCA17},
        doi = {10.1190/1.3223188},
	url = {https://doi.org/10.1190/1.3223188},
	author = {John Etgen and Samuel H. Gray and Yu Zhang}
}

@article {kowalski2009sparsity,
	title = {Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients},
	journal = {Signal, Image and Video Processing},
	volume = {3},
	number = {3},
	year = {2009},
	pages = {251-264},
	keywords = {Mixed-norms, Time-Frequency decompositions, Sparse representations},
        doi = {10.1007/s11760-008-0076-1},
	url = {http://dx.doi.org/10.1007/s11760-008-0076-1},
	author = {Kowalski, Matthieu and Torrésani, Bruno}
}


@article {Mansour11TRssma,
	title = {Randomized marine acquisition with compressive sampling matrices},
	journal = {Geophysical Prospecting},
	volume = {60},
	number = {4},
	year = {2012},
	month = {07},
	pages = {648-662},
	address = {University of British Columbia, Vancouver},
	abstract = {Seismic data acquisition in marine environments is a costly process that calls for the adoption of simultaneous-source or randomized acquisition - an emerging technology that is stimulating both geophysical research and commercial efforts. Simultaneous marine acquisition calls for the development of a new set of design principles and post-processing tools. In this paper, we discuss the properties of a specific class of randomized simultaneous acquisition matrices and demonstrate that sparsity-promoting recovery improves the quality of reconstructed seismic data volumes. We propose a practical randomized marine acquisition scheme where the sequential sources fire airguns at only randomly time-dithered instances. We demonstrate that the recovery using sparse approximation from random time-dithering with a single source approaches the recovery from simultaneous-source acquisition with multiple sources. Established findings from the field of compressive sensing indicate that the choice of the sparsifying transform that is incoherent with the compressive sampling matrix can significantly impact the reconstruction quality. Leveraging these findings, we then demonstrate that the compressive sampling matrix resulting from our proposed sampling scheme is incoherent with the curvelet transform. The combined measurement matrix exhibits better isometry properties than other transform bases such as a non-localized multidimensional Fourier transform. We illustrate our results with simulations of "ideal" simultaneous-source marine acquisition, which dithers both in time and space, compared with periodic and randomized time-dithering.},
	keywords = {curvelet transform, Fourier, Marine acquisition},
	doi = {10.1111/j.1365-2478.2012.01075.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01075.x/abstract},
	url2 = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/GeophysicalProspecting/2012/Mansour11TRssma/Mansour11TRssma.pdf},
	author = {Hassan Mansour and Haneet Wason and Tim T.Y. Lin and Felix J. Herrmann}
}

@article {michel2014grad,
	title = {Gradient calculation for waveform inversion of microseismic data in VTI media},
	journal = {Journal of Seismic Exploration},
	volume = {23},
	number = {3},
	year = {2014},
	author = {Michel, Oscar Jarillo and Tsvankin, Ilya}
}


@article {kim2011adjoint,
	title = {Adjoint centroid-moment tensor inversions},
	journal = {Geophysical Journal International},
	volume = {186},
	number = {1},
	year = {2011},
	pages = {264-278},
	keywords = {Inverse theory, Earthquake dynamics, Earthquake source observations, Computational seismology, Theoretical seismology},
        doi = {10.1111/j.1365-246X.2011.05027.x},
	url = {http://dx.doi.org/10.1111/j.1365-246X.2011.05027.x},
	author = {Kim, YoungHee and Liu, Qinya and Tromp, Jeroen}
}


@article {wu1996elastic,
	title = {Elastic full-waveform inversion for earthquake source parameters},
	journal = {Geophysical Journal International},
	volume = {127},
	number = {1},
	year = {1996},
	pages = {61-74},
	keywords = {earthquakes, source parameters, waveform inversion},
        doi = {10.1111/j.1365-246X.1996.tb01535.x},
	url = {http://dx.doi.org/10.1111/j.1365-246X.1996.tb01535.x},
	author = {Wu, Yafei and McMechan, George A.}
}


@article {bazargani2016opt,
	title = {Optimal source imaging in elastic media},
	journal = {Geophysical Journal International},
	volume = {204},
	number = {2},
	year = {2016},
	pages = {1134-1147},
	keywords = {Image processing, Inverse theory, Earthquake source observations,Theoretical seismology},
        doi = {10.1093/gji/ggv494},
	url = {http://dx.doi.org/10.1093/gji/ggv494},
	author = {Bazargani, Farhad and Snieder, Roel}
}

@article {osher2010flb,
	title = {Fast {Linearized} {Bregman} {Iterations} for {Compressive} {Sensing} and {Sparse} {Denoising}},
	journal = {Communications in Mathematical Sciences},
	volume = {8},
	number = {1},
	year = {2010},
	pages = {93-111},
	publisher = {2010 International Press},
	keywords = {$\ell_1$ - minimization, basis pursuit, compressed sensing, duality, sparse denoising, iterative regularization},
	url = {https://arxiv.org/abs/1104.0262},
	author = {Stanley Osher and Yu Mao and Bin Dong and Wotao Yin}
}

@article {berg2008SJSCpareto,
	title = {Probing the {Pareto} frontier for basis pursuit solutions},
	journal = {SIAM Journal on Scientific Computing},
	volume = {31},
	number = {2},
	year = {2008},
	month = {01},
	pages = {890-912},
	publisher = {SIAM},
	abstract = {The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the root-finding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems.},
	keywords = {basis pursuit, convex program, duality, Newton{\textquoteright}s method, one-norm regularization, Optimization, projected gradient, root-finding, sparse solutions},
	doi = {10.1137/080714488},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/SIAMJournalOnScientificComputing/2008/vanderberg08SIAMptp/vanderberg08SIAMptp.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}


@conference {esser2015CAMSAPrsa,
	title = {Resolving scaling ambiguities with the $\ell_1/\ell_2$ norm in a blind deconvolution problem with feedback},
	booktitle = {IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing},
	year = {2015},
	note = {(IEEE CAMSAP Workshop, Canc{\'u}n, Mexico)},
	month = {12},
	pages = {365-368},
	abstract = {Compared to more mundane blind deconvolution problems, blind deconvolution in seismic applications involves a feedback mechanism related to the free surface. The presence of this feedback mechanism gives us an unique opportunity to remove ambiguities that have plagued blind deconvolution for a long time. While beneficial, this feedback by itself is insufficient to remove the ambiguities even with $\ell_1$ constraints. However, when paired with an $\ell_1/\ell_2$ constraint the feedback allows us to resolve the scaling ambiguity under relatively mild assumptions. Inspired by lifting approaches, we propose to split the sparse signal into positive and negative components and apply an $\ell_1/\ell_2$ constraint to the difference, thereby obtaining a constraint that is easy to implement. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.},
	keywords = {$\ell_1/\ell_2$, blind deconvolution, CAMSAP, lifting, method of multipliers},
	doi = {10.1109/CAMSAP.2015.7383812},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa.pdf},
	presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_poster.pdf},
	url2 = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_ext.pdf},
	author = {Ernie Esser and Rongrong Wang and Tim T.Y. Lin and Felix J. Herrmann}
}


@conference {lakings2006SEGsurface,
	title = {Surface based microseismic monitoring of a hydraulic fracture well stimulation in the Barnett shale},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2006},
	pages = {605-608},
	doi = {10.1190/1.2370333},
	URL = {https://library.seg.org/doi/abs/10.1190/1.2370333},
	eprint = {https://library.seg.org/doi/pdf/10.1190/1.2370333},
	author = {James D. Lakings and Peter M. Duncan and Chris Neale and Todd Theiner}
}

@article{symes2007reverse,
  title={Reverse time migration with optimal checkpointing},
  author={Symes, William W.},
  journal={GEOPHYSICS},
  volume={72},
  number={5},
  pages={SM213-SM221},
  year={2007},
  url={http://dx.doi.org/10.1190/1.2742686}
}


@conference {kukreja2016OGHPClsm,
	title = {Leveraging symbolic math for rapid development of applications for seismic modeling},
	booktitle = {OGHPC},
	year = {2017},
	note = {(Oil and Gas HPC Conference, Rice University)},
	month = {03},
	abstract = {Wave propagation kernels are the core of many commonly used algorithms for inverse problems in exploration geophysics. While they are easy to write and analyze for the simplied cases, the code quickly becomes complex when the physics needs to be made more precise or the performance of these codes is to be optimized. Signicant eort is repeated every time new forms of physics need to be implemented, or a new computing platform to be supported. The use of symbolic mathematics as a domain specic language (DSL) for input, combined with automatic generation of high performance code customized for the target hardware platform is a promising approach to maximize code reuse. Devito is a DSL for nite dierence that uses symbolic mathematics to generate optimized code for wave propagation based on a provided wave equation. It enables rapid application development in a eld where the average time spent on development has historically been in weeks and months. The Devito DSL system is completely wrapped within the Python programming language and the fact that the running code is in C is completely transparent, making it simple to include Devito as part of a larger work ow including multiple applications over a large cluster.},
	keywords = {finite differences, HPC, Modelling, OGHPC, time domain},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/OGHPC/2017/kukreja2016OGHPClsm/kukreja2016OGHPClsm.pdf},
	presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/OGHPC/2017/kukreja2016OGHPClsm/kukreja2016OGHPClsm_pres.pdf},
	author = {Navjot Kukreja and Mathias Louboutin and Michael Lange and Fabio Luporini and Gerard Gorman}
}

@article{abbe1873beit,
  title={Beitr{\"a}ge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung},
  author={Abbe, E.},
  journal={Archiv f{\"u}r mikroskopische Anatomie},
  volume={9},
  number={1},
  pages={413–418},
  year={1873},
  url={http://dx.doi.org/10.1007/BF02956173}
}

@article{fink1997time,
  title={Time Reversed Acoustics},
  author={Fink, Mathias},
  journal={Physics Today},
  volume={50},
  number={3},
  pages={34–40},
  year={1997},
  url={http://dx.doi.org/10.1063/1.881692}
}

@conference{webster2013SEGdas,
	title = {Micro-seismic Detection using Distributed Acoustic Sensing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
        pages = {2459-2463},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Distributed Acoustic Sensing (DAS) deployed in a wellbore can be used to detect P-waves and S-waves generated in the subsurface. In a well which has geophones and a DAS cable deployed, micro-seismic events have been detected on both instruments at the same time, establishing the concept of using DAS as a micro-seismic detector. While DAS is still less sensitive than geophones, it has the advantage of being non intrusive and a permanent installation, so both recording in treatment wells and 4D recording concepts are realistic options that can be implemented once the fibered cable is installed.},
        keywords = {SEG},
	doi = {10.1190/segam2013-0182.1},
	url = {http://library.seg.org/doi/abs/10.1190/segam2013-0182.1},
	author = {P. Webster and J. Wall and C. Perkins and M. Molenaar}
}


@article{silver1982optimal,
  title={Optimal estimation of scalar seismic moment},
  author={Silver, Paul G. and Jordon, Thomas H.},
  journal={Geophysical Journal of the Royal Astronomical Society},
  volume={70},
  number={3},
  pages={755–787},
  year={1982},
  url={http://dx.doi.org/10.1111/j.1365-246X.1982.tb05982.x}
}


@article{vasco1989inversion,
  title={Inversion of Waveforms For Extreme Source Models With an application to the Isotropic Moment Tensor Component},
  author={Vasco, D.W. and Johnson, L.R.},
  journal={Geophysical Journal International},
  volume={97},
  number={1},
  pages={1-18},
  year={1989},
  url={http://dx.doi.org/10.1111/j.1365-246X.1989.tb00480.x}
}


@conference{ely2013IEEEmethods,
	title = {Methods for Large Scale Hydraulic Fracture Monitoring},
	booktitle = {5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
	volume = {35},
	year = {2013},
        pages = {272-275},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {In this paper we propose computationally efficient and robust methods for estimating the moment tensor and location of micro- seismic event(s) for large search volumes. Our contribution is two-fold. First, we propose a novel joint-complexity measure, namely the sum of nuclear norms which while imposing sparsity on the number of fractures (locations) over a large spatial volume, also captures the rank-1 nature of the induced wavefield pattern. This wavefield pattern is modeled as the outer-product of the source signature with the amplitude pattern across the receivers from a seismic source. A rank-1 factorization of the estimated wavefield pattern at each location can therefore be used to estimate the seismic moment tensor using the knowledge of the array geometry. In contrast to existing work this approach allows us to drop any other assumption on the source signature. Second, we exploit the recently proposed first-order incremental projection algorithms for a fast and efficient implementation of the resulting optimization problem and develop a hybrid stochastic & deterministic algorithm which results in significant computational savings.},
	url = {http://signalprocessingsociety.org/CAMSAP2013/papers/1569814265.pdf},
	author = {Gregory Ely and Shuchin Aeron}
}


@article{song1995freq,
  title={Frequency-domain acoustic-wave modeling and inversion of crosshole data: Part 1-2.5D modeling method},
  author={Song, Zhong-Min and Williamson, Paul R.},
  journal={GEOPHYSICS},
  volume={60},
  number={3},
  pages={784-795},
  year={1995},
  url={http://dx.doi.org/10.1190/1.1443817}
}


@conference{wang2016SEGmicro,
	title = {Micro-seismic imaging using a source independent full waveform inversion method},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {35},
	year = {2016},
        pages = {2596-2600},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic pro- cess (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of mi- croseismic events to invert for the source image, source func- tion and the velocity model. It is based on convolving refer- ence traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the ve- locity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.},
        keywords = {SEG},
	doi = {10.1190/segam2016-13946573.1},
	url = {http://dx.doi.org/10.1190/segam2016-13946573.1},
	author = {Hanchen Wang and Tariq Alkhalifah}
}

@article{nakata2016reverse,
  title={Reverse time migration for microseismic sources using the geometric mean as an imaging condition},
  author={Nakata, Nori and Beroza, Gregory C.},
  journal={GEOPHYSICS},
  volume={81},
  number={2},
  pages={K551–K560},
  year={2016},
  url={http://dx.doi.org/10.1190/GEO2015-0278.1}
}

@book{maxwell2014hydraulic,
  abstract={The objective of a hydraulic-fracture treatment is to stimulate production for a well, by injecting high-pressure fluids to stimulate a fracture network and enhance permeability and production (Montgomery and Smith, 2010). The first hydraulic-fracture treatment was performed in 1947 in the Hugoton field in Kansas, U.S.A. Since that time, technological advancements have transformed the process into a routine operation in most North American oil and gas well completions. Modern stimulations can involve injection of up to several thousand cubic meters of fluid (over a million gallons) using tens of thousands of pumping horsepower for high-rate injection. Depending on the total injection volume, individual hydraulic-fracture stimulations can cost anywhere between $10,000 (U. S. dollars) and several million. The current worldwide commercial fracturing market is estimated at nearly $30 billion per year — mainly in North America and consisting mostly of fracturing wells in unconventional reservoirs. Many modern wells are drilled horizontally and typically can be stimulated with 15 to 30 individual fracture treatments or stages at different positions along their length, although in some cases as many as 60 fracture stages have been performed.},
  author={Maxwell, Shawn},
  booktitle={Microseismic Imaging of Hydraulic Fracturing: Improved Engineering of Unconventional Shale Reservoirs},
  chapter={2},
  doi={10.1190/1.9781560803164.ch2},
  isbn={978-1-56080-316-4},
  number={17},
  pages={pp 15-30},
  publisher={Society of Exploration Geophysicists},
  series={Distinguished Instructor Series},
  title={2. Hydraulic-fracturing Concepts},
  url={http://dx.doi.org/10.1190/1.9781560803164.ch2},
  year={2014}
}

@article{yin2010analysis,
  title={Analysis and Generalizations of the Linearized Bregman Method},
  author={Yin, Wotao},
  journal={SIAM J. IMAGING SCIENCES},
  volume={3},
  number={4},
  pages={856–877},
  year={2010},
  url={http://dx.doi.org/10.1137/090760350}
}

@article{liu1989on,
  title={On the limited memory {B}{F}{G}{S} method for large scale optimization},
  author={Liu, Dong C. and Nocedal, Jorge},
  journal={J. Mathematical Programming},
  volume={45},
  number={1},
  pages={503–528},
  year={1989},
  url={http://dx.doi.org/10.1007/BF01589116}
}

@article{huang2013accel,
  title={Accelerated {L}inearized {B}regman {M}ethod},
  author={Huang, Bo and Ma, Shiqian and Goldfarb, Donald},
  journal={Journal of Scientific Computing},
  volume={54},
  number={2},
  pages={428–453},
  year={2013},
  url={http://dx.doi.org/10.1007/s10915-012-9592-9}
}

@article{bolton2001travel,
  title={Travel times of P and S from the global digital seismic networks: Implications for the relative variation of P and S velocity in the mantle},
  author={Bolton, Harold and Masters, Guy},
  journal={Journal of Geophysical Research: Solid Earth},
  volume={106},
  number={B7},
  pages={13527-13540},
  year={2001},
  url={https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000JB900378}
}

@article{rod2012sim,
  title={Simultaneous recovery of origin time, hypocentre location and seismic moment tensor using sparse representation theory},
  author={Rodriguez, Ismael Vera and Sacchi, Mauricio and Gu, Yu J.},
  journal={Geophysical Journal International},
  volume={188},
  number={3},
  pages={1188–1202},
  year={2012},
  url={http://dx.doi.org/10.1111/j.1365-246X.2011.05323.x}
}

@book{madariaga1989seismic,
  author={Madariaga, Raul},
  isbn={978-0-387-30752-7},
  pages={1129-1133},
  publisher={Springer US},
  title={Seismic source: Theory},
  url={http://dx.doi.org/10.1007/0-387-30752-4_137},
  year={1989}
}

@article{rie2015intro,
  title={Introduction to microseismic source mechanisms},
  author={Kamei, Rie and Nakata, Nori and Lumley, David},
  journal={The Leading Edge},
  volume={34},
  number={8},
  pages={876–880},
  year={2015},
  url={http://dx.doi.org/10.1190/tle34080876.1}
}

@article{Cance2015Validity,
  title={Validity of the acoustic approximation for elastic waves in heterogeneous media},
  author={Cance, Philippe and Capdeville, Yann},
  journal={GEOPHYSICS},
  volume={80},
  number={4},
  pages={T161–T173},
  year={2015},
  url={http://dx.doi.org/10.1190/GEO2014-0397.1}
}

@article{myung2003elastic,
  title={Elastic Properties of Overpressured and Unconsolidated Sediments},
  author={Lee, Myung W.},
  journal={U.S. Geological Survey Bulletin},
  volume={2214},
  year={2003},
  url={https://pubs.usgs.gov/bul/b2214/b2214-508.pdf}
}

@book{shawn2014micro,
  author={Maxwell, Shawn},
  isbn={978-1-56080-316-4},
  pages={81-100},
  publisher={Society of Exploration Geophysicists},
  booktitle={Microseismic Imaging of Hydraulic Fracturing: Improved Engineering of Unconventional Shale Reservoirs},
  title={Geomechanics of Microseismic Deformation},
  url={http://dx.doi.org/10.1190/1.9781560803164.ch5},
  year={2014}
}


@article{onge2011noise,
  title={Noise Examples from Two Microseismic Datasets},
  author={St-Onge, Andy and Eaton, David W.},
  journal={CSEG RECORDER},
  volume={36},
  number={8},
  pages={46–49},
  year={2011},
  url={https://csegrecorder.com/assets/pdfs/2011/2011-10-RECORDER-Noise_Examples_from_Two_Datasets.pdf}
}


@article{david2010the,
  title={Microseismic Moment Tensors: the Good, the Bad and the Ugly},
  author={Eaton, David W. and Forouhideh, Farshid},
  journal={CSEG RECORDER},
  volume={35},
  number={9},
  pages={44–47},
  year={2010},
  url={http://csegrecorder.com/assets/pdfs/2010/2010-11-RECORDER-Microseismic_Moment.pdf}
}

@conference{maxwell2013CSEGmicro,
	title = {Microseismic Signal Loss From Reservoir to Surface},
	year = {2013},
	publisher = {CSEG},
	organization = {CSEG},
        keywords = {Geoconvention},
	url = {https://cseg.ca/assets/files/resources/abstracts/2013/058_GC2013_Microseismic_Signal_Loss.pdf},
	author = {S.C. Maxwell and D. Raymer and M. Williams and P. Primiero}
}

@conference{eric2010CSPGbene,
	title = {Benefits of Hydrophones for Land Seismic Monitoring},
	year = {2010},
	publisher = {CSPG},
	organization = {CSPG},
	abstract = {CGGVeritas has conducted for Shell Canada a 4D project based on a network of buried mini- vibrators associated with buried sensors. This paper shows a comparison of signal and noise recorded on different types of sensors (surface DSU, buried geophones and hydrophones). We conclude that buried hydrophones provided the best data quality: a) they are free of shear wave, b) they present a better Signal to Noise ratio (20dB gain), c) they show better repeatability. Therefore, hydrophones are also well adapted for permanent seismic land acquisition used in 4D monitoring.},
        keywords = {CSPG},
	url = {http://www.cspg.org/cspg/documents/Conventions/Archives/Annual/2010/0872_GC2010_Benefits_of_Hydrophones_for_Land_Seismic_Monitoring.pdf},
	author = {Eric Forgues and Estelle Rebel}
}

@article{jost1989stu,
  title={A Student's Guide to and Review of Moment Tensors},
  author={Jost, M. L. and Herrmann, R. B.},
  journal={Seismological Research Letters},
  volume={60},
  number={2},
  pages={37–57},
  year={1989},
  url={https://doi.org/10.1785/gssrl.60.2.37}
}


@article{leo2013freq,
  title={The peak frequency of direct waves for microseismic events},
  author={Eisner, Leo and Gei, Davide and Hallo, Miroslav and Opršal, Ivo and Ali, Mohammed Y.},
  journal={GEOPHYSICS},
  volume={78},
  number={6},
  pages={A45–A49},
  year={2013},
  url={http://dx.doi.org/10.1190/GEO2013-0197.1}
}


@conference {kumar2017EAGEdha,
    title = {Denoising high-amplitude cross-flow noise using curvelet-based stable principle component pursuit},
    booktitle = {EAGE Annual Conference Proceedings},
    year = {2017},
    note = {(EAGE, Paris)},
    month = {06},
    abstract = {Removal of high-amplitude cross-flow noise in marine towed-streamer acquisition is of great interest because cross-flow noise hinders the success of subsequent processing (e.g. EPSI) and migration. However, the removal of cross-flow noise is a challenging process because cross-flow noise dominates steep angles and low-frequency components of the signal. As a result, applying a simple high-pass filter can result in a loss of coherent diving waves and reflected energy. We propose a stable curvelet-based principle-component pursuit approach that does not suffer from this shortcoming because it uses angle- and scale-adaptivity of the curvelet transform in combination with the low-rank property of cross-flow noise. As long as the cross-flow noise exhibits low-rank in the curvelet domain, our method successfully separates this signal component from the diving waves and seismic reflectivity, which is well-know to be sparse in the curvelet domain. Experimental results on a common-shot gather extracted from a coil shooting survey in the Gulf of Mexico shows the potential of our approach.},
    keywords = {coil data, cross-flow noise, curvelet, denoising, EAGE, SPCP},
    doi = {10.3997/2214-4609.201701055},
    url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2017/kumar2017EAGEdha/kumar2017EAGEdha.html},
    presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2017/kumar2017EAGEdha/kumar2017EAGEdha_poster.pdf},
    author = {Rajiv Kumar and Nick Moldoveanu and Felix J. Herrmann}
}


@conference{sharan2017SEGhigh,
	title = {High-resolution fast microseismic source collocation and source time-function estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {35},
	year = {2017},
        pages = {2778-2783},
	publisher = {SEG},
	organization = {SEG},
	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 ``2.5``D instead of ``2``D.},
        keywords = {SEG},
	doi = {10.1190/segam2017-17787749.1},
	url = {http://dx.doi.org/10.1190/segam2017-17787749.1},
	author = {Shashin Sharan and Rongrong Wang and Felix J Herrmann}
}


@conference{sharan2016SEGsparsity,
	title = {Sparsity-promoting joint microseismic source collocation and source-time function estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {35},
	year = {2016},
        pages = {2574-2579},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this work, we propose a new method to simultaneously locate microseismic events (e.g., induced by hydraulic fracturing) and estimate the source signature of these events. We use the method of linearized Bregman. This algorithm focuses unknown sources at their true locations by promoting sparsity along space and at the same time keeping the energy along time in check. We are particularly interested in situations where the microseismic data is noisy, sources have different signatures and we only have access to the smooth background-velocity model. We perform numerical experiments to demonstrate the usability of the proposed method. We also compare our results with full-waveform inversion based microseismic event collocation methods. Our method gives flexibility to simultaneously get a more accurate source image along with an estimate of the source-time function, which carries important information on the rupturing process and source mechanism.},
        keywords = {SEG},
	doi = {10.1190/segam2016-13871022.1},
	url = {http://dx.doi.org/10.1190/segam2016-13871022.1},
	author = {Shashin Sharan and Rongrong Wang and Tristan Van Leeuwen and Felix J Herrmann}
}


@conference{eisner2011SEGchallenges,
	title = {Challenges for microseismic monitoring},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
        pages = {1519-1523},
	publisher = {SEG},
	organization = {SEG},
        keywords = {SEG},
	doi = {10.1190/1.3627491},
	url = {http://dx.doi.org/10.1190/1.3627491},
	author = {Leo Eisner and Michael Thornton and Jessica Griffin}
}


@article{kitic2016physics,
  title={Physics-Driven Inverse Problems Made Tractable With Cosparse Regularization},
  author={Kitić, Srđan and Albera, Laurent and Bertin, Nancy and Gribonval, Rémi},
  journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING},
  volume={64},
  number={2},
  pages={335–348},
  year={2016},
  url={http://dx.doi.org/10.1109/TSP.2015.2480045}
}

@article{yin2008bregman,
  title={Bregman Iterative Algorithms for $\ell_1${-}minimization with Applications to Compressed Sensing},
  author={Yin, W and Osher, S and Goldfrab, D and Darbon, J},
  journal={SIAM J. IMAGING SCIENCES},
  volume={1},
  number={1},
  pages={143–168},
  year={2008},
  url={http://dx.doi.org/10.1137/070703983}
}

@conference{nakata2015SEGrtm,
	title = {Reverse-Time Migration for Microseismic Sources Using the Geometric Mean as an Imaging Condition},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {34},
	year = {2015},
        pages = {2451-2455},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Location and characterization of seismic sources provide insight into the physics of earthquakes/microseismic, fault zones, and extension of fractures. Time reversal is a powerful tool to image directly both microseismic location and mechanism. This technique assumes seismic velocities in the medium and propagates time reversed observations of ground motion at each receiver location. Assuming an accurate velocity model and adequate array aperture, the waves will focus at the source location. Because we do not know the location and the origin time a priori, we need to scan the entire 4D image (3D in space and 1D in time) to find focusing, which makes reverse time migration (RTM) computationally demanding. We propose a new approach to reverse-time imaging that reduces the scanning dimensions from 4D to 3D (no time) and increases the spatial resolution of the source image. We first individually extrapolate wavefields at each receiver, and then crosscorrelate these wavefields (product in the frequency do- main: Geometric-mean RTM, GmRTM). This crosscorrelation creates another imaging condition, and the focusing of the seis- mic wavefields occurs at the zero time lag of the correlation. Through this approach, we can reduce the dimensions of scan- ning, and hence the computational requirements, from 4D to 3D. The crosscorrelation effectively suppresses the side lobes and yields a high-resolution image. Also, GmRTM is robust for random noise because the crosscorrelation enhances the coherent signals. An added benefit is that, in contrast to conventional one-way RTM, GmRTM has potential to be used to retrieve velocity information by using time and/or space lags of crosscorrelation similar to what is done in active-source imaging.},
        keywords = {SEG},
	doi = {10.1190/segam2015-5851848.1},
	url = {http://dx.doi.org/10.1190/segam2015-5851848.1},
	author = {Nori Nakata and Gregory C. Beroza}
}

@conference{sun2015SEGitp,
	title = {Investigating the possibility of locating microseismic sources using distributed sensor networks},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {34},
	year = {2015},
        pages = {2485-2490},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Distributed sensor networks are designed to provide computation in-situ and in real-time. The conventional time-reversal imaging approach for microseismic event location may not be optimal for such an environment. To address this challenge, we develop a methodology of locating multiple microseismic events with unknown start times based on the cross-correlation imaging condition borrowed from active-source seismic imaging. The imaging principle states that a true microseismic source must correspond to the location where all the backward propagated events coincide in both space and time. Instead of simply stacking the backward-propagated seismic wavefields, as suggested by time-reversal imaging, we perform multiplication reduction to compute a high-resolution microseismicity map. The map has an extra dimension of time, indicating the start times of different events. Combined with a distributed sensor network, our method is designed for monitoring microseismic activities and mapping fracture development during hydraulic fracturing in-situ and in real-time. We use numerical examples to test the ability of the proposed technique to produce high-resolution images of microseismic locations.},
        keywords = {SEG},
	doi = {10.1190/segam2015-5888848.1},
	url = {http://dx.doi.org/10.1190/segam2015-5888848.1},
	author = {Junzhe Sun and Tieyuan Zhu and Sergey Fomel and Wen{\-}Zhan Song}
}

@conference{kad2015SEGmee,
	title = {Microseismic event estimation in noisy data via full waveform inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {34},
	year = {2015},
        pages = {1159-1164},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full waveform inversion accurately estimates the full spatial and temporal description of a microseismic source which includes not only the location and origin time of the source but also the waveform itself. Assuming two-dimensional acoustic wave propagation, the gradient is computed via the adjoint-state method for both the spatial radiation pattern and the temporal waveform of the source. Neither of these gradients requires storing the forward solution of the wave equation as is required by the imaging condition for velocity inversion. This approach identifies multiple sources, handles extremely low signal-to-noise ratio data, and produces accurate results in the absence of a good initial estimate.},
        keywords = {SEG},
	doi = {10.1190/segam2015-5867154.1},
	url = {http://dx.doi.org/10.1190/segam2015-5867154.1},
	author = {Jordan Kaderli and Matthew D. McChesney and Susan E. Minkoff}
}

@article{rutledge2003hydraulic,
  title={Hydraulic stimulation of natural fractures as revealed by induced microearthquakes, Carthage Cotton Valley gas field, east Texas},
  author={Rutledge, James T and Phillips, W. Scott},
  journal={GEOPHYSICS},
  volume={68},
  number={2},
  pages={441–452},
  year={2003},
  url={http://dx.doi.org/10.1190/1.1567214}
}

@article{carl2010frac,
  title={Hydraulic Fracturing: History Of An Enduring Technology},
  author={Montgomery, Carl T and Smith, Michael B},
  journal={Journal of Petroleum Technology},
  volume={62},
  number={12},
  pages={26–40},
  year={2010},
  url={http://dx.doi.org/10.2118/1210-0026-JPT}
}

@article{george1982det,
  title={Determination of source parameters by wavefield extrapolation},
  author={McMechan, George A},
  journal={Geophysical Journal of the Royal Astronomical Society},
  volume={71},
  number={3},
  pages={613–628},
  year={1982}
}

@article{rentsch2007fast,
  title={Fast location of seismicity: A migration-type approach with application to hydraulic-fracturing data},
  author={Rentsch, S and Buske, S and Lüth, S and Shapiro, S. A},
  journal={GEOPHYSICS},
  volume={72},
  number={1},
  pages={33–40},
  year={2007},
  url={http://dx.doi.org/10.1190/1.2401139}
}

@book{thurber2000earth,
  author={Thurber, Clifford H and Engdahl, E. Robert},
  isbn={978-90-481-5498-0},
  publisher={Springer Netherlands},
  title={Advances in Seismic Event Location},
  url={http://dx.doi.org/10.1007/978-94-015-9536-0_1},
  year={2000}
}

@article{waldhauser2000double,
  title={A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California},
  author={Waldhauser, Felix and Ellsworth, William L},
  journal={Bulletin of the Seismological Society of America},
  volume={90},
  number={6},
  pages={1353–1368},
  year={2000},
  url={http://dx.doi.org/10.1785/0120000006}
}

@article{dirk2014LBR,
  title={The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations},
  author={Lorenz, Dirk A and Schöpfer, Frank and Wenger, Stephan},
  journal={SIAM J. IMAGING SCIENCES},
  volume={7},
  number={2},
  pages={1237–1262},
  year={2014},
  url={http://dx.doi.org/10.1137/130936269}
}

@book{combettes2011proximal,
  abstract={The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of inverse problems and, especially, in signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.},
  author={Combettes, Patrick L and Pesquet, Jean{\-}Christophe},
  booktitle={Fixed-Point Algorithms for Inverse Problems in Science and Engineering},
  chapter={10},
  doi={10.1007/978-1-4419-9569-8_10},
  editor={Bauschke, Heinz H and Burachik, Regina S and Combettes, Patrick L and Elser, Veit and Luke, D. Russell and Wolkowicz, Henry},
  isbn={978-1-4419-9569-8},
  issn={1931-6828},
  number={1},
  pages={pp 185-212},
  publisher={Springer New York},
  series={Springer Optimization and Its Applications},
  title={Proximal Splitting Methods in Signal Processing},
  url={http://dx.doi.org/10.1007/978-1-4419-9569-8_10},
  volume={49},
  year={2011}
}

@article{sjogreen2014source,
  title={Source Estimation by Full Wave Form Inversion},
  author={Sjögreen, Björn and Petersson, N. Anders},
  journal={Journal of Scientific Computing},
  volume={59},
  number={1},
  pages={247–276},
  year={2014},
  url={http://dx.doi.org/10.1007/s10915-013-9760-6}
}

@article{dirk2005reverse,
  title={Reverse modelling for seismic event characterization},
  author={Gajewski, Dirk and Tessmer, Ekkehart},
  journal={Geophysical Journal International},
  volume={163},
  number={1},
  pages={276–284},
  year={2005},
  url={http://dx.doi.org/10.1111/j.1365-246X.2005.02732.x}
}

@article{nam2013cosparse,
  title={The cosparse analysis model and algorithms},
  author={Nam, S and Davies, M. E and Elad, M and Gribonval, R},
  journal={Applied and Computational Harmonic Analysis},
  volume={34},
  number={1},
  pages={30–56},
  year={2013},
  url={http://dx.doi.org/10.1016/j.acha.2012.03.006}
}

@conference{herrmann2015EAGEfast,
	title = {Fast “Online” Migration with Compressive Sensing},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
        month = {06},
	publisher = {EAGE},
	organization = {EAGE},
	abstract = {We present a novel adaptation of a recently developed relatively simple iterative algorithm to solve large-scale sparsity-promoting optimization problems. Our algorithm is particularly suitable to large-scale geophysical inversion problems, such as sparse least-squares reverse-time migration or Kirchoff migration since it allows for a tradeoff between parallel computations, memory allocation, and turnaround times, by working on subsets of the data with different sizes. Comparison of the proposed method for sparse least-squares imaging shows a performance that rivals and even exceeds the performance of state-of-the art one-norm solvers that are able to carry out least-squares migration at the cost of a single migration with all data.},
        keywords = {EAGE,LSRTM},
	url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2015/herrmann2015EAGEfom/herrmann2015EAGEfom.html},
        presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2015/herrmann2015EAGEfom/herrmann2015EAGEfom_pres.pdf},
        url2 = {http://www.earthdoc.org/publication/publicationdetails/?publication=80695},
	author = {Herrmann, Felix J and Tu, Ning and Esser, Ernie}
}

@article{lorentz2014ask,
  author={{Lorenz}, D.~A. and {Wenger}, S. and {Sch{\"o}pfer}, F. and {Magnor}, M.},
  title={A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing},
  journal={ArXiv e-prints},
  archivePrefix = "arXiv",
  eprint = {1403.7543},
  primaryClass = "math.OC",
  keywords = {Mathematics - Optimization and Control, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Information Theory, Mathematics - Numerical Analysis},
  year = 2014,
  month = mar,
  adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1403.7543L},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System},
  url={http://arxiv.org/pdf/1403.7543v1.pdf}
}
@article {herrmann2009GEOPcbm,
	title = {Curvelet-based migration preconditioning and scaling},
	journal = {Geophysics},
	volume = {74},
	year = {2009},
	month = {07-08},
	pages = {A41-A46},
	abstract = {The extremely large size of typical seismic imaging problems has been one of the major stumbling blocks for iterative techniques to attain accurate migration amplitudes. These iterative methods are important because they complement theoretical approaches that are hampered by difficulties to control problems such as finite-acquisition aperture, source-receiver frequency response, and directivity. To solve these problems, we apply preconditioning, which significantly improves convergence of least-squares migration. We discuss different levels of preconditioning that range from corrections for the order of the migration operator to corrections for spherical spreading, and position and reflector-dip dependent amplitude errors. While the first two corrections correspond to simple scalings in the Fourier and physical domain, the third correction requires phase-space (space spanned by location and dip) scaling, which we carry out with curvelets. We show that our combined preconditioner leads to a significant improvement of the convergence of least-squares {\textquoteleft}wave-equation{\textquoteright} migration on a line from the SEG AA{\textquoteright} salt model.},
	keywords = {Imaging, migration, SLIM},
	doi = {10.1190/1.3124753},
	url = {http://geophysics.geoscienceworld.org/content/74/4/A41.abstract},
	url2 = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcbm/herrmann2009GEOPcbm.pdf},
	author = {Herrmann, Felix J. and Brown, Cody R. and Erlangga, Yogi A. and Moghaddam, Peyman P.}
}
@article{MUSAFIR20133947,
title = "On non-radiating sources",
journal = "Journal of Sound and Vibration",
volume = "332",
number = "17",
pages = "3947 - 3955",
year = "2013",
note = "Philip Doak Commemorative Issue",
issn = "0022-460X",
doi = "https://doi.org/10.1016/j.jsv.2013.02.042",
url = "http://www.sciencedirect.com/science/article/pii/S0022460X13002459",
author = "Ricardo E. Musafir"
}
@article{Porter:82,
author = {R. P. Porter and A. J. Devaney},
journal = {J. Opt. Soc. Am.},
keywords = {},
number = {3},
pages = {327--330},
publisher = {OSA},
title = {Holography and the inverse source problem},
volume = {72},
month = {Mar},
year = {1982},
url = {http://www.osapublishing.org/abstract.cfm?URI=josa-72-3-327},
doi = {10.1364/JOSA.72.000327},
abstract = {The inverse source problem for monochromatic sources Re\[$\rho$(r, $\omega$)e{\textminus}i$\omega$t\] to the scalar-wave equation is investigated. It is shown that a unique solution to the inverse source problem can be obtained by imposing the constraint that the solution minimize the source energy E $=$ $\int$d3r{\textbar}$\rho$(r, $\omega$){\textbar}2. For certain recording geometries the time derivative of the real image produced by a point-reference hologram is shown to be directly proportional to the time-reversed minimum energy source Re\[$\rho$$\ast$ME(r, $\omega$)e{\textminus}i$\omega$t\] in the short-wavelength limit.},
}