@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}
}


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

@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 BFGS 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 Linearized Bregman Method},
  author={Huang, Bo and Ma, Shiqian and Goldfrab, 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{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{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{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{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}
}


@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}
}


@conference{eisner2011SEGchallenges,
	title = {Challenges for microseismic monitoring},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
        pages = {1519-1523},
	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 = {10.1190/1.3627491},
	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{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={2010}
}

@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},
  pages={271},
  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 = {Felix J. Herrmann and Ning Tu and Ernie Esser}
}

@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}
}