@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://slim.gatech.edu/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}
}
@mastersthesis {tu2015THfis,
	title = {Fast imaging with surface-related multiples},
	year = {2015},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Surface-related multiples, which are waves that bounce more than once between the water surface and the subsurface reflectors, constitute a significant part of the data acquired in marine seismic surveys. If left untreated, they can lead to misplaced phantom reflectors in the image, and result in erroneous interpretations of the subsurface structure. As a result, these multiples are removed before the imaging procedure in conventional seismic data processing. However, because they interact more with the subsurface medium, they may carry extra information that is not present in the primaries. Therefore instead of removing these multiples, a more desirable alternative is to make active use of them. We derive from the well-established "Surface-Related Multiple Elimination" relation, and arrive at a linearized expression of the wave-equation based modelling that incorporates the surface- related multiples. We then present a computationally efficient approach to iteratively invert this expression to obtain an image of the subsurface from data that contain multiples. We achieve the computational efficiency inside each iteration by (i) using the wave-equation solver to implicitly carry out the expensive multiple prediction; and (ii) reducing the number of wave-equation solves during data simulation by subsampling the monochromatic source experiments. We show that, compared with directly applying the cross-correlation/deconvolutional imaging conditions, the presented approach can suppress the coherent imaging artifacts from multiples more effectively. We also show that, by curvelet-domain sparsity promoting and occasionally drawing new data samples during the inversion, the proposed inversion method gains improved robustness to velocity errors in the background model, as well as modelling errors incurred during linearization of the wave-equation. To combine the information encoded in both the primaries and the multiples, we then propose a highly accurate source estimation method to jointly invert the total upgoing wavefield. We show with field data examples that we can reap benefits from both the relative noise-free primaries and the extra illumination coverage of the multiples. We also demonstrate that the inclusion of multiples help mitigate the amplitude ambiguity during source estimation. We conclude the thesis with an outlook for future research directions, as well as potential extensions of the proposed work.},
	keywords = {inversion, least-squares, multiples, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis_pres.pdf},
	author = {Ning Tu}
}
@article {tu2014fis,
	title = {Fast imaging with surface-related multiples by sparse inversion},
	journal = {Geophysical Journal International},
	volume = {201},
	number = {1},
	year = {2015},
	note = {(Geophysical Journal International)},
	month = {04},
	pages = {304-317},
	abstract = {In marine exploration seismology, surface-related multiples are usually treated as noise mainly because subsequent processing steps, such as migration velocity analysis and imaging, require multiple-free data. Failure to remove these wavefield components from the data may lead to erroneous estimates for migration velocity or result in strong coherent artefacts that interfere with the imaged reflectors. However, multiples can carry complementary information compared to primaries, as they interact with the free surface and are therefore exposed more to the subsurface. Recent work has shown that when processed correctly multiples can improve seismic illumination. Given a sufficiently accurate background velocity model and an estimate for the source signature, we propose a new and computationally efficient linearized inversion procedure based on two-way wave equations, which produces accurate images of the subsurface from the total upgoing wavefield including surface-related multiples. Modelling of the surface-related multiples in the proposed method derives from the well-known surface-related multiple elimination method. We incur a minimal overhead from incorporating the multiples by having the wave-equation solver carry out the multiple predictions via the inclusion of an areal source instead of expensive dense matrix-matrix multiplications. By using subsampling techniques, we obtain high-quality true-amplitude least-squares migrated images at computational costs of roughly a single reverse-time migration (RTM) with all the data. These images are virtually free of coherent artefacts from multiples. Proper inversion of the multiples would be computationally infeasible without using these techniques that significantly bring down the cost. By promoting sparsity in the curvelet domain and using rerandomization, out method gains improved robustness to errors in the background velocity model, and errors incurred in the linearization of the wave equation with respect to the model. We demonstrate the superior performance of the proposed method compared to the conventional RTM using realistic synthetic examples.},
	keywords = {approximate message passing, Compressive Sensing, curvelet, inversion, Kaczmarz, multiples},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2014/tu2014fis/tu2014fis.pdf},
	url2 = {http://gji.oxfordjournals.org/cgi/content/full/ggv020?ijkey=pKzrSXbtxjlOjzd\&keytype=ref},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {yang2015SINBADFfis,
	title = {Fast imaging with surface-related multiples: {\textendash} shallow water multiples},
	year = {2015},
	publisher = {SINBAD},
	abstract = {In this talk, we will show surface-related multiples imaging with source estimation. Here the algorithms are based on linearized bregman, and we give the source estimation formulation in this case. With the featured blocked structure of linearized bregman, we can do efficient imaging in straightforward way by randomly choosing sources and frequencies. Another benefit is the simplicity to delivery the algorithm.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/yang2015SINBADFfis/yang2015SINBADFfis.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/yang2015SINBADFfis/yang2015SINBADFfis.mov},
	author = {Mengmeng Yang and Ning Tu and Felix J. Herrmann}
}
@article {tu2015TLEfls,
	title = {Fast least-squares imaging with surface-related multiples: application to a North-Sea data set},
	journal = {The Leading Edge},
	volume = {34},
	number = {7},
	year = {2015},
	note = {(The Leading Edge)},
	month = {07},
	pages = {788{\textendash}794},
	abstract = {In marine seismic acquisition, surface-related multiples constitute a significant portion of the acquired data. Typically, multiples are removed during early-stage data-processing as they can lead to phantom reflectors during migration that may result in erroneous geological interpretations. However, if properly dealt with, multiples can provide valuable extra information and complement primaries in illuminating the subsurface. In this article, we demonstrate the limitation of the reverse-time migration in imaging these multiples, and present an alternative inversion procedure that is computationally efficient, that jointly maps both primaries and multiples to the true reflectors, and where the source function is estimated on the fly. As a result, we obtain high-quality, mostly artifact-free, broad-band images where the imprint of the source-function are partly removed at a computationally affordable expense compared to the combined costs of the wave-equation based surface-related multiple elimination and the reverse-time migration. We achieve all this by including the total downgoing wavefields as areal sources in the least-squares migration in combination with curvelet-domain sparsity promotion. We apply the proposed method to a shallow-water marine data set from the North sea, which contains abundant short-period surface-related multiples, and show its efficacy in eliminating coherent imaging artifacts associated with these multiples. We also demonstrate the benefits of joint imaging of primaries and multiples compared to imaging these signal components separately.},
	keywords = {field data, inversion, least squares, migration, multiples},
	doi = {10.1190/tle34070788.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2015/tu2015TLEfls/tu2015TLEfls.html},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {herrmann2015EAGEfom,
	title = {Fast "online" migration with Compressive Sensing},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	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},
	doi = {10.3997/2214-4609.201412942},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/herrmann2015EAGEfom/herrmann2015EAGEfom.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/herrmann2015EAGEfom/herrmann2015EAGEfom_pres.pdf},
	author = {Felix J. Herrmann and Ning Tu and Ernie Esser}
}
@conference {kumar2015CSEGlse,
	title = {Least-squares extended imaging with surface-related multiples},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2015},
	note = {(CSEG, Calgary)},
	month = {05},
	abstract = {Common image gathers are used in building velocity models, inverting anisotropy parameters, and analyzing reservoir attributes. Often primary reflections are used to form image gathers and multiples are typically attenuated in processing to remove strong coherent artifacts generated by multiples that interfere with the imaged reflectors. However, researchers have shown that, if correctly used, multiples can actually provide extra illumination of the subsurface in seismic imaging, especially for delineating the near-surface features. In this work, we borrow ideas from literatures on imaging with surface-related multiples, and apply these ideas to extended imaging. This way we save the massive computation cost in separating multiples from the data before using them during the formation of image gathers. Also, we mitigate the strong coherent artifacts generated by multiples which can send the migration velocity analysis type algorithms in wrong direction. Synthetic examples on a three-layer model show the efficacy of the proposed formulation.},
	keywords = {CSEG, image-gather, surface-related multiples},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2015/kumar2015CSEGlse/kumar2015CSEGlse.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2015/kumar2015CSEGlse/kumar2015CSEGlse_pres.pdf},
	author = {Rajiv Kumar and Ning Tu and Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {kumar2015EAGElse,
	title = {Least-squares extended imaging with surface-related multiples},
	number = {TR-EOAS-2015-1},
	year = {2015},
	month = {01},
	institution = {UBC},
	abstract = {Common image gathers are used in building velocity models, inverting for anisotropy parameters, and analyzing reservoir attributes. Typically, only primary reflections are used to form image gathers as multiples can cause artifacts that interfere with the events of interest. However, it has been shown that multiples can actually provide extra illumination of the subsurface, especially for delineating the near-surface features. In this paper, we aim to form common image gathers directly from the data with surface related multiples by applying concepts that have been used to successfully deal with surface-related multiples in imaging. We achieve this by effectively inverting an extended migration operator. This results in extended images with better near-surface illumination that are free of artifacts that can hamper velocity analysis. In addition, being able to generate extended images directly from the total data avoids the need for (time-consuming) pre-processing. Synthetic examples on a layered model show that the proposed formulation is promising.},
	keywords = {image gathers, surface-related multiples},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/kumar2015EAGElse/kumar2015EAGElse.html},
	author = {Rajiv Kumar and Ning Tu and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {oghenekohwo2015SINBADrdc,
	title = {Recent developments in compressive sensing for time-lapse studies},
	year = {2015},
	publisher = {SINBAD},
	abstract = {We present an overview of the advances we have made with respect to extending compressive sensing ideas to time-lapse studies. We show applications in compressive time-lapse seismic data acquisition, imaging and full-waveform inversion.},
	keywords = {Presentation, SINBAD, SINBADSPRING2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Spring/oghenekohwo2015SINBADrdc/oghenekohwo2015SINBADrdc.pdf},
	author = {Felix Oghenekohwo and Rajiv Kumar and Haneet Wason and Ernie Esser and Ning Tu and Felix J. Herrmann}
}
@conference {tu2015PIMSsls,
	title = {Sparse least-squares seismic imaging with source estimation utilizing multiples},
	booktitle = {PIMS Workshop on Advances in Seismic Imaging and Inversion},
	year = {2015},
	note = {(PIMS Workshop on Advances in Seismic Imaging and Inversion, University of Alberta, Edmonton)},
	month = {05},
	abstract = {We present an least-squares seismic imaging method that (1) is efficient by subsampling the monochromatic source experiments; (2) does not require the prior knowledge of the source wavelet, by inverting for the seismic image and the source wavelet simultaneously using variable projection; and (3) makes active use of surface-related multiples to increase the illumination and to resolve the scaling ambiguity in source estimation, by tightly integrating the well-established surface-related-multiple-prediction into the wave-equation based modelling. As a result, we are able to obtain ambiguity-resolved, high-fidelity least-squares inverted seismic images with computational costs that are comparable to conventional reverse-time migrations with all the data. We demonstrate the efficacy of the proposed method using synthetic examples.},
	keywords = {inversion, least-squares migration, multiples, PIMS, seismic imaging, source estimation, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/PIMS/2015/tu2015PIMSsls/tu2015PIMSsls_pres.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {witte2015IIPFWIspl,
	title = {Sparsity-promoting least-square migration with linearized Bregman and compressive sensing},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	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 = {Bregman, compressed sensing, FWI, migration, sparsity promotion, time domain},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/witte2015IIPFWIspl/witte2015IIPFWIspl_pres.pdf},
	author = {Philipp A. Witte and Ning Tu and Ernie Esser and Mengmeng Yang and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {kumar2014SINBADeia,
	title = {Extended images in action {\textendash}- image gather with surface-related multiples},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Common image gathers are used in building velocity models, invert anisotropy parameters and to analyze reservoir attributes. Often primary reflections are used to form the image gathers and multiples are typically attenuated in processing. However, researchers have shown that, if correctly used, they can provide useful information about the subsurface during reverse-time migration. In this work, i will show how we can use multiples along with primaries to form the image-gathers.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/kumar2014SINBADeia/kumar2014SINBADeia.pdf},
	author = {Rajiv Kumar and Ning Tu and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {tu2014SINBADfis2,
	title = {Fast imaging with source estimation},
	year = {2014},
	publisher = {SINBAD},
	abstract = {In seismic imaging, an inaccurate estimate of the source wavelet may result in degraded seismic images. While conventional reverse-time migration requires the knowledge of the source wavelet as prior information, we propose to include source estimation in the fast compressive imaging procedure. Using the proposed method, we can obtain seismic images that are comparable to those imaged with the true source wavelet, with computational costs that are comparable to conventional RTM images with all the data. We also extend the proposed method to image data with surface-related multiples, where these multiples help to mitigate the amplitude ambiguity in source estimation. We verify the proposed method using realistic synthetic examples.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADfis2/tu2014SINBADfis2.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {tu2014SINBADfis,
	title = {Fast imaging with surface-related multiples by sparse inversion},
	year = {2014},
	publisher = {SINBAD},
	abstract = {When used correctly, surface-related multiples can provide extra illumination coverage compared with primaries. In this talk, I will discuss how to jointly image primaries and surface-related multiples in a computationally efficient fashion. We bring down the computational cost by two means. First we use wave-equation solvers to implicitly carry out the expensive dense matrix-matrix multiplications in the prediction of surface-related multiples. Second we bring down the simulation cost by subsampling the frequencies and monochromatic source experiments together with curvelet-domain sparsity-promoting and rerandomization. As a result, we obtain true-amplitude least-squares migrated seismic images with computational costs that are comparable to a single RTM with all the data. We demonstrate the efficacy of the proposed method using realistic synthetic examples.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADfis/tu2014SINBADfis.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {herrmann2014SEGWSfli,
	title = {Fast linearized inversion with surface-related multiples with source estimation},
	booktitle = {SEG Workshop on Using Multiples as Signal for Imaging; Denver},
	year = {2014},
	note = {(SEG Workshop, Denver)},
	month = {10},
	abstract = {In the well-known SRME relation, multiples are expressed as the multi-dimensional convolution between the subsurface Green{\textquoteright}s function and the downgoing receiver wavefield. Therefore these multiples can be considered as the response of the subsurface to an "areal" source term given by the same downgoing receiver wavefield. This relation can be used to treat these multiples as signals instead of considering them as noise that must removed before seismic imaging. However, when we use conventional reverse-time migration to image these multiple events, it results in acausal imaging artifacts caused by cross-correlations between wrong pairs of up- and downgoing wavefields. We find that these artifacts can be removed by adopting a sparsity-promoting least-squares inversion approach. However, iterative inversions go at the expense of excessive computational costs. By combining the SRME relation and wave-equation based linearized modelling, we are able to significantly reduce the costs by avoiding the dense matrix-matrix multiplications of SRME and the number of wave-equation solves via source subsampling. As a result, we arrive at a method with a cost comparable to that of a single reverse-time migration with all shots.},
	keywords = {inversion, multiples, SEG, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/herrmann2014SEGWSfli/herrmann2014SEGWSfli.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/herrmann2014SEGWSfli/herrmann2014SEGWSfli_pres.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {tu2014SINBADind,
	title = {Imaging the Nelson data set using surface-related multiples},
	year = {2014},
	publisher = {SINBAD},
	abstract = {We will present out latest finding on migration with multiples on the Nelson dataset.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADind/tu2014SINBADind.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {tu2014SINBADsis,
	title = {Sparse inversion simplified},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Implementation of the SPGl1 solver in low-level computer languages such as C or Fortran may sound daunting to many. This talk is tailored for you if you would like to reap benefits from using sparse constraints to regularize your inversion problem, and at the same time want some easy-to-implement algorithm to solve it. We discuss in this talk the linearized Bregman projection method that embraces both ingredients, and show promising applications in fast least-squares imaging and seismic data interpolation problems.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADsis/tu2014SINBADsis.pdf},
	author = {Ning Tu and Navid Ghadermarzy and Rajiv Kumar and Felix J. Herrmann}
}
@conference {tu2013SEGcle,
	title = {Controlling linearization errors in $\ell_1$ regularized inversion by rerandomization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {4640-4644},
	abstract = {Linearized inversion is a data fitting procedure that tries to match the observed seismic data with data predicted by linearized modelling. In practice, the observed data is not necessarily in the column space of the linearized modelling operator. This can be caused by lack of an accurate background velocity model or by coherent noises not explained by linearized modelling. Through carefully designed experiments, we ob- serve that a moderate data mismatch does not pose an issue if we can use all the data in the inversion. However, artifacts do arise from the mismatch when randomized dimensionality reduction techniques are adopted to speed up the inversion. To stabilize the inversion for dimensionality reduction with randomized source aggregates, we propose to rerandomize by drawing independent simultaneous sources occasionally during the inversion. The effect of this rerandomization is remarkable because it results in virtually artifact-free images at a cost comparable to a single reverse-time migration. Implications of our method are profound because we are now able to resolve fine-scale steep subsalt features in a computationally feasible manner.},
	keywords = {inversion, message passing, rerandomization, SEG, sparsity},
	doi = {10.1190/segam2013-1302.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle_pres.pdf},
	author = {Ning Tu and Xiang Li and Felix J. Herrmann}
}
@presentation {tu2013SINBADrerand,
	title = {Controlling linearization errors with rerandomization},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Least squares migration aims to fit the observed seismic data with data predicted by linearized modelling, by solving an PDE-constrained optimization problem. This problem is challenging mostly because of its prohibitive computational cost. To address the issue, dimensionality reduction techniques were proposed in the literature. However, the solution of the reduced problem can deviate from that of the full problem when there are components in the observed data that cannot be explained by linearized modelling. We solve the problem by rerandomizing our $\ell_1$ regularized inversion. In this presentation, I will explain the method and demonstrate what we can achieve with rerandomization, especially for resolving fine sub-salt structures.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/tu2013SINBADrerand/tu2013SINBADrerand.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {tu2013SINBADfim,
	title = {Fast imaging with multiples and source estimation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {During this talk, we present a computationally efficient (cost of 1-2 RTMs with all data) iterative sparsity-promoting inversion framework where surface-related multiples are jointly imaged with primaries and where the source signature is estimated on the fly. Our imaging algorithm is computationally efficient because it works during each iteration with small independent randomized subsets of data. The multiples are handled by introducing an areal source term that includes the upgoing wavefield. We update the source signature for each iteration using a variable projection method. The resulting algorithm removes imaging artifacts from surface-related multiples, estimates and removes the imprint of the source, recovers true amplitudes, is fast, and robust to linearization errors by virtue of the statistical independence of the subsets of data we are working with at each iteration.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/tu2013SINBADfim/tu2013SINBADfim.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {tu2013SINBADvp,
	title = {Fast imaging with multiples and source estimation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Multiples are usually treated as unwanted components in seismic data. However, if correctly used, they can provide valuable information about the subsurface. In this presentation, I will talk about how to make use of multiples in $\ell_1$ regularized least-squares imaging, and how to estimate the source wavelet on the fly using multiples. Synthetic examples show that using multiples not only helps to retrieve the true-amplitude seismic image and the source wavelet, it also increases the wavenumber contents in the seismic image. By using dimensionality reduction techniques with rerandomization, we also greatly decrease the simulation cost without compromising the image quality.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/tu2013SINBADvp/tu2013SINBADvp.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {tu2013EAGElsm,
	title = {Fast least-squares migration with multiples and source estimation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {The advent of modern computing has made it possible to do seismic imaging using least-squares reverse-time migration. We obtain superior images by solving an optimization problem that recovers the true-amplitude images. However, its success hinges on overcoming several issues, including overwhelming problem size, unknown source wavelet, and interfering coherent events like multiples. In this abstract, we reduce the problem size by using ideas from compressive sensing, and estimate source wavelet by generalized variable projection. We also demonstrate how to invert for subsurface information encoded in surface-related multiples by incorporating the free-surface operator as an areal source in reverse-time migration. Our synthetic examples show that multiples help to improve the resolution of the image, as well as remove the amplitude ambiguity in wavelet estimation.},
	keywords = {EAGE, Imaging, multiples, source estimation, sparse},
	doi = {10.3997/2214-4609.20130727},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm_pres.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2013EAGEfrtm,
	title = {Fast RTM with multiples and source estimation},
	booktitle = {EAGE/SEG Forum - Turning noise into geological information: The next big step?},
	year = {2013},
	month = {11},
	abstract = {During this talk, we present a computationally efficient (cost of 1-2 RTM{\textquoteright}s with all data) iterative sparsity-promoting inversion framework where surface-related multiples are jointly imaged with primaries and where the source signature is estimated on the fly. Our imaging algorithm is computationally efficient because it works during each iteration with small independent randomized subsets of data. The multiples are handled by introducing an areal source term that includes the upgoing wavefield. We update the source signature for each iteration using a variable projection method. The resulting algorithm removes imaging artifacts from surface-related multiples, estimates and removes the imprint of the source, recovers true amplitudes, is fast, and robust to linearization errors by virtue of the statistical independence of the subsets of data we are working with at each iteration.},
	keywords = {EAGE, multiples, RTM, SEG, source estimation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/herrmann2013EAGEfrtm/herrmann2013EAGEfrtm_pres.pdf},
	author = {Felix J. Herrmann and Ning Tu}
}
@conference {tu2013SEGldi,
	title = {Limitations of the deconvolutional imaging condition for two-way propagators},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {3916-3920},
	abstract = {The deconvolutional imaging condition has gained wide attention in recent years, as it is often used to image surface-related multiples. However, we noticed on close inspection that this condition was derived from one-way propagation principles. Now that two-way wave-equation based simulations have become more affordable, we revisit the deconvolutional imaging condition and reveal its limitations for two-way propagators. First, it can distort the image due to receiver-side propagation effects. Second, when used to image surface-related multiples, it is not capable of removing all interfering phantom reflectors.},
	keywords = {inversion, migration, multiples, SEG},
	doi = {10.1190/segam2013-1440.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGldi/tu2013SEGldi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGldi/tu2013SEGldi_pres.pdf},
	author = {Ning Tu and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {tu2013SINBADmachar,
	title = {SLIM{\textquoteright}s findings on the Machar dataset},
	year = {2013},
	publisher = {SINBAD},
	abstract = {By courtesy of BP, we are able to get some hands-on experience imaging seismic data from the Machar field in North Sea. We performed reverse-time migration and sparsity-promoting migration with source-estimation to this dataset (or a cropped section of the dataset in many cases due to computational constraints), and had some interesting findings. In this presentation, we will show some conclusive results we have got, and explain the key techniques in imaging this dataset.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/tu2013SINBADmachar/tu2013SINBADmachar.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {aravkin2013ICASSPssi,
	title = {Sparse seismic imaging using variable projection},
	booktitle = {ICASSP},
	year = {2013},
	month = {05},
	abstract = {We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how this data was generated. For example, a sparse green{\textquoteright}s function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simulta- neously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with spar- sity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demon- strate the algorithm on a seismic imaging example.},
	keywords = {Imaging, Optimization, sparsity, variable projection},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2013/aravkin2013ICASSPssi/aravkin2013ICASSPssi.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Ning Tu}
}
@presentation {ning2012SINBADfim,
	title = {Fast imaging with multiples},
	year = {2012},
	publisher = {SINBAD},
	abstract = {If correctly used, multiple energy can be mapped to the correct subsurface locations. However, simply applying the cross-correlation imaging condition will introduce non-causal artifacts into the final image. Here we propose an inversion approach to image primaries and multiples simultaneously that yields an artifact-free image. To address the high computational cost associated with inversion, we propose to: i) have the wave-equation solver carry out the multi-dimensional convolutions implicitly, and ii) reduce the number of PDE solves by randomized subsampling. We then propose to improve the overall performance of this algorithm by a process called rerandomization, which helps to cancel the correlation built between model iterate and the subsampling operator. We show the merits of our approach on a number of examples.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/ning2012SINBADfim/ning2012SINBADfim_pres.pdf},
	author = {Ning Tu}
}
@presentation {ning2012SINBADSPRINGfim,
	title = {Fast imaging with multiples by sparse inversion},
	year = {2012},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADSPRING2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Spring/ning2012SINBADSPRINGfim/ning2012SINBADSPRINGfim_pres.pdf},
	author = {Ning Tu}
}
@conference {tu2012SEGima,
	title = {Imaging with multiples accelerated by message passing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {31},
	year = {2012},
	month = {11},
	pages = {1-6},
	publisher = {SEG},
	organization = {SEG},
	abstract = {With the growing realization that multiples can provide valuable information, there is a paradigm shift from removing them to using them. For instance, primary estimation by sparse inversion has demonstrated its superiority over surface-related multiple removal in many aspects. Inspired by this shift, we propose a method to image directly from the total up-going wavefield, including surface-related multiples, by sparse inversion. To address the high computational cost associated with this method, we propose to speed up the inversion by having the wave-equation solver carry out the multi-dimensional convolutions implicitly and cheaply by randomized subsampling. We improve the overall performance of this algorithm by selecting new independent copies of the randomized modeling operator, which leads to a cancellation of correlations that hamper the speed of convergence of the solver. We show the merits of our approach on a number of examples.},
	keywords = {Imaging, multiples, SEG},
	doi = {10.1190/segam2012-1552.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/tu2012SEGima/tu2012SEGima.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/tu2012SEGima/tu2012SEGima_pres.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {tu2012EAGElsm,
	title = {Least-squares migration of full wavefield with source encoding},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {Multiples can provide valuable information that is missing in primaries, and there is a growing interest in using them for seismic imaging. In our earlier work, we proposed to combine primary estimation and migration to image from the total up-going wavefield. The method proves to be effective but computationally expensive. In this abstract, we propose to reduce the computational cost by removing the multi-dimensional convolution required by primary estimation, and reducing the number of PDE solves in migration by introducing simultaneous sources with source renewal. We gain great performance boost without compromising the quality of the image.},
	keywords = {depth migration, EAGE, surface-related multiples},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/tu2012EAGElsm/tu2012EAGElsm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/tu2012EAGElsm/tu2012EAGElsm_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59688},
	author = {Ning Tu and Felix J. Herrmann}
}
@presentation {ning2011SINBADmsr,
	title = {Migration from surface-related multiples},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/ning2011SINBADmsr/ning2011SINBADmsr_pres.pdf},
	author = {Ning Tu}
}
@conference {tu2011SEGmult,
	title = {Migration with surface-related multiples from incomplete seismic data},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {3222-3227},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Seismic acquisition is confined by limited aperture that leads to finite illumination, which, together with other factors, hinders imaging of subsurface objects in complex geological settings such as salt structures. Conventional processing, including surface-related multiple elimination, further reduces the amount of information we can get from seismic data. With the growing consensus that multiples carry valuable information that is missing from primaries, we are motivated to exploit the extra illumination provided by multiples to image the sub- surface. In earlier research, we proposed such a method by combining primary estimation and sparsity-promoting migration to invert for model perturbations directly from the total up-going wavefield. In this abstract, we focus on a particular case. By exploiting the extra illumination from surface-related multiples, we mitigate the effects caused by migrating from incomplete data with missing sources and missing near-offsets.},
	keywords = {Imaging, Presentation, Processing, SEG},
	doi = {10.1190/1.3627865},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/tu11SEGmult/tu11SEGmult.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/tu11SEGmult/tu11SEGmult_pres.pdf},
	author = {Ning Tu and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {tu2011EAGEspmsrm,
	title = {Sparsity-promoting migration with surface-related multiples},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Multiples, especially the surface-related multiples, form a significant part of the total up-going wave- field. If not properly dealt with, they can lead to false reflectors in the final image. So conventionally practitioners remove them prior to migration. Recently research has revealed that multiples can actually provide extra illumination so different methods are proposed to address the issue that how to use multiples in seismic imaging, but with various kinds of limitations. In this abstract, we combine primary estimation and sparsity-promoting migration into one convex-optimization process to include information from multiples. Synthetic examples show that multiples do make active contributions to seismic migration. Also by this combination, we can benefit from better recoveries of the Greens function by using sparsity-promoting algorithms since reflectivity is sparser than the Greens function.},
	keywords = {EAGE, Imaging, Presentation, Processing},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/tu11EAGEspmsrm/tu11EAGEspmsrm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/tu11EAGEspmsrm/tu11EAGEspmsrm_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50369},
	author = {Ning Tu and Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {tu2010SINBADspm,
	title = {Sparsity promoting migration with surface-related multiples},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/tu2010SINBADspm/tu2010SINBADspm_pres.pdf},
	author = {Ning Tu}
}
@conference {lin2010SEGspm,
	title = {Sparsity-promoting migration from surface-related multiples},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {29},
	year = {2010},
	month = {10},
	pages = {3333-3337},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Seismic imaging typically begins with the removal of multiple energy in the data, out of fear that it may introduce erroneous structure. However, seismic multiples have effectively seen more of the earth{\textquoteright}s structure, and if treated correctly can potential supply more information to a seismic image compared to primaries. Past approaches to accomplish this leave ample room for improvement; they either require extensive modification to standard migration techniques, rely too much on prior information, require extensive pre-processing, or resort to full-waveform inversion. We take some valuable lessons from these efforts and present a new approach balanced in terms of ease of implementation, robustness, efficiency and well-posedness, involving a sparsity-promoting inversion procedure using standard Born migration and a data-driven multiple modeling approach based on the focal transform.},
	keywords = {Presentation, Processing, SEG},
	doi = {10.1190/1.3513540},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/lin10SEGspm/lin10SEGspm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/lin10SEGspm/lin10SEGspm_pres.pdf},
	author = {Tim T.Y. Lin and Ning Tu and Felix J. Herrmann}
}
