@mastersthesis {yang2020THsiw,
	title = {Seismic imaging with extended image volumes and source estimation},
	year = {2020},
	note = {(PhD)},
	month = {03},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic imaging is an important tool for the exploration and production of oil \& gas, carbon sequestration, and the mitigation of geohazards. Through the process of seismic migration, images of subsurface geological structures are created from data collected at the surface. These images reflect changes in the physical rock properties such as wave speed and density. While significant progress has been made in the development of 3D imaging technology for complex geological areas, several challenges remain, some of which are addressed in this thesis. The first main contribution of this thesis is in the area of creating so-called subsurface-offset gathers, which play an increasingly important role in seismic imaging because they provide a multitude of information ranging from the reflection mechanism itself to information of the dips of specific reflectors and the accuracy of the background velocity model. Unfortunately, the formation and manipulation of these gathers come with exceedingly high computational and storage costs because extended image volumes are quadratic in the image size. These high costs are avoided by using techniques from modern randomized linear algebra that allow for compression of extended image volumes into low-rank factorized form{\textemdash}i.e., the image volume is approximately written as an outer product of a tall and a wide matrix. It is demonstrated that this factorization provides access to different types of sub-surface offset gathers, including common-image (point) gathers, without the need to explicitly form this outer product. As a result, challenging steep dip imaging situations, where conventional horizontal offset gathers no longer focus, can be handled. Moreover, extended image volumes for one background velocity model can directly be mapped to those of another background velocity model. As a result, factorization costs are incurred only once when examining imaging scenarios for different background velocity models. The second main contribution of this thesis is on the development of computationally efficient sparsity-promoting imaging techniques and on-the-fly source estimation. In this work, an adaptive technique is proposed where the unknown time signature of the sources is estimated during imaging. Without accurate knowledge of these source signatures, seismic images can be wrongly positioned and can have the wrong amplitudes hampering subsequent geophysical and geological interpretations. With the presented technique, this problem is mitigated. Finally, a contribution is made to address the detrimental effects of surface-related multiples. If not handled correctly, these multiples give rise to unwanted artifacts in the image. A new technique is introduced to address this issue in realistic settings where there is a strong density contrast at the ocean bottom. As a result, the surface-related multiples are mapped to the reflectors. Because bounce points at the surface can be considered as sources, this mapping of the multiples rather than removal increases the subsurface illumination.},
	keywords = {extended image volumes, low rank, multiples, PhD, randomized linear algebra, source estimation, sparsity-promoting inversion},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/yang2020THsiw/yang2020THsiw.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/yang2020THsiw/yang2020THsiw_pres.pdf},
	author = {Mengmeng Yang}
}
@article {yang2020tdsp,
	title = {Time-domain sparsity promoting least-squares reverse time migration with source estimation},
	journal = {Geophysical Prospecting},
	volume = {68},
	number = {9},
	year = {2020},
	note = {(Geophysical Prospecting)},
	month = {08},
	pages = {2697-2711},
	abstract = {Least-squares reverse time migration is well-known for its capability to generate artifact-free true-amplitude subsurface images through fitting observed data in the least-squares sense. However, when applied to realistic imaging problems, this approach is faced with issues related to overfitting and excessive computational costs induced by many wave-equation solves. The fact that the source function is unknown complicates this situation even further. Motivated by recent results in stochastic optimization and transform-domain sparsity-promotion, we demonstrate that the computational costs of inversion can be reduced significantly while avoiding imaging artifacts and restoring amplitudes. While powerfull, these new approaches do require accurate information on the source-time function, which is often lacking. Without this information, the imaging quality deteriorates rapidly. We address this issue by presenting an approach where the source-time function is estimated on the fly through a technique known as variable projection. Aside from introducing negligible computational overhead, the proposed method is shown to perform well on imaging problems with noisy data and problems that involve complex settings such as salt. In either case, the presented method produces high resolution high-amplitude fidelity images including an estimates for the source-time function. In addition, due to its use of stochastic optimization, we arrive at these images at roughly one to two times the cost of conventional reverse time migration involving all data.},
	keywords = {penalty, source estimation, sparsity inversion},
	doi = {10.1111/1365-2478.13021},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2020/yang2020tdsp/yang2020tdsp.html},
	author = {Mengmeng Yang and Zhilong Fang and Philipp A. Witte and Felix J. Herrmann}
}
@mastersthesis {fang2018THsea,
	title = {Source estimation and uncertainty quantification for wave-equation based seismic imaging and inversion},
	year = {2018},
	note = {(PhD)},
	month = {04},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {In modern seismic exploration, wave-equation-based inversion and imaging approaches are widely employed for their potential of creating high-resolution subsurface images from seismic data by using the wave equation to describe the underlying physical model of wave propagation. Despite their successful practical applications, some key issues remain unsolved, including local minima, unknown sources, and the largely missing uncertainty analyses for the inversion. This thesis aims to address the following two aspects: to perform the inversion without prior knowledge of sources, and to quantify uncertainties in the inversion. The unknown source can hinder the success of wave-equation-based ap- proaches. A simple time shift in the source can lead to misplaced reflectors in linearized inversions or large disturbances in nonlinear problems. Unfortunately, accurate sources are typically unknown in real problems. The first major contribution of this thesis is, given the fact that the wave equation linearly depends on the sources, I have proposed on-the-fly source estimation techniques for the following wave-equation-based approaches: (1) time-domain sparsity-promoting least-squares reverse-time migration; and (2) wavefield-reconstruction inversion. Considering the linear dependence of the wave equation on the sources, I project out the sources by solving a linear least-squares problem, which enables us to conduct successful wave- equation-based inversions without prior knowledge of the sources. Wave-equation-based approaches also produce uncertainties in the resulting velocity model due to the noisy data, which would influence the subsequent exploration and financial decisions. The difficulties related to practical uncertainty quantification lie in: (1) expensive computation related to wave-equation solves, and (2) the nonlinear parameter-to-data map. The second major contribution of this thesis is the proposal of a computationally feasible Bayesian framework to analyze uncertainties in the resulting velocity models. Through relaxing the wave-equation constraints, I obtain a less nonlinear parameter-to-data map and a posterior distribution that can be adequately approximated by a Gaussian distribution. I derive an implicit formulation to construct the covariance matrix of the Gaussian distribution, which allows us to sample the Gaussian distribution in a computationally efficient manner. I demonstrate that the proposed Bayesian framework can provide adequately accurate uncertainty analyses for intermediate to large- scale problems with an acceptable computational cost.},
	keywords = {FWI, LS-RTM, PhD, source estimation, UQ, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea_pres.pdf},
	author = {Zhilong Fang}
}
@techreport {witte2017TRcls,
	title = {Compressive least-squares migration with source estimation},
	number = {TR-EOAS-2017-3},
	year = {2017},
	institution = {UBC},
	abstract = {Least-squares reverse-time migration is a powerful approach for true-amplitude seismic imaging of complex geological structures. The successful application of this method is hindered by its exceedingly large computational cost and required prior knowledge of the generally unknown source wavelet. We address these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration with source estimation. We adapt a recent algorithm from sparse optimization, which allows to work with randomized subsets of shots during each iteration of least-squares migration, while still converging to an artifact-free solution. We modify the algorithm to incorporate on-the-fly source estimation through variable projection, which lets us estimate the wavelet without additional PDE solves. The algorithm is easy to implement and allows imaging at a fraction of the cost of conventional least squares reverse-time migration, requiring only around two passes trough the data, making the method feasible for large-scale imaging problems with unknown source wavelets.},
	keywords = {LSRTM, migration, source estimation, sparsity, time domain},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/witte2017TRcls/witte2017TRcls.html},
	author = {Philipp A. Witte and Mengmeng Yang and Felix J. Herrmann}
}
@conference {fang2017AIPepm,
	title = {An efficient penalty method for PDE-constrained optimization problem with source estimation and stochastic optimization},
	booktitle = {Applied Inverse Problems Annual Conference Proceedings},
	year = {2017},
	note = {(AIP, Hangzhou)},
	month = {05-06},
	pages = {40},
	abstract = {Many inverse problems in applied science and engineering can be written as PDE-constrained optimization problems. Typically, one is interested in estimating the unknown medium parameters of the PDE describing the system, given multi-source measurements of the fields in the true medium. The objective function is often very oscillatory, which gives rise to problematic local minima, and merely evaluating one or more of its derivatives requires solving multiple PDEs, which are expensive. In many applications such as seismic exploration, only the source location is available and the source signature itself is unknown, which results in erroneous estimated parameters. In this work, we propose a penalty method to solve the PDE-constrained optimization problem, whereby we replace the PDE constraints by a two-norm penalty term, which leads to a bi-linear optimization problem with a much less oscillatory objective function. By applying the variable projection method, we develop an efficient method to invert the unknown parameters and source signatures simultaneously. To reduce the computational cost, we randomly select a subset of all data to update the parameters at each iteration. Numerical examples demonstrate that this method is less prone to becoming stuck in harmful local minima and is able to successfully invert the unknown parameters and source signature with less computational cost compared to using all the data.},
	keywords = {Optimization, penalty method, source estimation, Stochastic optimization},
	url = {http://aip2017.csp.escience.cn/dct/page/1},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AIP/2017/fang2017AIPepm/fang2017AIPepm_pres.pdf},
	author = {Zhilong Fang and Curt Da Silva and Felix J. Herrmann}
}
@conference {yang2016SEGtds,
	title = {Time-domain sparsity-promoting least-squares migration with source estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {4225-4229},
	abstract = {Traditional reverse-time migration (RTM) gives images with wrong amplitudes and low resolution. Least-squares RTM (LS-RTM) on the other hand, is capable of obtaining true-amplitude images as solutions of $\ell_2$-norm norm minimization problems by fitting the synthetic and observed reflection data. The shortcoming of this approach is that solutions of these $\ell_2$ problems are typically smoothed, tend to be overfitted, and computationally too expensive because it requires compared to standard RTM too many iterations. By working with randomized subsets of data only, the computational costs of LS-RTM can be brought down to an acceptable level while producing artifact-free high-resolution images without overfitting the data. While initial results of these "compressive imaging" methods were encouraging various open issues remain including guaranteed convergence, algorithmic complexity of the solver, and lack of on-the-fly source estimation for LS-RTMs with wave-equation solvers based on time-stepping. By including on-the-fly source-time function estimation into the method of Linearized Bregman (LB), on which we reported before, we tackle all these issues resulting in a easy-to-implement algorithm that offers flexibility in the trade-off between the number of iterations and the number of wave-equation solves per iteration for a fixed total number of wave-equation solves. Application of our algorithm on a 2D synthetic shows that we are able to obtain high-resolution images, including accurate estimates of the wavelet, for a single pass through the data. The produced image, which is by virtue of the inversion deconvolved with respect to the wavelet, is roughly of the same quality as the image obtained given the correct source function.},
	keywords = {least squares, RTM, SEG, source estimation, time domain},
	doi = {10.1190/segam2016-13850609.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/yang2016SEGtds/yang2016SEGtds.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/yang2016SEGtds/yang2016SEGtds_pres.pdf},
	author = {Mengmeng Yang and Philipp A. Witte and Zhilong Fang and Felix J. Herrmann}
}
@conference {fang2015EAGEsew,
	title = {Source estimation for Wavefield Reconstruction Inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Wavefield reconstruction inversion is a new approach to waveform based inversion that helps overcome the {\textquoteleft}cycle skipping{\textquoteright} problem. However, like most waveform based inversion methods, wavefield reconstruction inversion also requires good source wavelets. Without correct source wavelets, wavefields cannot be reconstructed correctly and the velocity model cannot be updated correctly neither. In this work, we propose a source estimation method for wavefield reconstruction inversion based on the variable projection method. In this method, we reconstruct wavefields and estimate source wavelets simultaneously by solving an extended least-squares problem, which contains source wavelets. This approach does not increase the computational cost compared to conventional wavefield reconstruction inversion. Numerical results illustrates with our source estimation method we are able to recover source wavelets and obtain inversion results that are comparable to results obtained with true source wavelets.},
	keywords = {EAGE, source estimation, WRI},
	doi = {10.3997/2214-4609.201412588},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/fang2015EAGEsew/fang2015EAGEsew.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/fang2015EAGEsew/fang2015EAGEsew_pres.pdf},
	author = {Zhilong Fang 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 {fang2015IIPFWIwri,
	title = {Wavefield Reconstruction Inversion with source estimation and its application to 2014 Chevron synthetic blind test dataset},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present a robust wavefield reconstruction inversion with source estimation. The source wavelet is estimated with the reconstruction of wavefield simultaneously by solving an extended data augmentation problem. We apply this method to the 2014 Chevron synthetic blind test dataset and show the robustness of our method.},
	keywords = {FWI, source estimation, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/fang2015IIPFWIwri/fang2015IIPFWIwri_pres.pdf},
	author = {Zhilong Fang 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}
}
