@mastersthesis {zhang2023THlsw,
	title = {Large scale wavefield reconstruction via weighted matrix factorization and seismic survey design},
	year = {2023},
	note = {(PhD)},
	month = {06},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic data acquisition plays a crucial role in identifying potential oil and gas reservoirs during the early phases of exploration. However, obtaining finely sampled seismic data can be costly and physically impossible. Recent developments in Compressive Sensing have resulted in seismic data being increasingly collected at random along spatial coordinates. Although random sampling improves acquisition efficiency, it shifts the burden from seismic acquisition to data processing. Wavefield recovery is one of the required processes for reconstructing fully seismic data from coarsely subsampled data. Among the various techniques proposed for wavefield reconstruction, matrix completion methods are computationally efficient and straightforward to implement. These methods exploit the low-rank structure of fully seismic data. However, matrix completion performs well at low-to-mid frequencies and degrades at higher frequencies due to the failure of low-rank structure to accurately approximate higher frequencies. To address this issue, this thesis proposed a recursively weighted matrix completion method. Although effective, this method is computationally expensive, and a more efficient method for handling 2D seismic data was also proposed. Compared to 2D seismic data, 3D seismic data can detect reflections outside of the 2D plane but poses a computational challenge due to its large scale. To overcome this challenge, this thesis proposed a parallel weighted reconstruction method to improve the reconstruction of 3D seismic data. Land seismic data presents a greater challenge due to contamination by ground roll, which consists of surface waves with a high spatial frequency content and large amplitude. To address this issue, a practical workflow was proposed in this thesis to improve the recovery of land seismic data. Although matrix completion is an efficient technique for reconstructing fully seismic data, the optimal acquisition design is still being investigated. Recent studies have shown that the spectral gap can be used to predict and characterize the quality of wavefield reconstruction via matrix completion for a given subsampling mask. Based on these findings, a simulation-free seismic survey design for both 2D and 3D seismic data was proposed in this thesis to obtain an improved subsampling survey by minimizing the spectral gap ratio. Furthermore, this concept was extended to the design of a time-lapse seismic survey, which is essential for reservoir management and monitoring geological carbon storage but is difficult and expensive to acquire. To improve the reconstruction of the time-lapse wavefield, a joint recovery model was proposed that leverages the benefits of the non-replicated baseline and monitor subsampled seismic data. A time-lapse seismic survey design that incorporates the joint recovery model with spectral gap was proposed to generate sparse, non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
	keywords = {5D reconstruction, Acquisition, compressed sensing, frequency-domain, JRM, matrix factorization, parallel, PhD, signal processing, spectral gap, survey design, time-lapse, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw/zhang2023THlsw.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw/zhang2023THlsw_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw},
	author = {Yijun Zhang}
}
@mastersthesis {siahkoohi2022THdgmf,
	title = {Deep generative models for solving geophysical inverse problems},
	year = {2022},
	note = {(PhD)},
	month = {07},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {My thesis presents several novel methods to facilitate solving large-scale inverse problems by utilizing recent advances in machine learning, and particularly deep generative modeling. Inverse problems involve reliably estimating unknown parameters of a physical model from indirect observed data that are noisy. Solving inverse problems presents primarily two challenges. The first challenge is to capture and incorporate prior knowledge into ill-posed inverse problems whose solutions cannot be uniquely identified. The second challenge is the computational complexity of solving inverse problems, particularly the cost of quantifying uncertainty. The main goal of this thesis is to address these issues by developing practical data-driven methods that are scalable to geophysical applications in which access to high-quality training data is often limited. There are six papers included in this thesis. A majority of these papers focus on addressing computational challenges associated with Bayesian inference and uncertainty quantification, while others focus on developing regularization techniques to improve inverse problem solution quality and accelerate the solution process. These papers demonstrate the applicability of the proposed methods to seismic imaging, a large-scale geophysical inverse problem with a computationally expensive forward operator for which sufficiently capturing the variability in the Earth{\textquoteright}s heterogeneous subsurface through a training dataset is challenging. The first two papers present computationally feasible methods of applying a class of methods commonly referred to as deep priors to seismic imaging and uncertainty quantification. I also present a systematic Bayesian approach to translate uncertainty in seismic imaging to uncertainty in downstream tasks performed on the image. The next two papers aim to address the reliability concerns surrounding data-driven methods for solving Bayesian inverse problems by leveraging variational inference formulations that offer the benefits of fully-learned posteriors while being directly informed by physics and data. The last two papers are concerned with correcting forward modeling errors where the first proposes an adversarially learned postprocessing step to attenuate numerical dispersion artifacts in wave-equation simulations due to coarse finite-difference discretizations, while the second trains a Fourier neural operator surrogate forward model in order to accelerate the qualification of uncertainty due to errors in the forward model parameterization.},
	keywords = {Bayesian inference, deep learning, Generative models, Geophysics, Inverse problems, PhD},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf_pres.pdf},
	author = {Ali Siahkoohi}
}
@mastersthesis {sharan2020THlsh,
	title = {Large scale high-frequency seismic wavefield reconstruction, acquisition via rank minimization and sparsity-promoting source estimation},
	year = {2020},
	note = {(PhD)},
	month = {11},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic data reconstruction on a dense periodic grid from seismic data acquired on a coarse grid is a common approach followed by most of the oil \& gas companies. This approach allows them to save on operationally challenging and expensive dense seismic data acquisition. Dense seismic data is one of the key requirements for generating high-resolution images of earth{\textquoteright}s subsurface for exploration and production decisions. Based on the Compressive Sensing (CS) paradigm, low-rank matrix factorization based seismic data reconstruction methods are computationally cheaper and scalable to large datasets in comparison to sparsity-promotion based methods. The sparsity-promotion based methods are based on transformation in certain transform domains that can be computationally expensive for large datasets. Although, low-rank matrix factorization based methods perform well at lower frequencies, their performance degrades at higher frequencies due to increase in rank of approximating matrix. One of the contributions of this thesis is a recursively weighted matrix factorization approach to improve the quality of reconstructed data at higher frequencies. This recursively weighted approach exploits the similarity between adjacent frequency slices. Although, recursively weighted method improves the data reconstruction quality at higher frequencies, it can be computationally expensive for large scale seismic datasets. This is because of the interdependence of frequencies preventing simultaneous reconstruction of frequencies. Another contribution of this thesis is a computationally efficient recursively weighted framework for large scale dataset by parallelizing data reconstruction over rows of low-rank factors of each frequency slices. To reduce the cost and turnaround time of seismic data acquisition simultaneous source acquisition is adapted by the oil and gas industry in last few years. Another contribution of this thesis is a low-rank based method for simultaneous separation and reconstruction of seismic data on a dense periodic grid from large scale seismic data acquired with simultaneous source acquisition. Next part of this thesis focuses on accurate detection of fractures created by hydraulic fracturing in unconventional reservoirs for economical production of oil and gas. Fracturing of rocks during hydraulic fracturing gives rise to microseismic events, which are localized along these fractures. In this work, a sparsity-promoting microseismic source estimation framework is proposed to detect closely spaced microseismic sources along with estimation of their associated source-time functions from noisy microseismic data recorded by receivers along the earth{\textquoteright}s surface or along monitor wells. Detecting closely spaced microseismic events helps in delineating fractures and estimation of source-time function is useful in estimating fracture{\textquoteright}s origin in time. Also, source-time functions can be potentially useful for estimating the source-mechanism. Also, this method does not make any prior assumption on number of microseismic sources or shape of their source-time functions. Therefore, this method is useful for detecting microseismic sources with different source signatures and frequency content. Last part of this thesis focuses on sparsity-promoting photoacoustic imaging to detect photoabsorbers along with estimating the associated source-time functions. Traditional photoacoustic imaging can only estimate the locations of photoacoustic absorbers. Also, traditional methods require dense transducer coverage whereas sparsity-promotion based method can work with reduced transducer sampling reducing the overall data storage cost.},
	keywords = {compressed sensing, low-rank, PhD, Sparsity-promoting, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh_pres.pdf},
	author = {Shashin Sharan}
}
@mastersthesis {louboutin2020THmfi,
	title = {Modeling for inversion in exploration geophysics},
	year = {2020},
	note = {(PhD)},
	month = {03},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic inversion, and more generally geophysical exploration, aims at better understanding the earth{\textquoteright}s subsurface, which is one of today{\textquoteright}s most important challenges. Firstly, it contains natural resources that are critical to our technologies such as water, minerals and oil and gas. Secondly, monitoring the subsurface in the context of CO2 sequestration, earthquake detection and global seismology are of major interests with regard to safety and the environment hazards. However, the technologies to monitor the subsurface or find resources are scientifically extremely challenging. Seismic inversion can be formulated as a mathematical optimization problem that minimizes the difference between field recorded data and numerically modeled synthetic data. The process of solving this optimization problem then requires to numerically model, thousands of times, wave-propagation in large three-dimensional representations of part of the earth subsurface. The mathematical and computational complexity of this problem, therefore, calls for software design that abstracts these requirements and facilitates algorithm and software development. My thesis addresses some of the challenges that arise from these problems; mainly the computational cost and access to the right software for research and development. In the first part, I will discuss a performance metric that improves the current runtime-only benchmarks in exploration geophysics. This metric, the roofline model, first provides insight at the hardware level of the performance of a given implementation relative to the maximum achievable performance. Second, this study demonstrates that the choice of numerical discretization has a major impact on the achievable performance depending on the hardware at hand and shows that a flexible framework with respect to the discretization parameters is necessary. In the second part, I will introduce and describe Devito, a symbolic finite-difference DSL that provides a high-level interface to the definition of partial differential equations (PDE) such as the wave equation. Devito, from the symbolic definition of PDEs, then generates and compiles highly optimized C code on-the-fly to compute the solution of the PDE. The combination of the high-level abstractions and the just-in-time compiler enable research for geophysical exploration and PDE-constrainted optimization based on the paradigm of separation of concerns. This allows researchers to concentrate on their respective field of study while having access to computationally performant solvers with a flexible and easy to use interface to successfully implement complex representations of the physics. The second part of my thesis will be split into two sub-parts; first describing the symbolic application programming interface (API), before describing and benchmarking the just-in-time compiler. I will end my thesis with concluding remarks, the latest developments and a brief description of projects that were enabled by Devito.},
	keywords = {finite-differences, FWI, HPC, Imaging, inversion, Modeling, performance, PhD, RTM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi_pres.pdf},
	author = {Mathias Louboutin}
}
@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}
}
@mastersthesis {witte2020THsal,
	title = {Software and algorithms for large-scale seismic inverse problems},
	year = {2020},
	note = {(PhD)},
	month = {02},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic imaging and parameter estimation are an import class of inverse problems with practical relevance in resource exploration, carbon control and monitoring systems for geohazards. The goal of seismic inverse problems is to image subsurface geological structures and estimate physical rock properties such as wave speed or density. Mathematically, this can be achieved by solving an optimization problem in which we minimize the mismatch between numerically modeled data and observed data from a seismic survey. As wave propagation through a medium is described by wave equations, seismic inverse problems involve solving a large number of partial differential equations (PDEs) during numerical optimization using finite difference modeling, making them computationally expensive. Additionally, seismic inverse problems are typically ill-posed, non-convex or ill-conditioned, thus making them challenging from a mathematical standpoint as well. Similar to the field of deep learning, this calls for software that is not only optimized for performance, but also enables geophysical domain specialists to experiment with algorithms in high-level programming languages and using different computing environments, such as high-performance computing (HPC) clusters or the cloud. Furthermore, they call for the adaption of dimensionality reduction techniques and stochastic algorithms to address computational cost from the algorithmic side. This thesis makes three distinct contributions to address computational challenges encountered in seismic inverse problems and to facilitate algorithmic development in this field. Part one introduces a large-scale framework for seismic modeling and inversion based on the paradigm of separation of concerns, which combines a user interface based on domain specific abstractions with a Python package for automatic code generation to solve the underlying PDEs. The modular code structure makes it possible to manage the complexity of a seismic inversion code, while matrix-free linear operators and data containers enable the implementation of algorithms in a fashion that closely resembles the underlying mathematical notation. The second contribution of this thesis is an algorithm for seismic imaging, that addresses its high computational cost and large memory imprint through a combination of on-the-fly Fourier transforms, stochastic sampling techniques and sparsity-promoting optimization. The algorithm combines the best of both time- and frequency-domain inversion, as the memory imprint is independent of the number of modeled time steps, while time-to-frequency conversions avoid the need to solve Helmholtz equations, which involve inverting ill-conditioned matrices. Part three of this thesis introduces a novel approach for adapting the cloud for high-performance computing applications like seismic imaging, which does not rely on a fixed cluster of permanently running virtual machines. Instead, computational resources are automatically started and terminated by the cloud environment during runtime and the workflow takes advantage of cloud-native technologies such as event-driven computations and containerized batch processing. The performance and cost analysis shows that this approach is able to address current shortcomings of the cloud such as inferior resilience, while at the same time reducing operating cost up to an order of magnitude. As such, the workflow provides a strategy for cost effectively running large-scale seismic imaging problems in the cloud and is a viable alternative to conventional HPC clusters.},
	keywords = {algorithms, AWS, FWI, Imaging, PhD, RTM, seismic, software},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal_pres.pdf},
	author = {Philipp A. Witte}
}
@mastersthesis {peters2019THiso,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	year = {2019},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Inverse problems in the imaging sciences encompass a variety of applications. The primary problem of interest is the identification of physical parameters from observed data that come from experiments governed by partial-differential-equations. The secondary type of imaging problems attempts to reconstruct images and video that are corrupted by, for example, noise, subsampling, blur, or saturation. The quality of the solution of an inverse problem is sensitive to issues such as noise and missing entries in the data. The non-convex seismic full-waveform inversion problem suffers from parasitic local minima that lead to wrong solutions that may look realistic even for noiseless data. To meet some of these challenges, I propose solution strategies that constrain the model parameters at every iteration to help guide the inversion. To arrive at this goal, I present new practical workflows, algorithms, and software, that avoid manual tuning-parameters and that allow us to incorporate multiple pieces of prior knowledge. Opposed to penalty methods, I avoid balancing the influence of multiple pieces of prior knowledge by working with intersections of constraint sets. I explore and present advantages of constraints for imaging. Because the resulting problems are often non-trivial to solve, especially on large 3D grids, I introduce faster algorithms, dedicated to computing projections onto intersections of multiple sets. To connect prior knowledge more directly to problem formulations, I also combine ideas from additive models, such as cartoon-texture decomposition and robust principal component analysis, with intersections of multiple constraint sets for the regularization of inverse problems. The result is an extension of the concept of a Minkowski set. Examples from non-unique physical parameter estimation problems show that constraints in combination with projection methods provide control over the model properties at every iteration. This can lead to improved results when the constraints are carefully relaxed.},
	keywords = {FWI, Optimization, PhD, regularization, Sets},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso_pres.pdf},
	author = {Bas Peters}
}
@mastersthesis {zhang2018THlss,
	title = {Large-scale seismic data compression: application to full waveform inversion and extended image volume},
	year = {2018},
	note = {(MSc)},
	month = {04},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Conventional oil and gas fields are increasingly difficult to explore and im- age, resulting in a call for more complex wave-equation based inversion al- gorithms that require dense long-o↵set samplings. Consequently, there is an exponential growth in the size of data volumes and prohibitive demands on computational resources. In this work, we propose a method to com- press and process seismic data directly in a low-rank tensor format, which drastically reduces the amount of storage required to represent the data. We first outline how seismic data exhibits low-rank structure in a particular transform-domain, which can be exploited to compress the dense data in one extremely storage-efficient tensor format when the data is fully sampled. In the more realistic case of missing data, we can use interpolation techniques based on the same tensor format to recover fully sampled data volume in compressed form. In either case, once we have our data represented in its compressed tensor form, we design an algorithm to extract source or receiver gathers directly from the compressed parameters. This extraction process can be done on-the-fly directly on the compressed data, in the full wave- form inversion context, and does not require scanning through the entire dataset in order to form shot gathers. To the best of our knowledge, this work is one of the first major contributions to working with seismic data applications directly in the compressed domain without reconstructing the entire data volume. We use a stochastic inversion approach, which works with small subsets of source experiments at each iteration, further to reduce the computational and memory costs of full waveform inversion. We also demonstrate how this data compression and extraction technique can be ap- plied to forming full subsurface image gathers through probing techniques.},
	keywords = {compression, extended image volume, FWI, hierarchical tucker, MSc, multilinear algebra, on-the-fly, thesis},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2018/zhang2018THlss/zhang2018THlss.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2018/zhang2018THlss/zhang2018THlss_pres.pdf},
	author = {Yiming Zhang}
}
@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}
}
@mastersthesis {oghenekohwo2017THetl,
	title = {Economic time-lapse seismic acquisition and imaging{\textendash}-Reaping the benefits of randomized sampling with distributed compressive sensing},
	year = {2017},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis presents a novel viewpoint on the implicit opportunities randomized surveys bring to time-lapse seismic - which is a proven surveillance tool for hydrocarbon reservoir monitoring. Time-lapse (4D) seismic combines acquisition and processing of at least two seismic datasets (or vintages) in order to extract information related to changes in a reservoir within a specified time interval. The current paradigm places stringent requirements on replicating the 4D surveys, which is an expensive task often requiring uneconomical dense sampling of seismic wavefields. To mitigate the challenges of dense sampling, several advances in seismic acquisition have been made in recent years including the use of multiple sources firing at near simultaneous random times, and the adaptation of Compressive Sensing (CS) principles to design practical acquisition engines that improve sampling efficiency for seismic data acquisition. However, little is known regarding the implications of these developments for time-lapse studies. By conducting multiple experiments modelling surveys adhering to the principles of CS for 4D seismic, I propose a model that demonstrates the feasibility of randomized acquisitions for time-lapse seismic. The proposed joint recovery model (JRM), which derives from distributed CS, exploits the common information in time-lapse data during recovery of dense wavefields from measured subsampled data, providing highly repeatable and high-fidelity vintages. I show that we obtain better vintages when randomized surveys are not replicated, in contrast to standard practice, paving the way for an opportunity to relax the rigorous requirement to replicate surveys precisely. We assert that the vintages obtained using our proposed model are of sufficient quality to serve as inputs to processes that extract time-lapse attributes from which subsurface changes are deduced. Additionally, I show that recovery with the JRM is robust with respect to errors due to differences between actual and recorded postplot information. Finally, I present an opportunity to adapt our model to problems related to time-lapse seismic imaging where the main finding is that we can better delineate time-lapse changes by adapting the joint recovery model to wave-equation based inversion methods.},
	keywords = {Acquisition, Compressive Sensing, distributed compressive sensing, joint recovery, PhD, thesis, time lapse},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl_pres.pdf},
	author = {Felix Oghenekohwo}
}
@mastersthesis {kumar2017THels,
	title = {Enabling large-scale seismic data acquisition, processing and waveform-inversion via rank-minimization},
	year = {2017},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {In this thesis, I adapt ideas from the field of compressed sensing to mitigate the computational and memory bottleneck of seismic processing workflows such as missing-trace interpolation, source separation and wave-equation based inversion for large-scale 3- and 5-D seismic data. For interpolation and source separation using rank-minimization, I propose three main ingredients, namely a rank-revealing transform domain, a subsampling scheme that increases the rank in the transform domain, and a practical large-scale data-consistent rank-minimization framework, which avoids the need for expensive computation of singular value decompositions. We also devise a wave-equation based factorization approach that removes computational bottlenecks and provides access to the kinematics and amplitudes of full-subsurface offset extended images via actions of full extended image volumes on probing vectors, which I use to perform the amplitude-versus- angle analyses and automatic wave-equation migration velocity analyses on complex geological environments. After a brief overview of matrix completion techniques in Chapter 1, we propose a singular value decomposition (SVD)-free factorization based rank-minimization approach for large-scale matrix completion problems. Then, I extend this framework to deal with large-scale seismic data interpolation problems, where I show that the standard approach of partitioning the seismic data into windows is not required, which use the fact that events tend to become linear in these windows, while exploiting the low-rank structure of seismic data. Carefully selected synthetic and realistic seismic data examples validate the efficacy of the interpolation framework. Next, I extend the SVD-free rank-minimization approach to remove the seismic cross-talk in simultaneous source acquisition. Experimental results verify that source separation using the SVD-free rank-minimization approaches are comparable to the sparsity-promotion based techniques; however, separation via rank-minimization is significantly faster and memory efficient. We further introduce a matrix-vector formulation to form full-subsurface extended image volumes, which removes the storage and computational bottleneck found in the convention methods. I demonstrate that the proposed matrix-vector formulation is used to form different image gathers with which amplitude-versus-angle and wave-equation migration velocity analyses is performed, without requiring prior information on the geologic dips. Finally, I conclude the thesis by outlining potential future research directions and extensions of the thesis work.},
	keywords = {Acquisition, extended image volumes, migration velocity analysis, PhD, Processing, rank minimization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/kumar2017THels/kumar2017THels.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/kumar2017THels/kumar2017THels_pres.pdf},
	author = {Rajiv Kumar}
}
@mastersthesis {dasilva2017THlso,
	title = {Large-scale optimization algorithms for missing data completion and inverse problems},
	year = {2017},
	note = {(PhD)},
	month = {09},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Inverse problems are an important class of problems found in many areas of science and engineering. In these problems, one aims to estimate unknown parameters of a physical system through indirect multi-experiment measurements. Inverse problems arise in a number of fields including seismology, medical imaging, and astronomy, among others. An important aspect of inverse problems is the quality of the acquired data itself. Real-world data acquisition restrictions, such as time and budget constraints, often results in measured data with missing entries. Many inversion algorithms assume that the input data is fully sampled and relatively noise free and produce poor results when these assumptions are violated. Given the multidimensional nature of real-world data, we propose a new low-rank optimization method on the smooth manifold of Hierarchical Tucker tensors. Tensors that exhibit this low-rank structure can be recovered from solving this non-convex program in an efficient manner. We successfully interpolate realistically sized seismic data volumes using this approach. If our low-rank tensor is corrupted with non-Gaussian noise, the resulting optimization program can be formulated as a convex-composite problem. This class of problems involves minimizing a non-smooth but convex objective composed with a nonlinear smooth mapping. In this thesis, we develop a level set method for solving composite-convex problems and prove that the resulting subproblems converge linearly. We demonstrate that this method is competitive when applied to examples in noisy tensor completion, analysis-based compressed sensing, audio declipping, total-variation deblurring and denoising, and one-bit compressed sensing. With respect to solving the inverse problem itself, we introduce a new software design framework that manages the cognitive complexity of the various components involved. Our framework is modular by design, which enables us to easily integrate and replace components such as linear solvers, finite difference stencils, preconditioners, and parallelization schemes. As a result, a researcher using this framework can formulate her algorithms with respect to high-level components such as objective functions and hessian operators. We showcase the ease with which one can prototype such algorithms in a 2D test problem and, with little code modification, apply the same method to large-scale 3D problems.},
	keywords = {convex composite, interpolation, low-rank, Optimization, PhD, software design, tensor, tensor completion},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/dasilva2017THlso/dasilva2017THlso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/dasilva2017THlso/dasilva2017THlso_pres.pdf},
	author = {Curt Da Silva}
}
@mastersthesis {wason2017THsss,
	title = {Simultaneous-source seismic data acquisition and processing with compressive sensing},
	year = {2017},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {The work in this thesis adapts ideas from the field of compressive sensing (CS) that lead to new insights into acquiring and processing seismic data, where we can fundamentally rethink how we design seismic acquisition surveys and process acquired data to minimize acquisition- and processing-related costs. Current efforts towards dense source/receiver sampling and full azimuthal coverage to produce high-resolution images of the subsurface have led to the deployment of multiple sources across survey areas. A step ahead from multisource acquisition is simultaneous-source acquisition, where multiple sources fire shots at near-simultaneous/random times resulting in overlapping shot records, in comparison to no overlaps during conventional sequential-source acquisition. Adoption of simultaneous-source techniques has helped to improve survey efficiency and data density. The engine that drives simultaneous-source technology is simultaneous-source separation {\textendash}- a methodology that aims to recover conventional sequential-source data from simultaneous-source data. This is essential because many seismic processing techniques rely on dense and periodic (or regular) source/receiver sampling. We address the challenge of source separation through a combination of tailored simultaneous-source acquisition design and sparsity-promoting recovery via convex optimization using l1 objectives. We use CS metrics to investigate the relationship between marine simultaneous-source acquisition design and data reconstruction fidelity, and consequently assert the importance of randomness in the acquisition system in combination with an appropriate choice for a sparsifying transform (i.e., curvelet transform) in the reconstruction algorithm. We also address the challenge of minimizing the cost of expensive, dense, periodically-sampled and replicated time-lapse surveying and data processing by adapting ideas from distributed compressive sensing. We show that compressive randomized time-lapse surveys need not be replicated to attain acceptable levels of data repeatability, as long as we know the shot positions (post acquisition) to a sufficient degree of accuracy. We conclude by comparing sparsity-promoting and rank-minimization recovery techniques for marine simultaneous-source separation, and demonstrate that recoveries are comparable; however, the latter approach readily scales to large-scale seismic data and is computationally faster.},
	keywords = {Acquisition, Compressive Sensing, marine, Optimization, PhD, simultaneous source, source separation},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss_pres.pdf},
	author = {Haneet Wason}
}
@mastersthesis {bougher2016THmla,
	title = {Machine learning applications to geophysical data analysis},
	year = {2016},
	note = {(MSc)},
	month = {08},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The sedimentary layers of the Earth are a complex amorphous material formed from chaotic, turbulent, and random natural processes. Exploration geophysicists use a combination of assumptions, approximate physical models, and trained pattern recognition to extract useful information from complex remote sensing data such as seismic and well logs. In this thesis I investigate supervised and unsupervised machine learning models in geophysical data analysis and present two novel applications to exploration geophysics. Firstly, interpreted well logs from the Trenton-Black River study are used to train a classifier that results in a success rate of 67\% at predicting stratigraphic units from gamma ray logs. I use the scattering transform, a multiscale analysis transform, to extract discriminating features to feed a K-nearest neighbour classifier. A second experiment frames a conventional pre-stack seismic data characterization workflow as an unsupervised machine learning problem that is free from physical assumptions. Conventionally, the Shuey model is used to fit the angle dependent reflectivity response of seismic data. I instead use principle component based approaches to learn projections from the data that improve classification. Results on the Marmousi II elastic model and an industry field dataset show that unsupervised learning models can be effective at segmenting hydrocarbon reservoirs from seismic data.},
	keywords = {AVA, machine learning, MSc, PCA, scattering transform, thesis, well logs},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2016/bougher2016THmla/bougher2016THmla.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2016/bougher2016THmla/bougher2016THmla_pres.pdf},
	author = {Ben B. Bougher}
}
@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}
}
@mastersthesis {lin2015THpes,
	title = {Primary estimation with sparsity-promoting bi-convex optimization},
	year = {2015},
	note = {(PhD)},
	month = {10},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis establishes a novel inversion methodology for the surface-related primaries from a given recorded seismic wavefield, called the Robust Estimation of Primaries by Sparse Inversion (Robust EPSI, or REPSI). Surface-related multiples are a major source of coherent noise in seismic data, and inferring fine geological structures from active-source seismic recordings typically first necessitates its removal or mitigation. For this task, current practice calls for data-driven approaches which produce only approximate multiple models that must be non-linearly subtracted from the data, often distorting weak primary events in the process. A recently proposed method called Estimation of Primaries by Sparse Inversion (EPSI) avoids this adaptive subtraction by directly inverting for a discrete representation of the underlying multiple-free subsurface impulse response as a set of band-limited spikes. However, in its original form, the EPSI algorithm exhibits a few notable shortcomings that impede adoption. Although it was shown that the correct impulse response can be obtained through a sparsest solution criteria, the current EPSI algorithm is not designed to take advantage of this finding, but instead approximates a sparse solution in an ad-hoc manner that requires practitioners to decide on a multitude of inversion parameters. The Robust EPSI method introduced in this thesis reformulates the original EPSI problem as a formal bi-convex optimization problem that makes obtaining the sparsest solution an explicit goal, while also reliably admit satisfactory solutions using contemporary self-tuning gradient methods commonly seen in large-scale machine learning communities. I show that the Robust EPSI algorithm is able to operate successfully on a variety of datasets with minimal user input, while also producing a more accurate model of the subsurface impulse response when compared to the original algorithm. Furthermore, this thesis makes several contributions that improves the capability and practicality of EPSI: a novel scattering-based multiple prediction model that allows Robust EPSI to deal with wider near-offset receiver gaps than previously demonstrated for EPSI, as well as a multigrid-inspired continuation strategy that significantly reduces the computation time needed to solve EPSI-type problems. These additions are enabled by and built upon the formalism of the Robust EPSI as developed in this thesis.},
	keywords = {biconvex, EPSI, inversion, multiples, Optimization, PhD, sparsity},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes_pres.pdf},
	author = {Tim T.Y. Lin}
}
@mastersthesis {li2015THsps,
	title = {Sparsity promoting seismic imaging and full-waveform inversion},
	year = {2015},
	note = {(PhD)},
	month = {07},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis will address the large computational costs of solving least-squares migration and full-waveform inversion problems. Least-squares seismic imaging and full-waveform inversion are seismic inversion techniques that require iterative minimizations of large least-squares misfit functions. Each iteration requires an evaluation of the Jacobian operator and its adjoint, both of which require two wave-equation solves for all sources, creating prohibitive computational costs. In order to reduce costs, we utilize randomized dimensionality reduction techniques, reducing the number of sources used during inversion. The randomized dimensionality reduction techniques create subsampling related artifacts, which we mitigate by using curvelet-domain sparsity-promoting inversion techniques. Our method conducts least-squares imaging at the approximate cost of one reverse-time migration with all sources, and computes the Gauss-Newton full-waveform inversion update at roughly the cost of one gradient update with all sources. Finally, during our research of the full-waveform inversion problem, we discovered that we can utilize our method as an alternative approach to add sparse constraints on the entire velocity model by imposing sparsity constraints on each model update separately, rather than regularizing the total velocity model as typically practiced. We also observed this alternative approach yields a faster decay of the residual and model error as a function of iterations. We provided empirical arguments why and when imposing sparsity on the updates can lead to improved full-waveform inversion results.},
	keywords = {Full-waveform inversion, Gauss-Newton method, least-squares imaging, seismic imaging, sparsity promoting},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps_pres.pdf},
	author = {Xiang Li}
}
@mastersthesis {li2015THwmd,
	title = {A weighted $\ell_1$-minimization for distributed compressive sensing},
	year = {2015},
	note = {(MSc)},
	month = {09},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Distributed Compressive Sensing (DCS) studies the recovery of jointly sparse signals. Compared to separate recovery, the joint recovery algorithms in DCS are usually more effective as they make use of the joint sparsity. In this thesis, we study a weighted l1-minimization algorithm for the joint sparsity model JSM-1 proposed by Baron et al. Our analysis gives a sufficient null space property for the joint sparse recovery. Furthermore, this property can be extended to stable and robust settings. We also presents some numerical experiments for this algorithm.},
	keywords = {distributed compressive sensing, MSc, thesis, weighted $\ell_1$},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THwmd/li2015THwmd.pdf},
	author = {Xiaowei Li}
}
@mastersthesis {petrenko2014THaih,
	title = {Accelerating an iterative Helmholtz solver using reconfigurable hardware},
	year = {2014},
	note = {(MSc)},
	month = {04},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {An implementation of seismic wave simulation on a platform consisting of a conventional host processor and a reconfigurable hardware accelerator is presented. This research is important in the field of exploration for oil and gas resources, where a 3D model of the subsurface of the Earth is frequently required. By comparing seismic data collected in a real-world survey with synthetic data generated by simulated waves, it is possible to deduce such a model. However this requires many time-consuming simulations with different Earth models to find the one that best fits the measured data. Speeding up the wave simulations would allow more models to be tried, yielding a more accurate estimate of the subsurface. The reconfigurable hardware accelerator employed in this work is a field programmable gate array (FPGA). FPGAs are computer chips that consist of electronic building blocks that the user can configure and reconfigure to represent their algorithm in hardware. Whereas a traditional processor can be viewed as a pipeline for processing instructions, an FPGA is a pipeline for processing data. The chief advantage of the FPGA is that all the instructions in the algorithm are already hardwired onto the chip. This means that execution time depends only on the amount of data to be processed, and not on the complexity of the algorithm. The main contribution is an implementation of the well-known Kaczmarz row projection algorithm on the FPGA, using techniques of dataflow programming. This kernel is used as the preconditioning step of CGMN, a modified version of the conjugate gradients method that is used to solve the time-harmonic acoustic isotropic constant density wave equation. Using one FPGA-based accelerator, the current implementation allows seismic wave simulations to be performed over twice as fast, compared to running on one Intel Xeon E5-2670 core. I also discuss the effect of modifications of the algorithm necessitated by the hardware on the convergence properties of CGMN. Finally, a specific plan for future work is set-out in order to fully exploit the accelerator platform, and the work is set in its larger context.},
	keywords = {CG, CGMN, FPGA, Helmholtz, Kaczmarz, linear solver, Maxeler, MSc, thesis, wave equation},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2014/petrenko2014THaih/petrenko2014THaih.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2014/petrenko2014THaih/petrenko2014THaih_pres.pdf},
	author = {Art Petrenko}
}
@mastersthesis {miao2014THesi,
	title = {Efficient seismic imaging with spectral projector and joint sparsity},
	year = {2014},
	note = {(MSc)},
	month = {03},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {In this thesis, we investigate the potential of improving the eciency of seismic imaging with two advanced techniques: the spectral projector and the {\textquoteright}joint sparsity{\textquoteright}. The spectral projector offers an eigenvalue decomposition free computation routine that can filter out unstable evanescent wave com- ponents during wave equation based depth extrapolation. {\textquoteright}Joint sparsity{\textquoteright} aims to improve on the pure sparsity promoting recovery by making use of additional structure information of the signal. Besides, a new sparsity optimization algorithm - PQNL1 - is proposed to improve both theoretical convergence rate and practical performance for extremely large seismic imaging problems.},
	keywords = {MSc, thesis},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2014/miao2014THesi/miao2014THesi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2014/miao2014THesi/miao2014THesi_pres.pdf},
	author = {Lina Miao}
}
@mastersthesis {hargreaves2014THssr,
	title = {Sparse signal recovery: analysis and synthesis formulations with prior support information},
	year = {2014},
	note = {(MSc)},
	month = {04},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The synthesis model for signal recovery has been the model of choice for many years in compressive sensing. Various weighting schemes using prior support information to adjust the objective function associated with the synthesis model have been shown to improve the recovery of the signal in terms of accuracy. Generally, even with no prior knowledge of the support, iterative methods can build support estimates and incorporate that into the recovery which has also been shown to increase the speed and accuracy of the recovery. However when the original signal is sparse with respect to a redundant dictionary (rather than an orthonormal basis) there is a counterpart model to synthesis, namely the analysis model, which has been less popular but has recently attracted more attention. The analysis model is much less understood and thus there are fewer theorems available in both the context of non-weighted and weighted signal recovery. In this thesis, we investigate weighting in both the analysis model and synthesis model in weighted $\ell_1$-minimization. Theoretical guarantees on reconstruction and various weighting strategies for each model are discussed. We give conditions for weighted synthesis recovery with frames which do not require strict incoherency conditions, this is based on recent results of regular synthesis with frames using optimal dual $\ell_1$ analysis. A novel weighting technique is introduced in the analysis case which outperforms its traditional counterparts in the case of seismic wavefield reconstruction. We also introduce a weighted split Bregman algorithm for analysis and optimal dual analysis. We then investigate these techniques on seismic data and synthetically created test data using a variety of frames.},
	keywords = {analysis, MSc, sparse, synthesis, thesis, weighted $\ell_1$},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2014/hargreaves2014THssr/hargreaves2014THssr.pdf},
	author = {Brock Hargreaves}
}
@mastersthesis {johnson2013THswr,
	title = {Seismic wavefield reconstruction using reciprocity},
	year = {2013},
	note = {(MSc)},
	month = {03},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The primary focus of most reflection seismic surveys is to help locate hydrocarbon recourses. Due to an ever increasing scarcity of these recourses, we must increase the size and quality of our seismic surveys. However, processing such large seismic data volumes to accurately recover earth properties is a painstaking and computationally intensive process. Due to the way reflection seismic surveys are conducted there are often holes in the collected data, where traces are not recorded. This can be due to physical or cost constraints. For some of the initial stages of processing these missing traces are of little consequence. However processes like multiple prediction and removal, interferometric ground roll prediction, and migration require densely sampled data on a regular grid. Thus the need to interpolate undersampled data cannot be ignored. Using the fact that reflection seismic data sets obey a reciprocal relationship in source and receiver locations, combined with recent advances in the field of compressed sensing, we show that properly regularized the wavefield reconstruction problem can be solved with a high degree of accuracy. We exploit the compressible nature of seismic data in the curvelet domain to solve regularized l1 recovery problems that seek to match the measured data and enforce the above mentioned reciprocity. Using our method we were able to achieve results with a 20.45 dB signal to noise ratio when reconstructing a marine data set that had 50\% of its traces decimated. This is a 13.44 dB improvement over using the same method run without taking reciprocity into account.},
	keywords = {MSc, thesis},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2013/johnson2013THswr.pdf},
	author = {James Johnson}
}
@mastersthesis {ghadermarzy2013THups,
	title = {Using prior support information in compressed sensing},
	year = {2013},
	note = {(MSc)},
	month = {08},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Compressed sensing is a data acquisition technique that entails recovering estimates of sparse and compressible signals from $n$ linear measurements, significantly fewer than the signal ambient dimension $N$. In this thesis we show how we can reduce the required number of measurements even further if we incorporate prior information about the signal into the reconstruction algorithm. Specifically, we study certain weighted nonconvex $\ell_p$ minimization algorithms and a weighted approximate message passing algorithm. In Chapter 1 we describe compressed sensing as a practicable signal acquisition method in application and introduce the generic sparse approximation problem. Then we review some of the algorithms used in compressed sensing literature and briefly introduce the method we used to incorporate prior support information into these problems. In Chapter 2 we derive sufficient conditions for stable and robust recovery using weighted $\ell_p$ minimization and show that these conditions are better than those for recovery by regular $\ell_p$ and weighted $\ell_1$. We present extensive numerical experiments, both on synthetic examples and on audio, and seismic signals. In Chapter 3 we derive weighted AMP algorithm which iteratively solves the weighted $\ell_1$ minimization. We also introduce a reweighting scheme for weighted AMP algorithms which enhances the recovery performance of weighted AMP. We also apply these algorithms on synthetic experiments and on real audio signals.},
	keywords = {compressed sensing, MSc, thesis, weighted $\ell_1$},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2013/ghadermarzy2013THups.pdf},
	author = {Navid Ghadermarzy}
}
@mastersthesis {jumah2012THdre,
	title = {Dimensionality-reduced estimation of primaries by sparse inversion},
	year = {2012},
	note = {(MSc)},
	month = {02},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Data-driven methods{\textemdash}such as the estimation of primaries by sparse inversion suffer from the curse of dimensionality that leads to disproportional growth in computational and storage demands when moving to realistic 3D field data. To remove this fundamental impediment, we propose a dimensionality-reduction technique where the data matrix is approximated adaptively by a randomized low-rank factorization. Compared to conventional methods, which need passes through all the data possibly including on-the-fly interpolations for each iteration, our approach has the advantage that the passes is reduced to one to three. In addition, the low-rank matrix factorization leads to considerable reductions in storage and computational costs of the matrix multiplies required by the sparse inversion. Application of the proposed formalism to synthetic and real data shows that significant performance improvements in speed and memory use are achievable at a low computational overhead required by the low-rank factorization.},
	keywords = {MSc, thesis},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2012/jumah2012THdre.pdf},
	author = {Bander Jumah}
}
@mastersthesis {moghaddam10phd,
	title = {Curvelet-based migration amplitude recovery},
	year = {2010},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Migration can accurately locate reflectors in the earth but in most cases fails to correctly resolve their amplitude. This might lead to mis-interpretation of the nature of reflector. In this thesis, I introduced a method to accurately recover the amplitude of the seismic reflector. This method relies on a new transform-based recovery that exploits the expression of seismic images by the recently developed curvelet transform. The elements of this transform, called curvelets, are multi-dimensional, multi-scale, and multi-directional. They also remain approximately invariant under the imaging operator. I exploit these properties of the curvelets to introduce a method called Curvelet Match Filtering (CMF) for recovering the seismic amplitude in presence of noise in both migrated image and data. I detail the method and illustrate its performance on synthetic dataset. I also extend CMF formulation to other geophysical applications and present results on multiple removal. In addition of that, I investigate preconditioning of the migration which results to rapid convergence rate of the iterative method using migration.},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2010/moghaddam10phd.pdf},
	author = {Peyman P. Moghaddam}
}
@mastersthesis {almatar10THesd,
	title = {Estimation of surface-free data by curvelet-domain matched filtering and sparse inversion},
	year = {2010},
	note = {(MSc)},
	month = {12},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {A recent robust multiple-elimination technique, based on the underlying principle that relates primary impulse response to total upgoing wavefield, tries to change the paradigm that sees surface-related multiples as noise that needs to be removed from the data prior to imaging. This technique, estimation of primaries by sparse inversion (EPSI), (van Groenestijn and Verschuur, 2009; Lin and Herrmann, 2009), proposes an inversion procedure during which the source function and surface- free impulse response are directly calculated from the upgoing wavefield using an alternating optimization procedure. EPSI hinges on a delicate interplay between surface-related multiples and pri- maries. Finite aperture and other imperfections may violate this relationship. In this thesis, we investigate how to make EPSI more robust by incorporating curvelet-domain matching in its formulation. Compared to surface-related multiple removal (SRME), where curvelet-domain matching was used successfully, incorporating this step has the additional advantage that matches multiples to multiples rather than predicated multiples to total data as in SRME.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2010/almatar10THesd.pdf},
	author = {Mufeed H. AlMatar}
}
@mastersthesis {kumar09THins,
	title = {Incoherent noise suppression and deconvolution using curvelet-domain sparsity},
	year = {2009},
	note = {(MSc)},
	month = {06},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Curvelets are a recently introduced transform domain that belongs to a family of multiscale and also multidirectional data expansions. As such, curvelets can be applied to resolution of the issues of complicated seismic wavefronts. We make use of this multiscale, multidirectional and hence sparsifying ability of the curvelet transform to suppress incoherent noise from crustal data where the signal-to-noise ratio is low and to develop an improved deconvolution procedure. Incoherent noise present in seismic reflection data corrupts the quality of the signal and can often lead to misinterpretation. The curvelet domain lends itself particularly well for denoising because coherent seismic energy maps to a relatively small number of significant curvelet coefficents.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2009/kumar09THins.pdf},
	author = {Vishal Kumar}
}
@mastersthesis {alhashim09THsdp,
	title = {Seismic data processing with the parallel windowed curvelet transform},
	year = {2009},
	note = {(MSc)},
	month = {08},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The process of obtaining high quality seismic images is very challenging when exploring new areas that have high complexities. The to be processed seismic data comes from the field noisy and commonly incomplete. Recently, major advances were accomplished in the area of coherent noise removal, for example, Surface Related Multiple Elimination (SRME). Predictive multiple elimination methods, such as SRME, consist of two steps: The first step is the prediction step, in this step multiples are predicted from the seismic data. The second step is the separation step in which primary reflection and surface related multiples are separated, this involves predicted multiples from the first step to be matched with the true multiples in the data and eventually removed. A recent robust Bayesian wavefield separation method have been recently introduced to improve on the separation by matching methods. This method utilizes the effectiveness of using the multi scale and multi angular curvelet transform in processing seismic images. The method produced excellent results and improved multiple removal. A considerable problem in the seismic processing field is the fact that seismic data are large and require a correspondingly large memory size and processing time. The fact that curvelets are redundant also increases the need for large memory to process seismic data. In this thesis we propose a parallel approach based windowing operator that divides large seismic data into smaller more managable datasets that can fit in memory so that it is possible to apply the Bayesian separation process in parallel with minimal harm to the image quality and data integrity. However, by dividing the data, we introduce discontinuities. We take these discontinuities into account and compare two ways that different windows may communicate. The first method is to communicate edge information at only two steps, namely, data scattering and gathering processes while applying the multiple separation on each window separately. The second method is to define our windowing operator as a global operator, which exchanges window edge information at each forward and inverse curvelet transform. We discuss the trade off between the two methods trying to minimize complexity and I/O time spent in the process. We test our windowing operator on a seismic denoising problem and then apply the windowing operator on our sparse-domain Bayesian primary-multiple separation.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2009/alhashim09THsdp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2009/alhashim09THsdp_pres.pdf},
	author = {Fadhel Abbas Alhashim}
}
@mastersthesis {lin08THccl,
	title = {Compressed computation of large-scale wavefield extrapolation in inhomogeneous medium},
	year = {2008},
	month = {04},
	school = {University of British Columbia},
	type = {mastersmasters},
	abstract = {In this work an explicit algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3-D. By using ideas from {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright}, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by \emphnonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can successfully be recovered when the measurement basis is \emphincoherent with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with sparsity transforms that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wave modes and on the complexity of the wavefield. A proof of principle for the {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright} method is given for inverse wavefield extrapolation in 2-D. The results show that our method is stable, has reduced dip limitations and handles evanescent waves in inverse extrapolation.},
	keywords = {BSc, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/lin08THccl.pdf},
	author = {Tim T.Y. Lin}
}
@mastersthesis {maysami08THlcs,
	title = {Lithology constraints from seismic waveforms: application to opal-A to opal-CT transition},
	year = {2008},
	note = {(MSc)},
	month = {02},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {In this work, we present a new method for seismic waveform characterization, which is aimed at extracting detailed litho-stratigraphical information from seismic data. We attempt to estimate the lithological attributes from seismic data according to our parametric representation of stratigraphical horizons, where the parameter values provide us with a direct link to nature of lithological transitions. We test our method on a seismic dataset with a strong diagenetic transition (opal-A to opal-CT transition). Given some information from cutting samples of well, we use a percolation-based model to construct the elastic profile of lithological transitions. Our goal is to match parametric representation for the diagenetic transition in both real data and synthetic data given by these elastic profiles. This match may be interpreted as a well-seismic tie, which reveals lithological information about stratigraphical horizons.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/maysami08THlcs.pdf},
	author = {Mohammad Maysami}
}
@mastersthesis {fenelon08msc,
	title = {Nonequispaced discrete curvelet transform for seismic data reconstruction},
	year = {2008},
	month = {08},
	type = {masters},
	abstract = {Physical constraints during seismic acquisitions lead to incomplete seismic datasets. Curvelet Reconstruction with Sparsity promoting Inversion (CRSI) is one of the most efficient interpolation method available to recover complete datasets from data with missing traces. The method uses in its definition the curvelet transform which is well suited to process seismic data. However, its main shortcoming is to not be able to provide an accurate result if the data are acquired at irregular positions. This come from the curvelet transform implementation which cannot handle this type of data. In this thesis the implementation of the curvelet transform is modified to offer the possibility to CRSI to give better representation of seismic data for high quality seismic imaging.},
	keywords = {BSc, SLIM},
	pdf = {http://slim.gatech.edu/Publications/Public/Theses/2008/fenelon08msc.pdf},
	author = {Lloyd Fenelon}
}
@mastersthesis {hennenfent08phd,
	title = {Sampling and reconstruction of seismic wavefields in the curvelet domain},
	year = {2008},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Wavefield reconstruction is a crucial step in the seismic processing flow. For instance, unsuccessful interpolation leads to erroneous multiple predictions that adversely affect the performance of multiple elimination, and to imaging artifacts. We present a new non-parametric transform-based reconstruction method that exploits the compression of seismic data by the recently developed curvelet transform. The elements of this transform, called curvelets, are multi-dimensional, multi-scale, and multi-directional. They locally resemble wavefronts present in the data, which leads to a compressible representation for seismic data. This compression enables us to formulate a new curvelet-based seismic data recovery algorithm through sparsity-promoting inversion (CRSI). The concept of sparsity-promoting inversion is in itself not new to geophysics. However, the recent insights from the field of {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright} are new since they clearly identify the three main ingredients that go into a successful formulation of a reconstruction problem, namely a sparsifying transform, a sub-Nyquist sampling strategy that subdues coherent aliases in the sparsifying domain, and a data-consistent sparsity-promoting program. After a brief overview of the curvelet transform and our seismic-oriented extension to the fast discrete curvelet transform, we detail the CRSI formulation and illustrate its performance on synthetic and real datasets. Then, we introduce a sub-Nyquist sampling scheme, termed jittered undersampling, and show that, for the same amount of data acquired, jittered data are best interpolated using CRSI compared to regular or random undersampled data. We also discuss the large-scale one-norm solver involved in CRSI. Finally, we extend CRSI formulation to other geophysical applications and present results on multiple removal and migration-amplitude recovery.},
	keywords = {curvelet transform, reconstruction, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/hennenfent08phd.pdf},
	author = {Gilles Hennenfent}
}
@mastersthesis {yarham08THsgs,
	title = {Seismic ground-roll separation using sparsity promoting $\ell_1$ minimization},
	year = {2008},
	note = {(MSc)},
	month = {05},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The removal of coherent noise generated by surface waves in land based seismic is a prerequisite to imaging the subsurface. These surface waves, termed as ground roll, overlay important reflector information in both the t-x and f-k domains. Standard techniques of ground roll removal commonly alter reflector information as a consequence of the ground roll removal. We propose the combined use of the curvelet domain as a sparsifying basis in which to perform signal separation techniques that can preserve reflector information while increasing ground roll removal. We examine two signal separation techniques, a block-coordinate relaxation method and a Bayesian separation method. The derivations and background for both methods are presented and the parameter sensitivity is examined. Both methods are shown to be effective in certain situations regarding synthetic data and erroneous surface wave predictions. The block-coordinate relaxation method is shown to have ma jor weaknesses when dealing with seismic signal separation in the presence of noise and with the production of artifacts and reflector degradation. The Bayesian separation method is shown to improve overall separation for both seismic and real data. The Bayesian separation scheme is used on a real data set with a surface wave prediction containing reflector information. It is shown to improve the signal separation by recovering reflector information while improving the surface wave removal. The abstract contains a separate real data example where both the block-coordinate relaxation method and the Bayesian separation method are compared.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/yarham08THsgs.pdf},
	author = {Carson Yarham}
}
@mastersthesis {lebed08THssr,
	title = {Sparse signal recovery in a transform domain},
	year = {2008},
	note = {(MSc)},
	month = {08},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {The ability to efficiently and sparsely represent seismic data is becoming an increasingly important problem in geophysics. Over the last thirty years many transforms such as wavelets, curvelets, contourlets, surfacelets, shearlets, and many other types of x-lets have been developed. Such transform were leveraged to resolve this issue of sparse representations. In this work we compare the properties of four of these commonly used transforms, namely the shift-invariant wavelets, complex wavelets, curvelets and surfacelets. We also explore the performance of these transforms for the problem of recovering seismic wavefields from incomplete measurements.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/lebed08THssr.pdf},
	author = {Evgeniy Lebed}
}
@mastersthesis {dupuis05THssc,
	title = {Seismic singularity characterization with redundant dictionaries},
	year = {2005},
	note = {(MSc)},
	month = {07},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {We consider seismic signals as a superposition of waveforms parameterized by their fractional- orders. Each waveform models the reflection of a seismic wave at a particular transition between two lithological layers in the subsurface. The location of the waveforms in the seismic signal corresponds to the depth of the transitions in the subsurface, whereas their fractional-order constitutes a measure of the sharpness of the transitions. By considering fractional-order transitions, we generalize the zero-order transition model of the conventional deconvolution problem, and aim at capturing the different types of transitions. The goal is to delineate and characterize transitions from seismic signals by recovering the locations and fractional-orders of its corresponding waveforms. This problem has received increasing interest, and several methods have been proposed, including multi- and monoscale analysis based on Mallat{\textquoteright}s wavelet transform modulus maxima, and seismic atomic decomposition. We propose a new method based on a two-step approach, which divides the initial problem of delineating and characterizing transitions over the whole seismic signal, into two easier sub-problems. The algorithm first partitions the seismic signal into its major components, and then estimates the fractional-orders and locations of each component. Both steps are based on the sparse decomposition of seismic signals in overcomplete dictionaries of waveforms parameter- ized by their fractional-orders, and involve $\ell_1$ minimizations solved by an iterative thresholding algorithm. We present the method and show numerical results on both synthetic and real data.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2005/dupuis05THssc.pdf},
	author = {Catherine Dupuis}
}
