@article {yang2020lrpo,
	title = {Low-rank representation of omnidirectional subsurface extended image volumes},
	journal = {Geophysics},
	volume = {86},
	number = {3},
	year = {2021},
	note = {(Geophysics)},
	month = {1},
	pages = {1MJ-WA152},
	abstract = {Subsurface-offset gathers play an increasingly important role in seismic imaging. These gathers are used during velocity model building and inversion of rock properties from amplitude variations. While powerful, these gathers come with high computational and storage demands to form and manipulate these high dimensional objects. This explains why only limited numbers of image gathers are computed over a limited offset range. We avoid these high costs by working with highly compressed low-rank factorizations. We arrive at these factorizations via a combination of probings with the double two-way wave equation and randomized singular value decompositions. In turn, the resulting factorizations give us access to all subsurface offsets without having to form the full extended image volumes. The latter is computationally prohibitive because extended image volumes are quadratic in image size. As a result, we can easily handle situations where conventional horizontal offset gathers are no longer focused. More importantly, the factorization also provides a mechanism to use the invariance relation of extended image volumes for velocity continuation. With this technique, extended image volumes for one background velocity model can directly be mapped to those of another background velocity model. Our low-rank factorization inherits this invariance property so we incur factorization costs only once when examining different imaging scenarios. Because all imaging experiments only involve the factors, they are computationally cheap with costs that scale with the rank of the factorization. We validate our methodology on 2D synthetics including a challenging imaging example with salt. Our experiments show that our low-rank factorization parameterizes extended image volumes naturally. Instead of brute force explicit cross-correlations between shifted source and receiver wavefields, our approach relies on the underlying linear-algebra structure that enables us to work with these objects without incurring unfeasible demands on computation and storage.},
	keywords = {extended image volumes, invariance relationship, low rank, power schemes, randomized linear algebra},
	doi = {10.1190/geo2020-0152.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2021/yang2020lrpo/Paper_final.html},
	author = {Mengmeng Yang and Marie Graff and Rajiv Kumar and Felix J. Herrmann}
}
@article {kumar2018toi,
	title = {Target-oriented imaging using extended image volumes{\textemdash}a low-rank factorization approach},
	journal = {Geophysical Prospecting},
	volume = {67},
	number = {5},
	year = {2019},
	note = {(Geophysical Prospecting)},
	pages = {1312-1328},
	abstract = {Imaging in geological challenging environments has led to new developments, including the idea of generating reflection responses by means of interferometric redatuming at a given target datum in the subsurface, when the target datum lies beneath a complex overburden. One way to perform this redatuming is via conventional model-based wave-equation techniques. But those techniques can be computationally expensive for large-scale seismic problems since the number of wave-equation solves is equal to two-times the number of sources involved during seismic data acquisition. Also conventional shot-profile techniques require lots of memory to save full subsurface extended image volumes. Therefore, they only form subsurface image volumes in either horizontal or vertical directions. We now present a randomized singular value decomposition based approach built upon the matrix probing scheme, which takes advantage of the algebraic structure of the extended imaging system. This low-rank representation enables us to overcome both the computational cost associated with the number of wave-equation solutions and memory usage due to explicit storage of full subsurface extended image volumes employed by conventional migration methods. Experimental results on complex geological models demonstrate the efficacy of the proposed methodology and allow practical reflection-based extended imaging for large-scale 5D seismic data.},
	keywords = {extended image volumes, randomized linear algebra, target-oriented imaging},
	doi = {10.1111/1365-2478.12779},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2019/kumar2018toi/kumar2018toi.html},
	author = {Rajiv Kumar and Marie Graff-Kray and Ivan Vasconcelos and Felix J. Herrmann}
}
@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}
}
