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Multidimensional seismic data reconstruction using tensor analysis Open Access


Other title
Type of item
Degree grantor
University of Alberta
Author or creator
Kreimer, Nadia
Supervisor and department
Sacchi, Mauricio D. (Physics)
Examining committee member and department
Vorobyov, Sergiy A. (Electrical and Computer Engineering)
Fomel, Sergey B. (University of Texas at Austin)
van der Baan, Mirko (Physics)
Sacchi, Mauricio D. (Physics)
Fenrich, Frances R. (Physics)
Department of Physics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on tensor algebra and proposes three methods that exploit the tensor nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the tensor slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the tensor and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods proposed in this thesis and other two reconstruction methods. This thesis demonstrates the suitability of tensor completion techniques for solving the simultaneous denoising and reconstruction problem.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Kreimer, N., and M. D. Sacchi, 2012, A tensor higher-order singular value decomposition for prestack seismic data noise reduction and interpolation: Geophysics, 77, no. 3, V113–V122.Kreimer, N., and M. D. Sacchi, 2012, Rank reduction of unfolded tensors for pre-stack de-noising and reconstruction: The Recorder, 37, no. 9, 24–27.Kreimer, N., and M. D. Sacchi, 2012, Reconstruction of seismic data via tensor completion: Statistical Signal Processing Workshop (SSP), 2012 IEEE, 29–32.Kreimer, N., and M. D. Sacchi, 2012, Tensor completion via nuclear norm minimization for 5D seismic data reconstruction: SEG Technical Program Expanded Abstracts, 1–5.Kreimer, N., and M. D. Sacchi, 2013, Nuclear norm minimization and tensor completion in exploration seismology: Presented at the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

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File title: Multidimensional seismic data reconstruction using tensor analysis, Ph. D. Thesis
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