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Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization

Publication ,  Journal Article
Charléty, J; Voronin, S; Nolet, G; Loris, I; Simons, FJ; Sigloch, K; Daubechies, IC
Published in: Journal of Geophysical Research: Planets
September 1, 2013

We present a realistic application of an inversion scheme for global seismic tomography that uses as prior information the sparsity of a solution, defined as having few nonzero coefficients under the action of a linear transformation. In this paper, the sparsifying transform is a wavelet transform. We use an accelerated iterative soft-thresholding algorithm for a regularization strategy, which produces sparse models in the wavelet domain. The approach and scheme we present may be of use for preserving sharp edges in a tomographic reconstruction and minimizing the number of features in the solution warranted by the data. The method is tested on a data set of time delays for finite-frequency tomography using the USArray network, the first application in global seismic tomography to real data. The approach presented should also be suitable for other imaging problems. From a comparison with a more traditional inversion using damping and smoothing constraints, we show that (1) we generally retrieve similar features, (2) fewer nonzero coefficients under a properly chosen representation (such as wavelets) are needed to explain the data at the same level of root-mean-square misfit, (3) the model is sparse or compressible in the wavelet domain, and (4) we do not need to construct a heterogeneous mesh to capture the available resolution. Key Points Global tomography with solution sparsity in a certain basis as prior informationOne-norm of model wavelet coefficients as constraint regularizes the inversionFirst realistic application on actual data for global seismic tomography. © 2013 American Geophysical Union. All Rights Reserved.

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Published In

Journal of Geophysical Research: Planets

DOI

EISSN

2169-9100

ISSN

0148-0227

Publication Date

September 1, 2013

Volume

118

Issue

9

Start / End Page

4887 / 4899

Related Subject Headings

  • Meteorology & Atmospheric Sciences
 

Citation

APA
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MLA
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Charléty, J., Voronin, S., Nolet, G., Loris, I., Simons, F. J., Sigloch, K., & Daubechies, I. C. (2013). Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization. Journal of Geophysical Research: Planets, 118(9), 4887–4899. https://doi.org/10.1002/jgrb.50326
Charléty, J., S. Voronin, G. Nolet, I. Loris, F. J. Simons, K. Sigloch, and I. C. Daubechies. “Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization.” Journal of Geophysical Research: Planets 118, no. 9 (September 1, 2013): 4887–99. https://doi.org/10.1002/jgrb.50326.
Charléty J, Voronin S, Nolet G, Loris I, Simons FJ, Sigloch K, et al. Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization. Journal of Geophysical Research: Planets. 2013 Sep 1;118(9):4887–99.
Charléty, J., et al. “Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization.” Journal of Geophysical Research: Planets, vol. 118, no. 9, Sept. 2013, pp. 4887–99. Scopus, doi:10.1002/jgrb.50326.
Charléty J, Voronin S, Nolet G, Loris I, Simons FJ, Sigloch K, Daubechies IC. Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization. Journal of Geophysical Research: Planets. 2013 Sep 1;118(9):4887–4899.

Published In

Journal of Geophysical Research: Planets

DOI

EISSN

2169-9100

ISSN

0148-0227

Publication Date

September 1, 2013

Volume

118

Issue

9

Start / End Page

4887 / 4899

Related Subject Headings

  • Meteorology & Atmospheric Sciences