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Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity

Publication ,  Journal Article
Simons, FJ; Loris, I; Nolet, G; Daubechies, IC; Voronin, S; Judd, JS; Vetter, PA; Charléty, J; Vonesch, C
Published in: Geophysical Journal International
November 1, 2011

We propose a class of spherical wavelet bases for the analysis of geophysical models and for the tomographic inversion of global seismic data. Its multiresolution character allows for modelling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We describe benefits and drawbacks of these constructions and apply them to analyse the information in two published seismic wave speed models of the mantle, using the statistics of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the ℓ2 norm of the data residuals and the ℓ1 norm of the model wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains from our new approach in future inversions of finite-frequency seismic data. © 2011 The Authors Geophysical Journal International © 2011 RAS.

Duke Scholars

Published In

Geophysical Journal International

DOI

EISSN

1365-246X

ISSN

0956-540X

Publication Date

November 1, 2011

Volume

187

Issue

2

Start / End Page

969 / 988

Related Subject Headings

  • Geochemistry & Geophysics
  • 4013 Geomatic engineering
  • 3706 Geophysics
  • 3705 Geology
  • 0909 Geomatic Engineering
  • 0404 Geophysics
  • 0403 Geology
 

Citation

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Simons, F. J., Loris, I., Nolet, G., Daubechies, I. C., Voronin, S., Judd, J. S., … Vonesch, C. (2011). Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity. Geophysical Journal International, 187(2), 969–988. https://doi.org/10.1111/j.1365-246X.2011.05190.x
Simons, F. J., I. Loris, G. Nolet, I. C. Daubechies, S. Voronin, J. S. Judd, P. A. Vetter, J. Charléty, and C. Vonesch. “Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity.” Geophysical Journal International 187, no. 2 (November 1, 2011): 969–88. https://doi.org/10.1111/j.1365-246X.2011.05190.x.
Simons FJ, Loris I, Nolet G, Daubechies IC, Voronin S, Judd JS, et al. Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity. Geophysical Journal International. 2011 Nov 1;187(2):969–88.
Simons, F. J., et al. “Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity.” Geophysical Journal International, vol. 187, no. 2, Nov. 2011, pp. 969–88. Scopus, doi:10.1111/j.1365-246X.2011.05190.x.
Simons FJ, Loris I, Nolet G, Daubechies IC, Voronin S, Judd JS, Vetter PA, Charléty J, Vonesch C. Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity. Geophysical Journal International. 2011 Nov 1;187(2):969–988.
Journal cover image

Published In

Geophysical Journal International

DOI

EISSN

1365-246X

ISSN

0956-540X

Publication Date

November 1, 2011

Volume

187

Issue

2

Start / End Page

969 / 988

Related Subject Headings

  • Geochemistry & Geophysics
  • 4013 Geomatic engineering
  • 3706 Geophysics
  • 3705 Geology
  • 0909 Geomatic Engineering
  • 0404 Geophysics
  • 0403 Geology