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

Jean Charléty, Sergey Voronin, Guust Nolet, Ignace Loris, Frederik J. Simons, Karin Sigloch, Ingrid C. Daubechies

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)4887-4899
Number of pages13
JournalJournal of Geophysical Research E: Planets
Volume118
Issue number9
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Forestry
  • Oceanography
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Palaeontology

Keywords

  • compressed sensing
  • finite-frequency tomography
  • inversion
  • l1 regularized least squares

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