Parametrizing surface wave tomographic models with harmonic spherical splines

Amirbekyan Abel, Volker Michel, Frederik J. Simons

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We present a mathematical framework and a new methodology for the parametrization of surface wave phase-speed models, based on traveltime data. Our method is neither purely local, like block-based approaches, nor is it purely global, like those based on spherical harmonic basis functions. Rather, it combines the well-known theory and practical utility of the spherical harmonics with the spatial localization properties of spline basis functions. We derive the theoretical foundations for the application of harmonic spherical splines to surface wave tomography and summarize the results of numerous numerical tests illustrating the performance of a practical inversion scheme based upon them. Our presentation is based on the notion of reproducing-kernel Hilbert spaces, which lends itself to the parametrization of fully 3-D tomographic earth models that include body waves as well.

Original languageEnglish (US)
Pages (from-to)617-628
Number of pages12
JournalGeophysical Journal International
Issue number2
StatePublished - Aug 2008

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology


  • Fourier analysis
  • Inverse theory
  • Numerical approximation and analysis
  • Seismic tomography
  • Surface waves and free oscillations
  • Tomography


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