Open AccessParametrizing surface wave tomographic models with harmonic spherical splines
Author(s) -
Amirbekyan Abel,
Michel Volker,
Simons Frederik J.
Publication year - 2008
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2008.03809.x
Subject(s) - spherical harmonics , parametrization (atmospheric modeling) , surface (topology) , inversion (geology) , basis function , tomography , mathematics , basis (linear algebra) , mathematical analysis , zonal spherical harmonics , geometry , physics , geology , vector spherical harmonics , optics , paleontology , structural basin , radiative transfer
SUMMARY 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.