We present a mathematical framework and a new methodology for the
parametrization of surface-wave phase-speed models based on
travel-time 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 may lend itself to
the parametrization of fully-three dimensional tomographic Earth
models including body waves as well.
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