Astronomy and Astrophysics – Astronomy
Scientific paper
May 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006geoji.165..668e&link_type=abstract
Geophysical Journal International, Volume 165, Issue 2, pp. 668-671.
Astronomy and Astrophysics
Astronomy
3
Seismic Anisotropy, Surface Waves, Tomography
Scientific paper
We describe a method of expressing azimuthally anisotropic surface wave velocities on the Earth using a local and smooth spherical-spline parametrization. Anisotropy in the Earth leads to azimuthally varying Love and Rayleigh wave velocities that can be expressed as (cos2ζ, sin2ζ) and (cos4ζ, sin4ζ) perturbations to the isotropic velocities, where ζ is the direction of surface-wave propagation. The strength of the perturbations varies laterally, and a current goal of seismic tomography is the detailed global mapping of these variations. Several parametrizations have previously been used to describe azimuthally varying velocities. The representation proposed here uses spherical splines and is designed to describe smooth variations in both the strength and geometry of azimuthal anisotropy. The method builds on a simple geometrical approximation for the local azimuth of propagation expressed at the defining spline knot points. It avoids the singularities at the poles that result when azimuthal variations are parametrized using traditional scalar spherical harmonics. Compared with a generalized spherical-harmonic expansion of the tensor fields that represent 2ζ and 4ζ azimuthal variations smoothly on a sphere, the new method offers the advantages of local geographical support and simplicity of implementation.
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