Open AccessA simple method of representing azimuthal anisotropy on a sphere
Author(s) -
Ekström Göran
Publication year - 2006
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.2006.02895.x
Subject(s) - spherical harmonics , azimuth , anisotropy , isotropy , physics , geometry , parametrization (atmospheric modeling) , mathematical analysis , classical mechanics , computational physics , mathematics , optics , radiative transfer
SUMMARY 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 (cos 2ζ, sin 2ζ) and (cos 4ζ, sin 4ζ) 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.