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USGS1999

An inverse method using toroidal mode data

The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1 %. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data .

Inverse Problems↗

USGS1984

Inverse problems for torsional modes.

Considers a spherically symmetric, non-rotating Earth consisting of an isotropic, perfect elastic material where the density and the S-wave velocity may have one or two discontinuities in the upper mantle. Shows that given the velocity throughout the mantle and the crust and given the density in the lower mantle, then the freqencies of the torsional oscillations of one angular order (one torsional spectrum), determine the density in the upper mantle and in the crust uniquely. If the velocity is known only in the lower mantle, then the frequencies of the torsional oscillations of two angular orders uniquely determine both the density and the velocity in the upper mantle and in the crust. In particular, the position and size of the discontinuities in the density and velocity are uniquely determined by two torsional spectra.-Author

Geophysical Journal of the Royal Astronomical Soci↗