Determination of structure coefficients from splitting matrices

Details Determination of structure coefficients from splitting matrices Determination of structure coefficients from splitting matrices

Sep 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000geoji.142....1g&link_type=abstract

Geophysical Journal International, Volume 142, Issue 1, pp. 1-3.

Astronomy and Astrophysics

Astronomy

2

Splitting Matrix, Structure Coefficients

Scientific paper

The splitting matrix for a set of coupled multiplets is a linear combination of structure coefficients, first-order Coriolis terms and terms for ellipticity and centrifugal force. These latter terms are calculated for a good 1-D earth model and removed. The first-order Coriolis terms are then uniquely determined. They are linear functionals of the density of the 1-D model. The remaining splitting matrix is an orthogonal transformation of the structure coefficients. The inverse orthogonal transformation is easily constructed and the set of structure coefficients is then obtained linearly from the splitting matrix. The structure coefficients are linear functionals of 3-D structure.

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