Determination of structure coefficients from splitting matrices

Abstract

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.