The Diagonal Sum Rule and Averaged Eigenfrequencies

Abstract

The average value of the eigenfrequencies of a multiplet, split by a linear, aspherical perturbation, is the multiplet's degenerate eigenfrequency belonging to an unperturbed, spherically symmetric Earth. This result is a consequence of the diagonal sum rule. Methods are proposed to analyse simultaneously a large number of seismograms to recover any particular line in the multiplet structure. The diagonal sum rule can be used to find the multiplet's degenerate eigenfrequency. The frequency perturbations are then constraints on lateral heterogeneities in the Earth. Copyright © 1971, Wiley Blackwell. All rights reserved