Open AccessThe Diagonal Sum Rule and Averaged Eigenfrequencies
Author(s) -
Gilbert Freeman
Publication year - 1971
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1971.tb01806.x
Subject(s) - multiplet , diagonal , degenerate energy levels , perturbation (astronomy) , physics , mathematical analysis , mathematics , geometry , quantum mechanics , spectral line
Summary 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.