Principles of Geodynamics

Abstract

Theoretical normal-mode spectra for four spheroidal and four toroidal multiplets at six different locations of WWSSN stations are computed for a rotating elliptical Earth with a given dissipation and double-couple source models for Chilean and Alaskan earthquakes. The most important difference between these spectra and those computed for a spherical nonrotating Earth is in the former being susceptible to the effect of mutual constructive or destructive interferences among excitations of individual singlets within a multiplet. Although this effect is expected because of fine-structure splittings within a multiplet, a calculation is necessary to determine the extent of interferences. In some cases, spectral shapes of split multiplets are sizeably narrower, broader, higher or smaller than those of respective degenerate multiplets; it is also not uncommon to find at least two peaks within a multiplet, causing an ambiguity as to where within that multiplet is the appropriate position for assigning an observed period associated with that multiplet. Such ambiguity arises only because description of a whole multiplet is constrained to one single spectral peak -a prevalent practice thus far in interpreting observed spectra-while actually (21 + 1) spectral peaks should be simultaneously considered.However, mutual interferences among singlets render such consideration impossible at present due to limited amount of data of imperfect quality and due to our lack of knowledge on dissipation and lateral inhomogeneities within the Earth's interior. Thus, as shown by the results of this study, care must be administered when one interprets real data by using those methods that are appropriate for studying spherically symmetric, nonrotating Earths. On the average, the relative deviation between the location of the maximum amplitude of a split peak and the respective degenerate one and, similarly, between the two values of Q is found to be 0.1 and 20 per cent respectively, while maximum amplitudes differ by 30 per cent.

Source mechanism of the deep Colombian earthquake of 1970 July 31 from the free oscillation data

“…While part of the scattering is doubtless due to instrumental noise, probably the dominant is due to lateral heterogeneities of the Earth. Luh & Dziewonski (1976)ihave shown that ellipticity and rotation of the Earth produce a change in spectral peak amplitude which, on average is 30 per cent of the amplitude corresponding to a non-rotating spherical earth. We should expect changes even larger if lateral heterogeneities wer?…”

Amplitudes of the earth's split normal modes.

“…GELLER (1976). LUH and DZIEWONSKI (1976) modified the moment tensor solution to include the effects of rotation and ellipticity.…”