An Application of Normal Mode Theory to the Retrieval of Structural Parameters and Source Mechanisms from Seismic Spectra

A cyclic process of refining models of the mechanical structure of the Earth and models of the mechanism of one or more earthquakes is developed. The theory of the elastic-gravitational free oscillations of the Earth is used to derive procedures for resolving nearly degenerate multiplets of normal modes. We show that a global network of seismographs (W.W.S.S.N.) permits resolution for angular orders l ≤ 76 and for frequencies a) w ≤ 0.090 s -1 . The peak or centre frequency of each nearly degenerate multiplet is interpreted to be a gross Earth datum. Together, the data are used to refine models of the mechanical structure of the Earth. The theory of free oscillations is used further to derive procedures for retrieving the mechanism, or moment tensor, of an earthquake point source. We show that a globa network of seismographs permits retrieval for frequencies 0.0125 s-1 ≤ w ≤ 0.0825 s-1 . We show that refined models of structure and mechanism lead to improved resolution and retrieval, and that an array of sources further complements the resolution of multiplets. We present a ‘standardized dataset’ of 1064 distinct, observed eigenfrequencies ol the elastic-gravitational free oscillations of the Earth. These gross-Earth data are compiled from 1461 modes reported in five studies: 2 modes reported by Derr (1969), 159 modes observed by Brune & Gilbert (1974), 240 modes observed by Mendiguren ( 1973), 248 modes observed by Dziewonski & Gilbert (1972,1973) and 812 modes reported here. It is our opinion that the establishment of a standardized dataset should precede the establishment of a standardized model of the Earth. Two new Earth models are presented that are compatible with the modal data. One is derived from model 508 (Gilbert & Dziewonski 1973) and the other from model B1 (Jordan & Anderson 1974). In the outer core and in the lower mantle, below a depth of about 950 km, the differences between the two models are negligibly small. In the inner core there are minor differences and in the upper mantle there are major differences in detail. The two models and the modal data are compatible with traditional ray data, provided that appropriate baseline corrections are made to the latter. The source mechanisms, or moment tensors, of two deep earthquakes, Colombia (1970 July 31) and Peru-Bolivia (1963 August 15), have been retrieved from the seismic spectra. In both cases the moment tensor possesses a compressive (implosive) isotropic part. There is good evidence that isotropic stress release begins gradually, over 80s before the origin time derived from the onset of short-period P and S waves. During the process of stress release the principal axes of the moment rate tensor migrate. The axis of compression is relatively stable, the compressive stress rate is dominant, and the other two axes rotate about the axis of compression. We speculate that earthquakes, occurring deep within descending lithospheric plates, are not sudden shearing movements alone but do exhibit compressive changes in volume such as would be associated with a phase change. We further speculate that compressive changes in volume may occur without sudden shearing movements, that there may be 9 silent earthquakes’.