Amplitudes of the earth's split normal modes.

Abstract

This paper develops the theory necessary to explain the amplitudes of the earth's split normal modes. Expressions are derived for the amplitudes of the free oscillations of a laterally homogeneous rotating and elliptical earth excited by a point double couple. The eigenfunctions for this problem are the complex vector spherical harmonics about the north pole. The amplitudes of the normal modes are obtained by transforming SAITO'S (1967) results, expressed in vector spherical harmonics about the earthquake source, into geographic coordinates. We explicitly show the dependence of the excitation of each singlet within a multiplet on geometric fault parameters, seismic moment, source depth, earth structure and the geographic coordinates of the source and receiver. We present synthetic torsional and spheroidal displacement and strain spectra for low order fundamental modes (0S2-0S5, 0T2-0T5) excited by four basic fault geometries. Our results are suitable for the synthesis of observed spectra and time domain records in which splitting is an important effect. We have applied these results elsewhere to the Chilean and Alaskan earthquakes and have obtained very good agreement with observations.

Spheroidal oscillations of the Earth stimulated by the Sumatra-Andaman earthquake with CDSN data

“…Therefore, the singlet amplitudes of Earth's free oscillations contain a great deal of information such as source location, geometric parameter, slip direction and amount of slip. According to Stein and Geller (1977), the pattern of singlet magnitude of spectral splitting stimulated by a double-couple source will be symmetric around m 0 , while on the contrary, the observed ones are strongly asymmetric, especially at the stations of HIA, LSA, ENH and WMQ, which implies impropriety in describing seismic rupture with one double-couple source. This viewpoint is also supported by the results of Ammon et al (2005) and Subarya et al (2006).…”

“…The focal mechanism of the event is from Harvard CMT catalogue (http://www.seismology.harvard.edu). We first calculated the spectrum of free oscillations according to the analytic expression given by Stein and Geller (1977), then multiplyed it with instrumental response of CDSN stations to get the theoretical singlet amplitudes, and finally compared the result with instrumental records.…”

“…To study the splitting of Earth's free oscillations in low-frequency band, we applied the theory developed by Stein and Geller (1977), which explains the splitting of normal modes of Earth oscillations, to the simulation of power spectral density. By transforming spherical harmonic expansion of the source from source reference frame into geographic coordinates, this theory gives an explicit expression of free oscillation amplitude stimulated by a double-couple point source in the laterally homogeneous, rotating and elliptical Earth.…”

Wavelet filter analysis of splitting and coupling of seismic normal modes below 1.5 mHz with superconducting gravimeter records after the December 26, 2004 Sumatra earthquake

“…The amplitude of each singlet depends on the location of the earthquake and seismic station, earthquake depth and focal mechanism, and seismic moment [34] . Calculating the seismic moment according to observed amplitude of singlets of 0 S 2 can be used to properly estimate the magnitude of earthquakes.…”

Penetration of the Earth's free oscillations at 54 minute period into the atmosphere

“…Aki and Richards, 1980). It is established for the 0 S 2 oscillations forced by a well-identi®ed earthquake that the observed distribution of the Earth 0 S 2 components over power depends on latitude and longitude of both a measurement site and earthquake source as well as on other parameters of the earthquake (e.g., Mendiguren, 1973;Stein and Geller, 1977). As for detecting the 0 S 2 components with microbarographic measurements, the gravity waves of atmospheric sources can hinder detection of these components.…”