The use of the coda for determination of the earthquake source spectrum

Abstract

abstract We studied the spectral content and variations in time of the coda of seismic oscillations following the body and surface waves of local earthquakes. Within narrow frequency bands, the form of the envelope of the coda is remarkably stable—independent of epicenter (and therefore epicentral distance), depth of focus, and all other parameters of the source. Only the absolute amplitude of the coda differs from event to event. Similarly, the forms of the coda at two stations from the same earthquake overlap one another, differing only in absolute amplitude by a factor that is the same for all events. Hence given the form of the coda, its amplitude in any frequency band may be parameterized by one number—the amplitude at a certain time. Therefore, the spectrum of the coda as a function of time can be described as the product of two factors—one, independent of time, is dependent only on the source, and the other, reflecting the effects of the medium and the same for all sources, gives the time dependence for each frequency band. Segments of the envelopes with time can be matched by simple theories of scattering. Using the theoretical relationships, estimates of Q can be made and show that for any time interval, Q increases with frequency, approximately proportional to the square root of frequency. As longer elapsed times are considered, the estimates of Q increase, suggesting greater penetration of seismic energy into the higher Q parts of the Earth. The spectra of different events can be compared directly by comparing the spectra of the codas at the same elapsed time. Such a comparison reveals a wide variety of different source spectra. By using empirical relations among coda spectra, observed S-wave spectra, and theoretical constraints, an estimate of the spectrum radiated by the source can be calculated from the coda spectrum. Source parameters (seismic moment, corner frequency of the radiated spectrum, calculated stress drop, etc.) can be determined from coda spectra of events with many different moments and in different regions, with the same station. The results show several interesting features dependent on the seismic moments and on the regions in which the earthquakes occurred.