Determination of seismic source parameters from the coherence of body wave phases
A method is described for determining parameters that characterize the earthquake rupture process fitted by a time-dependent point source. Several teleseismic records of $P$, $pP$, and $sP$ made at different sites on the Earth's surface are used to find the moment tensor, depth, and time history of the source. All these phases are theoretically coherent when considered in the ray approximation, that is, the phase spectra at any two stations are identical, apart from a linear function of the frequency, while the amplitude spectra are identical apart from a constant factor. These theoretical properties reduce the determination of components of the seismic moment tensor to the solution of linear equations given by spectral characteristics of recorded waves. In practice the procedure is more complex, because a broadband record usually shows a superposition of $P$, $pP$, and $sP$ which arrive close to one another. The spectra of an earlier part of a record consisting of a superposition of these phases are coherent only at periods that are substantially larger than the arrival time differences between direct $P$ and the reflected waves. For this reason the procedure is implemented in three steps. The first involves an analysis of the long-period part of the $P$ wave spectrum. The moment tensor is estimated by assuming that signals recorded at different stations are coherent. The second step considers a broader frequency range; using the moment tensor previously obtained and varying the hypocenter depth, we corrected the spectra for each depth value in order to eliminate the theoretical delay of the interfering phases. The true source depth was taken to be that value for which the corrected spectra showed the ``highest coherence." The third step consisted in calculating the source time history. The method was tested using synthetic seismograms and records of the 1991 Khailino earthquake.