Summary: Accurate determination of the source depth of a seismic event is a potentially important goal for better discrimination between deeper earthquakes and more shallow nuclear tests. Earthquakes and explosions generate depth phases such as \(pP\) and \(sP\) as reflections of the underlying \(P\) signal generated by the event. The delay time between the original signal and the \(pP\) phase can be used to estimate the depth of the seismic event. Cepstral methods, first used by Tukey and later by others, offer natural nonparametric means for estimating general echo patterns in a single series. Here, we extend the single series methodology to arrays by regarding the ensemble of log spectra as sums of nonstationary smooth functions and a common additive signal whose periods are directly related to the time delays of the seismic phases. Detrending the log spectra reduces the problem to one of detecting a common signal with multiple periodicities in noise. Plotting an approximate cepstral \(F\)-statistic over pseudo-time yields a function that can be considered as a deconvolution of the seismic phases. We apply the array methodology to determining focal depths using three component recordings of earthquakes.
For the entire collection see [Zbl 1051.86001].