A Cepstral F Statistic for Detecting Delay-Fired Seismic Signals

Abstract

Time- and frequency-domain approaches to detecting a consistent pattern of reflections on an ensemble of seismic recordings are developed. Such patterns are characteristic of mining bursts and not of nuclear explosions or earthquakes so that detecting a ripple delay structure can serve as one component for discrimination. In the frequency-domain approach, a generalization of cepstral analysis is used to derive an F statistic for detecting delay-fired events observed on an array. Detrended log-spectra are considered as realizations of stationary processes whose periodic components are frequencies, with periods proportional to delay-time differences. An F statistic is derived that is proportional to the stacked or summed cepstra and the spectrum of the stacked log-spectra. Advantages of the cepstral F statistic accrue from better resolution and the fact that statistical significance can be established for delay peaks. It is also easily incorporated into automatic detection systems. The frequency-domain approach is compared to a time-domain approach that involves searching seasonal autoregressive models with a fixed regular delay structure. Simulated array data and data from several mining explosions, measured at an array in northern Norway, are analyzed by both approaches.