Time–quefrency analysis of overlapping similar microseismic events

Abstract

In this paper, I describe a new technique to determine the interval between P-waves in similar, overlapping microseismic events. The similar microseismic events that occur with overlapping waveforms are called ‘proximate microseismic doublets’ herein. Proximate microseismic doublets had been discarded in previous studies because we had not noticed their usefulness. Analysis of similar events can show relative locations of sources between them. Analysis of proximate microseismic doublets can provide more precise relative source locations because variation in the velocity structure has little influence on their relative travel times. It is necessary to measure the interval between the P-waves in the proximate microseismic doublets to determine their relative source locations.A ‘proximate microseismic doublet’ is a pair of microseismic events in which the second event arrives before the attenuation of the first event. Cepstrum analysis can provide the interval even though the second event overlaps the first event. However, a cepstrum of a proximate microseismic doublet generally has two peaks, one representing the interval between the arrivals of the two P-waves, and the other representing the interval between the arrivals of the two S-waves. It is therefore difficult to determine the peak that represents the P-wave interval from the cepstrum alone. I used window functions in cepstrum analysis to isolate the first and second P-waves and to suppress the second S-wave. I change the length of the window function and calculate the cepstrum for each window length. The result is represented in a three-dimensional contour plot of length–quefrency–cepstrum data. The contour plot allows me to identify the cepstrum peak that represents the P-wave interval. The precise quefrency can be determined from a two-dimensional quefrency–cepstrum graph, provided that the length of the window is appropriately chosen. I have used both synthetic and field data to demonstrate that this method can be used to identify the cepstrum peak that represents the interval between the arrivals of successive P-waves.