Precise detection of a P‐wave in low S/N signal by using time‐frequency representations of a triaxial hodogram
We have developed a signal processing technique for three‐component microseismic data that allows the precise determination of P‐wave arrival times. The method is based on a time‐frequency representation of the signal that allows the evaluation of the 3-D particle motion from seismic waves in both time and frequency domains. A spectral matrix is constructed using the time‐frequency distributions. A crosscorrelation coefficient for the three‐component signal is derived through eigenvalue analysis of the spectral matrix. The P‐wave arrival time is determined through a statistical test of hypotheses using the crosscorrelation coefficient. This signal processing method is evaluated using a synthetic signal and it is compared to the local stationary autoregressive method for determining P‐wave arrival times. We also show that the proposed method is capable of determining the arrival time of a synthetic P‐wave to within 1 ms (five points in the discrete time series) in the presence of a signal‐to‐noise ratio of −5dB. The method can detect the arrival time of different frequency components of the P‐wave, which is a possibility for the evaluation of velocity dispersion of the seismic wave. We demonstrate the feasibility of the method further by applying it to microseismic data from a geothermal field.