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.