Precise arrival time detection of polarized seismic waves using the spectral matrix

I present a statistical method for detecting the arrival times of polarized seismic waves on three-component seismic observations in the time and frequency domains. In this method, the polarization, which is a representation of the 3D particle motion of seismic waves, is evaluated on the basis of a spectral matrix in the time and frequency domains and the statistical parameters are defined by using the eigenvalues of the spectral matrix for detecting the arrival times of linearly and elliptically polarized waves, where the idea of a statistical test of hypothesis is introduced. An evaluation of a synthetic signal revealed that the method can detect the arrival times of linearly and elliptically polarized waves within 10 sampling points at signal-to-noise ratios of ?7 dB. Application of the method to an earthquake suggested that it can be used to detect the arrival times of both linearly and elliptically polarized waves, which are difficult to identify manually.