Complex polarization analysis based on windowed Hilbert transform and its application

The implying assumption of the traditional Hilbert transform is that the length of time series is infinite. Considering its actual limitation, a multi-taper method (MTM) is introduced into the Hilbert transform of three short-time series to construct a complex covariance matrix. Time-varying polarization parameters can be measured by computing the eigenvalues and eigenvectors of the covariance matrix analytically. Combining with the polarization characteristics of special wave types and the measured parameters of actual seismic data, some signals can be identified, and then be separated using some adaptive filters, such as linear-cosine function or Gaussian weighting function filters. Application example of actual three-component earthquake data demonstrates that this method can be used to identify and separate some special seismic responses with special polarization.