基于加窗Hilbert变换的复偏振分析方法及其应用

Complex polarization analysis based on windowed Hilbert transform and its application

考虑到传统Hilbert变换所隐含的无限长序列假设的实际局限性,本文将多窗分析法引入到短时序列Hilbert变换中,通过构建复协方差矩阵和对该矩阵的特征值与特征向量的求解,获得三分量地震记录的时变偏振参数;基于不同波型的偏振特性与实测偏振参数,采用线性_余弦权重函数或高斯权重函数自适应空间滤波,识别与分离具有特定偏振特性的不同地震响应.针对天然地震三分量记录的处理结果表明,该方法在识别、分离具有特定偏振特性的不同地震响应方面具有一定的潜力.

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.