Degree of polarization filter for frequency-dependent signal enhancement through noise suppression

We construct and examine a new frequency-dependent polarization filter to attenuate less polarized signals and noise in single and multichannel seismic data. The filter uses a degree of polarization measure which is defined as a measure of the variations of an arbitrary instantaneous polarization through the course of the signal. Small variations indicate a high degree of polarization. The frequency-dependent degree of polarization is based on the eigen analysis of the data covariance matrices and is used to weight the decomposed time series in the time-frequency domain. This approach permits the frequency-dependent detection of polarized signals and their enhancement through less polarized signal and noise suppression. Further, interfering signals with different frequency contents can be separated. With densely spaced data the degree of polarization can be averaged locally to include the wave-field directivity. This procedure is important since, through the averaging, isolated polarized noise can be removed, but isolated unpolarized signals are not suppressed. In contrast to waveform stacks or stacks of data covariance matrices our approach does not punish signals with spatially changing characteristics, such as happens in the transition from precritical to postcritical reflections. Our data adaptive filter is analyzed with theoretical test data before it is applied to a complex wide-angle record section from the West Pyrenees.