Multichannel maximum-entropy method for the Wigner-Ville distribution

The Wigner-Ville distribution is a powerful technique for the time-frequency spectral analysis of nonstationary seismic data. However, the Wigner-Ville distribution suffers from cross-term interference between different wave components in seismic data. To mitigate cross-term interference, we have developed a multichannel maximum-entropy method (MEM) to modify the Wigner-Ville kernel. The method is related to the conventional maximum-entropy spectral analysis (MESA) algorithm because both algorithms use Burg’s reflection coefficients for the calculation of the prediction-error filter (PEF). The MESA algorithm works on the standard autocorrelation sequence, but it does not work for the Wigner-Ville kernel, which is an instantaneous autocorrelation sequence. Our multichannel MEM algorithm uses the PEF to modify any single Wigner-Ville kernel sequence by exploiting multiple Wigner-Ville kernel sequences simultaneously. This multichannel implementation is capable of robustly determining the reflection coefficient and a minimum-phased PEF for the Wigner-Ville kernel sequence. The Wigner-Ville distribution and the multichannel MEM algorithm in conjunction with each other in turn can produce a high-resolution time-frequency spectrum by mitigating the cross-term interferences and suppressing the spurious energy in the spectrum.