The Multichannel Maximum-Entropy Method (2020)

The Wigner-Ville distribution (WVD) is a powerful technique for the time-frequency spectral analysis of nonstationary seismic data. However, the Wigner-Ville distribution suffers from the cross-term interference between different wave components in the seismic data. To mitigate the cross-term interference, Professor Wang invented 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 in the calculation of the prediction-error filter (PEF). The MESA algorithm works on the standard autocorrelation sequence but does not work for the Wigner-Ville kernel, which is an instantaneous autocorrelation sequence. The multichannel MEM algorithm uses the prediction-error filter 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. In the example above, the left panel is the Wigner-Ville kernel sequences obtained by the multichannel MEM algorithm, and the right panel is the resultant time-frequency spectrum. 

This example demonstrates that the multichannel MEM algorithm and the Wigner-Ville distribution 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. 

This article is published in the GEOPHYSICS (2020, vol. 85, no. 1), doi: 10.1190/geo2019-0347.1.