Wigner distribution analysis of acoustic well logs

We use the Wigner distribution(WD) mixed time-frequency representation(TFR) to design two heuristic algorithms that can be used to analyze and separate the compressional(P), shear(S), Pseudo-Rayleigh (PR), and Stoneley(ST) wave components of the multi-component time-varying borehole seismic signals recorded in well logging velocity surveys. The first algorithm uses auto WD analysis, modification, and synthesis techniques to successively isolate each of the four components. The second algorithm uses a cross WD synthesis technique which is developed in this paper.