Warped P-SV wavelet distortion correction by using a time-frequency adaptive shaping filter

To perform joint PP/PS amplitude-variation-with-angle inversion or attribute analysis, we usually map converted-wave (PS) data to the PP time domain to guarantee that the reflection events from similar reflectors have the same two-way traveltimes. Mapping PS data to the PP time domain leads to a nonstationary characteristic of the PS data. Nonstationary here means varying spectral content of the wavelet in PS data, which will degrade inversion results. We propose a zero-phase time-frequency adaptive shaping filter to filter the nonstationary PS data to be stationary. This adaptive filter can correct the distorted wavelets in the PS data without introducing numerical noise and artifacts. In addition, we use the dynamic time warping algorithm to estimate the time shifts between the PP and PS data and the local seismic attribute estimation method to estimate the subsurface VP/ VS ratios from the time shifts. The estimated VP/ VS ratios will be used to calculate the time- and location-varying wavelets by the Fourier scaling theorem, and then the adaptive shaping filter is constructed. Based on the synthetic and field data examples, we determine the better performance of the adaptive shaping filter over the conventional shaping filter in attenuating numerical noise and artifacts.