A new type of analyzing wavelet and its applications for extraction of instantaneous spectrum bandwidth

A new type of analyzing wavelets which optimally match seismic wavelets (SW wavelets) is presented. It is proved that these wavelets are admissible. The advantages of the SW wavelets are shown for the seismic data processing and attributes analysis. By taking one of the SW wavelets as analyzing wavelet, a wavelet transform method (WT method) of calculating the instantaneous spectrum bandwidth (ISB) is given as an example of their applications. For a comparison between WT method and the commonly used Hilbert Transform (HT method), the ISB maps of a noisy synthetic data are calculated using both methods. The results demonstrated the advantages of WT method over HT method both in precision and in antinoise performance. The WT method was used for calculating the ISB map of a seismic recording from an oilfield; the map of the ISB distinctly displayed the position and pattern of an ancient subsurface ditch.