Three parameter wavelet and its applications to seismic data processing

In this paper, we develop a new type of analyzing wavelet with three parameters, and termed as the three parameter (TP) wavelet. The choice of parameter values enables the wavelet to be optimized for a given problem. By forcing some constraints upon the TP wavelet parameters, we obtain a new type of analyzing wavelet that is an approximate analytic wavelet. We demonstrate that a TP wavelet, through appropriate choice of its parameters, is suitable for the analysis of not only signals containing slowly varying frequency and amplitude components, but also rapidly varying ones. We propose a new method for studying the seismic data of thin interbeds using a TP wavelet as the analyzing wavelet. This method can characterize the deposit gyration of thin interbeds, in addition to exploring their local structure. Its performance is evaluated with synthetic data and real data.