A Seismic Wavelet Extraction Of High-end Cumulative Amount Method

Seismic wavelet extraction is one of the important long-standing research works in seismic data processing. Traditional wavelet extraction methods usually have the hypothesis that the wavelet is in a certain form, such as the minimum phase. This may limit their practical uses in a general case. It is desirable to have an accurate wavelet extraction approach that has no hypothesis on the wavelet phase form. In this thesis, a new frequency domain method of high-order cumulants is presented. It firstly computes the phase spectrum and then gets the solution of wavelet of time domain. Theoretically the approach is capable of extraction for almost all kinds of wavelets except for the zero-phase one.The high-order cumulant method is a kind of one that gives the characteristics of seismic records in the higher order sense and is sensitive to phase. Using high-order cumulants to extract wavelet becomes one of the hot research problems in recent years. Since that the higher the order of cumulants, the more the complexity of calculations, the third-order or fourth-order cumulants are usually used in practice for seismic wavelet extraction (note that the second-order cumulant is known as autocorrelation). Wavelet extraction using high-order cumulants can be mainly computed either in time domain or in frequency domain. The time domain methods are directly to find the solution of wavelet by optimally approaching or solving a matrix equation, and are more popularly studied than the frequency domain methods because of the sensitivity of the phase spectrum. However phase spectrum contains all the relative information of signals, and there is more information in phase than in amplitude. The time domain wavelet can be achieved by solving a linear equation containing the wavelet phase parameters.The computing flow of the presented fourth-order cumulant method is that (1) calculate the phase of the fourth-order cumulants of the seismic records; (2) calculate the phase of the seismic wavelet by unwrapping the phase of the fourth-order cumulants of the seismic records; (3) correct the time shift according to a smoothness criteria; (4) stabilize and smooth the phase of the wavelet; (5) find the time domain wavelet by solving the linear matrix equation.High-order cumulants belongs to the statistical methods and needs to be calculated in different time windows. It is found that the length of the time window may seriously affect the accuracy of the result, and it is proposed that this problem may be overcome by scanning the length of time window. The optimum wavelet is finally evaluated based on the varimax criterion for a zero-phasing seismic record or section.Numerical and real data tests demonstrate that the method presented is capable of both minimum and mix phase wavelet with relatively higher accuracy.