Higher-order Statistics Of The Seismic Wavelet Phase Analysis Study

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 any hypothesis on the wavelet phase form. High-order statistics analysis is in front of domestic and international signal process realm in nearly twenty years. High-order statistic applied to all problem that need consider non-gauss,non-minimum phase,non-linear and calm circular condition. In the seismic signal process realm, high-order statistics can be used to eliminate color noise.lt also is a powerful tool for identification and estimation non-minimum phase wavelet. In this thesis, a new method of high-order cumulant to identify phase is presented.The high-order cumulant method is a kind of one that gives the characteristics of seismic records in the higher-order dimension. Since that the higher-order cumulant, the more the complexity of calculations, the three-order and four-order cumulant are usually used in practice for seismic wavelet extraction (note that the second-order cumulant is known as self-correlation). Three-order cumulant is greatly distinguished from fourth-order cumulant in character. Besides that four-order cumulant of gauss rand serial and third-order cumulant of gauss serial both are zero, three-order cumulant of the symmetry distribute rand serial also is zero. But the four-order cumulant of the non-gauss rand serial is not zero usually.So the fourth-order cumulant is adopted.The presented fourth-order cumulant method consists of three parts:(l)Analyzing the main section of the fourth-order cumulant of the wavlet and find the representative one, and finding out the relationship between the wavelet phase and the representative section of the fourth-order cumulant of the wavlet ;(2)Research on fourth-order cumulant of different distribute rand serials for the next work e to look for the quite ideal result ;(3)As the way of wavelet, analyzing the four-order cumulant of the record,and finding the relationship between the wavelet phase and fourth-order cumulant of the record. Finally, compared the result of wavelet and result of record, they are very similar. So the relationship is surely existed.The high-order cumulant method is a kind of Statistic method, and need to adequate data. The fourth-order cumulant experiment of reflection coefficient which comes from the log data proves that the method is useful in practise.