
Frequency extension method for seismic data based on time-domain fractional differential fusion
YouXi YUE, ChuanYou GE, JunNan FU, YiDu CHEN
Prog Geophy ›› 2025, Vol. 40 ›› Issue (4) : 1440-1450.
Frequency extension method for seismic data based on time-domain fractional differential fusion
Time-domain fractional differentiation of seismic signals is a signal processing method in the field of differentiation. Compared with the traditional integer order differential processing and frequency domain seismic signal extension methods, the multi-scale characteristics of seismic signals can be better described and the data reliability can be improved. In order to deal with complex seismic signals with narrow frequency bands and obtain more refined seismic data, this paper proposes a seismic data extension method based on multi-level fractional differential adaptive fusion in time domain, which automatically obtains the weighted fusion coefficient by using the method of adaptive dynamic adjustment of the weighted coefficient according to the characteristics of fractional differential signals in different frequency bands in different frequency bands and the envelope of the spectrum of differentially differentiated signals of different orders. The seismic signal after frequency extension processing effectively reduces the influence of seismic wavelet band limiting. The model test and practical application show that the fractional differential operation in the time domain of the seismic signal highlights the high-frequency component of the original seismic signal and maintains the low-frequency component of the original signal. With the increase of the differential order, the main frequency of the differential signal increases, and the number of sidelobes increases while the width of the sidelobes narrows, and the ratio of the sidelobe value to the mainlobe value also increases gradually. After multi-level fractional differential adaptive fusion processing, the sidelobe amplitude can be effectively suppressed, the frequency band range can be broadened, and the ability to explain and characterize the reservoir can be provided more clearly, which can improve the ability to identify thin interbeds to a certain extent.
Time-domain / Fractional differentiation / Frequency extension / Resolution / Multi-level adaptive fusion
|
|
|
|
|
|
|
|
|
|
|
|
Wang X D. 2008. Riemann-Liouville fractional calculus and the proving of the properties [Master's thesis](in Chinese). Taiyuan: Taiyuan University of Technology.
|
Yang Y B. 2017. Spectral methods for some fractional differential equations [Ph. D. thesis](in Chinese). Shanghai: Shanghai University.
|
|
|
|
|
Zhao Y Y. 2013. Some theoretical properties and examples of the fractional calculus [Master's thesis](in Chinese). Zhengzhou: Zhengzhou University.
|
|
|
|
|
|
|
|
王小东. 2008. Riemann-Liouville分数阶微积分及其性质证明[硕士论文]. 太原: 太原理工大学.
|
杨宇博. 2017. 若干分数阶微分方程的谱方法[博士论文]. 上海: 上海大学.
|
|
|
|
|
赵莹莹. 2013. 分数阶微积分的若干理论及应用[硕士论文]. 郑州: 郑州大学.
|
|
感谢审稿专家提出的修改意见和编辑部的大力支持!
/
〈 |
|
〉 |