分数阶导数在地震奇异性分析中的应用

Application of fractional order derivative in analyzing seismic singularity

（中国石油大学(华东)，山东东营257061）

China University of Petroleum, Dongying 257061, China

传统的地震解释主要是观测地震资料的振幅及相位的变化，而振幅往往并不能反映真实的地质情况。地震界面可能是岩性分界面也可能是岩性过渡带，岩性过渡带的地震反射波是入射波的分数阶导数，因此将分数阶导数引入地震属性计算中，构建一种对波形敏感而对振幅变化不敏感的新属性——奇异性，用以刻画反射界面的横向变化。方法的基本原理是：首先计算地震子波的不同分数阶导数；然后利用匹配追踪算法将地震数据分解成地震子波的不同分数阶导数，进而获得反射波同相轴的分数阶。对胜利油田某区块实际二维地震资料进行了试处理，结果表明分数阶导数剖面能很好地描述不整合面，反映实际界面的横向变化。

Traditional seismic data interpretation focuses on changes of amplitude and phase. However, amplitude in most cases cannot reflect the actual geologic situation. Seismic interface can be either a lithologic interface or a lithologic transitional zone. The reflection of lithologic transitional zone is the fractional order derivative of incident wavelet. So the fractional order derivative is introduced into the calculation of seismic attribute to establish a new attribute called singularity which is sensitive to waveform but insensitive to amplitude. The singularity can be used to describe the lateral changes of seismic reflection interface. The principles of this method are as follows: firstly, fractional derivatives of various orders are calculated from a given seismic wavelet; then, matching pursuit algorithm is used to decompose seismic data into different orders of fractional derivatives of wavelet and then to obtain the fractional order of reflection events. This method was applied to preprocess the 2-D seismic data of Shengli oilfield, showing that the fractional order derivative profile can effectively describe the unconformity and reflect the lateral changes of actual interface.