基于傅里叶级数分析的各向异性参数估计及裂缝预测  

Anisotropy parameter estimation and fracture prediction based on Fourier series analysis

作　　者：宋维琪[1] 徐月森 张云银[2] 张营革[2] 高秋菊[2] 魏欣伟[2] 张明秀[2] SONG Weiqi;XU Yuesen;ZHANG Yunyin;ZHANG Geying;GAO Qiuju;WEI Xinwei;ZHANG Mingxiu(School of Geosciences,China University of Petroleum,Qingdao 266555,China;Geophysical Research Institute of Shengli Oilfield Branch of Sinopec,Dongying 257055,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,山东青岛266555 [2]中国石油化工股份有限公司胜利油田分公司物探研究院,山东东营257055

出　　处：《石油物探》2020年第1期108-113,共6页Geophysical Prospecting For Petroleum

基　　金：渤海湾盆地济阳坳陷致密油开发示范工程(2017ZX05072)任务一“致密油藏储层地震预测方法及地应力研究”资助。

摘　　要：利用Ruger反射系数近似公式进行地震方位各向异性椭圆拟合,研究裂缝密度与走向,在实际应用时因为待拟合点中存在奇异点,且椭圆拟合存在90°旋转问题,因而计算的方位角无法准确指示椭圆的长短轴方向。为此,将HTI模型纵波反射系数近似公式展开成傅里叶级数形式,利用最小二乘拟合提取傅里叶级数系数,从而提高各向异性参数估计和裂缝预测的准确性。针对不同方位角范围的数据,利用二倍角公式将纵波反射系数傅里叶级数展开式进一步展开,避免拟合提取傅里叶级数系数时因为同一个cos nφ项对应两个各向异性反射系数而导致拟合结果出错。将该方法应用于HTI介质模型和实际地震资料,结果表明:对于HTI介质模型,展开后提取的拟合傅里叶级数系数与理论公式计算结果一致;对于实际地震资料,展开后提取傅里叶级数系数与工区裂缝发育及井资料指示的结果吻合,效果优于椭圆拟合结果和未展开时的傅里叶级数系数拟合结果。In practical applications,an approximated formula of Ruger reflection coefficient is used for the elliptic fitting of seismic azimuth anisotropy;this is aimed at studying the density and direction of the fracture in rock masses.As a result,because there are singularities in the fitting points and the elliptic fitting has a 90°rotation issue,the calculated angle of azimuth does not accurately indicate the direction of the elliptical axis.In this study,the approximate formula for the P-wave reflection coefficient of a horizontal transverse isotropic(HTI)medium was expanded through Fourier series;the coefficient of which was extracted by least square fitting.This procedure improved the accuracy in the estimation of the anisotropic parameter,and thus provided a better crack prediction.For data with different azimuth ranges,the Fourier series expansion of the P-wave reflection coefficient was further expanded with the double angle formula;this was to avoid incorrect fitting results caused by the same items corresponding to two values.Further,the method was applied to a HTI model and actual seismic data.The results for the HTI model showed that the fitting Fourier series coefficients obtained after the expansion were consistent with the predicted results of the theoretical formula.For the actual seismic data,the coefficients obtained after the expansion were in agreement with the observations of fracture development,and wells in the applied working area.Furthermore,the results were more accurate than those obtained through elliptic fitting or from the Fourier series coefficients without expansion;thereby it was demonstrated that the proposed approach exhibited a superior capability.

关 键 词：裂缝预测 各向异性参数 傅里叶级数展开 最小二乘拟合 方位各向异性 椭圆拟合 HTI模型 

分 类 号：P631[天文地球—地质矿产勘探]