方位弹性阻抗傅里叶级数裂缝预测方法

目前裂缝预测方法主要分为两类:第一类方法基于方位地震数据的振幅或振幅导出属性(频率、衰减等)预测裂缝,仅能得到界面两侧地层的综合响应,无法确定上覆、下伏地层的裂缝信息;第二类方法基于方位AVO叠前地震反演获得不同方位的弹性参数,可直接求取目的层内的裂缝信息,但待反演参数维度高,且各向异性参数值较弹性参数值小得多,反演稳定性有待提升。为此,提出了基于方位弹性阻抗傅里叶级数的裂缝预测方法。基于Rüger的方位AVO反射系数近似方程,首先推导了方位弹性阻抗方程,将裂缝介质的界面信息转化为地层内部的弹性信息,方位弹性阻抗差异体现了地层的各向异性;其次,利用傅里叶级数展开方位弹性阻抗方程求取二阶傅里叶系数,通过方位弹性阻抗与余弦函数的互相关求取裂缝法向。模型测试表明,基于方位弹性阻抗傅里叶级数展开的裂缝预测方法能较好地预测裂缝发育情况以及裂缝法向,精度较高且抗噪性较强。实际数据预测结果表明,裂缝预测结果与成像测井结果一致,具有较高精度。

Fracture prediction method based on Fourier series of azimuthal elastic impedance

At present, there are mainly two categories of fracture prediction methods. The first type is based on the amplitude or attributes (such as frequency and attenuation) derived from the amplitude of azimuth seismic data. It can only provide the comprehensive response information of the strata on both sides of the interface and fails to determine the fracture information of the overlying or underlying strata. The second type obtains the elastic parameters with the help of azimuthal AVO prestack seismic inversion, which can directly achieve the fracture information of target strata. However, the dimension of the parameters to be inverted is high, and the anisotropic parameter is much smaller than the elastic parameter, with the inversion stability needing to be improved. In response, this paper proposes a fracture prediction method based on the Fourier series of azimuthal elastic impedance. Firstly, the azimuthal elastic impedance equation is derived on the basis of the Rüger’s approximation of the azimuthal AVO reflection coefficient. The interface information of a fractured medium is transformed into the elastic information of the formation. The difference in azimuthal elastic impedance reflects the anisotropy of the formation. Secondly, the azimuthal elastic impedance equation is expanded by Fourier series to obtain the second-order Fourier coefficient . Finally, the normal direction of fracture is obtained through the cross-correlation between azimuthal elastic impedance and cosine function. The model test shows that the fracture prediction method based on the Fourier series expansion of azimuthal elastic impedance can well predict the development and normal direction of fracture with high accuracy and strong noise resistance. The performance on actual data indicates that the fracture prediction results are consistent with the imaging logging results, which proves that the method has high accuracy.