直流电测深中各向异性层状地层的视电阻率响应特征

Response characteristics of apparent resistivity of anisotropic laminar formation in direct current electric sounding

基于各向异性介质的电磁场方程,利用极向型与环向型标量位函数,得到了任意各向异性层状介质的电磁场响应和视电阻率响应关系。利用界面上电磁场切向分量的连续性及地面激励源的耦合条件,导出不同层之间电磁场的传播状态矩阵和递归计算关系。针对递归计算中指数项的数值不稳定性,借助状态矩阵的性质,构造稳定的计算格式。针对横向各向同性(TI)介质中极向位与环向位解耦的特点,地面磁场的计算采用格林函数积分方法,用均匀各向异性介质的解析解检验所提算法的正确性。结果表明:对于水平薄交互储层或水平裂缝带,地面测得的视电阻率小于实际地层的真电阻率,由此计算的含油气饱和度偏低;对于发育倾斜裂缝的储层,方位视电阻率的极向图表现出明显的反常现象,即随方位视电阻率呈椭圆状分布,长轴方向指向裂缝分布的走向;利用方位视电阻率的椭圆特征参数可以估算地下地层的裂缝分布参数。

The relation between electromagnetic field response and apparent resistivity response was expressed in potentials of poloidal and toroidal scalars based on the electromagnetic equations in the arbitrarily anisotropic formation. Based on the continuity of the electricmagnetic fields within layer boundaries and the coupling of the source on the earth surface, the propagation state matrix of the electricmagnetic fields from the upper layer to the lower layers was derived, and the electricmagnetic fields were calculated recursively from the bottom layer to the top layer. For the instability of the exponential term, a stable formulation was deduced through the state matrix. An integral of the Green＇s function was used in the computation of the magnetic field because of the decoupling of the poloidal and toroidal functions. The validity of the numerical method was checked with an analytic solution of a homogeneous half space with arbitrary anisotropy. The results show that for horizontal thin overlapping formation and horizontal fractured formation, the measured apparent resistivity will be less than the true resistivity, which results in low hydrocarbon saturation. The polar diagram of azimuthal apparent resistivity of the formations that exist slanting fractures shows evident paradox; that is, its distribution shows elliptical configuration of the apparent resistivity and the long axis points to the strike of the fracture extension. The elliptical characteristics of the azimuthal apparent resistivity can be used to estimate the parameters of the distribution of the subsurface fractures.