2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟

2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric FEM for the conductivity orthotropic medium

本文实现了2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟.利用傅里叶变换导出了电导率正交各向异性2.5维海洋可控源电磁法波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行剖分,在单元中进行双二次插值,将有限元方程化为线性代数方程组;最后,求解线性方程组并进行反傅里叶变换获得空间域电磁场值.这个方法可以模拟海底起伏地形条件下地下任意形状电导率正交各向异性的复杂模型.与一维模型的数值模拟结果对比表明,电磁场数值解与解析解吻合.二维模型的计算结果与二维自适应非结构有限元模拟结果也吻合.水平海底二维地电模型考察了不同各向异性系数对海洋可控源电磁响应的影响特征.海底起伏地形地电模型的数值结果表明,电导率各向异性对海洋可控源电磁响应影响明显,有可能淹没海底地形和高阻油气藏引起的异常.

We have made a 2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric finite element method for the conductivity orthotropic medium. The electromagnetic field coupling equations of wave number are derived by Fourier transformation, and the corresponding finite element equation is deduced by adopting the Galerkin weighted residual approach. The surveyed region is subdivided by arbitrary quadrilateral elements, and the biquadratic interpolation is conducted in the element turning the finite element equation into linear algebraic equations~ finally, the linear equations are solved and the spatial domain electromagnetic field value is obtained through inverse Fourier transformation. This method can simulate the complex model of any shape of the conductivity orthotropic medium under submarine rugged topography. By comparison with the analytical result of the conductivity anisotropy of horizontal layered earth, the validity of the method is verified. The numerical solutions also match well with the results of marine controlled-source electromagnetic adaptive unstructured finite element method in two-dimensional anisotropic conductivity model in existing literature, which further verifies program correctness. The horizontal submarine 2D geoelectric model inspects the influence of various anisotropy coefficients on marine controlled-source electromagnetic response. The value of submarine rugged topography geoelectric model indicates that the resistivity anisotropy will bring obvious influence on marine controlled-source electromagnetic response, and it may mask the abnormal phenomenon caused by submarine topography and highly resistive oil and gas reservoirs.