井间电磁测量的2．5维层析成像方法

利用正则化最小二乘反演方法实现了井间电磁测量数据的层析成像，对井间地层电阻率进行了重建。在成像算法中，我们假设了井间电磁的激发与接收采用电磁偶极子源，井间介质仅在二维（xoz）平面内变化。在数值模拟中，通过对构造走向（y方向）的Fourier变换，将三维电磁场问题转化为一系列二维问题，用等参有限元方法在波数域求解，使实际地层模型的处理得以实现。对于波数域中每个波数对应的电磁场方程采用等参有限元求解，并用高斯积分将波数域解变换为空间域电磁场。利用源与接收器电磁场的互易原理，实现了电磁场响应对电导率分布灵敏度的快速计算。针对正演模拟中源点的奇异性，我们采用具有一定面积的伪艿函数表达源电流分布，使数值解精度得到提高。用层状介质的解析解与数值计算结果的对比，验证了模拟算法的精度。用介质扰动产生的电磁场变化检验互易性定理计算灵敏度的有效性。对简单块状模型、斜向裂缝带模型及“大”字模型的模拟数据成像结果表明，本文介绍的层析成像方法是正确有效的。

Tomography of the Cross-Hole Electro magnetic Measurements

The regularized least-squares inversion scheme is used to reconstruct the formation resistivity within boreholes from the tomography of the cross-hole electromagnetic measurements.In the tomography,a two-dimensional conductivity variation profile with point dipole sources and receivers in it are assumed.The forward modeling was fulfilled by the iso-parametric finite element method in wave-number domain,and the 3-D problem was converted to a series of 2-D problems in K_y wave-number domain,thus make it possible to deal with the practical model.For the requisite number of K_y values,the coupled equations are solved by the finite element method on the iso-parametric element on the xoz plane.In order to improve the accuracy of the numeric solution, Gauss integral was applied to the wave-number numeric solution in the inverse Fourier transformation of the wavenumber domain solution to real space domain.The sensitivities of the electromagnetic measurements to the formation conductivity are effectively calculated by using of the reciprocity principle of the electromagnetic fields in source locations and receiver locations.Our method validated by using of the simulation data and field data.For the singularity of the source point in modeling of cross-hole electromagnetic measurement,a pseudo-delta function was adopted to distribute the dipole source current,and the numeric accuracy is enhanced.A quantitative test of accuracy is presented which compares the numeric results with the analytic solutions for a dipole source in layer medium for different wave number K_y to validate the code.Through the perturbation of the conductivity of a single block,the difference between two simulations was compared with that from the reciprocity principle,and the effectiveness has been verified.The sound tomography results of the simple block,slant fracture zones and the big character model,verify the effectiveness of the tomography procedures.