中文摘要：

在现有计算机内存和运算速度条件下，电性各向异性地层中频率域电磁响应的数值模拟是一个难点．为探索各向异性介质模型电磁响应的有效算法，同时为进一步研究各向异性地层测量响应的校正方法奠定基础，从Maxwell电磁响应方程出发，使用由三个彼此垂直的发射线圈和三个彼此垂直的接收线圈组成的线圈结构模型，应用交错网格有限差分法推导了三维频率域电磁响应的差分计算格式，采用预条件双共轭梯度法对所形成的复系数矩阵进行了迭代求解，从而得到电性各向异性地层模型下的线圈测量响应．应用这些方法进行了多种条件下电磁响应的计算，计算结果表明，所形成的计算方法是准确可靠的，预条件双共轭梯度法的运算效率也较高；电性各向异性地层的电磁响应与地层倾角（或井斜角）、仪器测量方位、地层的水平电阻率和垂直电阻率有关；根据水平方向磁场强度分量可以确定地层界面；在电磁响应计算过程中，背景电导率的取值要尽量接近整个计算区域的平均电导率．

英文摘要：

The numeric simulation of electromagnetic responses in frequency domain for electrical anisotropic formation is a challenge in current conditions of computer memory and operation speed. In order to investigate the calculation method of electromagnetic responses in anisotropic formation models and further lay a foundation for the study of the correct method to the effect of formation anisotropy on the tool responses, the difference equations to compute 3-D electromagnetic responses of the sonde configuration which comprises of three mutually orthogonal transmitter-receiver pairs are derived from the Maxwell＇ s equations by using staggered-grid finite difference method and solved by the iteration of pre-conditioned bi-conjugate gradient method, so the responses of receiving coils can be calculated in electrical anisotropic formations. These methods have been applied to calculate the electromagnetic responses in various conditions. The results show that the computation method is correct and credible, the computation efficiency of the pre-conditioned bi-conjugate gradient method is high to solve equations. The electromagnetic responses of electrical artisotropic formation are related with borehole angle （or formation dip）, the measuring orientation of tool, and the horizontal and vertical resistivities of formation. The formation interfaces can be determined by horizontal components of magnetic intensions, and the taken value of background conductivity should be close to the average conductivity of the computed area in calculation of electromagnetic responses.