用改进的逐次逼近解法计算二维井间电磁场

Computation of 2D Cross-well Electromagnetic Fields by Modified Successive Approximation Method

提出了一种计算积分方程的新方法——改进的逐次逼近解法 (MSAM) ,并用该方法计算了轴对称二维井间电磁场。与传统的逐次逼近解法 (SAM)相比 ,该方法收敛性强 ,应用范围广 ,可适用于高电导率对比地层。由于不必进行直接的大型矩阵求逆运算 ,因此与积分方程的直接解法 (IE)相比 ,该方法计算速度更快 ,所需内存更少。采用矩阵求逆方法计算了成层介质中的二维 Green函数 ,并对含 Green函数的积分进行了简化 ,从而加快了计算速度。数值计算结果显示 ,在地层电导率对比度达到 2个数量级时 MSAM仍收敛 ,且计算结果与直接求解积分方程的结果一致 ,因此

A novel approach for computing integral equations——modified successive approximation method (MSAM) is introduced herein, by which the cylindrically symmetric 2D cross well electromagnetic fields are calculated. The method converges faster than conventional successive approximation method (SAM) and can be applied to high conductivity contrast formation. The method has a faster computational speed and less computer memory requirements than direct computation of the integral equations (IE) since the direct large scale matrix inversion is avoided. The 2D Greens functions in layered medium are calculated by a method of matrix inversion, thus the integrals comprising Greens functions can be simplified and the computational speed enhanced. Numerical results indicate that MSAM also converges and has the same precision as the direct computation when the conductivity contrast is two orders of magnitudes. MSAM is an efficient approach to compute the cylindrically symmetric 2D cross well electromagnetic fields.