【摘要】 系数矩阵存储和线性方程组求解是限制三维电磁积分方程方法发展的主要因素。Zhdanov提出准线性(QL)近似技术,建立了复杂散射场与背景场的线性关系,有效地避免了积分方程中大型线性方程组的求解,但是该算法用于多源问题航空电磁正演模拟时精度不高。因此,本文提出一种基于多重网格准线性(MGQL)近似的算法,并利用系数矩阵的Toeplitz性质存储矩阵和快速傅里叶变换,实现了矩阵与向量的快速乘积、降低了计算复杂度,采用多重网格结合了积分方程方法和准线性近似解法的优点,在保证精度的条件下提高计算速度、减少存储量。针对不同类型网格的模拟实验表明,相比于传统积分方程方法,本文算法在保证计算精度的同时,可以将计算速度极大地提高(>10倍)。更多还原

【Abstract】 In an integral equation(IE)method,the storage of Green’s coefficient matrix and solution of linear equation system are always challenging for its development and application.Quasi-linear(QL)approximation method assumes that a linear relationship exists between the background and abnormal field.It can deal with nonlinear problems effectively.For a multiple-transmitter airborne EM(AEM)problem,however,the calculation is substantially slowed down.In this paper we present an algorithm based on quasi-linear approximation(MGQL)of multiple grids,through utilizing the Toeplitz property of the coefficient matrix to store it and the fast fourier transform to achieve the matrix-vector multiplication so as to reduce the computational complexity.This method combines the advantages of IE and QL,and can be a fast and accurate tool for a numerical modeling for the multiple-transmitter airborne EM.Numerical experiments show that the MGQL method is efficient for AEM modeling.The memory and time requirement for MGQL method is much less than that of the existing IE methods.Especially for large grids,the computation of this method can be accelerated by over 10 times than before.It is expected that its extraordinary computational efficiency will fundamentally improve 3D AEM inversions.更多还原