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.

Key words: multigrid quasi-linear (MGQL) approximation, airborne electromagnetic method, three-dimensional modeling, integral equation (IE)