Large-scale forward modeling of magnetic data using an adaptive multi-level fast multipole method

In this paper, we propose a fast and high-precision approach for large-scale magnetic forward modeling using the adaptive multi-level fast multipole (AMFM) method and an unstructured grid. The algorithm can overcome the shortcomings of the Fast fourier transfom (FFT) method which cannot adopt unstructured grids. In addition, the adaptive multi-level fast multipole (AMFM) method is chosen to solve the problem of high computational cost in traditional integral summation methods. Firstly, the unstructured tetrahedral meshing technique is used to properly approximate the complex model, for instance the terrain model, and realize the high-precision simulation of the magnetic model. Secondly, an adaptive multi-level fast multipole (AMFM) method is employed to accelerate large-scale magnetic forward modeling. Then, we divide the integral region into two parts. One is the near part in which we use analytical solution to get high-precision results, and the other is far part in which we choose the the adaptive multilevel fast multipole method to accelerate the calculation. The computational complexity can be reduced from in the traditional integral summation method to, where M and N are the numbers of observation sites and source elements, respectively. A combinational model and a complex model based on the digital elevation model (DEM) of Huaining County in Anhui province are used to test the proposed method. The results indicate that the proposed method is effective and accurate in three-dimensional magnetic forward modeling.