基于自适应多层快速多极算法的大规模磁法正演模拟

提出了一种基于非结构化四面体以及带地形模型的自适应多层快速多极大规模磁法快速正演算法.该算法弥补了传统积分方法采用FFT加速计算时不能采用非结构化网格的缺陷；同时采用自适应快速多极算法突破积分求和方法求解大规模磁法问题耗时长的突出问题.首先，采用非结构化的四面体网格剖分技术能够更好的模拟复杂模型以及带地形模型，实现磁法模型的高精度模拟；其次，采用一种自适应多层快速多极（AMFM）算法实现大规模磁法正演求解.通过将计算区域划分为近区和远区，对近区采用解析计算高精度求解，对远区采用自适应多层快速多极算法进行加速计算，假设有M个观测点，N个四面体源单元，可将计算复杂度由传统积分求和法的O（MN）减少到O（MlogN）.本文设计了组合体模型以及安徽怀宁地区的实际地形模型，模型计算结果体现了采用该方法进行大规模复杂模型三维磁法正演模拟的高效性和准确性.

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 multi-level 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.