基于积分解的空间-波数混合域二度体磁异常数值模拟

Two-dimensional numerical modeling of magnetic anomaly in a mixed space-wavenumber domain based on integral solution

提出一种基于积分解的空间-波数混合域二度体磁异常数值模拟快速算法。该方法将磁异常二维空间域卷积问题,通过傅里叶变换转换为空间-波数混合域垂向一维积分问题,将一个复杂问题分解为多个小问题,不同波数的小问题之间具有高度并行性;保留深度方向为空间域,采用二次插值的形函数计算垂向一维积分,便于浅层网格适当加密,深层网格适当稀疏,兼顾计算精度、计算效率及模拟复杂地形。在此基础上,根据一维形函数积分的特点,提出了一种适用于起伏地形条件下的磁异常快速计算方法,核心思想是对于相同的单元积分进行存储,避免重复计算,进一步提高了计算效率,尤其适用于复杂地形条件下的模拟。模型算例中分别设计了突变介质模型、起伏地形模型和复杂模型,通过数值解与解析解对比结果表明:本算法正确、可靠,且具有数值模拟精度高、计算速度快,适用于任意复杂地形的特点。

A new 2-D numerical modeling of magnetic anomaly in a mixed space-wavenumber domain based on integral solution is proposed in this paper.The convolution problem in 2-D space domain of magnetic anomaly is transformed into a 1-D integration problem using a mixed space-wavenumber domain by Fourier transform.A large problem is decomposed into several small problems,and the minor problems with different wave numbers are highly parallel each other.The method preserves the vertical component in the space domain,thus,a mesh for modeling can be fine at shallow depths and coarse at deep depths.This is beneficial to modeling with complex topography.Based on the characteristics of 1-D shape function integration,the core idea is to store the same element integral,avoid repeated calculation,and further improve the calculation efficiency,especially for the simulation of complex terrain conditions.The catastrophe medium model,alpine terrain model and complex model are designed respectively,and the comparison results of numerical solution and analytical solution show that the algorithm proposed in this paper is correct and reliable.It has the characteristics of high numerical simulation accuracy and less computational cost,which is suitable for any complex terrain.