磁化强度矢量反演方程及二维模型正反演研究

导了磁化强度矢量层析成像方程，并与磁化强度标量层析成像方程进行了对比. 使该矢量层析成像方程既适用于三维的也适用于二维，既适用于使用磁场垂直分量资料，也适用于使用磁场总强度资料. 本文采用改进的高斯-赛德尔迭代求解磁化强度矢量层析成像方程，在求解方程中引进了与深度有关的权系数. 并对二维模型开展了正反演研究. 当模型层数为二层，且每层51个柱体时，采用零初始模型就能获得较好的磁化强度垂直分量和水平分量反演结果，除了异常体边部外，磁化方向比较可靠. 当模型层数为五层，且每层51个柱体时，采用零初始模型不能得到较好结果，改用接近背景值的均匀初始模型，反演的磁化强度垂直分量和水平分量大致接近真实，但不能刻划某些细节.

Magnetization vector inversion equations and 2D forward and inversed model study

We derive magnetization vector tomography imaging equations and compare them with the magnetization scalar tomoqraphy imaging equations. The derived equations are applicable to 3D and 2D magnetization vector inversion problems, to vertical component magnetic data or total magnitude of magnetic data. In the inversion process, an improved Gauss Sadel interative method with a weight coefficient determined according prism's berried depth is introduced. 2D model forward and inversed studies show that when the model consists two layers, each has 51 prisms, the inversed vertical and horizontal magnetization component with the zero magnetization initial model are consistent well with the model's parameters, except the edge effect near the boundary. When the model consists five layers, each has 51 prisms, the inversed vertical and horizontal magnetization components can be obtained with a homogeneous initial magnetization model instead of the zero initial magnetization one, and the boundary effect all so exists instead. But we can not get detail fine magnetization structures from the inversion results. These problems should to further studied in the future.