大地电磁法三维快速松弛反演

实现大地电磁法快速三维反演的关键在于找到快速计算灵敏度矩阵的方案. 本文在对大地电磁三维张量阻抗表达式进行深入分析的基础上，获得了三维快速松弛反演算法的灵敏度函数表达式，解决了三维快速松弛反演的核心问题；为了减小反演解的多解性，针对三维问题定义了最小构造函数，实现了求最小构造的三维快速松弛反演算法. 对二维棱柱体、三维棱柱体理论模型的大地电磁合成数据进行了反演试算，反演结果与理论模型相吻合. 对日本Kayabe地区实测资料进行了XY模式反演，反演得到的地电模型较好地反映了地热资源的分布. 反演试算结果表明大地电磁三维快速松弛反演具有计算速度快、结果稳定可靠等特点；使三维快速松弛反演在普通微机上得以实现.

THREE-DIMENSIONAL RAPID RELAXATION INVERSION FOR THE MAGNETOTELLURIC METHOD

The crucial step in doing 3D inversion for the magnetotelluric method is to find an effective way to calculate the sensitivity matrix. By detailedly analyzing the expressions of 3D impedences, Frechet kernel functions are derived for 3D case. Defining the object function to smooth the 3D electrical structures, we finally obtained the iteration procedure of 3D Rapid Relaxation Inversion (RRI) for the minimum structure. The 3D RRI algorithm is tested by a synthetic data set with added Gaussian noise of 1 %. The designed models are 2d prism and 3D prism. The inverted resistivity models fit the true models well. The 3D RRI algorithm is also tested on the Kayabe data, which were collected in Kayabe area of Japan for the purpose of prospecting geothermal resource. Tests results show that our 3D RRI inversion algorithm works well on a PC.