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针对铁磁性物质反演中正则化参数自适应选择的问题,提出了基于x2准则的磁梯度张量3D聚焦反演方法.利用深度加权矩阵和最小支撑矩阵对经典Tikhonov正则化理论框架下的反演模型进行约束得到目标函数,避免了由于反演参数多于采集点数而导致反演解的多解性,并有效解决了核函数随深度增大而快速衰减的问题.通过对目标函数进行迭代奇异值分解获得最佳物性参数,并根据x 2准则自适应地确定目标函数在迭代过程中的正则化参数,提高了迭代速度和求解精度.仿真和实验结果表明:该方法能准确还原磁性异常体的轮廓形态,具有较好的模型分辨率.“,”The method of magnetic gradient tensor three-dimensional pose inversion is researched.Three-dimensional focusing inversion of magnetic gradient tensor data based on the x2 principle was proposed for regularization parameter adaptively selected issues of small target ferromagnetic materials in the inversion process.Depth weighting matrix and minmal support matrix were added in the inversion model of Tikhonov regularization theoretical framework to obtain the objective function to avoid the multiple solutions of inversion problem caused by the number of inverse parameter far than observational points and compensate kernel function avoid diminshing rapidly with depth.This function was calculated the optimal physical parameters by singular value decomposition.and according the x2principle to adaptively determine the regularization parameter in the iterative process,thereby this principle increased the iterative speed and the solver accuracy.Three-dimensional focusing inversion of magnetic gradient tensor data produces models with non-smooth properties,for which typical implementations in this field use the iterative minmum support stabilizer and both regularizer and regularizing parameter are updated each iteration.The x2 principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem.For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and,when the stabilizing,or regularization,term is considered to be weighted by unknown inverse covariance information on the model parameters,the minmum of the Tikhonov functional becomes a random variable that follows a x2-distribution.Simulation and experimental results show that:this inversion method can reflect the outline shade of the magnetic anomaly and has good model resolution,which provide the theoretical foundation and practical experience for the application of the inversion method of magnetic gradient tensor.