针对铁磁物质反演方法中反演解的病态性问题，提出基于光滑约束的磁梯度张量3D正则化反演方法。首先，利用积分灵敏度矩阵和粗糙度矩阵对经典Tikhonov正则化理论框架下的反演模型进行约束，避免由于反演参数多于采集点数而导致的不稳定；然后，通过定义正则化修正系数确定合理的初始正则化因子，从而减少因正则化因子引入而在反演结果中介入的误差；最后，利用物性参数上下限约束函数，将反演过程中的解转换到合理的值域范围内，得到与原始模型更加吻合的反演结果。仿真及实验结果表明：该反演方法能够准确还原磁性异常体的轮廓形态，具有较好的横向和纵向分辨率。
For the ill-posed problem of ferromagnetic materials inversion method, the method based on 3D magnetic gradient tensor regularization inversion method was proposed based on smooth constraint condition. First, the unstable defect caused by the number of inverse parameter far than observational points by using the integral sensitivity matrix and the roughness matrix in the classical Tikhonov regularization under the framework of the theory to constrain the model is avoided. Then, errors are reduced due to regularization factor introduced in the inversion results, by defining regularization correction factor to determine a reasonable initial regularization factor. Finally, by using the upper and lower constraint function of physical parameters, the solution to a reasonable value range in the inversion process is converted and the inversion results which are more consistent with the original model are obtained. Simulation and experimental results show that this inversion method can reflect the outline shade of the magnetic anomaly, and has good lateral and vertical resolution.
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