非结构化网格渐进自适应正则化反演算法

以二维大地电磁(Magneto-telluric,MT)为例研究了自适应网格细化正则化反演方法。在反演的初期使用粗网格,通过减少反演单元数的方式降低反问题的不适定性;随着反演的迭代进行,基于网格细化策略对网格进行自适应加密,以提高正则化反演效果;反演过程中,细化网格反演以前一重网格的反演结果作为参考模型与初始模型,保证反演沿正确的方向进行,以提高反演的效果和稳定性。另外,还深入研究了基于模型灵敏度、模型改变量、模型梯度和"边-角"检测四种网格细化方案,对比了它们的特点和自适应反演结果,并通过Hessian矩阵的特征值分布分析了这四种网格细化方案对反演结果的影响。最后,通过理论模型与实测数据反演证明了自适应反演算法的实用性。

Study on step-by-step regularization inversion based on adaptive unstructured mesh

A step-by-step regularization inversion scheme based on adaptive mesh by taking two-dimensional magnetotelluric (MT) inversion as an example. In the initial stage of the inversion，coarse mesh is adopted for the inversion，and the ill-posedness of the inversion is decreased by reducing the number of inversion elements. During the iterative inversion process，mesh is adaptively refined according to mesh refinement strategies to get better imaging of abnormal bodies. The inversion results of the previous mesh are used as the reference model and the initial model in the inversion of the next mesh，so as to ensure the model improvements along the correct direction of the inversion，and then improve the inversion stability and inversion results. Four mesh refinement strategies were proposed，including model sensitivity，model variation，model gradient and “edge-angle” detection. The characteristics of the four mesh optimization schemes are analyzed by Hessian matrix eigenvalue distribution，and the adaptive inversion results of four mesh refinement schemes are compared. Finally，the practicability of the adaptive inversion algorithm is proved by the inversion of synthetic model and field data.