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Three-dimensional magnetotelluric inversion using L-BFGS
Acta Geophysica ( IF 2.3 ) Pub Date : 2020-06-30 , DOI: 10.1007/s11600-020-00456-7
Libin Lu , Kunpeng Wang , Handong Tan , Qingkun Li

The gradient-based optimization methods are preferable for the large-scale three-dimensional (3D) magnetotelluric (MT) inverse problem. Compared with the popular nonlinear conjugate gradient (NLCG) method, however, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method is less adopted. This paper aims to implement a L-BFGS-based inversion algorithm for the 3D MT problem. And we develop our code on top of the ModEM package, which is highly extensible and popular among the MT community. To accelerate the convergence speed, the preconditioning technique by the affine linear transformation of the original model parameters is used. Two modifications of the conventional L-BFGS algorithm are also made to get a comparable convergence rate with the NLCG method. The impacts of the preconditioner parameters, the regularization parameters, the starting model, etc., on the inversion are evaluated by synthetic examples for both L-BFGS and NLCG methods. And the real MT Kayabe dataset is also inverted by the inversion algorithms. The synthetic tests show that through our L-BFGS inversion algorithm the similar resistivity models can be obtained with that from the NLCG method. For the real data inversion, the L-BFGS method performs more efficiently and reasonable results could be obtained by less iterations of the inversion process than the NLCG method. Thus, we suggest the common usage of the L-BFGS method for the 3D MT inverse problem.

中文翻译:

使用L-BFGS进行三维大地电磁反演

对于大规模三维(3D)大地电磁(MT)反问题,基于梯度的优化方法更可取。与流行的非线性共轭梯度法(NLCG)相比,有限内存的Broyden–Fletcher–Goldfarb–Shanno(L-BFGS)方法较少采用。本文旨在为3D MT问题实现基于L-BFGS的反演算法。而且我们在ModEM软件包的基础上开发代码,该软件包高度可扩展并且在MT社区中很流行。为了加快收敛速度​​,使用了通过对原始模型参数进行仿射线性变换的预处理技术。还对常规L-BFGS算法进行了两次修改,以与NLCG方法获得可比的收敛速度。预调节器参数,正则化参数,反演的起始模型等通过L-BFGS和NLCG方法的综合示例进行评估。真实的MT Kayabe数据集也通过反演算法反演。综合测试表明,通过我们的L-BFGS反演算法,可以使用NLCG方法获得相似的电阻率模型。对于实际数据反演,与NLCG方法相比,L-BFGS方法执行效率更高,并且反演过程的迭代次数更少,可以获得合理的结果。因此,我们建议将L-BFGS方法用于3D MT反问题。综合测试表明,通过我们的L-BFGS反演算法,可以使用NLCG方法获得相似的电阻率模型。对于实际数据反演,与NLCG方法相比,L-BFGS方法执行效率更高,并且反演过程的迭代次数更少,可以获得合理的结果。因此,我们建议将L-BFGS方法用于3D MT反问题。综合测试表明,通过我们的L-BFGS反演算法,可以使用NLCG方法获得相似的电阻率模型。对于实际数据反演,与NLCG方法相比,L-BFGS方法执行效率更高,并且反演过程的迭代次数更少,可以获得合理的结果。因此,我们建议将L-BFGS方法用于3D MT反问题。
更新日期:2020-06-30
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