Magnetic inversion to recover the subsurface block structures based on L1 norm and total variation regularization
Magnetic inversion to recover the subsurface block structures based on L1 norm and total variation regularization
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DOI：
10.1093/gji/ggab355
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发表时间：
2021-09
影响因子：
2.8
通讯作者：
M. Utsugi
中科院分区：
文献类型：
--
作者：
M. Utsugi
提出了一种基于L1范数正则化的三维磁测数据稀疏反演方法。孤立地说，L1范数正则化产生不受输入数据约束的模型元素，使其精确为零，从而产生具有紧凑和集中结构的稀疏模型。在这里，我们补充了L1范数的惩罚最小化总变差，模型梯度的L1范数;预计地下结构的尖锐边界不会受到影响，通过纳入此惩罚。虽然这种惩罚被广泛用于地球物理反演研究中，它往往被替代的二次惩罚，以减轻惩罚反演问题的解决方案，在这项研究中，使用的总变差的原始定义，即模型梯度的L1范数的形式。为了解决这种L1范数和全变分的组合惩罚问题，本文引入了基于增广拉格朗日函数优化的原-对偶优化算法--交替方向乘子法。为了提高算法的计算效率，使该方法适用于大规模的磁反问题，本研究采用矩阵压缩，利用小波变换和预条件共轭梯度法。将该反演方法应用于合成试验和真实的资料，合成试验表明，当地下结构为块状时，可以较好地再现地下结构。
This paper presents a new sparse inversion method based on L1 norm regularization for 3-D magnetic data. In isolation, L1 norm regularization yields model elements which are unconstrained by the input data to be exactly zero, leading to a sparse model with compact and focused structure. Here, we complement the L1 norm with a penalty minimizing total variation, the L1 norm of the model gradients; it is expected that the sharp boundaries of the subsurface structure are not compromised by incorporating this penalty. Although this penalty is widely used in the geophysical inversion studies, it is often replaced by an alternative quadratic penalty to ease solution of the penalized inversion problem; in this study, the original definition of the total variation, that is form of the L1 norm of the model gradients, is used. To solve the problem with this combined penalty of L1 norm and total variation, this study introduces alternative direction method of multipliers, which is a primal-dual optimization algorithm that solves convex penalized problems based on the optimization of an augmented Lagrange function. To improve the computational efficiency of the algorithm to make this method applicable to large-scale magnetic inverse problems, this study applies matrix compression using the wavelet transform and the preconditioned conjugate gradient method. The inversion method is applied to both synthetic tests and real data, the synthetic tests demonstrate that, when subsurface structure is blocky, it can be reproduced almost perfectly.