Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem
Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem
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DOI：
10.1088/0266-5611/20/3/017
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发表时间：
2004-06
期刊：
影响因子：
2.1
通讯作者：
M. Zhdanov;Ekaterina V. Tolstaya
中科院分区：
文献类型：
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作者：
M. Zhdanov;Ekaterina V. Tolstaya
在本文中，我们描述了一种锐边界地球物理反演的新方法。我们证明，可以通过使用专门设计的模型参数非线性参数化来实现具有最小支撑稳定器的正则化反演。这种参数化与聚焦反演的原始论文中介绍的加权模型参数空间的变换起到相同的作用。它允许我们将非二次最小支撑稳定器转化为传统的二次最小范数稳定器，从而简化了反问题的求解。这种转换会自动确保解决方案属于具有最小支持度的模型类别。该方法通过地球电导率结构的 3D 大地电磁反演的综合示例进行说明。为了简化计算，在迭代反演的初始阶段，我们使用 Zhdanov 和 Hursan 开发的准解析近似（2000 Inverse Problems 16 1297–322）。然而，为了提高反演的精度，我们在反演的最后阶段应用了基于积分方程方法的严格的正演建模。为了获得 3D 反问题的稳定解，我们使用带有新非线性参数化的 Tikhonov 正则化方法。该技术可以生成异常电导率分布的清晰图像。反演基于正则化共轭梯度法。
In this paper we describe a new approach to sharp boundary geophysical inversion. We demonstrate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonlinear parametrization of the model parameters. This parametrization plays the same role as transformation into the space of the weighted model parameters, introduced in the original papers on focusing inversion. It allows us to transform the nonquadratic minimum support stabilizer into the traditional quadratic minimum norm stabilizer, which simplifies the solution of the inverse problem. This transformation automatically ensures that the solution belongs to the class of models with a minimum support. The method is illustrated with synthetic examples of 3D magnetotelluric inversion for an earth conductivity structure. To simplify the calculations, in the initial stage of the iterative inversion we use the quasi-analytical approximation developed by Zhdanov and Hursan (2000 Inverse Problems 16 1297–322). However, to increase the accuracy of inversion, we apply rigorous forward modelling based on the integral equation method at the final stage of the inversion. To obtain a stable solution of a 3D inverse problem, we use the Tikhonov regularization method with a new nonlinear parametrization. This technique leads to the generation of a sharp image of anomalous conductivity distribution. The inversion is based on the regularized conjugate gradient method.