We present an inversion algorithm to reconstruct the spatial distribution of the electrical conductivity from the analysis of magnetometric resistivity (MMR) data acquired at the ground surface. We first review the theoretical background of MMR connecting the generation of a magnetic field in response to the injection of a low-frequency current source and sink in the ground given a known distribution of electrical conductivity in the subsurface of the Earth. The forward modelling is based on sequentially solving the Poisson equation for the electrical potential distribution and the magnetostatic (Biot and Savart) equation for the magnetic field. Then, we introduce a Gauss–Newton inversion algorithm in which the logarithm of the electrical conductivity field is parametrized by using the chaos polynomial expansion in order to reduce the number of model parameters. To illustrate how the method works, the algorithm is successfully applied on four synthetic models with 3-D heterogeneous distribution of the electrical conductivity. Finally, we apply our algorithm to a field case study in which seepage was known to be occurring along an embankment of a headrace channel to a power station.

中文翻译：

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使用混沌多项式展开的磁电阻率层析成像

我们提出了一种反演算法，可通过对在地面获得的磁电阻率（MMR）数据的分析来重建电导率的空间分布。我们首先回顾一下MMR的理论背景，该模型将响应于低频电流源的注入与磁场的产生联系起来，该磁场响应于地面中地下已知的电导率分布而注入地下。正向建模基于依次求解电势分布的泊松方程和磁场的静磁方程（Biot和Savart）。然后，我们引入了一种高斯-牛顿反演算法，其中通过使用混沌多项式展开来参数化电导率场的对数，以减少模型参数的数量。为了说明该方法是如何工作的，该算法已成功应用于电导率具有3-D异质分布的四个合成模型。最后，我们将我们的算法应用于现场案例研究，在该案例研究中，已知沿通往电站的引水通道的堤岸发生渗漏。