Abstract

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical for near-surface characterization in many fields of applications, for example, precision agriculture, pollution assessments, and shallow geological investigations. To this end, the inversion of either the real (in-phase) or the imaginary (quadrature) component of the signal has already been studied. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. The present work discusses an algorithm for the inversion of the complex signal in its entirety, as well as a regularization method that promotes the sparsity of the reconstructed electrical conductivity distribution. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The results of the implementation of this sparsity-enhancing regularization at each step of a damped Gauss–Newton inversion algorithm (based on a nonlinear forward model) are compared with the solutions obtained via a standard smooth stabilizer. An approach for estimating the depth of investigation, that is, the maximum depth that can be investigated by a chosen instrument configuration in a particular experimental setting, is also discussed. The effectiveness and limitations of the whole inversion algorithm are demonstrated on synthetic and real data sets.

中文翻译：

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具有最小梯度支持正则化的多配置复杂EMI数据反演：一个案例研究

摘要

频域电磁仪器允许以不同的配置收集数据，即，改变线圈间距，频率和地上高度。它们方便的尺寸使这些工具在许多应用领域（例如精确农业，污染评估和浅层地质调查）中的近地表表征非常实用。为此，已经研究了信号的实分量（同相）或虚分量（正交）的求逆。此外，在许多情况下，盲目应用检索平滑解的正则化方案，而无需考虑现有的现有知识。本工作讨论了一种用于对整个复杂信号进行反演的算法，以及促进重建的电导率分布稀疏性的正则化方法。此正则化策略将最小梯度支持稳定器合并到截断的广义奇异值分解方案中。将在阻尼高斯-牛顿反演算法（基于非线性正向模型）的每个步骤上执行此稀疏增强正则化的结果与通过标准平滑稳定器获得的解进行比较。还讨论了一种估计调查深度的方法，即可以通过在特定实验设置中选择的仪器配置调查的最大深度。整个反演算法的有效性和局限性在合成和真实数据集上得到了证明。