最小梯度支持正则化反演多组态复EMI数据：一个实例研究
Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study
摘要：
频域电磁仪器允许以不同的配置收集数据，即改变线圈间的间距、频率和离地高度。它们方便的尺寸使这些工具在许多应用领域的近地表表征中非常实用，例如精准农业，污染评估和浅层地质调查。为此，已经研究了信号的实部（同相）或虚部（正交）分量的反转。此外，在许多情况下，一个正则化方案检索光滑的解决方案是盲目的，没有考虑到现有的知识。本工作讨论了一种算法的复杂信号的反演在其整体上，以及正则化方法，促进重建的电导率分布的稀疏性。该正则化策略将最小梯度支撑稳定器引入到截断广义奇异值分解方案中。在阻尼高斯-牛顿反演算法（基于非线性正演模型）的每一步中执行这种稀疏增强正则化的结果与通过标准平滑稳定器获得的解决方案进行比较。还讨论了一种用于估计调查深度的方法，即在特定的实验设置中，所选择的仪器配置可以调查的最大深度。在合成数据和实际数据上验证了整个反演算法的有效性和局限性。
英文摘要：
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.
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