基于小波和尺度相关正则化项的电磁感应数据反演
Inversion of electromagnetic induction data using a novel wavelet-based and scale-dependent regularization term
摘要：
用电磁感应数据反演电导率剖面是一个不适定问题。正则化提高了反演的稳定性，并且基于奥卡姆剃刀原理，通常使用平滑约束。然而，电导率曲线并不总是预期平滑的。在这里，我们开发了一种新的反演方案，其中我们将模型变换到小波空间并施加稀疏性约束。这种稀疏约束反演方案将最小化具有最小二乘数据失配和小波域中模型的稀疏度量的目标函数。小波域中的模型具有时间和空间分辨率两者，并且惩罚小尺度系数有效地降低了模型的复杂度。根据预期的电导率分布，可以选择最佳小波基函数。因此，该方案是自适应的。最后，我们将这个新方案应用于频域电磁测深（FDEM）数据集，但该方案同样适用于任何其他一维地球物理方法。
英文摘要：
The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used. However, the conductivity profiles are not always expected to be smooth. Here, we develop a new inversion scheme in which we transform the model to the wavelet space and impose a sparsity constraint. This sparsity constrained inversion scheme will minimize an objective function with a least-squares data misfit and a sparsity measure of the model in the wavelet domain. A model in the wavelet domain has both temporal as spatial resolution, and penalizing small-scale coefficients effectively reduces the complexity of the model. Depending on the expected conductivity profile, an optimal wavelet basis function can be chosen. The scheme is thus adaptive. Finally, we apply this new scheme on a frequency domain electromagnetic sounding (FDEM) dataset, but the scheme could equally apply to any other 1D geophysical method.
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