论文标题
使用新型小波和规模依赖的正则化项来反转电磁感应数据
Inversion of electromagnetic induction data using a novel wavelet-based and scale-dependent regularization term
论文作者
论文摘要
电磁感应数据对电导率轮廓的反转是一个问题。正则化改善了反转的稳定性，并基于OCCAM的剃须刀原理，通常使用平滑约束。但是，并非总是期望电导率曲线光滑。在这里，我们开发了一种新的反转方案，在该方案中，我们将模型转换为小波空间并施加了稀疏性约束。这种稀疏性限制了反转方案，将使用最小二乘数据失配的目标函数和小波域中模型的稀疏度度量。小波域中的模型既有时间为空间分辨率，又可以有效地降低模型的复杂性。根据预期电导率曲线，可以选择最佳的小波基函数。因此，该方案是自适应的。最后，我们将此新方案应用于频域电磁音（FDEM）数据集，但该方案可以同样适用于任何其他1D地球物理方法。
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.
