论文标题
使用基于小波的复杂度度量
Flexible quasi-2D inversion of time-domain AEM data, using a wavelet-based complexity measure
论文作者
论文摘要
正则化方法通过引入解决方案（例如平滑度或清晰度）的一些先验特征来提高逆问题的稳定性。在这一贡献中，我们提出了一个基于多维的，依赖于规模的小波的L1调节项，以治愈空降（时域）电磁诱导倒数问题的不良性。正则化项是灵活的，因为它可以基于合适的小波基函数恢复反转模型之间的块状，光滑且可调的。对于每个方向，可以使用不同的小波基函数，从而引入附加的相对正规化参数。我们提出了一种校准方法，以确定（受过教育的初始猜测）此相对正则化参数，该参数减少了对此参数进行优化的需求，因此，总体计算时间正在控制。我们将新的方案应用于比利时盐水入侵环境中的时域空降电磁数据集，但是该方案可以同样适用于任何其他2D或3D地球物理逆问题。
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent wavelet-based L1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, introducing an additional relative regularization parameter. We propose a calibration method to determine (an educated initial guess for) this relative regularization parameter, which reduces the need to optimize for this parameter, and, consequently, the overall computation time is under control. We apply our novel scheme to a time-domain airborne electromagnetic data set in Belgian saltwater intrusion context, but the scheme could equally apply to any other 2D or 3D geophysical inverse problem.
