The solution to an inverse problem is often resolved by inverting the perturbation to a reference model of physical parameters and using regularizations. However, the most commonly used higher-order Tikhonov regularizations, which are unrelated to the reference model, are generally unable to correct false variations in the reference model, since these regularizations tend to minimize the model variations in the inverted perturbations. A viable approach to overcome this shortcoming is to adapt the regularization for the reference model such that a sharp variation around a given position in the reference model (regardless of whether the variation is true or false) receives a smaller weighting in the regularizations. Linear and nonlinear inversion tests show that this new adaptive regularization can improve the inversion results at or around positions with either badly constructed or true variations in the reference model.

中文翻译：

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逆问题中参考模型的自适应正则化

逆问题的解决方案通常通过将扰动逆向物理参数的参考模型并使用正则化来解决。然而，与参考模型无关的最常用的高阶 Tikhonov 正则化通常无法纠正参考模型中的错误变化，因为这些正则化倾向于最小化反向扰动中的模型变化。克服这个缺点的一个可行方法是调整参考模型的正则化，使得参考模型中给定位置周围的急剧变化（无论变化是真还是假）在正则化中获得较小的权重。