In this article, we validate the neuro-fuzzy kinematic finite-fault inversion method by studying the rupture process of the , Aug/24/2016, Amatrice, central Italy, earthquake. We jointly invert three different datasets to infer the spatio-temporal slip distribution, namely static and high-rate GNSS data (<= Hz) and strong-motion data ( Hz). Each data set is used to constrain a different frequency range of the source model, depending on the sensitivity of the data set. The inferred slip shows a slow nucleation phase at shallow depths of 3–4 km, followed by a bilateral rupture that forms two asperities, one to the NW (Norcia) and another to the SE (Amatrice) of the hypocenter. Our inferred slip is compared with those previously obtained using well-established methods. In order to select an adequate number of fuzzy basis functions, we propose two alternative procedures, which yield the same general slip features. The first approach consists of ensuring that the inverse problem is formally over-determined and uses the same number of basis functions at all frequencies. The second approach is based on a maximum-likelihood analysis of the model misfit and selects a different number of basis functions for each frequency. The maximum-likelihood approach allows for more basis functions at high frequencies, where more detail in the spatial slip distribution is needed. The solution obtained with the maximum-likelihood approach provides a more physically plausible source time function, which shows less back slip artifacts. The accurate prediction of high-rate GNSS traces not used in the inversion attests the robustness of the inferred slip model.

中文翻译：

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Neuro-Fuzzy Kinematic Finite-Fault Inversion: 2. Application to the Mw6.2, August/24/2016, Amatrice Earthquake

在本文中，我们通过研究2016 年 8 月 24 日意大利中部阿马特里切地震的破裂过程验证了神经模糊运动学有限断层反演方法。我们联合反转三个不同的数据集来推断时空滑动分布，即静态和高速 GNSS 数据（<= Hz）和强运动数据（赫兹）。每个数据集用于约束源模型的不同频率范围，具体取决于数据集的敏感性。推断的滑动显示了 3-4 公里浅层的缓慢成核阶段，然后是双边破裂，形成两个凹凸不平，一个到 NW (Norcia)，另一个到 SE (Amatrice) 的震源。我们推断的滑移与先前使用完善的方法获得的滑移进行了比较。为了选择足够数量的模糊基函数，我们提出了两种替代程序，它们产生相同的一般滑动特征。第一种方法包括确保逆问题在形式上是超定的，并在所有频率上使用相同数量的基函数。第二种方法基于模型失配的最大似然分析，并为每个频率选择不同数量的基函数。最大似然方法允许在高频下使用更多基函数，在这种情况下需要更多空间滑移分布的细节。使用最大似然方法获得的解决方案提供了一个在物理上更合理的源时间函数，它显示出更少的回滑伪影。反演中未使用的高速 GNSS 轨迹的准确预测证明了推断滑动模型的稳健性。使用最大似然方法获得的解决方案提供了一个在物理上更合理的源时间函数，它显示出更少的回滑伪影。反演中未使用的高速 GNSS 轨迹的准确预测证明了推断滑动模型的稳健性。使用最大似然方法获得的解决方案提供了一个在物理上更合理的源时间函数，它显示出更少的回滑伪影。反演中未使用的高速 GNSS 轨迹的准确预测证明了推断滑动模型的稳健性。