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Neuro-Fuzzy Kinematic Finite-Fault Inversion: 1. Methodology
Journal of Geophysical Research: Solid Earth ( IF 3.9 ) Pub Date : 2021-07-16 , DOI: 10.1029/2020jb020770
Navid Kheirdast 1 , Anooshiravan Ansari 1 , Susana Custódio 2
Affiliation  

Kinematic finite-fault source inversions aim at resolving the spatio-temporal evolution of slip on a fault given ground motion recorded on the Earth's surface. This type of inverse problem is inherently ill posed due to two main factors. First, the number of model parameters is typically greater than the number of independent observed data. Second, small singular values are generated by the discretization of the physical rupture process and amplify the effect of noise in the inversion. As a result, one can find different slip distributions that fit the data equally well. This ill posedness can be mitigated by decreasing the number of model parameters, hence improving their relationship to the observed data. In this study, we propose a fuzzy function approximation approach to describe the spatial slip function. In particular, we use an Adaptive Network-based Fuzzy Inference System (ANFIS) to find the most adequate discretization for the spatial variation of slip on the fault. The fuzzy basis functions and their respective amplitudes are optimized through hybrid learning. We solve this earthquake source problem in the frequency domain, searching for optimal spatial slip distribution independently for each frequency. The approximated frequency-dependent spatial slip functions are then used to compute the forward relationship between slip on the fault and ground motion. The method is constrained through Tikhonov regularization, requiring a smooth spatial slip variation. We discuss how the number of model parameters can be decreased, while keeping the inversion stable and achieving an adequate resolution. The proposed inversion method is tested using the SIV1-benchmark exercise.

中文翻译:

神经模糊运动学有限故障反演:1. 方法论

运动学有限断层源反演旨在解决给定地球表面记录的地面运动的断层滑动的时空演化。由于两个主要因素,这种类型的逆问题本质上是不合适的。首先,模型参数的数量通常大于独立观测数据的数量。其次,物理破裂过程的离散化会产生小的奇异值,并在反演中放大噪声的影响。因此,人们可以找到同样适合数据的不同滑移分布。这种病态可以通过减少模型参数的数量来减轻,从而改善它们与观察数据的关系。在这项研究中,我们提出了一种模糊函数近似方法来描述空间滑移函数。特别是,我们使用基于自适应网络的模糊推理系统 (ANFIS) 来为断层上滑动的空间变化找到最合适的离散化。通过混合学习优化模糊基函数及其各自的幅度。我们在频域中解决了这个震源问题,为每个频率独立地寻找最佳空间滑移分布。然后使用近似的频率相关空间滑移函数来计算断层上的滑移和地震动之间的前向关系。该方法通过 Tikhonov 正则化受到约束,需要平滑的空间滑移变化。我们讨论了如何减少模型参数的数量,同时保持反演稳定并获得足够的分辨率。
更新日期:2021-08-23
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