Neuro‐Fuzzy Kinematic Finite‐Fault Inversion: 1. Methodology. Issue 8 (22nd August 2021)

• Record Type: Journal Article
• Authors: Kheirdast, Navid; Ansari, Anooshiravan; Custódio, Susana
• Is Part Of: Journal of geophysical research. Volume 126:Issue 8(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-08-22
• Subjects: earthquake source kinematics -- fuzzy logic -- instability analysis -- inverse theory -- neural networks; Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2020JB020770
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: 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. Plain Language Summary: Earthquake kinematic source inversions help seismologists infer key features of fault ruptures from the available recorded data. The technique faces inherent ill posedness from the viewpoint of its mathematical formulation. Furthermore, the limited available datasets render the problem even more challenging. In this study, we use an adaptive function approximation methodology that describes slip on the fault using a reduced number of model parameters. This innovative formulation helps us to achieve a good balance between available data (information) and model parameters (unknowns). The proposed technique decreases the degree of ill posedness of the inverse problem by adaptively improving the slip discretization and the slip amplitude using neural network learning. Key Points: We present a new method to kinematically image finite‐fault rupture which reduces the number of basis to spatially discretize the slip The inversion employs a neural‐network based evolutionary method that improves model estimation We discretize the fault using fuzzy basis functions that stabilizes the inversion and reduces the number of small singular values