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\begin{document}

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



\author[1]{Navid Kheirdast}%
\author[1]{Anooshiravan Ansari}%
\author[2]{Susana Custódio}%
\affil[1]{International Institute of Earthquake Engineering and Seismology (IIEES)}%
\affil[2]{University of Lisbon}%


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  \date{June 16, 2024}


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\begin{abstract}
We validate the fuzzy kinematic finite-fault inversion method by
studying the rupture process of the \$M\_w 6.2\$, 24/Aug/2016, Amatrice,
central Italy, earthquake. We jointly invert three different datasets to
infer the spatio-temporal slip distribution, including static and
high-rate GNSS data (\$\textless{}=0.06\$ Hz) and strong-motion data
(\$\textgreater{}0.06-0.5\$ Hz). Each dataset is used to constrain a
different frequency range of the source model, depending on the
sensitivity of each dataset. Our slip solution confirms the main rupture
features revealed by previous studies, including a slow nucleation phase
at shallow depths, between 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. To select an adequate number of fuzzy
basis functions, we propose two alternative procedures, that yield the
same general slip features concerning the amplitude, distribution, and
velocity of slip. The first approach consists of ensuring the inverse
problem is formally over-determined and uses a constant number of basis
functions at all frequencies. The second 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 obtained. 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 testifies
the robustness of the inversion%
\end{abstract}%



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