A generalized slip-rate function for kinematic modeling

Over the last decades, many types of slip-rate functions (SRFs) have been introduced into kinematic rupture modeling. Commonly used SRFs are the Haskell-type rectangular pulse, cosine and trapezoidal windows and the Kostrov-/Yoffe functions. All these functions and many functional shapes inferred from multiwindow inversion techniques can be well described or are even identical to the functional form of the generalized beta distribution—a widely used and well studied probability density function (pdf) in statistics. The generalized beta pdf has three parameters, where one parameter relates to the SRF duration and two describe the shape of the pulse. The shape parameters have simple analytic expressions for their estimators. Using the generalized beta pdf with free shape parameters as SRF can effectively reduce the number of required free parameters in the inversion when compared to multiwindow SRF techniques. The generalized beta pdf provides us not only with analytic solutions of the derivative (slip-rate change) and antiderivative (slip) of the slip-rate function but also analytic expressions for their Fourier spectra. We apply the beta SRF for rupture modeling of two well studied earthquakes in Taiwan—the 2016 M_W 6.4 Meinong earthquake and the M_W 6.3 2018 Hualien earthquake—and compare results in terms of slip distribution and model uncertainties.