A seismologically consistent surface rupture length model for unbounded and width-limited events

Abstract

A new surface-rupture-length (SRL) relationship as a function of magnitude $\left(\mathbf{M}\right)$ , fault thickness, and fault dip angle is presented in this article. The objective of this study is to model the change in scaling between unbounded and width-limited ruptures. This is achieved through the use of seismological-theory-based relationships for the average displacement scaling and the aid of dynamic fault rupture simulations to constrain the rupture width scaling. The empirical data set used in the development of this relationship is composed of $122$ events ranging from $\mathbf{M}$ 5 to $8.1$ and SRL 1.1 to 432 km. The dynamic rupture simulations data set includes $554$ events ranging from $\mathbf{M}$ 4.9 to 8.2 and $\mathrm{SRL}$ 1 to 655 km. For the average displacement $\left(\overline{D}\right)$ scaling, three simple models and two composite models were evaluated. The simple average displacement models are a square root of the rupture area $\left(\sqrt{A}\right)$ , a down-dip width $\left(W\right)$ , and a rupture length $\left(L\right)$ proportional model. The two composite models have a $\sqrt{A}$ scaling for unbounded ruptures and transition to $W$ and $L$ scaling for width-limited events, respectively. The empirical data favors a $\overline{D}~\sqrt{A}$ scaling for the entire regime (unbounded and width-limited ruptures) followed by a $\sqrt{A}$ scaling for unbounded that changes to $L$ scaling for width-limited ruptures. The selected models exhibit better predictive performance compared to linear $\log (\mathrm{SRL})~\mathbf{M}$ type models, especially in the large magnitude range, which is dominated by width-limited events. A comparison with published SRL models shows consistent scaling for different fault types and tectonic environments.