A Source Model for Earthquakes near the Nucleation Dimension

Abstract:

Since first proposed by Aki (1967), the concept of earthquake self-similarity has been the subject of intense debate, both from an observational and theoretical standpoint. Self-similar models assume that ruptures start at a point and propagate at constant speed, which results in an inverse relationship between source radius and corner frequency. In contrast, elasto-frictional theory predicts acceleration over a finite nucleation length, confirmed by numerical simulations and recent laboratory experiments. For an accelerating rupture starting with a finite area, the inverse relationship between radius and corner frequency no longer holds. Here we use dynamic simulations and fracture mechanics to derive a seismic source model for nucleation, and quantify how source properties vary with source dimension in this regime.

We model circular asperities with rate-state friction, loaded by creep, with dimensions between 1 and 2 critical nucleation lengths. In this regime, creep penetrates inwards and reaches the center of the asperity; seismic ruptures begin there and expand radially as constant stress drop cracks. Surprisingly, we find that far-field ground motion pulses have nearly constant duration, independent of the asperity radius. We derive an equation of motion for accelerating circular ruptures based on an energy balance: the dynamic energy release rate, which is a function of crack size and rupture velocity, must equal the fracture energy, assumed constant. In the early phases of nucleation, rupture velocity increases exponentially with time, and the same time dependence is reflected in synthetic far-field ground motion. As a consequence, theoretical far-field pulses for events of different size collapse on the same curve once normalized by final displacement, giving rise to the apparent constant duration found in the simulations. These results imply: 1) that source duration is not a reliable proxy for rupture dimension near the nucleation length, and 2) that the break in self-similarity would manifest as an apparent decrease in stress drop for smaller earthquakes since their relative size is overestimated.