TOWARD A PHYSICAL UNDERSTANDING OF EARTHQUAKE SCALING RELATIONS

In seismological literature, there exist two competing theories (the s o-called W model and L model) treating earthquake scaling relations be tween mean slip and rupture dimension and between seismic moment and r upture dimension. The core of arguments differentiating the two theori es is whether the mean slip should scale with the rupture width or wit h the rupture length for large earthquakes. In this paper, we apply th e elastic theory of dislocation to clarify the controversy. Several st atic dislocation models are used to simulate strike-slip earthquakes. Our results show that the mean slip scales linearly with the rupture w idth for small earthquakes with a rupture length smaller than the thic kness of the seismogenic layer. However, for large earthquakes with a rupture length larger than the thickness of the seismogenic layer, our models show a more complicated scaling relation between mean slip and rupture dimension. When the rupture length is smaller than a cross-ov er length; the mean slip scales nearly linearly with the rupture lengt h. When the rupture length is larger than a cross-over length, the mea n slip approaches asymptotically a constant value and scales approxima tely with the rupture width. The cross-over length is a function of th e rupture width and is about 75 km for earthquakes with a saturated ru pture width of 15 km. We compare our theoretical predictions with obse rved source parameters of some large strike-slip earthquakes, and they match up well. Our results also suggest that when large earthquakes h ave a fixed aspect ratio of rupture length to rupture width (which see ms to be the case for most subduction earthquakes) the mean slip scale s with the rupture dimension in the same way as small earthquakes.