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.