In this paper, I propose the scaling relation W=C1Lβ (where β≈2/3) to describe the scaling of rupture width with rupture length. I also propose a new displacement relation , where A is the area (LW). By substituting these equations into the definition of seismic moment (), I have developed a series of self-consistent equations that describe the scaling between seismic moment, rupture area, length, width, and average displacement. In addition to β, the equations have only two variables, C1 and C2, which have been estimated empirically for different tectonic settings. The relations predict linear log–log relationships, the slope of which depends only on β.
These new scaling relations, unlike previous relations, are self-consistent, in that they enable moment, rupture length, width, area, and displacement to be estimated from each other and with these estimates all being consistent with the definition of seismic moment. I interpret C1 as depending on the size at which a rupture transitions from having a constant aspect ratio to following a power law and C2 as depending on the displacement per unit area of fault rupture and so static stress drop. It is likely that these variables differ between tectonic environments; this might explain much of the scatter in the empirical data.
I suggest that these relations apply to all faults. For small earthquakes (M<∼5) β=1, in which case L3 fault scaling applies. For larger (M>∼5) earthquakes β=2/3, so L2.5 applies. For dip-slip earthquakes this scaling applies up to the largest events. For very large (M>∼7.2) strike-slip earthquakes, which are fault width-limited, β=0 and assuming , then L1.5 scaling applies. In all cases, M0∝A1.5 fault scaling applies.