Earthquake Fault Scaling: Self-Consistent Relating of Rupture Length, Width, Average Displacement, and Moment Release

In this paper, I propose the scaling relation W = C1L beta (where beta approximate to 2/3) to describe the scaling of rupture width with rupture length. I also propose a new displacement relation (D) over bar = C-2 root A, where A is the area ( W). By substituting these equations into the definition of seismic moment (M-0 = mu(D) over bar LW), 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 beta, the equations have only two variables, C-1 and C-2, which have been estimated empirically for different tectonic settings. The relations predict linear log-log relationships, the slope of which depends only on beta. 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 C-1 as depending on the size at which a rupture transitions from having a constant aspect ratio to following a power law and C-2 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 < similar to 5) beta = 1, in which case L-3 fault scaling applies. For larger (M > similar to 5) earthquakes beta = 2/3, so L-2.5 applies. For dip-slip earthquakes this scaling applies up to the largest events. For very large (M > similar to 7.2) strike-slip earthquakes, which are fault width-limited, beta = 0 and assuming (D) over bar proportional to root A, then L-1.5 scaling applies. In all cases, M-0 proportional to A(1.5) fault scaling applies.