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

Abstract

In this paper, I propose the scaling relation W = C 1 L β (where β ≈2/3) to describe the scaling of rupture width with rupture length. I also propose a new displacement relation ![Graphic][1] , where A is the area ( LW ). By substituting these equations into the definition of seismic moment (![Graphic][2] ), 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, 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 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 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 ∼5) earthquakes β =2/3, so L 2.5 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 ![Graphic][3] , then L 1.5 scaling applies. In all cases, M ∝ A 1.5 fault scaling applies. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif