New Empirical Source-Scaling Laws for Crustal Earthquakes Incorporating Fault Dip and Seismogenic-Thickness Effects

Abstract New global source-scaling relations for the aspect ratio and rupture area for crustal earthquakes that include the width-limited effect and a possible free-surface effect are derived using a global dataset of finite-fault rupture models. In contrast to the commonly used scaling relations between moment magnitude (M), fault length (L), width (W), and area, we built self-consistent scaling relations by relating M to the aspect ratio (L/W) and to the fault area to model the change in the aspect ratio once the rupture width reaches the down-dip width limit of the fault. The width-limited effect of large-magnitude earthquakes depends on the fault dip and a regional term for the seismogenic thickness. The magnitude scaling of the aspect ratio includes a break in the magnitude scaling that is dip angle dependent. This dip angle-dependent magnitude scaling in the magnitude–area relation is modeled by a trilinear relation incorporating a dip-related transition range. The effect of the free surface was observed using a normalized depth term and parameterizing the source by the depth of the top of the fault rupture; it is more apparent in the area scaling relation. The scaling differences are related to the fault geometry, not to the rake angle, as commonly assumed. Finally, the corresponding L and W scaling relations obtained by converting the area and aspect ratio models to L and W models not only show good agreement with the previous regional scaling laws on average but also provide better fault-specific application due to the inclusion of a fault-specific dip angle and seismogenic thickness.