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.