Variation of Proportionality Between Stress Drop and Slip, With Implications for Megathrust Earthquakes

• Published in: Geophysical research letters Vol. 50; no. 4
• Main Authors: Wu, Baoning, Kyriakopoulos, Christodoulos, Oglesby, David D., Ryan, Kenny J.
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 28.02.2023; Wiley
• Subjects: crack model; Depth; Dimensions; Dipping; Earth surface; earthquake scaling relation; earthquake source processes; Earthquakes; Elastostatics; free surface effects; Geological hazards; Ground motion; Hazard assessment; Mathematical models; megathrust earthquakes; Parameters; proportionality factor C; Seismic activity; Seismic hazard; Seismology; Shear modulus; Slip; Stiffness; Stress; Three dimensional models; Tsunami hazard; Tsunamis; Weather hazards
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2022GL100568

Earthquake stress drop Δσ is related to fault slip via Δσ=C⋅μ⋅DLc ${\Delta }\sigma =C\cdot \mu \cdot \frac{D}{{L}_{c}}$, where μ, D, and Lc denote shear modulus, average slip, and fault dimension. C is controlled by the system geometry, characterizes the effective stiffness of the system, and is commonly assumed to be a constant near 1. We use 3D elastostatic models to systematically investigate how C is controlled by fault burial depth, dip angle, and slip direction. We find that C decreases with smaller burial depth and dip angle, with a value for a shallow‐dipping surface‐rupturing fault roughly one‐fifth that of the deeply buried case. Our results help explain the apparent magnitude‐dependent stress drops of megathrust earthquakes in Thingbaijam et al. (2017), https://doi.org/10.1785/0120150291. There may also be implications for the apparent depth‐ and magnitude‐dependence in other source parameters, and for reducing uncertainties in the seismic and tsunami hazard assessments of megathrust earthquakes. Plain Language Summary Characterizing earthquake stress drops is important for both understanding earthquake processes as well as assessing seismic hazards. Estimating stress drops for earthquakes often involves a non‐dimensional parameter C, which characterizes the effective elastic stiffness of the faulting system. In this study, we investigate how interactions between the Earth's surface and the fault affect the theoretical C value, which has not been systematically studied. We find that C decreases with a smaller earthquake depth, and its depth‐dependence exceeds the general “rule of thumb.” Seismological studies for stress drop commonly assume C is a constant. With the SRCMOD earthquake source model catalog (Mai & Thingbaijam, 2014, https://doi.org/10.1785/0119990126; Thingbaijam et al., 2017, https://doi.org/10.1785/0120150291), we show that it is necessary to consider the depth‐dependence of C when measuring stress drops for large earthquakes; otherwise, with a “constant C” assumption, the estimated stress drops would appear to be magnitude‐dependent. Since C factor plays an important role in many theories that relate earthquake sources to their ground motion, our results here may help improve our current seismic and tsunami hazard assessments. Key Points We conduct numerical experiments to investigate the variation of proportionality between earthquake stress drop and slip The proportionality factor C between stress drop and slip is low for a shallow‐buried fault with a small dip angle The systematic variation in C can be significant enough to affect the source parameter analyses that assume a constant C