How do inertia, free surface interaction, and absolute friction coefficient level affect the final slip amplitude in a theoretical earthquake rupture model?

Abstract:

Estimating the fault slip amplitude for a future large earthquake is a key problem in earthquake physics with important implications for mitigating earthquake hazards. Theoretically, one can estimate the fault slip with a mechanical model: when initial conditions are given, the corresponding fault slip can be calculated by solving the equations of fundamental physical laws.

Although advancements in computational power have allowed us to simulate earthquakes of great complexity, simplified “generic” models are still widely used as they can provide clear physical insights into earthquake processes. One classic example is the static crack model with a planar fault embedded in an unbounded elastic whole space. This model yields the result that fault slip is proportional to the shear stress change before and after the event (often referred to as “static shear stress drop”) and to the length of the rupture/slipping region. In such a simple model, there is no normal stress change due to the slip process. Nonetheless, there are many other parameters to consider other than “static shear stress drop” and “rupture length”. For example, when considering inertial effects, the final slip is typically larger than in a static model (known as dynamic overshoot). Most importantly, the classic whole space model suggests that the absolute level of friction coefficient and the absolute level of stress does not affect the final slip amplitude; however, for a dipping fault that ruptures close to the ground surface, the topography can induce a normal stress interaction that in turn can alter the shear stress on the fault through friction coefficient.

In this study, we investigate how inertia, free surface interactions, and absolute friction coefficient level affect the final slip. We obtain a set of analytical relations that quantitatively relate these factors to the final slip. These analytical relations, while containing the whole space static crack model as a special case, can also generally explain the effect of inertia and normal stress change. With numerical models, we demonstrate that the above factors can significantly affect the final slip and surface displacement in a dipping fault setting, which has important implications of estimating tsunami generation in subduction zones, as well as for ground motion on continental dipping faults.