How Earthquake Risk Depends on the Closeness to a Fault: Symmetry-Based Geometric Analysis

Abstract

Earthquakes can lead to a huge damage-and the big problem is that they are very difficult to predict. To be more precise, it is very difficult to predict the time of a future earthquake. However, we can estimate which earthquake locations are probable. In general, earthquakes are mostly concentrated around the corresponding faults. For some faults, all the earthquakes occur in a narrow vicinity of the fault, while for other faults, areas more distant from the fault are risky as well. To properly estimate the earthquake's risk, it is important to understand when this risk is limited to a narrow vicinity of a fault and when it not thus limited. This problem has been thoroughly studied for the most well-studied fault in the world: San Andreas fault. This fault consists of somewhat different Northern and Southern parts. The Northern part is close to a straight line, and in this part, earthquake are mostly limited to a narrow vicinity of this line. In contrast, the Southern part is different: it is curved, and earthquakes can happen much further from the main fault. In this paper, we provide a general general explanation for this phenomenon. The existence of such a general explanations makes us expect that the same phenomenon will be observed at other not-so-well-studied faults as well.