Scaling laws in earthquake memory for interevent times and distances

Earthquakes involve complex processes that span a wide range of spatial and temporal scales. The limited earthquake predictability is partly due to the erratic nature of earthquakes and partly due to the lack of understanding of the underlying mechanisms of earthquakes. To improve our understanding and possibly the predictability of earthquakes, we develop here a lagged conditional probability method to study the spatial and temporal long-term memory of interevent earthquakes above a certain magnitude. We find, in real data from different locations, that the lagged conditional probabilities show long-term memory for both the interevent times and interevent distances and that the memory functions obey scaling and decay slowly with time, while, at a characteristic time (crossover), the decay rate becomes faster. We also show that the epidemic-type aftershock sequence model, which is often used to forecast earthquake events, fails in reproducing the scaling function of real catalogs as well as the crossover in the scaling function. Our results suggest that aftershock rate is a critical factor to control the long-term memory.