A simple physical model for deep moonquake occurrence times
The physical process that results in moonquakes is not yet fully understood. The periodic occurrence times of events from individual clusters are clearly related to tidal stress, but also exhibit departures from the temporal regularity this relationship would seem to imply. Even simplified models that capture some of the relevant physics require a large number of variables. However, a single, easily accessible variable - the time interval I(n) between events - can be used to reveal behavior not readily observed using typical periodicity analyses (e.g., Fourier analyses). The delay-coordinate (DC) map, a particularly revealing way to display data from a time series, is a map of successive intervals: I(n+. 1) plotted vs. I(n). We use a DC approach to characterize the dynamics of moonquake occurrence. Moonquake-like DC maps can be reproduced by combining sequences of synthetic events that occur with variable probability at tidal periods. Though this model gives a good description of what happens, it has little physical content, thus providing only little insight into why moonquakes occur. We investigate a more mechanistic model. In this study, we present a series of simple models of deep moonquake occurrence, with consideration of both tidal stress and stress drop during events. We first examine the behavior of inter-event times in a delay-coordinate context, and then examine the output, in that context, of a sequence of simple models of tidal forcing and stress relief. We find, as might be expected, that the stress relieved by moonquakes influences their occurrence times. Our models may also provide an explanation for the opposite-polarity events observed at some clusters. ?? 2010.