Mechanisms of stress transfer and probabilistic models have been widely investigated to explain earthquake clustering features. However, these approaches are still far from being able to link individual events and to determine the number of earthquakes caused by a single event. An alternative approach based on proximity functions allows us to generate hierarchical clustering trees and to identify pairs of nearest-neighbors between consecutive levels of hierarchy. Then, the productivity of an earthquake is the number of events of the next level to which it is linked. Using a relative magnitude threshold ΔM to account for scale invariance in the triggering process, we show that the ΔM-productivity attached to each event is a random variable that follows an exponential distribution. The exponential rate of this distribution does not depend on the magnitude of triggering events and systematically decreases with depth. These results could now be used to characterize active fault systems and improve epidemic models of seismicity.

Earthquakes are usually followed by aftershocks. The number of aftershocks—the so-called productivity—depends on the magnitude of the earthquake. In seismic modeling it is usually assumed that the number of aftershocks is approximately the same for earthquakes with the same magnitude. This is one of the key assumptions on which the calculations are based. Although it is known that in reality this number can vary widely, only recently a pattern of such changes, called the earthquake productivity law, has been established. If we consider only direct aftershocks in a fixed magnitude range relative to the magnitude of the main shocks, then their number for a set of earthquakes in some spatiotemporal volume has an exponential distribution form. This means that fewer aftershocks are more likely. The most likely outcome is the complete absence of aftershocks. This pattern is quite counterintuitive, especially when considering aftershocks over a wide range of magnitudes. Here we managed to confirm the fulfillment of the earthquake productivity law for the wide range of magnitudes. For earthquakes of magnitude 6 and higher in the land part of Japan, it is confirmed that the frequency distribution of the number of their direct aftershocks with a minimum magnitude of 5 units less has an exponential shape. In seismicity modeling the validated earthquake productivity law makes it possible to replace the incorrect assumption of constant earthquake productivity with an exponential distribution. The single parameter of this regularity is easily determined from the actual data.

In seismology according to Båth’s well-known law, the magnitude of the strongest aftershock is on average by unity lower than the magnitude of the main shock. At the same time, most of the strongest...

This paper provides the results of an experiment for seismic-infrasonic monitoring of the glaciers situated on the northern coast of Isfjorden Bay, Svalbard. Monitoring is done by a single BRBB seismicinfrasonic station placed in the geophysical test area of the Russian Academy of Sciences, on the southern coast of Isfjorden Bay. BRBB station is complemented with a three-component seismic station on the northern bank of the fjord. The experiment shows that glaciers produce a seismic emission, which is enhanced from the second part of July to the end of September. The diurnal variations of the seismic emission are close to the behavior of the air temperature near the Earth surface. The seismic-infrasonic events produced by the glaciers destruction have been revealed in Spitsbergen for the first time. To detect and localize seismic-infrasonic events, methods based on joint use of seismic records and the data of infrasound monitoring are suggested. The experiment has shown convincing evidence for the possibility of monitoring glacier-destruction processes and iceberg formation by means of seismic-infrasonic methods.