Statistical study of the occurrence of shallow earthquakes

ABSTRACT

Summary. The time—space-magnitude interaction of shallow earthquakes has been investigated for three catalogues: worldwide (M≥ 7.0), Southern and Northern California (M≥ 4.0) and Central California (M≥ 1.5). The earthquake sequences are considered as a multi-dimensional stochastic point process; the estimates of the parameters for a branching model of the seismic process are obtained by a maximum-likelihood procedure. After applying magnitude—time and magnitude—distance scaling, the pattern of relationship among earthquakes of different magnitude ranges is almost identical. The number of foreshocks diminishes as the magnitude difference between the main shock and the foreshocks increases, while the magnitude distribution of aftershocks has the opposite property. The strongest aftershocks are likely to occur at the beginning of the sequence; later they migrate away with velocities of the order of km/day. The sequences which are composed of smaller aftershocks last longer and there are indications that they remain essentially in the focal region. Foreshocks also appear to migrate, but in this case, toward the main shock. The rate of occurrence of dependent shocks increases as t^-1 as the origin time of the main shock is approached, effectively making every earthquake a multi-shock event. This interaction of earthquakes was modelled by a Monte-Carlo simulation technique. The statistical inversion of simulated catalogues was undertaken to derive the information we would be able to retrieve from actual data, as well as possible errors of estimates. The possibility of using these results as a tool for seismic risk prediction is discussed and evaluated.