A seismically active region is modelled as a system of absolutely rigid blocks separated by infinitely thin plane faults. The interaction of the blocks along the fault planes and with the underlying medium is viscous-elastic. The system of blocks moves as a consequence of prescribed motion of the boundary blocks and of the underlying medium. When, for some part of a fault plane the stress exceeds a certain strength level, a stress-drop (''a failure'') occurs, and it can cause failures in other parts of the fault planes. In our model the failures represent earthquakes. As a result of the numerical simulation a synthetic earthquake catalog is produced.The procedure is applied to the numerical modelling of the dynamics of the block-structure, which approximates the tectonic structure of the Vrancea region. The result of the numerical experiment is a synthetic earthquake catalog with the space distribution of epicenters close to the real distribution and the frequency-magnitude relations (Gutenberg-Richter curves) obtained for the synthetic and real catalogs possessing some common features.

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We propose a multiscale method to map the spatial variations of the completeness magnitude M c of earthquake catalogs. The Gutenberg-Richter law describing the earthquake frequency-magnitude distribution (FMD) might not hold over the entire magnitude range, and small areas may exhibit a specific type of seismicity, especially in volcanotectonic contexts. For these reasons, any scaling relation should be obtained by adapting the dimension of the studied zone to the range of the event magnitude. Here, we associate ranges of larger magnitudes with increasing areas for data selection based on empirical relations in seismotectonics. Then, for each point in space, we document the earthquake FMD at all length scales within the corresponding earthquake magnitude ranges. High resolution of the M c -value is achieved through the determination of the smallest space-magnitude scale in which the Gutenberg-Richter law is verified. The multiscale procedure isolates the magnitude range that meets the best local seismicity and local record capacity. Using artificial catalogs and earthquake catalogs of the Lesser Antilles arc, this M c -mapping method is shown to be efficient in regions with mixed types of seismicity, a variable density of epicenters, and various levels of registration.