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In this paper we consider the statistics of the aftershock sequence of the m = 7.65 20 September 1999 Chi-Chi, Taiwan earthquake. We first consider the frequency-magnitude statistics. We find good agreement with Gutenberg-Richter scaling but find that the aftershock level is anomalously high. This level is quantified using the difference in magnitude between the main shock and the largest inferred aftershock $$ {{\Updelta}}m^{ *}. $$ Typically, $$ {{\Updelta}}m^{ *} $$ is in the range 0.8-1.5, but for the Chi-Chi earthquake the value is $$ {{\Updelta}}m^{ *} $$ = 0.03. We suggest that this may be due to an aseismic slow-earthquake component of rupture. We next consider the decay rate of aftershock activity following the earthquake. The rates are well approximated by the modified Omori's law. We show that the distribution of interoccurrence times between aftershocks follow a nonhomogeneous Poisson process. We introduce the concept of Omori times to study the merging of the aftershock activity with the background seismicity. The Omori time is defined to be the mean interoccurrence time over a fixed number of aftershocks. [ABSTRACT FROM AUTHOR]

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Båth’s law for the magnitude of the largest aftershock, and (3) the modified Omori’s law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Båth’s law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omori’s law. [ABSTRACT FROM AUTHOR]

— The study of surface deformation due to seismic activity is often made using dislocations with uniform slip and simple geometries. A better modeling of coseismic and postseismic surface displacements can be obtained by using dislocations with variable slip and nonregular shapes. This is consistent with the asperity model of fault surfaces, assuming a friction distribution on faults made of locked zones with much higher friction than surrounding zones. In this paper we consider the 1997–1998 Colfiorito seismic sequence. The coseismic surface displacements in the Colfiorito zone are used in order to infer the slip distribution on the fault surface at different stages of the sequence. The displacement field has been modeled varying the slip distribution on the fault, and comparing the deformation observed by SAR and GPS techniques with model results. The slip distribution is calculated by Monte Carlo simulations on a normal fault with the dip angle equal to 40°. A good approximation is obtained by using square asperity units of 1.5×1.5 km2. In the first stage, we employed a simplified model with uniform slip, in which each asperity unit is allowed to slip a constant amount or not to slip at all, and in the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results show that the 1997 seismic events of the sequence can be modeled by irregular dislocations, obtaining a good fit to the DInSAR and GPS observations. The model also confirms the results of previous studies by a different methodology, defining the distribution of asperities on the fault plane using the fault geometry, the geodetic data and the seismic moment of the 1997–1998 Colfiorito seismic sequence. Furthermore, the analysis of 1997 aftershocks in the seismogenic region shows a strong correlation between most events and the asperity distribution, which can be considered as an independent test of the validity of the model. [ABSTRACT FROM AUTHOR]

Strong mining-induced earthquakes exhibit various aftershock patterns. The aftershock productivity is governed by the geomechanical properties of rock in the seismogenic zone, mining-induced stress and coseismic stress changes related to the main shock's magnitude, source geometry and focal mechanism. In order to assess the quantitative aftershock productivity potential in the mining environment we apply a forecast model based on natural seismicity properties, namely constant tectonic loading and the Gutenberg-Richter frequency-magnitude distribution. Although previous studies proved that mining-induced seismicity does not obey the simple power law, here we apply it as an approximation of seismicity distribution to resolve the number of aftershocks, not considering their magnitudes. The model used forecasts the aftershock productivity based on the background seismicity level estimated from an average seismic moment released per earthquake and static stress changes caused by a main shock. Thus it accounts only for aftershocks directly triggered by coseismic process. In this study we use data from three different mines, Mponeng (South Africa), Rudna and Bobrek (Poland), representing different geology, exploitation methods and aftershock patterns. Each studied case is treated with individual parameterization adjusted to the data specifics. We propose the modification of the original model, i.e. including the non-uniformity of M , resulting from spatial correlation of mining-induced seismicity with exploitation. The results show that, even when simplified seismicity distribution parameters are applied, the modified model predicts the number of aftershocks for each analyzed case well and accounts for variations between these values. Such results are thus another example showing that coseismic processes of mining-induced seismicity reflect features of natural seismicity and that similar models can be applied to study the aftershock rate in both the natural and the mining environment. [ABSTRACT FROM AUTHOR]

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (“fertility”), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities µ is characterized by a power law ~1/µ1+?. For earthquakes we expect such a power-distribution of fertilities with ?=b/a based on the Gutenberg-Richter magnitude distribution ~ 10-bm and on the increase ~ 10-am of the number of aftershocks with the mainshock magnitudem. We derive the asymptotic distributionsp r(r) andp g(g) of the total numberrof offsprings and of the total numbergof generations until extinction following a mainshock. In the regime ?<2 for which the distribution of fertilities has an infinite variance, we findThis should be compared with the distributionsobtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values a=0.8-1 andb=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother [ABSTRACT FROM AUTHOR]

— A seismic data file of 3,740 earthquakes from January 1987 to December 1994 has been elaborated for Morocco and the border regions, with 10 main events registering magnitudes from 5 to 5.6. Such seismicity is particularly important for Morocco as the released seismic energy constitutes a considerable part of the total energy radiated during the 20th century. Relative seismicity maps confirm the persistence of the major features of the seismicity of Morocco. An important seismic activity is observed in the Alboran region continental crust, which absorbs the maximum deformation resulting from the convergence of the African and Iberian plates. However, in the longitude window 3.5°– 6° W at depths of 25 to 50 km, a seismic gap zone seems to take place. An explanation of this phenomenon may be provided by the slab breakoff model. Even if the seismicity of Morocco remains moderate, heavy damage is observed when the magnitude of earthquakes exceeds 4.5, especially in the case of traditional buildings. [ABSTRACT FROM AUTHOR]