Statistical analysis of fractal properties of point processes modeling seismic sequences

Abstract Fractal stochastic point processes are described by power-law statistics, and therefore, are suited to model the time-occurrence sequence of seismic events, that are generally characterized by a time-clustering phenomenon. In this paper we quantified the temporal clustering in earthquake sequences by means of the Fano factor and the Allan factor, that can be used to reveal the fractality of such processes. These methods are applied to model the fractality of the 1983–1997 seismicity of one of the most seismically active area of southern Apennine Chain (southern Italy), that has shown the presence of temporal clusterization.

[1]  G. Luongo,et al.  A FRACTAL APPROACH TO CLUSTERING OF THE 1983–1984 SEISMICITY IN THE CAMPI FLEGREI CALDERA, SOUTHERN ITALY , 1996 .

[2]  B. C. Lesieutre.  Self-organizing criticality , 2002, Proceedings of the 35th Annual Hawaii International Conference on System Sciences.

[3]  W. D. Stuart,et al.  Earthquake instability on a strike‐slip fault , 1979 .

[4]  Hans G. Feichtinger,et al.  Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes , 1997, adap-org/9709006.

[5]  D. W. Allan,et al.  A statistical model of flicker noise , 1966 .

[6]  Yan Y. Kagan,et al.  Long-term earthquake clustering , 1991 .

[7]  L. Telesca,et al.  INVESTIGATING CLUSTERING STRUCTURES IN TIME-OCCURRENCE SEQUENCES OF SEISMIC EVENTS OBSERVED IN THE IRPINIA-BASILICATA REGION (SOUTHERN ITALY) , 1999 .

[8]  Yan Y. Kagan,et al.  Observational evidence for earthquakes as a nonlinear dynamic process , 1994 .

[9]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[10]  L. Telesca,et al.  Analysis of the time-scaling behaviour in the sequence of the aftershocks of the Bovec (Slovenia) April 12, 1998 earthquake , 2000 .

[11]  Malvin C. Teich.  Fractal character of the auditory neural spike train , 1989 .

[12]  Didier Sornette,et al.  Self-Organized Criticality and Earthquakes , 1989 .

[13]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[14]  Gianluca Valensise,et al.  Faulting mechanism and complexity of the November 23, 1980, Campania-Lucania Earthquake, inferred from surface observations , 1990 .

[15]  Jean-Luc Chatelain,et al.  A fractal approach to the clustering of earthquakes: Applications to the seismicity of the New Hebrides , 1987 .

[16]  A. Aldroubi,et al.  Wavelets in Medicine and Biology , 1997 .

[17]  Keisuke Ito,et al.  Earthquakes as self-organized critical phenomena , 1990 .

[18]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[19]  D. Sornette,et al.  Are sequences of volcanic eruptions deterministically chaotic , 1991 .

[20]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[21]  L. Telesca,et al.  Self-similarity properties of seismicity in the Southern Aegean area , 2000 .

[22]  Y. Kagan.  Correlations of earthquake focal mechanisms , 1992 .

[23]  M. Teich,et al.  The periodogram and Allan variance reveal fractal exponents greater than unity in auditory-nerve spike trains. , 1996, The Journal of the Acoustical Society of America.

[24]  Steven B. Lowen,et al.  ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES , 1995 .

[25]  Enzo Boschi,et al.  Forecasting where larger crustal earthquakes are likely to occur in Italy in the near future , 1995, Bulletin of the Seismological Society of America.

[26]  Teich,et al.  Fractal renewal processes generate 1/f noise. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Malte Meesmann,et al.  General relation between variance-time curve and power spectral density for point processes exhibiting 1/fβ-fluctuations, with special reference to heart rate variability , 1995, Biological Cybernetics.

[28]  B. Bodri.  A FRACTAL MODEL FOR SEISMICITY AT IZU-TOKAI REGION, CENTRAL JAPAN , 1993 .

[29]  Steven B. Lowen,et al.  Estimating the dimension of a fractal point process , 1993, Optics & Photonics.

[30]  D. W. Allan,et al.  Statistics of atomic frequency standards , 1966 .

[31]  S. Lowen,et al.  Point process models for self-similar network traffic, with applications , 1998 .

[32]  S. Porfido,et al.  Detailed study of the Potentino seismic zone in the Southern Apennines, Italy , 1995 .

[33]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[34]  Kerry E Sieh,et al.  Prehistoric large earthquakes produced by slip on the San Andreas Fault at Pallett Creek, California , 1978 .

[35]  Obukhov,et al.  Self-organized criticality in a crack-propagation model of earthquakes. , 1991, Physical review. A, Atomic, molecular, and optical physics.