Back
 GEP  Vol.6 No.11 , November 2018
Conventional and Fractal Variogram Based on Time—Space Analysis of Seismicity Distribution—Case Study: Algeria Seismicity (1673-2010)
Abstract: Geostatistics belongs to the wide class of statistical methods. It is used and applied to analyze and predict the values associated with spatial or spatio-temporal phenomena such as seismological events. Thus, in addition to its adaptability to perform spatial data analysis based on the principles of variography, many other methods more representative of the spatial distributions of the epicentres have been experimented. The unidirectional or isotropic fractal variogram associates the criterion of variance with the fractal dimension which is a better descriptive parameter of the spatial organization of events. The same analysis procedure carried out through a directional or azimuthal variogram introduces the context of a preferential direction of earthquake evolution. Moreover, b-value is a privileged seismological parameter that can be studied alone or in combination with other more advanced geostatistical analysis factors such as fractals, fractal dimensions and the anisotropic variogram. All these concepts were used as methodology for a protocol of analysis of the catalog of the Algeria seismicity including 1919 events for the period extending from 1673 to 2010. This catalog is provided by the compilation of partial catalogs synthesized by the CRAAG (Research Centre in Astronomy, Astrophysics and Geophysics).
Cite this paper: Aitouche, M. and Djeddi, M. (2018) Conventional and Fractal Variogram Based on Time—Space Analysis of Seismicity Distribution—Case Study: Algeria Seismicity (1673-2010). Journal of Geoscience and Environment Protection, 6, 147-172. doi: 10.4236/gep.2018.611012.
References

[1]   Aitouche, M. A., Djeddi, M., & Baddari, K. (2012). Fracal Variogram Based Aftershock Sequences Analysis-Case Study: The May 21, 2003 Boumerdes Algeria Earthquake MW = 6.8. Arabian Journal of Geosciences, 6.

[2]   Aki, K., & Richards, P. (1980). Quantitative Seismology Theory and Methods. San Francisco: H. Freeman Co.

[3]   Amorese, F. W. H. D., Grass, J.-R., & Rydelek, P. (2010). On Varying b-Value with Depth: Results from Computer Intensive Tests for Southern California. Geophysical Journal International, 180, 347-360.

[4]   Barnes, R. (1991). The Variogram Sill and the Sample Variance. Mathematical Geology, 23, 673-678. https://doi.org/10.1007/BF02065813

[5]   Bellalem, F., Mobarki, M., & Talbi, A. (2008). Analysis of Spatio-Temporal Seismic Activity in in Northern Algeria. Proceeding of the 14 World Conference on Earthquake Engineering. Beijing.

[6]   Benouar, D. (1994). Materials for the Investigation of the Seismicity of Algeria and Adjacent Regions during the Twentieth Century. Annals of Geophysics, 37, 459-860.

[7]   Carminati, C., Doglioni, C., & lastrino, M. (2012). Geodynamic Evolution of the Central and Western Mediterranean Tectonic vs. Igneous Petrology Constraints. Tectonophysics, 579, 173-192. https://doi.org/10.1016/j.tecto.2012.01.026

[8]   Cressie, N. A. (1993). Statistics for Spatial Data. New York: Wiley & Sons.

[9]   Crownover, R. (1995). Introduction to Fractals and Chaos. Burlington: Johns and Barlett Publishers.

[10]   Feder, J. (1989). Fractals. New York: Plenum Press.

[11]   Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford: Oxford University Press.

[12]   Gutenberg, B., & Richter, C. F. (1942). Earthquake Magnitude Intensity and Acceleration. Bulletin of the Seismological Society of America, 32, 163-191.

[13]   Hirata, T. (1989). A Correlation between b Value and Fractal Dimension of Earthquakes, JGR Solid Earth, 94, 7507-7514. https://doi.org/10.1029/JB094iB06p07507

[14]   Kenzi, Mc. D. P. (1972). Active Tectonic of the Mediterranean Region (Soc. 30). Geophy. J.R. Astronomy.

[15]   Klinkenberg, B. (1994). A Review of Methods Used to Determine the Fractal Dimension of Linear Features. Mathematical Geology, 26, 23-46.

[16]   Kouadri, A., Aitouche, M. A., & Zelmat, M., (2012). Variogram Based Fault Diagnosis in an Interconnected Tank System. ISA Transactions.

[17]   Legrand, D. (2002). Fractal Dimensions of Small, Intermediate and Large Earthquakes. Bulletin of the Seismological Society of America, 92, 3318. https://doi.org/10.1785/0120020025

[18]   Mandelbrot, B. B. (1982). The Fractal Geometry of Nature (2nd ed.). Londra: W. H. Freeman.

[19]   Mathéron, G. (1970). La théorie des variables régionalisées et ses applications, Cahiers du Centre de Morphologie Mathématique de Fontainebleau. Paris: Ecole des mines.

[20]   Mc Nutt, S. R., Sanchez, J. J., & Wyss, M. (2004). Spatial Variations in the Frequency-Magnitude Distribution of Earthquakes at Mount Pinatubo Volcano. Bulletin of the Seismological Society of America, 94, 430-438.

[21]   Ogata, Y., & Katsura, K. (1993). Analysis of Temporal and Spatial Heterogeneity of Magnitude-Frequency Distribution Inferred from Earthquake Catalogues. Geophysical Journal international, 113, 727-738. https://doi.org/10.1111/j.1365-246X.1993.tb04663.x

[22]   Olea, R. A. (2009). A Practical Prime on Geostatistics. USG Geology Survey.

[23]   Schaefer, A. M., Danielle, J. E. & Wenzel, E. (2014). Application of Geostatistical Methods and Machine Learning for Spatio-Temporal Earthquake Cluster Analysis. American Geophysical Union Fall Meeting.

[24]   Smalley, R. F., Chatelain, J.-L., & Prevot, R. (1987). A Fractal Approach to the Clustering of Earthquakes. Bulletin of the Seismological Society of America, 62.

[25]   Turcotte, D. L. (1981). Fractals and Chaos in Geology and Geophysics. Cambridge: Cambridge University Press.

[26]   Wackermagel, H. (2003). Variogram Cloud. In Multivariate Geostatistics. Berlin: Springer.

[27]   Wierner, S. (2001). A Software Package to Analyse Seismicity ZMAP. Seismological Research Letters, 72, 373-382.

[28]   Wiemer, S., & Wiss, M. (2002). Mapping Spatial Variability of the Frequency-Magnitude Distribution of Earthquakes. Advances in Geophysics, 45, 1-40.

[29]   Wierner, S. (1996). ZMAP User Guide. XYZ Corporation.

[30]   Yarus, S., & Chambers, M. A. (1994). Stochastic Modelling and Geostatistics: Principles, Methods and Case Studies (No. 3). AAPG Computer Applications in Geology.

 
 
Top