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Fractal Methods in Self-Potential Signals Measured in Seismic Areas

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Fractal Behaviour of the Earth System

Summary

The self-potential (SP) signals are mainly generated by the streaming potential, which causes a voltage difference when a fluid flows in a porous rock. In seismic focal areas, this effect is strengthened by the increasing accumulation strain, which can produce dilatancy of rocks. Therefore, tectonic processes can be directly revealed by the investigation of the temporal fluctuations of SP signals, which may be useful to monitor and understand complex phenomena related with earthquakes.

Can the concept of fractal be used to qualitatively and quantitatively characterize an SP signal? Fractals are featured by power-law statistics, and, if applied to time series, can be a powerful tool to investigate their temporal fluctuations, in terms of correlations structures and memory phenomena. In the present review we describe monofractal and multifractal methods applied to SP signals measured in seismic areas. Persistent scaling behaviour characterizes SP signals, which, therefore, are not realizations of a white noise process. Furthermore, in multifractal domain SP signals measured in intense-seismicity areas and those recorded in low-seismicity areas are discriminated.

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References

  • Ashkenazy Y, Ivanov PC, Havlin S, Peng C-H, Goldberger AL, Stanley HE (2001) Magnitude and sign correlations in heartbeat fluctuations. Phys Rev Lett 86: 1900–1903

    Article  Google Scholar 

  • Ashkenazy Y, Havlin S, Ivanov PC, Peng C-K, Schulte-Frohlinde V, Stanley HE (2003) Magnitude and sign scaling in power-law correlated time series. Physica A 323: 19–41

    Article  Google Scholar 

  • Berry MV (1979) Diffractals. J Phys A Math Gentile 12: 781–792

    Google Scholar 

  • Buldyrev SV, Goldberger AL, Havlin S, Peng C-K, Stanley HE (1994) Fractals in biology and medicine: From DNA to the Heartbeat. In: Bunde A, Havlin S (eds) Fractals in Science, Springer-Verlag, Berlin Heidelberg New York, pp 48–87

    Google Scholar 

  • Burlaga LF, Klein LW (1986) Fractal structure of the interplanetary magnetic field. J Geophys Res 91: 347

    Google Scholar 

  • Brace WF, Paulding Jr BW, Scholz CH (1966) Dilatancy in the fracture of cristalline rocks. J Geophys Res 71: 3939–3953

    Google Scholar 

  • Box GEP, Jenkins GM (1976) Time Series Analysis. Holden-Day, S. Francisco

    Google Scholar 

  • Colangelo G, Lapenna V, Telesca L (2003) Analysis of correlation properties in geoelectrical data. Fractals 11: 27–38

    Google Scholar 

  • Corwin RF, Hoover DB (1979) The SP method in geothermal exploration. Geophysics 44: 226–245

    Article  Google Scholar 

  • Cuomo V, Lapenna V, Macchiato M, Serio C, Telesca L (1999) Stochastic behaviour and scaling laws in geoelectrical signals measured in a seismic area of southern Italy. Geophys J Int 139: 889–894

    Article  Google Scholar 

  • Davis A, Marshak A, Wiscombe W (1994) Wavelet-based multifractal analysis of non-stationary and/or intermittent geophysical signals. In: Foufoula-Georgiou E, Kumar P (eds) Wavelets in geophysics: Academic Press, New York, pp 249–298

    Google Scholar 

  • Di Bello G, Heinicke J, Koch U, Lapenna V, Macchiato M, Martinelli G, Piscitelli S (1998) Geophysical and geochemical parameters jointly monitored in a seismic area of Southern Apennines (Italy). Phys Chem Earth 23: 909–914

    Google Scholar 

  • Diego JM, Martinez-Gonzales E, Sanz JL, Mollerach S, Mart VJ (1999) Partition function based analysis of cosmic microwave background maps. Mon Not R Astron Soc 306: 427–436

    Article  Google Scholar 

  • Di Maio R, Patella D (1991) Basic theory of electrokinetic effects associated with earthquake. Boll Geof Teor Appl 33: 130–131

    Google Scholar 

  • Di Maio R, Mauriello P, Patella D, Petrillo Z, Piscitelli S, Siniscalchi A, Veneruso M (1997) Self-potential, geoelectric and magnetotelluric studies in Italian active volcanic areas. Annali di Geofisica 40: 519–537

    Google Scholar 

  • Dimri VP, Ravi Prakash M (2001) Scaling of power spectrum of extinction events in the fossil record. Earth Planet Sci Lett 186: 363–370

    Article  Google Scholar 

  • Dobrovolsky, IP (1993) Analysis of preparation of a strong tectonic earthquake. Phys Solid Earth 28: 481–492

    Google Scholar 

  • Dobrovolsky IP, Zubkov SI, Miachkin VI (1979) Estimation of the size of earthquake preparation zones. Pure Appl Geoph 117: 1025–1044

    Google Scholar 

  • Kantelhardt JW, Koscienly-Bunde E, Rego HHA, Havlin S, Bunde A (2001) Detecting long-range correlations with detrended fluctuation analysis. Physica A 295: 441–454

    Article  Google Scholar 

  • Kantelhardt JW, Zschiegner SA, Konscienly-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316: 87

    Article  Google Scholar 

  • Keller GV, Frischknecht FC (1966) Electrical Methods in Geophysical Prospecting, Pergamon Press, Oxford

    Google Scholar 

  • Havlin S, Amaral LAN, Ashkenazy Y, Goldberger AL, Ivanov PCh, Peng C-K, Stanley HE (1999) Application of statistical physics to heartbeat diagnosis. Physica A 274: 99–110

    Article  Google Scholar 

  • Hayakawa M (1994) Direction finding of seismogenic emissions. In: Hayakawa M, Fujinawa Y, (eds). Electromagnetic phenomena related to earthquake prediction. Terra Sci. Pub. Co., Tokyo, pp 493–494

    Google Scholar 

  • Hayakawa M, Hattori K, Itoh T, Yumoto K (2000) ULF electromagnetic precursors for an earthquake at Biak, Indonesia on February 17, 1996. Geophys Res Lett 27: 1531–1534

    Article  Google Scholar 

  • Hayakawa M, Ito T, Smirnova N (1999) Fractal analysis of ULF geomagnetic data associated with the Guam earthquake on August 8, 1993. Geophys Res Lett 26: 2797–2800

    Article  Google Scholar 

  • Higuchi T (1988) Approach to an irregular time series on the basis of the fractal theory. Physica D 31: 277–283

    Article  Google Scholar 

  • Higuchi T (1990) Relationship between the fractal dimension and the power law index for a time series: a numerical investigation. Physica D 46: 254–264

    Article  Google Scholar 

  • Feder J (1988) Fractals, Plenum Press, New York

    Google Scholar 

  • Lapenna V, Patella D, Piscitelli S (2000) Tomographic analysis of SP data in a seismic area of Southern Italy. Annali di Geofisica 43: 361–373

    Google Scholar 

  • Lei X, Kusunose K, Nishizawa O, Satoh T (2003) The hierarchical rupture process of a fault: an experimental study. Phys Earth Planet Int 137: 213

    Google Scholar 

  • Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophyisics and Space Science 39: 447–462

    Google Scholar 

  • Martinelli G, Albarello D (1997) Main constraints for siting monitoring networks devoted to the study of earthquake related hydrogeochemical phenomena in Italy. Annali di Geofisica 40: 1505–1522

    Google Scholar 

  • Mizutani H, Ishido T, Yokokura T, Ohnishi S (1976) Electrokinetic phenomena associated with earthquakes. Geophys Res Lett 3: 365–368

    Google Scholar 

  • Nur A (1972) Dilatancy pore fluids and premonitory variations of ts/tp travel times. Bull Seism Soc Am 62: 1217–1222

    Google Scholar 

  • O’Brien GS, Bean CJ, McDermott F (2003) A numerical study of passive transport through fault zones. Earth Planet Sci Lett 214: 633–643

    Google Scholar 

  • Ogilvy AA, Ayed MA, Bogoslovsky VA (1969) Geophysical studies of water leakages from reservoirs. Geophys Prosp 22: 36–62

    Google Scholar 

  • Parasnis DS (1986) Principles of Applied Geophysics. Chapman and Hall, London/ New York

    Google Scholar 

  • Park SK (1997) Monitoring resistivity changes in Parkfield, California 1988–1995. J Geophy Res 102: 24545–24559

    Article  Google Scholar 

  • Patella D (1997) Introduction to ground surface SP tomography. Geophys Prospect 45: 653–681

    Google Scholar 

  • Peng C.-K, Havlin S, Stanley HE, Goldberger AL (1995) Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. CHAOS 5: 82–87

    Article  Google Scholar 

  • Rikitake T(1988) Earthquake prediction: an empirical approach. Tectonophysics 148: 195–210

    Google Scholar 

  • Scholz CH (1990) The mechanics of earthquakes and faulting. Cambridge University Press, Cambridge

    Google Scholar 

  • Sharma PS (1997) Environmental and engineering geophysics. Cambridge University Press, Cambridge

    Google Scholar 

  • Shimizu Y, Thurner S, Ehrenberger K (2002) Multifractal spectra as a measure of complexity in human posture. Fractals10:103–116

    Google Scholar 

  • Stanley HE, Afanasyev V, Amaral LAN, Buldyrev SV, Goldberger AL, Havlin S, and Leschhorn H, Maass P, Mantegna RN, Peng C.-K., Prince PA, Salinger RA, Stanley MHR, Viswanathan GM (1996) Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics. Physica A 224: 302–321

    Article  Google Scholar 

  • Stanley HE, Amaral LAN, Goldberger AL, Havlin S, Ivanov PCh, Peng C-K (1999) Statistical physics and physiology: Monofractal and multifractal approaches. Physica A 270: 309–324

    Article  Google Scholar 

  • Telesca L, Cuomo V, Lapenna V, Macchiato M (2001) A new approach to investigate the correlation between geoelectrical time fluctuations and earthquakes in a seismic area of southern Italy. Geophys Res Lett 28: 4375–4378

    Google Scholar 

  • Telesca L, Lapenna V, Macchiato M (2002) Fluctuation analysis of the hourly time variability in observational geoelectrical signals. Fluctuation Noise Lett 2: L235–L242

    Google Scholar 

  • Telesca L, Colangelo G, Lapenna V, Macchiato M (2003) Monofractal and multifractal characterization of geoelectrical signals measured in southern Italy. Chaos Solitons & Fractals 18: 385–399

    Google Scholar 

  • Telesca L, Balasco M, Colangelo G, Lapenna V, Macchiato M (2004a). Investigating the multifractal properties of geoelectrical signals measured in southern Italy. Phys Chem Earth 29: 295–303

    Google Scholar 

  • Telesca L, Colangelo G, Lapenna V, Macchiato M (2004b) A preliminary study of the site-dependence of the multifractal features of geoelectric measurements. Annals of Geophysics 47: 11–20

    Google Scholar 

  • Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D 58: 77–94

    Article  Google Scholar 

  • Thurner S, Lowen SB, Feurstein MC, Heneghan C, Feichtinger HC, Teich MC (1997) Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes. Fractals 5: 565–596

    Google Scholar 

  • Tramutoli V, Di Bello G, Pergola N, Piscitelli S (2001) Robust satellite techniques for remote sensing of seismically active areas. Annali di Geofisica 44: 295–312

    Google Scholar 

  • Troyan VN, Smirnova NA, Kopytenko YA, Peterson T, Hayakawa M (1999) Development of a complex approach for searching and investigation of electromagnetic precursors of earthquakes: Organization of experiments and analysis procedures. In: Hayakawa, M., (ed) Atmospheric and ionospheric electromagnetic phenomena associated with earthquakes, Terra Sci. Pub. Co., Tokyo, pp 147–170

    Google Scholar 

  • Vallianatos F, Tzanis A (1999) On possible scaling laws between Electric Earthquake Precursors (EEP) and Earthquake Magnitude. Geophys Res Lett 26: 2013–2016

    Article  Google Scholar 

  • Zhao Y, Qian F (1994) Geoelectric precursors to strong earthquakes in China Tectonophysics 233: 99–113

    Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Methodologies for Environmental Analysis, National Research Council, C.da S.Loja, 85050, Tito (PZ), Italy

    Luciano Telesca & Vincenzo Lapenna

Authors
  1. Luciano Telesca
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  2. Vincenzo Lapenna
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Editors and Affiliations

  1. National Geophysical Research Institute, Uppal Road, Hyderabad, 500 007, India

    V. P. Dimri

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Telesca, L., Lapenna, V. (2005). Fractal Methods in Self-Potential Signals Measured in Seismic Areas. In: Dimri, V.P. (eds) Fractal Behaviour of the Earth System. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26536-8_8

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