Fractal Analysis of Data from Seismometer Array Monitoring Virgo Interferometer

Abstract

The local Hurst exponent H(t) has been computed for an array of 38 seismometers, deployed at the Virgo West End Building for Newtonian Noise characterisation purposes. The analysed period is from January 31st, 2018 to February 5th, 2018. The Hurst exponent H is a fractal index quantifying the persistent behaviour of a time series, higher H corresponding to higher persistency. The adopted methodology makes use of the local Hurst exponent computed using small sliding windows, in order to characterise the properties of the seismometers. Hourly averages and averages of H(t) have been computed over the whole analysed period. Results show that seismometers placed on a concrete slab closer to the centre of the room systematically exhibit higher persistency than the ones that are not placed on it. Seismometers placed next to the outer walls also exhibit higher persistency. The seismometer placed on a thin metal plate exhibits instead very low values of persistency during the analysed period, compared to the rest of the array.

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References

  1. Ausloos, M., & Ivanova, K. (2001). Power-law correlations in the southern-oscillation-index fluctuations characterizing El Nino. Physical Review E, 63(4), 047201.

    Article  Google Scholar 

  2. Ausloos, M., Vandewalle, N., Boveroux, P., Minguet, A., & Ivanova, K. (1999). Applications of statistical physics to economic and financial topics. Physica A: Statistical Mechanics and its Applications, 274(1–2), 229–240.

    Article  Google Scholar 

  3. Beccaria, M., Bernardini, M., Braccini, S., Bradaschia, C., Bozzi, A., Casciano, C., et al. (1998). Relevance of Newtonian seismic noise for the virgo interferometer sensitivity. Classical and Quantum Gravity, 15(11), 3339.

    Google Scholar 

  4. Bianchi, S., Longo, A., & Plastino, W. (2018). A new methodological approach for worldwide beryllium-7 time series analysis. Physica A: Statistical Mechanics and its Applications, 501, 377–387.

    Article  Google Scholar 

  5. Bianchi, S., Longo, A., Plastino, W., & Povinec, P. (2018). Evaluation of 7Be and 133Xe atmospheric radioactivity time series measured at four ctbto radionuclide stations. Applied Radiation and Isotopes, 132, 24–28.

    Article  Google Scholar 

  6. Bianchi, S., & Plastino, W. (2018). Uranium time series analysis: A new methodological approach for event screening categorisation. Journal of Environmental Radioactivity, 183, 37–40.

    Article  Google Scholar 

  7. Bianchi, S., Plastino, W., Brattich, E., Djurdjevic, V., Longo, A., Hernández-Ceballos, M. A., et al. (2019). Analysis of trends, periodicities, and correlations in the beryllium-7 time series in northern europe. Applied Radiation and Isotopes, 148, 160–167.

    Article  Google Scholar 

  8. Buldyrev, S., Goldberger, A., Havlin, S., Mantegna, R., Matsa, M., Peng, C.-K., et al. (1995). Long-range correlation properties of coding and noncoding dna sequences: Genbank analysis. Physical Review E, 51(5), 5084.

    Article  Google Scholar 

  9. Driggers, J., Harms, J., & Adhikari, R. (2012). Subtraction of Newtonian noise using optimized sensor arrays. Physical Review D, 86(10), 102001.

    Article  Google Scholar 

  10. Eichner, J. F., Koscielny-Bunde, E., Bunde, A., Havlin, S., & Schellnhuber, H.-J. (2003). Power-law persistence and trends in the atmosphere: A detailed study of long temperature records. Physical Review E, 68(4), 046133.

    Article  Google Scholar 

  11. Eke, A., Herman, P., Bassingthwaighte, J., Raymond, G., Percival, D., Cannon, M., et al. (2000). Physiological time series: distinguishing fractal noises from motions. Pflügers Archiv, 439(4), 403–415.

    Article  Google Scholar 

  12. Fraedrich, K., & Blender, R. (2003). Scaling of atmosphere and ocean temperature correlations in observations and climate models. Physical Review Letters, 90(10), 108501.

    Article  Google Scholar 

  13. Grau-Carles, P. (2000). Empirical evidence of long-range correlations in stock returns. Physica A: Statistical Mechanics and its Applications, 287(3–4), 396–404.

    Article  Google Scholar 

  14. Harms, J. (2015). Terrestrial gravity fluctuations. Living Reviews in Relativity, 18(1), 3.

    Article  Google Scholar 

  15. Ihlen, E. A. F. E. (2012). Introduction to multifractal detrended fluctuation analysis in Matlab. Frontiers in Physiology, 3, 141.

    Article  Google Scholar 

  16. Ivanova, K., Ackerman, T., Clothiaux, E., Ivanov, P. C., Stanley, H., & Ausloos, M. (2003). Time correlations and 1/f behavior in backscattering radar reflectivity measurements from cirrus cloud ice fluctuations. Journal of Geophysical Research: Atmospheres, 108(D9).

  17. Ivanov, P. C., Yuen, A., Podobnik, B., & Lee, Y. (2004). Common scaling patterns in intertrade times of us stocks. Physical Review E, 69(5), 056107.

    Article  Google Scholar 

  18. Jánosi, I. M., Janecskó, B., & Kondor, I. (1999). Statistical analysis of 5 s index data of the budapest stock exchange. Physica A: Statistical Mechanics and its Applications, 269(1), 111–124.

    Article  Google Scholar 

  19. Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications, 316(1–4), 87–114.

    Article  Google Scholar 

  20. Kavasseri, R. G., & Nagarajan, R. (2004). Evidence of crossover phenomena in wind-speed data. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(11), 2255–2262.

    Article  Google Scholar 

  21. Koscielny-Bunde, E., Bunde, A., Havlin, S., Roman, H. E., Goldreich, Y., & Schellnhuber, H.-J. (1998). Indication of a universal persistence law governing atmospheric variability. Physical Review Letters, 81(3), 729.

    Article  Google Scholar 

  22. Liu, Y., Gopikrishnan, P., Stanley, H. E., et al. (1999). Statistical properties of the volatility of price fluctuations. Physical Review E, 60(2), 1390.

    Article  Google Scholar 

  23. Longo, A., Bianchi, S., & Plastino, W. (2018). Xenon and radon time series analysis: A new methodological approach for characterising the local scale effects at ctbt radionuclide network. Applied Radiation and Isotopes, 139, 209–216.

    Article  Google Scholar 

  24. Longo, A., Bianchi, S., & Plastino, W. (2019). tvf-EMD based time series analysis of 7Be sampled at the CTBTO-IMS network. Physica A: Statistical Mechanics and its Applications, 523, 908–914.

    Article  Google Scholar 

  25. Matsoukas, C., Islam, S., & Rodriguez-Iturbe, I. (2000). Detrended fluctuation analysis of rainfall and streamflow time series. Journal of Geophysical Research: Atmospheres, 105(D23), 29165–29172.

    Article  Google Scholar 

  26. Moret, M. A., Zebende, G., Nogueira, E, Jr., & Pereira, M. (2003). Fluctuation analysis of stellar X-ray binary systems. Physical Review E, 68(4), 041104.

    Article  Google Scholar 

  27. Pattantyús-Abrahám, M., Király, A., & Jánosi, I. M. (2004). Nonuniversal atmospheric persistence: Different scaling of daily minimum and maximum temperatures. Physical Review E, 69(2), 021110.

    Article  Google Scholar 

  28. Peng, C.-K., Havlin, S., Stanley, H. E., & Goldberger, A. L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos: An Interdisciplinary Journal of Nonlinear Science, 5(1), 82–87.

    Article  Google Scholar 

  29. Plastino, W., Plenteda, R., Azzari, G., Becker, A., Saey, P., & Wotawa, G. (2010). Radioxenon time series and meteorological pattern analysis for CTBT event categorisation. Pure and Applied Geophysics, 167(4–5), 559–573.

    Article  Google Scholar 

  30. Raberto, M., Scalas, E., Cuniberti, G., & Riani, M. (1999). Volatility in the italian stock market: an empirical study. Physica A: Statistical Mechanics and its Applications, 269(1), 148–155.

    Article  Google Scholar 

  31. Robinson, P. (2003). Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology. Physical Review E, 67(3), 032902.

    Article  Google Scholar 

  32. Siwy, Z., Ausloos, M., & Ivanova, K. (2002). Correlation studies of open and closed state fluctuations in an ion channel: Analysis of ion current through a large-conductance locust potassium channel. Physical Review E, 65(3), 031907.

    Article  Google Scholar 

  33. Talkner, P., & Weber, R. O. (2000). Power spectrum and detrended fluctuation analysis: Application to daily temperatures. Physical Review E, 62(1), 150.

    Article  Google Scholar 

  34. Vandewalle, N., & Ausloos, M. (1998). Crossing of two mobile averages: A method for measuring the roughness exponent. Physical Review E, 58(5), 6832.

    Article  Google Scholar 

  35. Varotsos, C., Assimakopoulos, M.-N., & Efstathiou, M. (2007). Long-term memory effect in the atmospheric CO$_2$ concentration at mauna loa. Atmospheric Chemistry and Physics, 7(3), 629–634.

    Article  Google Scholar 

  36. Varotsos, P., Sarlis, N., & Skordas, E. (2003a). Long-range correlations in the electric signals that precede rupture: Further investigations. Physical Review E, 67(2), 021109.

    Article  Google Scholar 

  37. Varotsos, P., Sarlis, N., & Skordas, E. (2003b). Attempt to distinguish electric signals of a dichotomous nature. Physical Review E, 68(3), 031106.

    Article  Google Scholar 

  38. Zebende, G., Da Silva, M., Rosa, A, Jr., Alves, A., De Jesus, J., & Moret, M. (2004). Studying long-range correlations in a liquid-vapor-phase transition. Physica A: Statistical Mechanics and its Applications, 342(1–2), 322–328.

    Article  Google Scholar 

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Acknowledgements

The data acquisition was supported by the TEAM/2016-3/19 grant from the Foundation for Polish Science. Data shown in the paper were taken using the Advanced Virgo environmental monitoring system. We acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium.

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Longo, A., Bianchi, S., Plastino, W. et al. Fractal Analysis of Data from Seismometer Array Monitoring Virgo Interferometer. Pure Appl. Geophys. 177, 2597–2603 (2020). https://doi.org/10.1007/s00024-019-02395-x

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Keywords

  • Newtonian Noise
  • virgo
  • detector characterisation
  • fractal time series analysis
  • DFA
  • local hurst exponent