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Statistically-based approach for monitoring of micro-seismic events

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Abstract

We consider the problem of optimal statistical estimation of micro-seismic source parameters using multichannel data from surface arrays of seismometers affected by a strong seismic noise. The problem is treated as a statistical task of parameter estimation for a general type multidimensional linear model with random or completely unknown input time functions. The maximum-likelihood generic estimators are derived and their relationship with the well-known seismic emission tomography (SET) algorithm is established. The proposed estimation algorithms perform processing of multichannel discrete observations in the frequency domain and can be implemented in on-line mode. Using the method of successive independent trials (Monte-Carlo), we demonstrate that a proposed statistical estimation algorithm provides much higher accuracy of the micro-seismic event source location in real noise conditions than the widely used SET algorithm and, as a consequence, is more reliable in practical applications.

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Notes

  1. Symbols \(\overline{1,m}\) denote the set of all integers with values between 1 and m.

  2. We call a “segment” of the stationary time series \(\eta _k, \; k\in \mathbb Z \), the set of this time series values with indexes \(k\) belonging to the discrete time interval \(k\in \overline{1,n} \).

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Acknowledgments

The authors are grateful to the companies Synapse Science Center Inc. (Russia) and Earth Imaging Inc. (USA) for their support and assistance during the research and to the company ISTI Inc. (USA) for permission to use the records of surface seismic noise registered during hydraulic fracturing in the hydrocarbon field.

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Authors and Affiliations

  1. Institute for Earthquakes Prediction theory and Mathematical Geophysics RAS, Profsoyuznaya str., 84/32, 117997 , Moscow, Russia

    A. Kushnir

  2. Synapse Science Center, Artamonova str., d.16, korp. 3, 121357 , Moscow, Russia

    A. Kushnir, N. Rozhkov & A. Varypaev

  3. Moscow State Institute of Electronics and Mathematics—Higher School of Economics, Bol. Trekhsvjatitel’skij per., 1-3/12, build. 8, 109028 , Moscow, Russia

    A. Varypaev

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  1. A. Kushnir
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  2. N. Rozhkov
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  3. A. Varypaev
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Correspondence to A. Varypaev.

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Kushnir, A., Rozhkov, N. & Varypaev, A. Statistically-based approach for monitoring of micro-seismic events. Int J Geomath 4, 201–225 (2013). https://doi.org/10.1007/s13137-013-0049-6

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  • DOI: https://doi.org/10.1007/s13137-013-0049-6

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