High resolution temperature monitoring in a borehole, detection of the deterministic signals in noisy environment

Studia Geophysica et Geodaetica volume 52, pages 413–437 (2008)Cite this article

Abstract

Temperature was monitored as a function of time at several selected depth levels in a slim experimental borehole. The hole is 15 cm in diameter, 150 m deep, and effectively sealed from the influx of ground water by a plastic tube of 5 cm diameter. The mean temperature gradient is 19.2 mK/m. The borehole was drilled in 1993 and has been in equilibrium since then. The data obtained reveal that: (1) the temperature-time series showed a complex, apparently random oscillation pattern with amplitudes of up to 25 mK; (2) irregular temperature variations characterized by larger oscillations may alternate with relatively “quiet” intervals; and (3) the character of the oscillation may vary both in depth as well as in time and the transition between two distinct regimes may be sudden.

The Fourier analysis detected “red noise” behavior of the signal but did not highlight any specific peak(s) corresponding to periodicity in the measured temperature series. We employed a variety of techniques (roughness coefficient, local growth of the second moment, recurrence and cross recurrence plots) to reveal the deterministic framework of the system behavior. All above methods were proven to be quite robust in the face of noise, and enabled the discovery of structures hidden in the signals produced by complex natural processes.

Statistical analysis suggested the existence of a quasi-periodic intra-hole oscillatory convection. The temperature field in the hole has a dual-frequency structure, in which short period oscillations of about 10–30 minutes are superposed on longer variations of up to several hours. At certain conditions, so far not fully understood, the temperature oscillations may practically stop. The temperature remains within 1–2 mK for a period of several days when the oscillation pattern (convection ?) suddenly resumes.

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Affiliations

  1. Institute of Geophysics, Acad. Sci. Czech Republic, Boční II/1401, 141 31, Praha 4, Czech Republic

    V. Čermák, J. Šafanda & M. Krešl

Authors
  1. V. Čermák
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  2. J. Šafanda
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  3. M. Krešl
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Correspondence to V. Čermák.

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Čermák, V., Šafanda, J. & Krešl, M. High resolution temperature monitoring in a borehole, detection of the deterministic signals in noisy environment. Stud Geophys Geod 52, 413–437 (2008). https://doi.org/10.1007/s11200-008-0029-8

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Key words

  • borehole correction
  • recurrence analysis
  • temperature monitoring