Spatial and Temporal Dependence of Temperature Variations Induced by Atmospheric Pressure Variations in Shallow Underground Cavities

Pressure-induced temperature (PIT) variations are systematically observed in the atmosphere of underground cavities. Such PIT variations are due to the compressibility of the air, damped by heat exchange with the rock surface. It is important to characterize such processes for numerous applications, such as the preservation of painted caves or the assessment of the long-term stability of underground laboratories and underground waste repositories. In this paper we thoroughly study the spatiotemporal dependence of the PIT response versus frequency using vertical and horizontal profiles of temperature installed in an abandoned underground quarry located in Vincennes, near Paris. The PIT response varies from about 20 × 10−3°C hPa−1 at a frequency of 2 × 10−4 Hz to 2–3 × 10−3°C hPa−1 at a frequency of one cycle per day. An analytical expression based on a simple heat exchange model accounts for the observed features of the PIT response and allows for correcting the measured time series, having standard deviations of about 10−2°C, to residual variations with a standard deviation of about 2 × 10−3°C. However, a frequency-dependent attenuation of the response, corresponding to a reduction in amplitude with a factor varying from 2 to 3, is observed near the walls. This effect is not included in the simple analytical expression, but it can be accounted for by a one-dimensional differential equation, solved numerically, where temperature variations in the atmosphere are damped by an effective radiative coupling with the rock surface, complemented by a diffusive coupling near the walls. The TIP response is observed to remain stable over several years, but a large transient enhancement of about a factor of two is observed near the roof at one location from July to October 2005. In a cavity located below the Paris Observatory, an additional contribution is identified in the PIT response function versus frequency for frequencies smaller than 2 × 10−5 Hz. This contribution can be described using a modified analytical expression that includes the effect of heat diffusion into the surrounding rock. Using this expression, in this case also, the temperature time series can then be corrected, giving a residual standard deviation smaller than 1.6 × 10−3°C. Transient temporal variations of the PIT response are observed in all sites, with possible nonlinear components in the PIT. Such effects are not properly understood at this stage, and limit the reduction of time series to standard deviations of the order of 2 × 10−3°C, and consequently limit the search for new transient or seasonal temperature signals, for example due to the presence of tiny heat sources in the cavity or to geodynamical effects.