Time Series Analysis of Groundwater Radon Using Stochastic Differential Equations

Abstract

This paper provides a new approach to detect changes in the groundwater radon concentration related to an earthquake. We express changes in radon concentration in a radon-detection chamber by using stochastic linear differential equations. These equations are represented by the state space notation, and then its solution is replaced by an estimation of the state vector at discrete points in time with an assumption that the coefficients describing the stochastic differential equations are constant for a sufficiently small time interval. Since the solubility of radon in water depends strongly on temperature, the separation of radon from liquid water, which is necessary for radon detection, causes fluctuations in the observed radon concentrations due to water temperature changes in the chamber. We applied our procedure to some actual data sets on groundwater radon concentration with those on simultaneously observed water temperature, and found that the temperature effects on the fluctuations in the observed radon concentration can be satisfactorily described by our procedure. Furthermore, we were able to estimate the original radon concentration in groundwater before it was introduced into the radon-detection chamber, which was not affected by water temperature changes. The obtained original radon concentrations are very stable during normal periods, and anomalous changes associated with earthquakes were easily detected. Our new method will be very useful to examine time-variation patterns of changes in groundwater radon and will provide important information about the mechanism of radon changes related to earthquakes.