The Estimation of Fluid Flow Properties from the Response of Water Levels in Wells to the Combined Atmospheric and Earth Tide Forces

The water level in an open well tapping a confined formation is influenced by natural forces including the solid Earth tide (SET) and atmospheric pressure variation (APV). The spectral method is used to analytically derive a model for well response to both random and periodic components of the combined SET and APV forcings (CSA). An inverse theory and algorithm are developed in order to provide improved results when using the model to estimate the hydraulic parameters associated with a given formation. An examination of the response surface of the estimation criterion reveals a uniqueness problem in estimating storativity (S). Since there is little correlation between the transmissivity (T) and S estimators, a good estimate for T is still possible independent of having accurate knowledge of S. An estimate of T is possible only if the data contain sufficient information so that the analysis occurs within an identifiability window. The CSA estimation methodology is compared to individual SET and APV schemes. The CSA scheme gives the greatest probability that sufficient information is contained in a data record so that T is indeed identifiable. The results of applications to synthetic data indicate that the CSA scheme gives a T estimate with the most precision and also that it requires collecting fewer observations. These results are discussed in light of practical considerations when designing data collection procedures