The use of well response to natural forces in the estimation of hydraulic parameters

Abstract

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 derive an analytical solution for well response to both the random and the periodic components of the combined SET and APV (CSA) forcings. Previously posed models for the individual SET and APV forcings are subsets of this more general model. An inverse theory and an algorithm are developed in order to provide improved results when using such models to estimate the hydraulic parameters associated with a given formation. A complex vector estimation criterion is used in developing a nonlinear, Gauss-Marquardt estimation algorithm. When compared to previous methods of fitting modulus and phase, the complex vector estimation methodology has less bias and variance, and is more robust. An examination of the response surface of the estimation criterion reveals that storativity (S) is relatively non-unique, and thus is not considered in the context of the parameter estimation problem. However, since there is little correlation between transmissivity (T) and S estimators, a good estimate for T is still possible independent of having 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, which is defined with respect to the dimensionless transmissivity of the system. 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 identifiable. The results of applications to synthetic data indicate that the OEA scheme gives a T estimate with the most precision, and also that it requires collecting fewer observations.