Theis' Solution by Nonlinear Least‐Squares and Finite‐Difference Newton's Method

A method using the nonlinear least‐squares and finite‐difference Newton's method to determine the aquifer parameters via a pumping test in a homogeneous and isotropic confined aquifer system is proposed. The nonlinear least‐squares is used to find the values of transmissivity and storage coefficient such that the sum of the squares of differences between the predicted drawdowns and observed drawdowns is minimized. The finite‐difference Newton's method is used to solve the system of nonlinear least‐squares equations for transmissivity and storage coefficient. Comparisons of the results between the proposed method and graphical methods including the Theis, Cooper‐Jacob, and Chow methods are discussed in detail, showing data of a 6‐hour pumping test. The proposed method has the advantages of high accuracy and quick convergence for most initial guesses.