Background Reports

Mathematical Derivations of Expressions for the Total Pumping-Induced Leakage Entering an Aquifer

Introduction

In this report, derivations of the Laplace-space expressions for the volume of pumping-induced leakage entering an aquifer (total leakage) are presented. These expressions, which are used by Butler and Tsou (in press) to demonstrate the scale invariance of total leakage, are obtained from the solutions of Hantush and Jacob (1955), Hantush (1960), and Butler et al. (2001). For the sake of generality, the expressions are presented in a dimensionless form. In all three cases, the Laplace-space expressions can be numerically inverted into real space using the Stehfest (1970) algorithm, as is done in Butler et al. (2001) and Butler and Tsou (in press).

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