Spatial averaging implied in aquifer test interpretation: The meaning of estimated hydraulic properties

Abstract

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Processing of aquifer test drawdowns to obtain estimates of transmissivity, and sometimes storativity, is an integral part of hydrogeological site investigations. Analysis of these data often relies on an assumption of hydraulic property uniformity. Aquifer properties are often estimated by fitting a Theis curve to measured drawdowns. Where an aquifer exhibits heterogeneity, quantities that are forthcoming from such analyses are assumed to represent spatially-averaged properties. However the nature of the averaging process, and the area over which averaging takes place are unknown. In this study we derive spatial averaging functions that link inferred hydraulic properties to real-world hydraulic properties. These functions employ Fréchet integrals derived by previous investigators that link observation well drawdowns to aquifer properties under an assumption of mild aquifer heterogeneity. It is shown that these hydraulic property spatial averaging functions are complex, especially at times that immediately follow the commencement of pumping. Furthermore, they cross hydraulic property boundaries, so that estimates of storativity can be contaminated by heterogeneities in real-world transmissivity, and vice versa. Because of its greater averaging area at later times, estimates of transmissivity are generally more immune to the effects of local hydraulic property heterogeneity than are those of storativity. They are therefore more reflective of broadscale real-world hydraulic properties, particularly those that prevail in areas that are removed from the immediate vicinity of the pumping and observation wells.

Keywords

• pumping tests
• resolution matrix
• sensitivity coefficient
• Fréchet kernel
• inversion
• Theis equation