Transmissivity Resolution Obtained from the Inversion of Transient and Pseudo-Steady Drawdown Measurements

A key aspect of estimating transmissivity distributions from pumping tests is the spatial resolution of the estimation. Some assumption of spatial structure is needed to make an inversion possible. Both the nature of groundwater flow and assumed structure cause a smeared estimate. This research is focused on the how information content of the data smears the estimate. The inversion procedure near the solution is approximated as iterative linear updates. Linear resolution analysis of the distributed sensitivity to transmissivity indicates the limit of detail possible from the inversion. To enable this research, adjoint-sensitivity calculations were added to MODFLOW-2000. The adjoint-sensitivity calculations significantly speed the calculation of the sensitivity matrix. To highlight the concepts, we use a homogeneous aquifer with known storativity. The analysis indicates resolution of transmissivity is finer near the pumping and monitoring wells than in the regions between wells. Transient data are highly redundant with respect to transmissivity information. Very early time data do provide different spatial information than later time data do. INTRODUCTION An important question in any endeavor is “How well can we do it?” This is often a very complicated question. Bounding the answer rather than answering it directly often turns a difficult question into one we can answer. Our endeavor is to estimate subsurface properties. Resolution analysis provides insight into how well we can estimate the properties. Resolution analysis is a common technique in the geophysical community (Menke, 1989; Tarantola, 1987). With the exception of Vasco et. al. (1997), resolution analysis has not received attention in the groundwater literature. Resolution analysis uses a linear approximation of the dependence of measurements on estimated parameters to determine how the inversion estimates relate to the actual subsurface properties. This is truly a bounding analysis because we assume that our groundwater model is accurate and that the estimated parameters are close enough to correct that non-linearity can be ignored. We also partially neglect the influence of errors in the measurements used in the inversion. In this paper, we consider the estimation of the distribution of transmissivity in a hypothetical aquifer from drawdown measurements in observation wells about a pumping well. The emphasis is on the resolution analysis not on a specific inversion procedure. As this is a conference on MODFLOW, the addition of the adjoint state method (Sun, 1994; Townley and Wilson, 1985) of calculating sensitives to MODFLOW-2000 (Harbaugh et al., 2000; Hill et al., 2000) and its use in this investigation is highlighted. SENSITIVITY CALCULATIONS The simulated hypothetical aquifer has a central region 12.9 m by 7.6 m of constant grid spacing of 0.25 m. Twelve wells are positioned in roughly concentric rings about the central well as shown in Figure 1. The central region is surrounded by a grid that expands with a growth ratio of 1.5 to 150 m. The grid extends beyond the central region far enough that no appreciable drawdown occurs at the boundary during the simulation period. A constant storativity of 0.3 is used. A uniform transmissivity of 0.0032 m /s is used. A constant pumping rate of 5 l/s is maintained for 10,000 s (170 min). No appreciable drawdown occurs at the boundary during the simulation period. A total of 122 observations were made from drawdown at the wells. Four drawdown observations per log base ten time interval were recorded. Early observations, before a well responds, were not included. MODFLOW and More 2003: Understanding through Modeling Conference Proceedings, Poeter, Zheng, Hill & Doherty www.mines.edu/igwmc/ The model has a total of 9409 cells. Estimating a distribution of