Importance of Smoothing Derivative Data

Derivative analysis is a powerful diagnostic tool that enhances the interpretation of pumping test data. Hydrogeologists use the technique to identify flow regimes, discern boundary conditions and refine the selection of aquifer models.

Derivatives are not measured directly in the field; rather, they are computed by numerical differentiation from drawdowns collected during a pumping test. Straightforward calculation of the derivative from neighboring drawdown measurements typically leads to noisy derivative data. Therefore, smoothing routines are employed to obtain a cleaner derivative signal (Bourdet et al. 1989; Spane and Wurstner 1993).

To appreciate the importance of derivative smoothing, consider field data measured in a deep piezometer during a constant-rate pumping test performed in an unconfined aquifer (Kruseman and de Ridder 1994). Figure 1 is a derivative plot for the piezometer showing drawdown (squares) and derivatives (crosses) computed without smoothing (nearest neighbor method). Without smoothing, the derivative data provide little useful information for the interpretation of this test.

Figure 1. Derivative plot showing derivatives computed without smoothing.

Application of the Bourdet method to smooth the derivatives leads to a derivative plot with useful information (Figure 2). The trough in the derivative curve shown in Figure 2 is typical for an unconfined aquifer with delayed yield. The derivative signature suggests the possibility of using a mathematical model by Neuman (1974) to interpret the data.

Figure 2. Derivative plot showing derivatives computed with Bourdet smoothing.

AQTESOLV features three smoothing methods for computing derivatives including the Bourdet and Spane methods.

More information on derivative analysis is available at Aquifer Testing 101.

Hydraulics of Wells

Hydraulics of Wells by M. S. Hantush (1964) is available for download. This classic work is a recommended reference for the bookshelf of every practicing hydrogeologist.

To find more aquifer testing materials including other links to downloadable resources, check out my reference list at the Aquifer Testing 101 web site.