The time and frequency response of tracer experiments

Two distinctly different approaches to the interpretation of advective and dispersive transport characteristics of an intermediate scale (0-6 m) tracer experiment are examined and compared. The first, or time domain method, is based on a direct analysis of the tracer breakthrough via the widely used moment method. The second, or frequency domain method, is based on a comparison of the Fourier transform of the tracer breakthrough and its theoretical counterpart the frequency response function. Both methods provide satisfactory estimates of the mean advective transport component of the experiment for both conservative and nonconservative tracers. For the sampling ports closest to the source (0-2 m), the moment method produces much larger estimates of the dispersivity than the frequency response method. This difference is attributed to a buildup of errors in the estimation of higher moments, resulting from local variations in the tracer and fluid migration rates within this zone. In the lower part of the caisson (> 2m), the tracer breakthrough is smoother, and both methods provide similar and smaller dispersivity estimates. Overall the frequency domain approach is less sensitive to random variations in the breakthrough response. This idea is illustrated with an example from optimal filtering theory.