RECOVERING THE HISTORY OF A GROUNDWATER CONTAMINANT PLUME - METHOD OFQUASI-REVERSIBILITY

The method of quasi-reversibility (QR) (Lattes and Lions, 1969) has be en used previously to solve the diffusion equation with reversed time. We develop a quasireversible solution to a convection-dispersion equa tion by solving the QR diffusion operator in a moving coordinate syste m. The solution procedure is applied to the problem of recovering the history of a groundwater contaminant plume from observations of its pr esent conditions. This approach to the plume history problem is potent ially superior to the Tikhonov regularization approach used by Skaggs and Kabala (1994) because it is easier to implement and readily allows for space- and time-dependent transport parameters. However, our resu lts for a few example problems suggest that the QR procedure is less a ccurate than the regularization technique. Thus the easy implementatio n and improved generality of the QR procedure come at the expense of a ccuracy; this trade-off will have to be weighed if the QR technique is to be used.