Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions

An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum Kmax/Kmin tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.