Geostatistical inversion of coupled problems: dealing with computational burden and different types of data

Practical application of geostatistical inversion to coupled problems is hampered by a number of difficulties. In this paper, we address two of them: first, the computational cost of sensitivity (Jacobian) matrices and, second, the evaluation of the relative weights of different types of data. Regarding the first, we revise the adjoint state equations to propose a form whose cost is independent of the number of unknown parameters and only grows with the number of observation wells. Regarding the second, we derive expressions for the relative weights of different types of data. These expressions are based on minimizing the expected likelihood, rather than the likelihood itself. The efficiency of both improvements is tested on a synthetic example. The example analyzes a wide range of groundwater flow and solute transport conditions. Yet, the expected likelihood consistently yields the optimal weights. The proposed form of the adjoint state equations leads to one order of magnitude reduction in CPU time with respect to the conventional sensitivity equations.