Sensitivity of temporal moments calculated by the adjoint-state method andjoint inversing of head and tracer data

Including tracer data into geostatistically based methods of inverse modeli ng is computationally very costly when all concentration measurements are u sed and the sensitivities of many observations are calculated by the direct differentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7) :1615-26) have suggested the use of the first temporal moment instead of th e complete concentration record at a point. We derive a computationally eff icient adjoint-state method for the sensitivities of the temporal moments t hat require the solution of the steady-state flow equation and two steady-s tate transport equations for the forward problem and the same number of equ ations for each first-moment measurement. The efficiency of the method make s it feasible to evaluate the sensitivity matrix many times in large domain s. We incorporate our approach for the calculation of sensitivities in the quasi-linear geostatistical method of inversing ("iterative cokriging"). Th e application to an artificial example of a tracer introduced into an injec tion well shows good convergence behavior when both head and first-moment d ata are used for inversing, whereas inversing of arrival times alone is les s stable. (C) 2000 Elsevier Science Ltd. All rights reserved.