Statistical inverse modeling and geostatistical analysis of the Avra Valley aquifer

Abstract

Avra Valley is a deep, elongate alluvial basin in southern Arizona, which contains an extensive unconfined aquifer. This aquifer was modeled by using a statistical inverse model. The input data required by the inverse model are (1) spatially averaged logtransmissivity estimates in zones of the aquifer, (2) steady-state hydraulic head estimates at points in the aquifer, and (3) the covariance matrices of log-transmissivity and hydraulic-head estimation errors. The geostatistical interpolation technique of kriging was used to assign the spatially averaged log-transmissivities and to compute the covariance matrix of the log-transmissivity estimation errors. Estimates of the steady-state hydraulic heads were made by interpolating between known data points. Two independent determinations of the covariance matrix of the hydraulic-head estimation errors were made. The output from the inverse model is a modified set of spatially averaged logtransmissivities and the covariance matrix of their associated estimation errors. The magnitude of the estimation errors of this modified set of log-transmissivities is less than the magnitude of the estimation errors of the kriged log-transmissivities. A conditional simulation analysis was also performed to assess the magnitude of errors in the hydraulic heads predicted by the kriged log-transmissivity field and the logtransmissivity field computed by the inverse model.