Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments

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Abstract
A new methodology for solution of the inverse problem in groundwater hydrology is proposed and applied to a site in southeastern New Mexico with extensive hydrogeologic data. The methodology addresses the issue of nonuniqueness of the inverse solutions by generating an ensemble of transmissivity fields considered to be equally likely, each of which is in agreement with the measured transmissivity and pressure data. It consists of generating a selected number of conditionally simulated transmissivity fields and then calibrating each of the fields to match the measured steady state or transient pressures, in a least squares sense. The calibration phase involves an iterative implementation of an automated pilot point approach coupled with conditional simulations. Pilot points are the parameters of calibration. They are synthetic transmissivity data which are added to the transmissivity database to produce a revised conditional simulation during calibration. Coupled kriging and adjoint sensitivity analysis is employed for the optimal location of pilot points, and gradient search methods are used to derive their optimal transmissivities. The pilot point methodology is well suited for characterizing the spatial variability of the transmissivity field in contrast to methods using zonation. Pilot points are located where their potential for minimizing the objective function is the highest. This minimizes the perturbations in the transmissivities which are optimally assigned to the pilot point and results in minimal changes to the covariance structure of the transmissivity field. The calibrated fields honor the transmissivity measurements at their locations, preserve the variogram, and match the measured pressures in a least squares sense. Since there are numerous options in the execution of this methodology, computational experiments have been conducted to identify the most efficient among them. The method has been applied to the Waste Isolation Pilot Plant (WIPP) site, in southeastern New Mexico, where the U.S. Department of Energy is conducting probabilistic system assessment for the permanent disposal of transuranic nuclear waste. The resulting calibrated transmissivity fields are input to a Monte Carlo analysis of the total system performance. The present paper, paper 1 of a two‐paper presentation, describes the methodology. Paper 2, a companion paper, presents the methodology's application to the WIPP site.