Application Of Pilot-points And Regularization In The Inversion Of Hydrogeological Parameters

Hydrogeological parameters are critical for groundwater numerical simulation. Up to now, most of the hydrogeological paremeters are still difficult to measure directly due to the limited fund, especially for a large study area. Therefore, it is usually to estimate the hydrogeological parameters by fitting the observation data during the process of model calibration. During the last decades, a number of methods have been developed for the estimation of hydrogeological parameters. However, most of them are still limited for low parameterized problem, which limited their application in the field cases.Highly parameterized groundwater models can create calibration difficulties. Pilot-points and regularization method implemented in PEST software combines use of large numbers of parameters with mathematical approaches for stable parameter estimation, which could address these difficulties and enhance the transfer of information contained in field measurements to parameters used to model that system.In this paper, firstly we described the principles of three kinds of regularization methods named Tikhonov, T-SVD and SVD-Assist, as well as the pilot-points method. Secondly, we applied the three kinds of regularization methods for a synthetic model and discussed the influences of the numbers of pilot-points on the inversion results of regularization methods. Finaly, three kinds of inversion methods including regularization method based on pilot-points, the zones of uniform property method and the Ensemble Kalman Filter (EnKF) algorithms are compared. The main conclusions of this paper are the following:(1) By using Tikhonov regularization method, ill-posed problems can be solved stably and the results are consistent with the prior regularization information. T-SVD regularization method can obtain the main directions of the parameter space by truncating the singular values. Then stable inversion is achievable where only parameter combinations belonging to the calibration solution space are estimated. SVD-Assist regularization method combines the advantages of the T-SVD regularization and the Tikhonov regularization, as a result, the computing efficiency has been greatly improved. The prior regularization information has a significant impact on the inversion results of the Tikhonov regularization, similarly, the initial parameter vector has a great impact on the inversion results of T-SVD and SVD-Assist regularizations.(2) The number of pilot points has an effect on the inversion results. Within a certain range, the accuracy of the inversion gradually improves with the increasing number of pilot points, but the inversion accuracy will begin to deteriorate once exceeding this range. Meanwhile, more the number of pilot points, more computation burden, therefore the number of pilot points should be controlled within a reasonable range.(3) Compared to the traditional zones of uniform property method, the pilot-points regularization method is not only able to automatically determine the spatial distribution of parameters, but also is better than the traditional zones of uniform property method in terms of the accuracy of estimated parameters and the fitness between simulation and observation data. Compared to the EnKF algorithms, the fitness between model simulaitons and observations, as well as the accuracy of the result of the pilot-points regularization method are better, but the latter takes a longer time to complete the inversion.