Robust estimation of hydrogeologic model parameters

Inverse modeling has become a standard technique for estimating hydrogeologic parameters. These parameters are usually inferred by minimizing the sum of the squared differences between the observed system state and the one calculated by a mathematical model. The robustness of the least squares criterion, however, has to be questioned because of the tendency of outliers in the measurements to strongly influence the outcome of the inversion. We have examined alternative approaches to the standard least squares formulation. The robustness of these estimators has been tested by means of Monte Carlo simulations of a synthetic experiment, in which both non-Gaussian random errors and systematic modeling errors have been introduced. The approach was then applied to data from an actual gas-pressure-pulse-decay experiment. The study demonstrates that robust estimators have the potential to reduce estimation bias in the presence of noisy data and minor systematic errors, which may be a significant advantage over the standard least squares method.

[1]  K. Pruess,et al.  TOUGH2-A General-Purpose Numerical Simulator for Multiphase Fluid and Heat Flow , 1991 .

[2]  Peter J. Huber,et al.  Robust Statistical Procedures: Second Edition , 1996 .

[3]  Stefan Finsterle,et al.  Determining permeability of tight rock samples using inverse modeling , 1997 .

[4]  S. Finsterle.  ITOUGH2 command reference. Version 3.1 , 1997 .

[5]  Guy Chavent.  On the theory and practice of non-linear least-squares , 1991 .

[6]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[7]  Don W. Vasco,et al.  Robust inversion of IASP91 travel time residuals for mantle P and S velocity structure, earthquake mislocations, and station corrections , 1994 .

[8]  J. Claerbout,et al.  Robust Modeling With Erratic Data , 1973 .

[9]  W. Yeh.  Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[10]  C. J. Lawrence.  Robust estimates of location : survey and advances , 1975 .

[11]  K. F. Gauss,et al.  Theoria combinationis observationum erroribus minimis obnoxiae , 1823 .

[12]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information , 1986 .

[13]  D. McLaughlin,et al.  A Reassessment of the Groundwater Inverse Problem , 1996 .

[14]  D. F. Andrews,et al.  Robust Estimates of Location: Survey and Advances. , 1975 .

[15]  N. Sun.  Inverse problems in groundwater modeling , 1994 .

[16]  Yanyong Xiang,et al.  A composite L1 parameter estimator for model fitting in groundwater flow and solute transport simulation , 1993 .

[17]  Jesús Carrera,et al.  State of the Art of the Inverse Problem Applied to the Flow and Solute Transport Equations , 1988 .

[18]  M. Th. van Genuchten,et al.  Parameter estimation for unsaturated flow and transport models — A review , 1987 .

[19]  D. Vasco.  Bounding seismic velocities using a tomographic method , 1991 .

[20]  Philip E. Gill,et al.  Practical optimization , 1981 .

[21]  S. P. Neuman.  Calibration of distributed parameter groundwater flow models viewed as a multiple‐objective decision process under uncertainty , 1973 .

[22]  G. Stewart,et al.  Theory of the Combination of Observations Least Subject to Errors , 1987 .

[23]  P. J. Huber.  Robust Statistical Procedures , 1977 .

[24]  Roland N. Horne,et al.  Automated Well Test Analysis Using Robust (LAV) Nonlinear Parameter Estimation , 1995 .

[25]  Karsten Pruess,et al.  A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media , 1996 .