*Water Resources Research, 34*(11), 2939-2947, 1998.
## Robust Estimation of Hydrogeologic Model Parameters

*Stefan Finsterle and Julie Najita*

Lawrence Berkeley National Laboratory, Earth Sciences Division

University of California, Berkeley, CA 94720

**Abstract.**
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.