A BRIEF INTRODUCTION TO INVERSE MODELING

Inverse modeling is a powerful tool for developing and calibrating simulation models used in the earth sciences. It is based on a model of a physical system that includes observable inputs to the system, observable outputs of the system, a well-defined mathematical relation between the inputs and the outputs, and parameters that specify the mathematical relation. The goal of the inverse modeling is to estimate those parameters using the observable inputs and outputs. There are two general methods of estimating the parameters: maximum likelihood estimation (including its many variations) and Bayesian inference. During inverse modeling, several key questions must be considered: Is the model a suitable representation of the physical system? How sensitive are the model parameters to the data? How do noise and measurement error in the inputs and outputs affect the estimated model parameters? How uncertain are the estimated model parameters? If using maximum likelihood estimation, has the optimal model been found? Inverse modeling, as well as the related methods of sensitivity analysis and uncertainty evaluation, provide tools to help answer these questions. For example, these methods enable improved understanding of the processes governing the physical system dynamics, effective data-model integration, and evaluation of the uniqueness of model parameters. Models developed with inverse modeling usually represent better the physical system than models developed with trial and error.