ABSTRACT
This chapter describes how to determine model parameter values, and introduces some inversion algorithms that are based on the least-squares method. In constructing a mathematical model, the problem of interest is usually generalized to produce a conceptual model, which is then formulated by relating model-defining parameters. Forward modeling is an integral part of inverse modeling because inversion requires minimizing the discrepancy between prediction and observation. A well-posed inverse problem requires demonstration of the existence of the problem, the uniqueness in solution of the problem, the stability in algorithm used to achieve a solution, and the efficiency of delivering a final product. Inversion can be achieved in two ways. One, a modeler iteratively modifies parameter values until attaining best match. The other, an inverse algorithm is adopted to automatically or semi-automatically obtain the parameter values from the observed data and an initial set of trial parameter values.
