## ABSTRACT

This chapter further considers the digital inversion of deterministic data to estimate m>2 unknown coefficients of a mathematical forward model. The objective is to complete the set of coefficients so that the model evaluates the data's differential and integral properties to within the inversion's error limits. The inversion process involves subjective conceptualization of a model for the observed data variations that is transformed via assumptions into a simplified mathematical model of known and unknown coefficients. Solutions for the unknown coefficients are tested by comparing the model's predictions against the observations until an acceptable fit is found. However, the solution is not unique due to the presence of data and modeling errors. Thus, to identify a plausible subset of solutions, constraints are invoked to reduce ambiguities and improve contextual reasonableness and computational efficiency. Popular inversion methods include trial-and-error testing of solutions, which is relatively effective with small numbers of unknowns [i.e., m≤5 -10] and observations and for training inexperienced investigators on the data's interpretation limits. For more complex inversions involving larger numbers of unknowns and observations, the matrix and spectral analysis methods are commonly implemented.