Stratigraphic Inversion Using a Genetic Algorithm: Lessons About Non-Uniqueness

Cornel Olariu¹ and John F. Ferguson^2
1 University of Texas at Austin, Austin, TX
² University of Texas at Dallas, Richardson, TX

Quantitative predictions of geological data can be made for a number of important sedimentary environments. These approximate and ad hoc models are difficult to verify and validate. An important problem involves the fitting of model parameters to geologic data. Inverse modeling is a widespread practice in geophysics, which produces estimates of model parameters from observed data. The primary interest is the non-uniqueness of inverse models; any given data can be fit to a range of model parameters. This paper presents an analysis of non-uniqueness in the inversion of a river delta model. Usually inversion procedures are cast in the form of optimization problems with respect to data misfit. The data misfit can be measured by correlation of a synthetic well log with an observed well log. The inverse problem for the delta model can be solved by application of a genetic algorithm to maximization of well log correlation. Non-uniqueness is explored by the creation of a large number of optimal models. These models can be “linearly close” and parameters may simply “trade off” or they may cluster into distinct classes. A set of “known” parameters for the delta model is specified and bed thickness logs are computed at distinct locations. The genetic algorithm inversion generates hundreds of models, all of which produce similar logs. The models are then analyzed using cluster analysis, principal components analysis and graphic displays.