Inverse Methods and Uncertainties in Stratigraphy and Basin Analysis

Abstract

Quantitative models are often constructed in attempts to uncover the evolution of stratigraphic and basinal systems from present-day data. These models contain parameters related to the imposed boundary and initial conditions, as well as intrinsic parameters connected to the intrinsic evolution of the systems through equations of state taken to describe dynamical, chemical and flow processes. The use of inverse methods to determine these parameters is often undertaken by optimizing the model development in order to minimize the disagreement of the model with observations. We show here that several methods of optimization are possible, and we compare and contrast their intrinsic assumptions and relative numerical speeds. The problems of finite data sampling, with uncertainty of precision, accuracy, sensitivity and sampling frequency and distribution also play a major role in attempting to obtain the parameters required. In addition, different choices of control functions chosen for the minimization are shown to lead to different optimum parameter values, so that there is also a uniqueness problem in any inverse method chosen. The three methods considered here are simulated annealing, genetic algorithms, and the fast path tomographic method. Newton line search methods and Simplex solvers are also mentioned, but they are already known to be very much slower than any of the other three methods. The implications of the investigation reported here are that extreme care must be exercised in using data, models, and methods in attempts to uncover the evolution of a system. Failure to be absolutely sharp in what is being done can easily lead to overstating the results of an inverse method beyond its level of ability to resolve the problem. And the manner in which a problem fails to be resolved is also one of the crucial factors to be determined from any inverse method applied to such problems.