Determining the uniqueness of best-fit trishear models

Abstract

We show the application of a simulated annealing algorithm to trishear inverse modeling. The algorithm traverses the parameter space in search for best-fit models without being trapped in local minima, and thus sampling for more possible solutions globally. Simulated annealing is a robust and efficient technique to determine the uniqueness of best-fit trishear models; the spread of possible trishear models that can fit a structure. We first apply the algorithm to a decameter-size, contractional fault-propagation fold in west-central Taiwan, for which there is an exceptional exposure of pre-growth and growth strata. Simulated annealing shows that even for this complete fold dataset with low uncertainties, there is a range of models and fault slip/uplift histories that can fit the data, with the consequent implications for the assessment of seismic hazard. We then apply the algorithm to a kilometer-size, extensional fault-propagation fold, the Hadahid monocline, Gulf of Suez Rift, Egypt. In this monocline there is only surface coverage in the footwall anticline areas and the algorithm was used to delimit the range of possible models that can fit the data and their uncertainties, thus avoiding biases in the interpretation. Simulated annealing suggests that the along-strike structural variability of the monocline can result from along-strike variability in fault slip, fault propagation to fault slip ratio and depth of fault nucleation. Both examples illustrate the benefits of searching for a possible range of models rather than a precise best-fit model when modeling fault-propagation folds. In an attempt to understand which parameters control fault development, and also how the spread of possible solutions varies with fold growth, we apply the algorithm to four sequential stages of a published, analog clay model of an extensional forced fold. The inversions of the natural examples and the analog model suggest that the spread of the possible models is a manifestation of the data uncertainties, the suitability of the trishear model, fold evolution, and rock mechanical properties.