INVERSE TRISHEAR MODELING OF BEDDING DIP DATA

A new method for inverse trishear modeling of bedding dip data is presented, and its capabilities and limitations are tested using synthetic and real data sets. Trishear is a model for fault-propagation fold kinematics that is able to reproduce fold shapes not adequately represented by kink-band models, but which requires numerical solution in order to fit a model to data. Where the geometry of an entire folded bed is known from seismic or outcrop data, the trishear model can be used to restore the bed to its prefolding orientation; this method can be used with a variety of inversion techniques to determine the best-fitting model parameters. When data consist only of surface measurements of bedding attitudes and contact locations, however, previous approaches have relied on the forward modeling of entire beds in order to match these surface data. We present an algorithm, using equations derived from the strain rate tensor for the trishear velocity field, for the direct restoration of dip data to their pre-folding values for comparison with an expected regional dip. By using the misfit between model and data to calculate a probability, dips and contact locations can be used together to calculate a best-fit model and to reconstruct the probability density functions for different model parameters. We demonstrate this approach using both grid search and Metropolis-Hastings algorithms. Tests on a synthetic cross-section show that the method is capable of identifying the correct best-fit model, but that the resulting probability density function is frequently multimodal. Dip or contact data alone are insufficient to uniquely identify the original model parameters of the test section, but when used together, they are able to constrain the model. The model also becomes much better constrained if one or more of the six trishear parameters to be fit is known ahead of time. In particular, fault ramp angle is difficult to identify from forelimb dip data alone, but if known allows the rest of the model parameters to be more confidently determined. The model is applied to a real-world example from the North Canterbury Fold and Thrust Belt of New Zealand, where two possible models that fit the data are identified.