USING A MATHEMATICAL MODEL TO HELP EXPLAIN OBSERVED STRAIN PATTERNS WITHIN THE MOINE THRUST ZONE, NW SCOTLAND

A salient-recess pair in the Moine thrust exhibits significant lateral variation in the strain patterns recorded in the footwall. In particular, the recess shows evidence for higher strain values and a larger, non-plane strain, flattening component to the deformation (i.e., lower Flinn’s k-values) than the adjoining salient. Additionally, some deformed grains are observed to have their long axes oriented perpendicular to the regional transport direction in this area. To help explain these features, we have developed a kinematics-based mathematical model of thrust sheet deformation.

We model the deformation of a thrust-perpendicular line of particles within a thrust sheet as the sheet is transported along the thrust surface. With each increment of deformation, an individual point experiences a horizontal contraction strain, vertical gravitational strain, fault normal reaction strain, fault parallel simple shear, and a component of slip. The relative amount of each of these components (except slip which is constant) is dependent on the position of that point. The model simulates particle path as well as strain path within a thrust sheet. It predicts an increase in strain magnitude as well as non-plane strain flattening in the vicinity of increased fault dip which corresponds to the recess within the Moine thrust zone.

The effects of lateral boundary condition strains can also be incorporated into the model. Without a lateral confining strain, much of the thrust sheet would experience transport-perpendicular, maximum extension. If the lateral confining strain is exceedingly high then all of the deformation will be plane strain. The model suggests that with lateral confining strains of approximately twice the total strain there is still the possibility of the existence of transport-perpendicular lineations where there is a local increase in the fault dip. Furthermore, the model suggests that areas within thrust sheets that are most likely to develop perpendicular lineations do not always coincide with areas of maximum transport-perpendicular motion. The model results are consistent with observations in the Moine thrust zone, suggesting that such models are useful in predicting strain paths and local strain variations within thrust sheets.