UNIFYING INCLINED SHEAR AND FLEXURAL SLIP

In structural balancing and restoration it is common to use an inclined shear algorithm when modeling regions that have undergone extension, and a flexural slip algorithm for regions that have experienced contraction. We have unified inclined shear and flexural slip into one algorithm for kinematic forward modeling of fault-bend folding. When modeling contraction, at each time step the cutoff and fault-bend angles are determined and the fault-bend fold equations are solved for the slip ratios and active-axial-surface (velocity-boundary) orientations. The folds produced conserve cross-sectional area, layer thickness, and line length. In cases where there is no solution to the fault-bend equations, such as large anticlinal bends or interfering kink bands, a minimum change in bed length is computed and cross sectional area is still conserved. The thrust sheets produced are quite realistic, typically parallel folds with localized bed thinning or thickening. When modeling extension the velocity boundary orientations are independently defined from fault shape, and the fault-bend folding equations are used to calculate slip ratios and the modeled structures conserve area. Realistic extensional fault-bend folds, such as rollover structures with growth, are produced.

The transformation at a fault bend is that of simple shear parallel to the velocity boundary with this orientation constituting a line of no elongation within the instantaneous strain ellipse. Thus when modeling extension this orientation is equivalent to inclined shear, with associated conservation of area. When modeling contraction the computation of the specific velocity boundary from the fault-bend folding equations is again an orientation no elongation and therefore also inclined shear, but a special case where the other orientation of no elongation is that of the folded bedding. Thus it is equivalent to flexural slip, conserving line length, layer thickness and area.

With this approach we can realistically model many structures that are difficult to achieve with previous algorithms, such as: gravity-driven systems with linked proximal extension and distal contraction in one section, rounded parallel folds in thrust sheets associated with curved thrusts and sections with spatially and temporarily varying inclined shear.