Kinematic modeling of cross‐sectional deformation sequences by computer simulation

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Abstract
We derive a kinematic algorithm which permits simulation of postulated cross‐sectional deformation sequences in sedimentary rocks affected by faulting, fault‐related folding, and simple shear. The transformations are to a more deformed state and are formulated analytically in terms of the less deformed configuration (forward modeling, Lagrangian description). The medium is subdivided into domains of constant dip and homogeneous displacement vector fields which are delimited by the axial planes of the fault inflections. The displacement trajectory is of constant length for all the displaced particles throughout the medium and parallel to the underlying active fault segment. As a consequence, the deformation path is continuous but not smooth and causes an angular style of parallel folding, except at the deformation front where the layer thickness is not conserved. The inhomogeneity of the displacement vector field across axial planes introduces longitudinal and angular shear strains, whereas the area of the medium remains constant. These strains, which are superposed on the externally applied simple shear, make the mapping transformation unconformal. We define the stratigraphic layering of the undeformed medium by an approximating body of finite quadrilateral elements, evaluate the defined displacement functions for the grid nodes, and graph the deformed mesh. Eventually, we create with the algorithm synthetic deformation sequences for simple boundary conditions and try in a specific case study to match the resulting synthetics with the available observational and experimental data.