Kinematic modeling of cross‐sectional deformation sequences by computer simulation

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.

Un modèle cinématique discret de déformation 3D d'un bassin sédimentaire

“…Pour ce faire, le point est translaté sur une droite parallèle au support, et à distance constante du support. Le maintien de cette distance est réalisé par l'introduction des plans bissecteurs du support (l'équiva-lent des kinks du modèle de Contreras et Sutter [12]) et par le système d'équations paramétriques décrit ci-dessous. Dans un premier temps, on calcule la distance du milieu d'arête M avec le point d'intersection du plan médiateur I. Soient la projection de sur le plan du support P S suivant la normale à P S , et P med le plan médiateur, tels que :…”

“…L'approche cinématique décrite ici permet de reconstituer un chemin de déformation géologiquement acceptable, prenant en compte une évolution incrémentale dans le temps, contrairement à des logiciels de dépliage du type Unfold [10] ou Patchwork [11] qui déplient instantané-ment. Jusqu'alors, les principaux travaux sur des modèles cinématiques ont été effectués en deux dimensions [12][13][14][15][16][17][18][19]. Par la suite, quelques modèles ont proposé des solutions « pseudo-3D ».…”

A geologically-sound representation for evolutionary multi-objective subsurface identification

“…The use of kink-band style folding with non-deforming footwalls (characteristic of such geometric models) has been criticized by Ramsay (1991) as being unrealistic. Another fault-bend folding model was proposed by Contreras and Suiter (1990), however it was also based on the conservation of area. Since their introduction, these geometric models have received a lot of attention (Medwedeff, 1989; Jordan et al, 1993) and have been used extensively to predict thrust fault geometries at depths based on observed fold geometries.…”

“…Contreras and Suiter (1990), kink model is used for the deformation of the model from the initial state to final state. After deformation, dip and fault location parameters are evaluated for optimization purpose.…”

“…This model also considers fault parallel simple shearing. A complete derivation Contreras fault bend folding (FBF) was provided by Contreras and Suiter (1990). The heterogeneity of the displacement vector field across axial planes introduces longitudinal and angular shear strains.…”