Restoration and balance of complex folded and faulted rock volumes: Flexural flattening, jigsaw fitting and decompaction in three dimensions

G. D. Williams, S. J. Kane, T. S. Buddin, and A. J. Richards, 'Restoration and balance of complex folded and faulted rock volumes: flexural flattening, jigsaw fitting and decompaction in three dimensions', Tectonophysics, Vol. 273, Issues 3-4, May 1997, pp. 203-218, DOI: https://doi.org/10.1016/S00040-1951 (96) 00282-X Copyright © 1997 Published by Elsevier B. V.Techniques of two-dimensional bed length and cross-sectional area restoration are extended into true, three-dimensional (3-D) restorations using the preservation of areas of individual surfaces plus conservation of volume between surfaces. The flexural flattening technique involves the restoration of a complexly folded surface to a horizontal plane while conserving surface area and minimising finite strain. Multiple surfaces showing superimposed non-co-axial folding may be restored using the flexural flattening method applied to successively deeper surfaces. In the process of sequential restoration, volumes between the uppermost flattened surface and underlying surfaces are preserved and therefore the method is volume-balanced. The jigsaw fit of footwall and hangingwall cut-offs of each flattened surface, in map view, provides a unique restoration solution based on a unique translation and/or rotation of the hangingwall block. Flexural flattening and jigsaw fit performed sequentially on successively deeper surfaces in a three-dimensional model may incorporate removal of the uppermost layer and three-dimensional decompaction at each restoration step. The method is applied to a synthetic 3-D growth fault structure which has been produced using multiple discrete slip vectors and bulk simple shear hangingwall deformation.Peer reviewe

A sensitivity analysis of 3-dimensional restoration techniques using vertical and inclined shear constructions

T. S. Buddin, S. J. Kane, G. D. Williams, and S. S. Egan, 'A sensitivity analysis of 3-dimensional restoration techniques using vertical and inclined shear constructions', Tectonophysics, Vol. 269, Issues 1-2, January 1997, pp. 33-50, DOI: http://doi.org/10.1016/S0040-1951 (96) 00099-6. © 1997 Elsevier Science B. V.The restoration of cross sections in extensional settings is commonly carried out with simple shear constructions which use either vertical or inclined shear geometrical construction techniques. These techniques assume plane strain and that the X and Z principal finite strain axes are contained within the plane of the cross-section. In 2-dimensional balanced cross sections the displacement vector is, of necessity, assumed to be in the plane of the section. In 3-dimensional restoration the main components are the horizontal displacement vector (heave), the deformation plane that contains the X and Z principal strain axes in plane strain deformation and the vertical/inclined shear angle (shear pins) parallel to which the hanging wall deforms during translation. During 3-dimensional restoration it is possible to vary the orientation of the displacement vector and shear pins in both azimuth and plunge. We can therefore test the sensitivity of artificial models, or natural examples, to variation in restoring parameters. The examples used here show that restorations are extremely sensitive to the shear angle chosen for the hanging wall, and in the case of an oblique ramp model and a natural fault example, to the movement direction assumed for the restoration. Using map view visualisation of faulted hanging-wall surfaces it is possible to obtain a good estimate of the original slip vector which would not be apparent from 2-D sections by matching hanging-wall and footwall cut-offs. Using this 3-D approach it is possible to minimise errors in restoration which result from erroneous restoring slip vectors. Any information on the angle of simple shear deformation of the hanging wall during deformation should be used when restoring the 3-D surface or cross-section.Peer reviewe

Computer modelling and visualisation of the structural deformation caused by movement along geological faults

S. S. Egan, S. Kane, T. S. Buddin, G. D. Williams, and D. Hodgetts, 'Computer modelling and visualisation of the structural deformation caused by movement along geological faults', Computers & Geosciences, Vol. 25 (3): 283-297, April 1999, doi: http://doi.org/10.1016/S00098-3004(98)00125-3 Copyright © 1999 Elsevier Science Ltd. All rights reserved.The computer modelling and visualisation of deformation caused by movement along faults has enhanced our understanding of the evolution of fault-related structures in the geological record. In particular, the development of computer software to carry out structural restoration and section balancing has provided earth scientists with an effective tool for validating structural interpretations constructed from geological and geophysical data. This paper describes both two- and three-dimensional geometric methods for modelling hanging wall deformation in response to fault movement. Equations are presented for the definition of two-dimensional fault geometries and for the determination of hanging wall geometry following movement over these faults. The Chevron and inclined shear constructions and fault-bend fold theory are described in a format to enable easy conversion into computer algorithms. The modelling of fault movement in three-dimensions is also considered in the context of the Chevron construction. Schematic models are presented which show hanging wall deformation caused by extensional, compressional and, most importantly, strike-slip movement over a complex fault surface. In addition, a new geometric technique for the restoration of deformed hanging wall surfaces is described. This technique has been called flexural flattening and involves flattening a surface represented as a mesh of triangles, back to horizontal. It has the advantages of maintaining the area of the surface before and after restoration and is relatively simple to apply in comparison to three-dimensional implementations of existing geometric methods.Peer reviewe