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Yakovlev Fedor



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FOLDING formation research




about the study of folded structures of several scale levels into thin-layered flysch-like sediments in a Hinterland



Folder 13. Retro-deformation for linear folding structures in cross-section (core of method) (ranks 3, 5) since 1987.

Description.  The idea of ellipsoid of strain (ellipse for 2D strain in case of linear folding) is used for the restoration of prefolded state of cross-section. Cross-section is divided to set of domains and three parameters of domain geometry measured (Fig. 1): axial surface dip inclination (AX), envelope dip inclination (EN), shortening of folds (SH) (see folders 6, 7). The domains part of cross-section line measured also as length and it angle of tilting. Three cinematic operations (Fig. 2) are used for transformation of ellipsoid to sphere (of ellipse to cycle): 1) rotation to horizontal position of envelope plane, 2) simple horizontal shearing to vertical position of axial plane and 3) pure shearing (horizontal extension) to folds disappearing (ellipse is transforming to cycle). Length of domains section line and it tilting have the same perturbations and new length of line and it tilting appear in horizontal prefolded layering. A consecutive junction of all domains is method of prefolded section restoration (Fig. 3). It is a single balancing sections method for hinterland structures now. The fault displacements may be calculated also (Fig. 4). Each fault plain is used as boundary of adjoining domains, of cause. The dip angle of fault plain should be measured for natural structure. It is assumed that this plain is part of domain and initial dip of plain may be calculated by the same three cinematic operations as for domain. Difference of stratigraphic levels between layers, which is contacting on fault on its sides, is vertical displacement. The horizontal displacement is calculating as function of vertical shift and initial dip of fault plain.

Publications. First publication of core of method is paper (Yakovlev F.L. A Study of the Kinematic, 1987, pages 319-320; PDF, N 3 in List-En,). The explanation of computer program was made in (Yakovlev F.L. Investigation of the processes , 2002, pages 323-325; PDF-R, N 12 in List-En,). Full new description has published in (Yakovlev F.L. Reconstruction of Linear Fold Structures , 2009, pp. 10231034. [in Russian, in English]. PDF-en N 36 in List-En)

Materials. There are computer program for recent section visualization (for each domain) and it transformation to prefolded state and it visualization also. The measurements of domain geometry are used as txt-files. Test examples exist for theoretic and natural; structures. Let me know about your interest by e-mail. *:

Fig. 1. The domain parameters: 1 horizontal plain, 2 envelope plain dip, 3 axial plain dip, 4 ellipsoid of strain for domain isometric layering rocks volume

Fig. 2. Three cinematic operations from recent state (1) to ptefolded one (4). A rotation up to horizontal position of envelope plain, B simple shearing up to vertical position of axial plain, C elongation (pure shearing) up to folds disappearing (ellipse became circl)

Fig. 3. (to right upper) The PC-program procedures and testing. Upper section: 10 domains were transformed by convection (1-st stage) and flattening 50% (2-nd stage). Last two domains parameters as measured (black) and restored (three lower blue lines) and total resume are shown in table. Restored prefolded states of domains as common structure are shown at lower section. The goal prefolded length of 10000 was calculated as 9906 with the error near 1%.

Fig. 4. The natural folded structure section (part of section number 7, North-West Caucasus) after measurements of domain parameters and construction by PC-program. Upper section recent structure,
including faults, colors of domains are conventional only. Lower section is prefolded state. One scale mark of vertical and horizontal axes is 1500 meters.

2009, ,