Abstract
Given the wealth of data concerning the kinematics of deforming fold-thrust belts (FTBs), first-order generalizations about how the major strain components vary within a deforming thrust wedges are considered. These generally observed strain patterns are used to constrain a general, kinematics-based, FTB-wedge model. We considered five strain components within a deforming thrust sheet: (1) thrust-parallel simple shear, (2) horizontal contractional strain, (3) thrust-normal reaction strain, (4) gravitational strain, and (5) a lateral confining boundary condition. After making assumptions about how these strain components vary within a model FTB-wedge, the incremental deformation matrix can be calculated for any given point within the deforming wedge. Thus, the material path of a given marker can be determined and an initially spherical marker’s strain path can be calculated as it moves through the deforming wedge. Furthermore, by illustrating various kinematic parameters of many initially spherical markers (for example, Flinn’s k-value, incremental octahedral shear strain, transport-perpendicular stretch), we have assembled representations of the kinematic properties of the entire model wedge. By including a flat-ramp-flat fault surface geometry for the model wedge, we are able to examine the kinematic effects of this relatively common structural geometry. Within the fault ramp segment there are greater incremental strain magnitudes, out-of-the-plane motion, and flattening strains. Additionally, data from this model suggests that gravitational strains potentially have a significant effect on the strain distribution within a deforming thrust wedge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bowen RM (1989) Introduction to continuum mechanics for engineers. Plenum Press, New York, 261 p
Chapple WM (1978) Mechanics of thin-skinned fold-and-thrust belts. Geol Soc Am Bull 81:1189–1198
Coward MP (1988) The Moine thrust and the Scottish Caledonides. In: Mitra G, Wojtal S (eds) Geometries and mechanisms of thrusting, with special reference to the Appalachians. Geol Soc Am Spec Paper, vol 222, pp 1–15
Coward MP, Kim JH (1981) Strain within thrust sheets. In: McClay KR, Price (eds) Thrust and nappe tectonics, Special publication geological society London, vol 9, pp 275–292
Davis D, Suppe J, Dahlen F (1983) Mechanics of fold-and-thrust belts and accretionary wedges. J Geophys Res B 88:1153–1172
DeCelles PG, Mitra G (1995) History of the Sevier orogenic wedge in terms of critical taper models, northeast Utah and southwest Wyoming. Geol Soc Am Bull 107(4):454–462
Donath FA (1970) Some information squeezed out of rock. Am Sci 58:54–72
Durney DW, Ramsay JG (1973) Incremental strains measured by syntectonic crystal growth. In: DeJong KA, Scholten R (eds) Gravity and tectonics. Wiley, New York, pp 67–96
Erickson SG, Jamison WR (1995) Viscous-plastic finite-element models of fault-bend folds. J Struct Geol 17:561–573
Flinn D (1962) On folding during three-dimensional progressive deformation. Q J Geol Soc Lond 118:385–433
Fossen H, Tikoff B (1993) The deformation matrix for simultaneous pure shear, simple shear, and volume change, and its application to transpression/transtension tectonics. J Struct Geol 15:413–425
Geiser PA (1988) The role of kinematics in construction and analysis of geological cross sections in deformed terranes. In: Mitra G, Wojtal S (eds) Geometries and mechanisms of thrusting, with special reference to the Appalachians. Geol soc Am spec paper, vol 222, pp 47–76
Gilotti JA (1992) The rheologically critical matrix in arkosic mylonites along the Särv Thrust, Swedish Caledonides. In: Mitra S, Fisher GW (eds) Structural geology of fold and thrust belts (the Elliott volume). Johns Hopkins University Press, Baltimore, pp 145–160
Gilotti JA, Kumpulainen R (1986) Strain softening induced ductile flow in the Särv thrust sheet, Scandinavian Caledonides. J Struct Geol 8:441–455
Gleason GC, Tullis J (1995) A flow law for dislocation creep of quartz aggregates determined with the molten salt cell. Tectonophysics 247:1–23
Gray MB, Mitra G (1999) Ramifications of four-dimensional progressive deformation in contractional mountain belts. J Struct Geol 21:1151–1160
Griggs DT, Turner FJ, Heard HG (1960) Deformation of rocks at 500° to 800°C. In: Griggs DT, Handin J (eds) Rock deformation. Geol soc of Am memoir, vol 79, pp 39–104
Gwinn V (1970) Kinematic patterns and estimates of lateral shortening, Valley and Ridge and Great Valley provinces, central Appalachians, south-central Pennsylvania. In: Studies of Appalachian geology, central and southern. Interscience, New York, pp 127–146
Handin J, Hager RV Jr, Friedman M, Feather JN (1963) Experimental deformation of sedimentary rocks under confining pressure: pore pressure tests. Am Assoc Pet Geol Bull 47:717–755
Holdsworth RE (1990) Progressive deformation structures associated with ductile thrusts in the Moine Nappe, Sutherland, N. Scotland. J Struct Geol 12:443–452
Hossack JR (1967) Pebble deformation and thrusting in the Bygdin Area (southern Norway). Tectonophysics 5:315–339
Hsu TC (1966) The Characteristics of coaxial and non-coaxial strain paths. J Strain Anal 1:216–222
Jiang D, Williams PF (1998) High-strain zones; a unified model. J Struct Geol 20:1105–1120
Kwon S, Mitra G (2004) Three-dimensional finite-element modeling of a thin-skinned fold-thrust belt wedge; Provo Salient, Sevier Belt, Utah. Geology 32(7):561–564
Law RD (1987) Heterogeneous deformation and quartz crystallographic fabric transitions: natural examples from the Moine Thrust zone at the Stack of Glencoul, northern Assynt. J Struct Geol 9:819–834
Lin S, Jiang D, Williams PF (1998) Transpressional (or transtensional) zones of triclinic symmetry: natural example and theoretical modelling. In: Holdsworth RE, Strachan RA, Dewey JF (eds) Continental transpressional and transtensional tectonics. Special publication of the geological society of London, vol 135, pp 41–57
Means WD (1976) Stress and strain: Basic concepts of continuum mechanics for geologists. Springer, New York, 339 pp
Mitra G (1979) Ductile deformation zones in the Blue Ridge basement rocks and estimation of finite strains. Geol Soc Am Bull 90:935–951
Mitra G (1994) Strain variation in thrust sheets across the Sevier fold-and-thrust belt (Idaho–Utah–Wyoming): implications for section restoration and wedge taper evolution. J Struct Geol 16(4):585–602
Mitra G (1997) Evolution of salients in a fold-and-thrust belt: the effects of sedimentary basin geometry, strain distribution and critical taper. In: Sengupta S (ed) Evolution of geological structures from macro- to micro- scales. Chapman and Hall, London, pp 59–90
Mukul M, Mitra G (1998) Finite strain and strain variation analysis in the Sheeprock thrust sheet: an internal thrust sheet in the Provo salient of the Sevier fold-and-thrust belt, Central Utah. J Struct Geol 20:403–417
Nadai A (1963) Theory of flow and fracture of solids. Engineering societies monographs. McGraw-Hill, New York, 705 pp
Price RA (1981) The Cordilleran foreland thrust and fold belt in the southern Canadian Rocky Mountains. In: Price NJ, McClay KR (eds) Thrust and nappe tectonics. Geological society of London special publication, vol 9, pp 427–428
Ramberg H (1975) Particle paths, displacement and progressive strain applicable to rocks. Tectonophysics 28:1–37
Ramsay JG (1967) Folding and Fracturing of Rocks. McGraw-Hill, New York, 568 p
Ramsay JG, Graham RH (1970) Strain variations in shear belts. Can J Earth Sci 7:786–813
Ramsay JG, Huber MI (1983) The techniques of modern structural geology, vol 1. Academic Press, London, 462 p
Smart KJ, Kreig RD, Dunne WD (1999) Deformation behavior during blind thrust translation as a function of fault strength. J Struct Geol 21:855–874
Strayer LM, Hudleston PJ (1997) Simultaneous folding and faulting and fold-thrust belt evolution. In: A distinct element model. Geol. soc. of Am. abstracts with programs, vol 29/6, p A44
Strayer LM, Hudleston PJ (1998) Controls of duplex formation: results from numerical models. Geol soc of Am abstracts with programs, vol 30/7, p A42
Strayer LM, Suppe J (2002) Out-of-plane motion of a thrust sheet during along-strike propagation of a thrust ramp; a distinct-element approach. J Struct Geol 24(4):637–650
Strine M, Mitra G (2004) Evidence for non-plane strain flattening along the Moine thrust, Loch Srath nan Aisinnin, northwest Scotland. J Struct Geol 26:1755–1772
Strine M, Wojtal S (2004) Evidence for non-plane strain flattening along the Moine thrust, Loch Strath nan Aisinnin, northwest Scotland. J Struct Geol 19:1755–1772
Tikoff B, Fossen H (1993) Simultaneous pure and simple shear: the unifying deformation matrix. Tectonophysics 217:267–283
Twiss RJ, Unruh JR (1998) Analysis of fault-slip inversions: Do they constrain stress or strain rate. J Geophys Res 103:12,205–12,222
White SH, Evans DJ, Zhong DL (1982) Fault rocks of the Moine thrust zone; microstructures and textures of selected mylonites. Textures Microstruct 5:33–61
Willet (1992) Dynamic and kinematic growth and change of a Coulomb wedge. In: McClay KR (ed) Thrust tectonics. Chapman and Hall, London, pp 19–31
Willet (1999) Orogeny and orography: The effects of erosion on the structure of mountain belts. J Geophys Res 104:28,957–28981
Author information
Authors and Affiliations
Corresponding author
Additional information
M. Mookerjee is formerly Matthew Strine.
Rights and permissions
About this article
Cite this article
Mookerjee, M., Mitra, G. Kinematics-Based Mathematical Model for Deforming Thrust Wedges. Math Geosci 40, 249–275 (2008). https://doi.org/10.1007/s11004-008-9149-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-008-9149-5