Abstract
Descriptions of the 3D geometry of ancient faults suggest that single, continuous normal faults have approximately elliptical tipline shapes, with (sub)horizontal major axes. However, many examples of normal faults are not continuous, but consist of distinct, overstepping segments. Individual segments may have complex shapes as well as a vertical height that exceeds the horizontal length. Where fault segments step laterally, their tiplines are relatively straight and steeply plunging. Tiplines in relays between vertically stepping normal fault segments are also relatively straight, but have a (sub)horizontal attitude. The fault shapes appear strongly related to the presence of neighboring faults and the positions of the fault segments relative to one another.
We evaluate these observations with quasi-static 3D boundary element models consisting of two frictionless, circular normal faults in a homogeneous, linearly-elastic medium, subjected to a uniform dip-slip stress drop. The local slip gradient at the fault tipline is used to calculate the propagation tendency. Mechanical interaction enhances fault propagation at levels where the faults underlap, but impede it where they overlap. For laterally echelon segments, the overlapped portion of the tipline is likely to become straighter, and approach parallelism with the slip vector. Such straight tiplines promote linkage of segments along a continuous line rather than at one or a few points. Also, the slip-parallel, steeply plunging attitude of the line of linkage tends to minimize kinematic constraints during simultaneous slip of adjacent segments. For vertically overlapping segments, horizontal relays are predicted. These relays are perpendicular to the slip vector and thus have a limited preservation potential.
These results suggest that normal faults may consist of a patchwork of segments, linked along lines parallel and perpendicular to the overall slip vector. Each segment in turn is likely to exist of a patchwork of smaller segments. Analysis of the propagation tendency suggests that the envelope of this whole patchwork of linked segments tends to re-establish a smooth elliptical tipline and a smooth distribution of total slip.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aki, K., Characterization of barriers on an earthquake fault, J. Geophys. Res, 84, 6140–6148, 1979.
Andrews, D.J., A Stochastic Fault model: 1. Static case, J. geophys. Res., 85, 3867–3877, 1980.
Aydin, A., and A.M. Johnson, Analysis of faulting in porous sandstones, J. Struct. Geol., 5, 19–31, 1983.
Aydin, A., and A. Nur, Evolution of pull-apart basins and their scale independence, Tectonics, 1, 91–105, 1982.
Aydin, A., and R.A. Schultz, Effect of mechanical interaction on the development of strike-slip faults with echelon patterns, J. Struct. Geol., 12, 123–129, 1990.
Barenblatt, G.I., Mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7, 55–129, 1962.
Barnett, J.M., J. Mortimer, J. Rippon, J.J. Walsh, and J. Watterson, Displacement geometry in the volume containing a single normal fault, Am. Assoc. Pet. Geol. Bull., 71, 925–937, 1987.
Becker, A.A., The boundary element method in engineering, 337 pp., McGraw-Hill Book Company, 1992.
Bouvier, J.D., C.H. Kaars-Sijpesteijn, D.F. Kluesner, C.C. Onyejekwe, and R.C. Van Der Pal, Three-Dimensional Seismic Interpretation and Fault Sealing investigations, Nun River Field, Nigeria, Am. Assoc. Pet. Geol. Bull., 73, 1397–1414, 1989.
Bürgmann, R., D.D. Pollard, and S.J. Martel, Slip distributions on faults: effects of stress gradients, inelastic deformation, heterogeneous host-rock stiffness, and fault interaction, J. Struct. Geol, 16, 1675–1690, 1994.
Childs, C, S.J. Easton, B.C. Vendeville, M.P.A. Jackson, S.T. Lin, J.J. Walsh, J. Watterson, Kinematic analysis of faults in a physical model of growth faulting above a viscous salt analogue, Tectonophysics, 228, 313–329, 1993.
Childs, D., J. Watterson, and J.J. Walsh, Fault overlap zones within developing normal fault systems, J. Geol. Soc. Lond., 152, 535–549, 1995.
Comninou, M.A., J. Dunders, The angular dislocation in a half-space, J. Elasticity, 5, 203–216, 1975. Cottrell, B., and J.R. Rice, Slightly curved or kinked cracks, Int. J. Fract., 16, 155–169, 1980.
Cowie, P.A., and C.H. Scholz, Physical explanation for the displacement-length relationship of faults, using a post-yield fracture mechanics model, J. Struct. Geol., 14, 1133–1148, 1992.
Cox, S.J.D., and C.H. Scholz, On the formation and growth of faults: an experimental study, J. Struct. Geol., 10, 413–430, 1988.
Crouch, S.L., A.M. Starheid, Boundary element methods in solid mechanics, 322 pp., George Allen & Unwin Ltc, London, 1983.
Cruikshank, K.M., G. Zhao, and A.M. Johnson, Duplex structures connecting fault segments in Entrada Sandstone, J. Struct. Geol., 13, 1185–1196, 1991.
Das, S., and K. Aki, Fault Plane with barriers: a versatile earthquake model, J. geophys. Res., 82, 5658–5670, 1977.
Davy, P., On the frequency-length distribution of the San Andreas Fault system, J. Geophys. Res., 98, 12141–12151, 1993.
Dawers, N.H., and M.H. Anders, Displacement-length scaling and fault linkage, J. Struct. Geol., 17 (5), 607–614, 1995.
Du, Y., and A. Aydin, The maximum distortional strain energy density criterion for shear fracture propagation with applications to the growth paths of en echelon faults, Geophys. Res. Let., 20, 1091–1094, 1993.
Du, Y., and A. Aydin, Shear fracture patterns and connectivity at geometric complexities along strike-slip faults, J. geophys. Res., 100, 18093–18102, 1995.
Dugdale, D.S., Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8, 100–104, 1960.
Gay, N.C., and W.D. Ortlepp, Anatomy of a mining-induced fault zone, Geol. Soc. Am. Bull., 90, 47–58, 1979.
Gillespie, P.A., J.J. Walsh, and J. Watterson, Limitations of dimension and displacement data from single faults and the consequences for data analysis and interpretation, J. Struct. Geol., 14, 1157–1172, 1992.
Ida, Y., Cohsive force across the tip of longitudinal shear crack and Griffith’s specific surface energy, J. Geophys. Res., 77, 3796–3805, 1972.
Irwin, G.R., Analyses of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., 24, 361–364, 1957.
Jev, B.I., C.H. Kaars-Sijpesteijn, M.P.A.M. Peters, N.L. Watts, & J.T. Wilkie, Akaso Field, Nigeria: Use of integrated 3-D seismic, fault slicing, clay smearing, & RFT-pressure data on fault trapping & dynamic leakage, Am. Assoc. Pet. Geol. Bull., 77, 1389–1404, 1993. Jeyakumaran, M.,
J.W. Rudnicki, and L.M. Keer, Modeling slip zones with triangular dislocation elements, Seis. Soc. Am. Bull., 82, 2153–2169, 1992.
Kanamori, H., The nature of seismicity patterns before large earthquakes., in Earth-quake prediction: an international review, edited by D. Simpson, Richards, AGU Maurice Ewing Series, 1981.
Kronberg, P., Geometries of extensional fault systems, observed and mapped on aerial and satellite photographs of Central Afar, (Ethiopia/Djibouti), Geologie en Mijnbouw, 70, 145–161, 1991.
Larsen, P.H., Relay structures in a Lower Permian basement-involved extension system, East Greenland, J. Struct. Geol., 10, 3–8, 1988.
Lawn, B.R., and T.R. Wilshaw, Fracture of Brittle Solids, Cambridge University Press, Cambridge, 1975.
Li, V.C., Mechanics of shear rupture, in Fracture mechanics of rocks, edited by B.K. Atkinson, pp. 351–428, Academic Press, London, 1987.
Mandl, G., Discontinuous fault zones, J. Struct. Geol., 9, 105–110, 1987.
Mandl, G., Mechanics of Tectonic Faulting: Models & Basic Concepts, 407 pp., Elsevier, Amsterdam, 1988.
Mansfield, C.S., and J.A. Cartwright, High resolution fault displacement mapping from 3-D seismic data: evidence for dip-linkage during fault growth, J. Struct. Geol., 18, 249–263, 1996.
McGarr, A., D.D. Pollard, N.C. Gay, & W.D. Ortlepp, Observations & analysis of structures in exhumed mine-induced faults, in Conference VIII: Analysis of actual fault zones in Bedrock., pp. 101–120, USGS, Menlo Park, California, 1979.
Moore, D.E., and D.A. Lockner, The role of microcracking in shear-fracture propagation in granite, J. Struct. Geol, 17, 95–114, 1995.
Morley, C.K., R.A. Nelson, T.L. Patton, and S.G. Munn, Transfer zones in the East African rift system and their relevance to hycrocarbon exploration in rifts, Am. Assoc. Pet. Geol. Bull., 74, 1234–1253, 1990.
Muraoka, H., and H. Kamata, Displacement distribution along minor fault traces, J. Struct. Geol, 5, 483–495, 1983.
Nicol, A., J.J. Walsh, J. Watterson, and P.G. Bretan, Three-dimensional geometry and growth of conjugate normal faults, J. Struct. Geol., 17 (6), 847–862, 1995.
Nicol, A., J. Watterson, J.J. Walsh, and C. Childs, The shapes, major axis orientations and displacement patterns of fault surfaces, J. Struct. Geol., 18, 235–248, 1996.
Olson, J., Fracture Mechanics analysis of joints and veins, PhD thesis, Stanford University, 1991.
Olson, J.E., D.D. Pollard, Inferring stress states from detailed joint geometry, in Key questions in Rock Mechanics, edited by P.A. Cundall, R.L. Sterling, A.M. Starheid, pp. 159–167, Balkema, Rotterdam, 1988.
Olson, J.E., and D.D. Pollard, The initiation and growth of en echelon veins, J. Struct. Geol., 13, 595–608, 1991.
Palmer, A.C., and J.R. Rice, The growth of slip surfaces in the progressive failure of overconsolidated clay, Proc. Roy. Soc. Lond., A332, 527–548, 1973.
Paris, P.C., G.C. Sih, Stress analysis of cracks, in Fracture Toughness Testing, pp. 30–83, American Society for Testing Materials, Special Technical Publication, 1965.
Peacock, D.C.P., Displacement & segment linkage in strike-slip fault zones, J. Struct. Geol., 13, 1025–1035, 1991. Peacock, D.C.P., D.J. Sanderson, Displacements, segment linkage and relay ramps in normal fault zones, J. Struct. Geol., 13, 721–733, 1991.
Peacock, D.C.P., and D.J. Sanderson, Displacements, segment linkage and relay ramps in normal fault zones, J. Struct. Geol., 13, 721–733, 1991.
Peacock, D.C.P., and D.J. Sanderson, Geometry and development of relay ramps in normal fault systems, Am. Assoc. Pet. Geol. Bull., 78, 147–165, 1994.
Peacock, D.C.P., and D.J. Sanderson, Strike-slip relay ramps, J. Struct. Geol., 17, 1351–1360, 1995.
Peng, S., and A.M. Johnson, Crack growth and faulting in cylindrical specimens of Chelmsford granite, Int. J. Rock Mech. and Mining Sci., 9, 37–86, 1972.
Petit, J.P., and M. Barquins, Can natural faults propagate under mode-II conditions?, Tectonics, 7, 1243–1256, 1988.
Pollard, D.D., and A. Aydin, Propagation and linkage of oceanic ridge segments, J. Geophys. Res., 89, 10017–10028, 1984.
Pollard, D.D., S.D. Saltzer, and A.M. Rubin, Stress inversion methods; are they based on faulty assumptions?, J. Struct. Geol., 15, 1045–1054, 1993.
Pollard, D.D., P. Segall, Theoretical displacements and stresses near fractures in rock: with applications to faults, joints, veins, dikes, and solution surfaces, inFracture mechanics of rocks, edited by B.K. Atkinson, Academic Press, London, 1987.
Pollard, D.D., P. Segall, and P. Delaney, Formation and interpretation of dilatant echelon cracks, Bull. Geol. Soc. Am., 93, 1291–1303, 1982.
Rice, J.R., Mathematical analysis in the mechanics of fracture, in Fracture: An advanced treatise, edited by H. Liebowitz, pp. 191–311, Academic Press, San Diego, 1968.
Rice, J.R., Theory of precursory processes in the inception of earthquake rupture, Gerlands Beitrage Geophys., 88, 91–127, 1979.
Rippon, J.H., Contoured patterns of throw and hade of normal faults in the coalmeasures (Westphalian) of northeast Derbyshire, Proc. Yorks. Geol. Soc, 45, 147–161, 1985.
Rudnicki, J.W., Fracture mechanics applied to the earth’s crust, Ann. Rev. Earth Planet. Sci., 8, 489–525, 1980. Segall, P., D.D.
Pollard, Mechanics of discontinuous faults, J. Geophys. Res., 85 (B8), 4337–4350, 1980.
Segall, P., and D.D. Pollard, Nucleation and growth of strike slip faults in granite, J. Geophys. Res., 88, 555–568, 1983.
Shen, B., O. Stephansson, H.H. Einstein, B. Ghahreman, Coalescence of fractures under shear stresses in experiments, J. Geophys. Res., 100 (B4), 5975–5990, 1995.
Sih, G.C., Three Dimensional Crack Problems, 452 pp., Noordhoff International, Leiden, 1975.
Sneddon, I.N., The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc. Roy. Soc. London, Section A, 187, 229–260, 1946.
Tada, H., P.C. Paris, and G.R. Irwin, The Stress Analysis of Cracks Handbook, Paris Productions Incorporated (and Del Research Corporation), St. Louis, 1985.
Thomas, A.L., Poly3D: a three-dimensional, polygonal element, displacement discontinuity boundary element computer program with applications to fractures, faults, and cavities in the Earth’s crust, MSc thesis, Stanford University, 1993.
Thomas, A.L., and D.D. Pollard, The geometry of echelon fractures in rock: implications from laboratory and numerical experiments, J. Struct. Geol., 15, 323–334, 1993.
Walsh, J.J., and J. Watterson, Analysis of the relationship bewteen displacements and dimensions of faults, J. Struct. Geol., 10, 239–247, 1988.
Walsh, J.J., and J. Watterson, Displacement gradients of fault surfaces, J. Struct. Geol., 11 (3), 307–316, 1989.
Walsh, J.J., J. Watterson, Geometric and kinematic coherence & scale effects in normal fault systems, in The Geometry of Normal Faults, edited by A.M. Roberts, G. Yielding, B. Freeman, pp. 193–203, Geol. Soc. Lond. Spec. Publ., 1991.
Willemse, E.J.M., Segmented normal faults: correspondence between three-dimensionalmechanical models and field data, J. Geophys. Res., 102, 675–692, 1997.
Willemse, E.J.M., D.D. Pollard, and A. Aydin, 3D analysis of slip distributions along echelon normal fault arrays with consequences for fault scaling, J. Struct. Geol., 18, 295–309, 1996.
Williams, M.L. , On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24 (109–114), 1957.
Wong, T.F., On the normal stress dependency of the shear fracture energy, in Earthquake source mechanics, edited by S. Das, J. Boatwright, C.H. Scholz, pp. 1–12, AGU, Washingon, D.C., 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Willemse, E.J.M., Pollard, D.D. (2000). Normal fault growth: Evolution of tipline shapes and slip distribution. In: Lehner, F.K., Urai, J.L. (eds) Aspects of Tectonic Faulting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59617-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-59617-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64053-7
Online ISBN: 978-3-642-59617-9
eBook Packages: Springer Book Archive