A comparison of numerical surface topography calculations in geodynamic modelling: An evaluation of the 'sticky air' method

Geophysical Journal International

Volumn 189, Issue 1, 2012, Pages 38-54

  Crameri, F ^a   Schmeling, H ^b   Golabek, G J ^a,c   Duretz, T ^a   Orendt, R ^b   Buiter, S J H ^d,e   May, D A ^a   Kaus, B J P ^a,f   Gerya, T V ^a   Tackley, P J ^a  

^a ETH ZURICH   (Switzerland)

^b GOETHE UNIVERSITY   (Germany)

^c UNIVERSITÉ DE LYON   (France)

^d GEOLOGICAL SURVEY OF NORWAY   (Norway)

^e UNIVERSITY OF OSLO   (Norway)

^f JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Dynamics of lithosphere and mantle; Geomechanics; Numerical approximations and analysis; Numerical solutions; Tectonics and landscape evolution

Indexed keywords

AIR LAYERS; ANISOTROPIC DISTRIBUTION; CALCULATION METHODS; CHARACTERISTIC VISCOSITY; DIRECT CALCULATION; EULERIAN GRIDS; FINITE DIFFERENCE; FINITE ELEMENT TECHNIQUES; FREE SURFACES; FREE-SLIP; GEODYNAMIC MODELS; LAGRANGIAN TRACKING; LATERAL FLUCTUATIONS; LENGTH SCALE; LOW DENSITY; LOW VISCOSITY FLUIDS; NORMAL STRESS; NUMERICAL APPROXIMATIONS; NUMERICAL CODE; NUMERICAL PROBLEMS; NUMERICAL SOLUTION; PHYSICAL CONDITIONS; TIME-SCALES;

GEODYNAMICS; GEOMECHANICS; SURFACE TOPOGRAPHY; TECTONICS; TOPOGRAPHY;

NUMERICAL METHODS;

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; GEODYNAMICS; GEOMECHANICS; LANDSCAPE EVOLUTION; LITHOSPHERIC STRUCTURE; MANTLE STRUCTURE; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; TECTONIC EVOLUTION; TOPOGRAPHY;

EID: 84858616804     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2012.05388.x     Document Type: Article

References (50)

1. Balay, S. et al., 2008. PETSc Users Manual, Technical Report ANL-95/11 - Revision 3.0.0, Argonne National Laboratory,.
2. Beaumont, C., Fullsack, P. & Hamilton, J., 1994. Styles of crustal deformation in compressional orogens caused by subduction of the underlying lithosphere, Tectonophysics, 232(1-4), 119-132.
3. Blankenbach, B. et al., 1989. A benchmark comparison for mantle convection codes, Geophys. J. Int., 98(1), 23-38.
4. Braun, J., 2006. Recent advances and current problems in modelling surface processes and their interaction with crustal deformation, in Analogue and Numerical Modelling of Crustal-Scale Processes, Geol. Soc. Lond. Spec. Publ. Vol. 253, pp. 307-325, eds Uiter, S.J.H.B. & Schreurs, G., The Geological Society, London, doi:.
5. Braun, J. & Yamato, P., 2010. Structural evolution of a three-dimensional, finite-width crustal wedge, Tectonophysics, 484(1-4), 181-192.
6. Braun, J., Thieulot, C., Fullsack, P., DeKool, M., Beaumont, C. & Huismans, R., 2008. DOUAR: a new three-dimensional creeping flow numerical model for the solution of geological problems, Phys. Earth planet. Inter., 171(1-4), 76-91.
7. Burkett, E.R. & Billen, M.I., 2009. Dynamics and implications of slab detachment due to ridge-trench collision, J. geophys. Res., 114(B12), B12402, doi:.
8. Crook, A.J.L., Willson, S.M., Yu, J.G. & Owen, D.R.J., 2006. Predictive modelling of structure evolution in sandbox experiments, J. Struct. Geol., 28(5), 729-744.
9. Dabrowski, M., Krotkiewski, M. & Schmid, D.W., 2008. MILAMIN: MATLAB-based finite element method solver for large problems, Geochem. Geophys. Geosyst., 9(4), Q04030, doi:.
10. Duretz, T., May, D.A., Gerya, T.V. & Tackley, P.J., 2011. Discretization errors and free surface stabilization in the finite difference and marker-in-cell method for applied geodynamics: a numerical study, Geochem. Geophys. Geosyst., 12(7), Q07004, doi:.
11. Fuchs, L., Schmeling, H. & Koyi, H., 2011. Numerical models of salt diapir formation by down-building: the role of sedimentation rate, viscosity contrast, initial amplitude and wavelength, Geophys. J. Int., 186(2), 390-400.
12. Fullsack, P., 1995. An arbitrary Lagrangian-Eulerian formulation for creeping flows and its application in tectonic models, Geophys. J. Int., 120(1), 1-23.
13. Gerya, T.V. & Yuen, D.A., 2003a. Rayleigh-Taylor instabilities from hydration and melting propel 'cold plumes' at subduction zones, Earth planet. Sci. Lett., 212(1-2), 47-62.
14. Gerya, T.V. & Yuen, D.A., 2003b. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties, Phys. Earth planet. Inter., 140(4), 293-318.
15. Gurnis, M., Eloy, C. & Zhong, S., 1996. Free-surface formulation of mantle convection-II. implication for subduction-zone observables, Geophys. J. Int., 127(3), 719-727.
16. Hager, B.H., Clayton, R.W., Richards, M.A., Comer, R.P. & Dziewonski, A.M., 1985. Lower mantle heterogeneity, dynamic topography and the geoid, Nature, 313(6003), 541-546.
17. Harlow, F.H. & Welsh, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8(10), 2182-2189.
18. Hassani, R. & Chéry, J., 1996. Anelasticity explains topography associated with basin and range normal faulting, Geology, 24(12), 1095-1098.
19. Kaus, B.J.P. & Becker, T.W., 2007. Effects of elasticity on the Rayleigh-Taylor instability: implications for large-scale geodynamics, Geophys. J. Int., 168(2), 843-862.
20. Kaus, B.J.P., Steedman, C. & Becker, T.W., 2008. From passive continental margin to mountain belt: insights from analytical and numerical models and application to Taiwan, Phys. Earth planet. Inter., 171(1-4), 235-251.
21. Kaus, B.J.P., Mühlhaus, H. & May, D.A., 2010. A stabilization algorithm for geodynamic numerical simulations with a free surface, Phys. Earth planet. Inter., 181(1-2), 12-20.
22. King, S.D., 2009. On topography and geoid from 2-d stagnant lid convection calculations, Geochem. Geophys. Geosyst., 10(3), Q03002, doi:.
23. Koons, P.O., 1989. The topographic evolution of collisional mountain belts: a numerical look at the Southern Alps, New Zealand, Am J Sci, 289(9), 1041-1069.
24. Lavier, L.L., Buck, W.R. & Poliakov, A.N.B., 2000. Factors controlling normal fault offset in an ideal brittle layer, J. geophys. Res., 105(B10), 23431-23442.
25. McKenzie, D., 1977. Surface deformation, gravity anomalies and convection, Geophys. J. R. astr. Soc., 48(2), 211-238.
26. Melosh, H.J. & Raefsky, A., 1980. The dynamical origin of subduction zone topography, Geophys. J. R. astr. Soc., 60(3), 333-354.
27. Moresi, L., Dufour, F. & Mühlhaus, H.-B., 2003. A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials, J. Comput. Phys., 184(2), 476-497.
28. Moresi, L., Quenette, S., Lemiale, V., Mériaux, C., Appelbe, B. & Mühlhaus, H.-B., 2007. Computational approaches to studying non-linear dynamics of the crust and mantle, Phys. Earth planet. Inter., 163(1-4), 69-82.
29. Mühlhaus, H., BourgouL. & Hale, A., 2007. Free surface modeling based on level sets, ICCES, 3(4), 225-232.
30. Pelletier, D., FortA. & Camarero, R., 1989. Are FEM solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!), Int. J. Numer. Methods Fluids, 9(1), 99-112.
31. Poliakov, A. & Podladchikov, Y., 1992. Diapirism and topography, Geophys. J. Int., 109(3), 553-564.
32. Pysklywec, R.N., Beaumont, C. & Fullsack, P., 2000. Modeling the behavior of the continental mantle lithosphere during plate convergence, Geology, 28(7), 655-658.
33. Quinquis, M.E.T., Buiter, S.J.H. & Ellis, S., 2011. The role of boundary conditions in numerical models of subduction zone dynamics, Tectonophysics, 497(1-4), 57-70.
34. Quinteros, J., Ramos, V.A. & Jacovkis, P.M., 2009. An elasto-visco-plastic model using the finite element method for crustal and lithospheric deformation, J. Geodyn., 48(2), 83-94.
35. Ramberg, H., 1967. Gravity, Deformation, and the Earth's Crust: In Theory, Experiments and Geological Application, Academic Press, London, 214pp.
36. Samuel, H. & Evonuk, M., 2010. Modeling advection in geophysical flows with particle level sets, Geochem. Geophys. Geosyst., 11(8), Q08020, doi:.
37. Schenk, O. & Gärtner, K., 2004. Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener. Comput. Syst., 20(3), 475-487.
38. Schmeling, H. & Marquart, G., 1991. The influence of second-scale convection on the thickness of continental lithosphere and crust, Tectonophysics, 189(1-4), 281-306.
39. Schmeling, H. et al., 2008. A benchmark comparison of spontaneous subduction modelsâ-towards a free surface, Phys. Earth planet. Inter., 171(1-4), 198-223.
40. Tackley, P.J., 1993. Effects of strongly temperature-dependent viscosity on time-dependent, three-dimensional models of mantle convection, Geophys. Res. Lett., 20(20), 2187-2190.
41. Tackley, P.J., 2008. Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Phys. Earth planet. Inter., 171(1-4), 7-18.
42. Tackley, P.J. & King, S.D., 2003. Testing the tracer ratio method for modeling active compositional fields in mantle convection simulations, Geochem. Geophys. Geosyst., 4(4), 8302, doi:.
43. Turcotte, D. & Schubert, G., 2002. Geodynamics, 2nd edn, Cambridge University Press, New York, NY.
44. Weinberg, R.F. & Schmeling, H., 1992. Polydiapirs: multiwavelength gravity structures, J. Struct. Geol., 14(4), 425-436.
45. Willett, S.D., 1999. Orogeny and orography: the effects of erosion on the structure of mountain belts, J. geophys. Res., 104(B12), 28957-28981.
46. Zaleski, S. & Julien, P., 1992. Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs, Tectonophysics, 206(1-2), 55-69.
47. Zhong, S., 2002. Effects of lithosphere on the long-wavelength gravity anomalies and their implications for the formation of the Tharsis rise on Mars, J. geophys. Res., 107(E7), 5054, doi:.
48. Zhong, S. & Gurnis, M., 1992. Viscous flow model of a subduction zone with a faulted lithosphere: long and short wavelength topography, gravity and geoid, Geophys. Res. Lett., 19(18), 1891-1894.
49. Zhong, S., Gurnis, M. & Hulbert, G., 1993. Accurate determination of surface normal stress in viscous flow from a consistent boundary flux method, Phys. Earth planet. Inter., 78(1-2), 1-8.
50. Zhong, S., Gurnis, M. & Moresi, L., 1996. Free-surface formulation of mantle convection-I. Basic theory and application to plumes, Geophys. J. Int., 127(3), 708-718.