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Earth, Planets and Space

, Volume 50, Issue 11–12, pp 1055–1065 | Cite as

Synthetic tests of geoid-viscosity inversion: A layered viscosity case

Open Access
Article

Abstract

We revisited the resolving power of viscosity inversion in terms of geoid misfit in a 2-D Cartesian geometry under the assumption that the mantle viscosity is laterally stratified. Firstly, we considered a simple case of two viscosity layers only, which is described by two parameters of the amount and the depth of the viscosity jump. The uniqueness of the inversion was examined by evaluating misfits between the reference geoid for a reference viscosity and that for a viscosity described by the changing two parameters. The misfits are mapped into 2-D model space as a function of the two parameters. Three types of density distribution are tested; they are vertically constant (1), taken from a tomographic model (2), and the same but includes artificial noise (3). We found that, at least for this simple case, the viscosity solution keeps unique in the entire 2-D model space using whole degree band (1–8) of geoid. This holds even if the artificial noise is rather large (70%), though the solution is slightly different from the reference viscosity. However, we also observed non-uniqueness, such as trade-off between the two parameters, when individual degree components of geoid are concerned. In the next, we employed a more realistic viscosity structure, having seven iso-viscous layers. It is no longer possible to describe 6-D model space easily. Therefore we tried to reconstruct a reference viscosity from the reference geoid using genetic algorithm search. According to this analysis, nearly the same solution with the reference viscosity can be reconstructed, while solutions apart from the reference viscosity with increase of noise in the density distribution.

Keywords

Model Space Density Anomaly Synthetic Test Mantle Viscosity Tomographic Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Čadek, O., Y. Ricard, Z. Martinec, and C. Matyska, Comparison between Newtonian and non-Newtonian flow driven by internal loads, Geophys. J. Int., 112, 103–114, 1993.CrossRefGoogle Scholar
  2. Čadek, O., H. Čížková, and D. A. Yuen, Can longwavelength dynamical signatures be compatible with layered mantle convection?, Geophys. Res. Lett., 24, 2091–2094, 1997.CrossRefGoogle Scholar
  3. Corrieu, V., C. Thoraval, and Y. Ricard, Mantle dynamics and geoid Green functions, Geophys. J. Int., 120, 516–523, 1995.CrossRefGoogle Scholar
  4. Doin, M.-P., L. Fleitout, and D. P. McKenzie, Geoid anomalies and the structure of continental and oceanic lithospheres, J. Geophys. Res., 101, 16119–16135, 1996.CrossRefGoogle Scholar
  5. Forte, A. M. and W. R. Peltier, Viscous flow models of global geophysical observables 1. Forward problems, J. Geophys. Res., 96, 20131–20159, 1991.CrossRefGoogle Scholar
  6. Forte, A. M. and W. R. Peltier, The kinematics and dynamics of poloidal-toroidal coupling in the mantle flow: The importance of surface plates and lateral viscosity variations, Adv. Geophys., 36, 1–119, 1994.CrossRefGoogle Scholar
  7. Forte, A. M. and R. L. Woodward, Global 3D mantle structure and vertical mass and heat transfer across the mantle from joint inversions of seismic and geodynamic data, J. Geophys. Res., 102, 17981–17994, 1997.CrossRefGoogle Scholar
  8. Forte, A. M., R. L. Woodward, and A. M. Dziewonski, Joint inversions of seismic and geodynamic data for models of three-dimensional mantle heterogeneity, J. Geophys. Res., 99, 21857–21877, 1994.CrossRefGoogle Scholar
  9. Forte, A. M., A. M. Dziewonski, and R. J. O’Connell, Thermal and chemical heterogeneity in the mantle: A seismic and geodynamic study of continental roots, Phys. Earth Planet. Inter., 92, 45–55, 1995.CrossRefGoogle Scholar
  10. Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, pp. 412, Addison-Wesley Publishing Company, Inc., 1989.Google Scholar
  11. Hager, B. H. and W. R. Clayton, Constraints on the structure of mantle convection using seismic observations, flow models and the geoid, in Mantle Convection, edited by W. R. Peltier, pp. 657–763, Pergamon Press, 1989.Google Scholar
  12. Hager, B. H. and M. A. Richards, Long-wavelength variations in Earth’s geoid: physical models and dynamical implications, Phil. Trans. R. Soc. Lond., A328, 309–327, 1989.CrossRefGoogle Scholar
  13. Jordan, T. H., Composition and development of the continental tectosphere, Nature, 274, 544–548, 1978.CrossRefGoogle Scholar
  14. Karato, S., Effects of water on seismic wave velocities in the upper mantle, Proc. Japan. Acad., 71, Ser. B, 61–66, 1995.CrossRefGoogle Scholar
  15. Kido, M. and O. Cadek, Inferences of viscosity from the oceanic geoid: Indication of a low viscosity zone below the 660-km discontinuity, Earth Planet. Sci. Lett., 151, 125–137, 1997.CrossRefGoogle Scholar
  16. Kido, M., D. A. Yuen, O. Cadek, and T. Nakakuki, Mantle viscosity derived by genetic algorithm using oceanic geoid and seismic tomography for whole-mantle versus blocked-flow situations, Phys. Earth Planet. Inter., 151, 503–525, 1998.Google Scholar
  17. King, S. D., Radial models of mantle viscosity: results from a genetic algorithm, Geophys. J. Int., 122, 725–734, 1995.CrossRefGoogle Scholar
  18. King, S. D. and G. Masters, An inversion for radial viscosity structure using seismic tomography, Geophys. Res. Lett., 19, 1551–1554, 1992.CrossRefGoogle Scholar
  19. Li, X.-D. and B. Romanowicz, Global mantle shear velocity model developed using nonlinear asymptotic coupling theory, J. Geophys. Res., 101, 22245–22272, 1996.CrossRefGoogle Scholar
  20. Mitrovica, J. X. and A. M. Forte, Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial rebound observables, J. Geophys. Res., 102, 2751–2769, 1997.CrossRefGoogle Scholar
  21. Panasyuk, S. V., B. H. Hager, and A. M. Forte, Understanding the effects of mantle compressibility on geoid kernels, Geophys. J. Int., 124, 121–133, 1996.CrossRefGoogle Scholar
  22. Ribe, N. M., The dynamics of thin shells with variable viscosity and the origin of toroidal flow in the mantle, Geophys. J. Int., 110, 537–552, 1992.CrossRefGoogle Scholar
  23. Ricard, Y., C. Froidevaux, and L. Fleitout, Global plate motion and the geoid: a physical model, Geophys. J., 93, 477–484, 1988.CrossRefGoogle Scholar
  24. Ricard, Y., C. Vigny, and C. Froidevaux, Mantle heterogeneities, geoid, and plate motion: A Monte Carlo inversion, J. Geophys. Res., 94, 13739–13754, 1989.CrossRefGoogle Scholar
  25. Ricard, Y., C. Doglioni, and R. Sabadini, Differential rotation between litho-sphere and mantle: A consequence of lateral mantle viscosity variation, J. Geophys. Res., 96, 8407–8415, 1991.CrossRefGoogle Scholar
  26. Ricard, Y., M. Richards, C. Lithgow-Bertelloni, and Y. Le Stunff, A geodynamic model of mantle density heterogeneity, J. Geophys. Res., 98, 21895–21909, 1993.CrossRefGoogle Scholar
  27. Ricard, Y., H.-C. Nataf, and J.-P. Montagner, The 3-SMAC model: Confrontation with seismic data, J. Geophys. Res., 1995 (submitted). Richards, M. A. and B. H. Hager, Geoid anomalies in a dynamic earth, J. Geophys. Res., 89, 5987–6002, 1984.Google Scholar
  28. Richards, M. A. and B. H. Hager, Effects of lateral viscosity variation on long-wavelength geoid anomalies and topography, J. Geophys. Res., 94, 10299–10313, 1989.CrossRefGoogle Scholar
  29. Sen, M. K. and P. L. Stoffa, Rapid sampling of model space using genetic algorithms: examples from seismic waveform inversion, Geophys. J. Int., 108, 281–292, 1992.CrossRefGoogle Scholar
  30. Tarantola, A. and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. Space Phys., 20, 219–232, 1982.CrossRefGoogle Scholar
  31. Thoraval, C., Ph. Machetel, and A. Cazenave, Influence of mantle compressibility and ocean warping on dynamical models of the geoid, Geophys. J. Int., 117, 566–573, 1994.CrossRefGoogle Scholar
  32. Thoraval, C., Ph. Machetel, and A. Cazenave, Locally layered convection inferred from dynamic models of the Earth’s mantle, Nature, 375, 777–789, 1995.CrossRefGoogle Scholar
  33. Wen, L. and D. L. Anderson, Layered mantle convection: A model for geoid and topography, Earth Planet. Sci. Lett., 146, 367–378, 1997.CrossRefGoogle Scholar
  34. Zhang, S. and U. R. Christensen, The effect of lateral viscosity variations on geoid, topography and plate motions induced by density anomalies in the mantle, Geophys. J. Int., 114, 531–547, 1993.CrossRefGoogle Scholar

Copyright information

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. 1998

Authors and Affiliations

  1. 1.Ocean Research InstituteUniversity of TokyoJapan
  2. 2.Department of Earth and Planetary System ScienceUniversity of HiroshimaJapan

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