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.
Similar content being viewed by others
References
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.
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.
Corrieu, V., C. Thoraval, and Y. Ricard, Mantle dynamics and geoid Green functions, Geophys. J. Int., 120, 516–523, 1995.
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.
Forte, A. M. and W. R. Peltier, Viscous flow models of global geophysical observables 1. Forward problems, J. Geophys. Res., 96, 20131–20159, 1991.
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.
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.
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.
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.
Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, pp. 412, Addison-Wesley Publishing Company, Inc., 1989.
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.
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.
Jordan, T. H., Composition and development of the continental tectosphere, Nature, 274, 544–548, 1978.
Karato, S., Effects of water on seismic wave velocities in the upper mantle, Proc. Japan. Acad., 71, Ser. B, 61–66, 1995.
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.
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.
King, S. D., Radial models of mantle viscosity: results from a genetic algorithm, Geophys. J. Int., 122, 725–734, 1995.
King, S. D. and G. Masters, An inversion for radial viscosity structure using seismic tomography, Geophys. Res. Lett., 19, 1551–1554, 1992.
Li, X.-D. and B. Romanowicz, Global mantle shear velocity model developed using nonlinear asymptotic coupling theory, J. Geophys. Res., 101, 22245–22272, 1996.
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.
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.
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.
Ricard, Y., C. Froidevaux, and L. Fleitout, Global plate motion and the geoid: a physical model, Geophys. J., 93, 477–484, 1988.
Ricard, Y., C. Vigny, and C. Froidevaux, Mantle heterogeneities, geoid, and plate motion: A Monte Carlo inversion, J. Geophys. Res., 94, 13739–13754, 1989.
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.
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.
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.
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.
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.
Tarantola, A. and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. Space Phys., 20, 219–232, 1982.
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.
Thoraval, C., Ph. Machetel, and A. Cazenave, Locally layered convection inferred from dynamic models of the Earth’s mantle, Nature, 375, 777–789, 1995.
Wen, L. and D. L. Anderson, Layered mantle convection: A model for geoid and topography, Earth Planet. Sci. Lett., 146, 367–378, 1997.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kido, M., Honda, S. Synthetic tests of geoid-viscosity inversion: A layered viscosity case. Earth Planet Sp 50, 1055–1065 (1998). https://doi.org/10.1186/BF03352200
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1186/BF03352200