The normal modes of a layered, incompressible Maxwell half-space

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D. Wolf

Abstract

The theory describing the relaxation of an incompressible, layered Maxwell half-space is developed. The approach is based on the analytic solution of the associated elastic model and the subsequent application of the correspondence principle. The viscoelastic theory follows normal-mode theory, which allows the independent and exact determination of the relaxation-time and amplitude spectra for each mode of relaxation. The solution is tested by calculating the response of several models in the wavenumber and spatial domains. The examples are selected with regard to postglacial adjustment in Fennoscandia and analyse effects caused by (a) varying lithospheric thickness, (b) adding an asthenosphere, (c) increasing lower-mantle viscosity, (d) permitting relaxation of the lower lithosphere or (e) introducing density contrasts at 400-km and 670-km depths.


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Wolf, D. 1985. “The Normal Modes of a Layered, Incompressible Maxwell Half-Space”. Journal of Geophysics 57 (1), 106-17. https://journal.geophysicsjournal.com/JofG/article/view/245.
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References

Balling, N. (1980) The land uplift in Fennoscandia, gravity field anomalies and isostasy. In: Morner, N.-A. (Ed.) Earth rheology, isostasy, and eustasy. pp. 297-321. Wiley, New York

Beaumont, C. (1978) The evolution of sedimentary basins on a viscoelastic lithosphere: theory and examples. Geophys. J. R. Astron. Soc. 55:471-497

Cathi es, L.M. (1975) The viscosity of the Earth's mantle. Princeton University Press

Courtney, R.C. (1982) On the rheology of the oceanic and continental lithospheres. M.Sc. thesis, Dalhousie University

Dziewonski, A.M., Anderson, D.L. (1981) Preliminary reference Earth model. Phys. Earth Planet. Inter. 25:297-356

Farrell, W.E. (1972) Deformation of the Earth by· surface loads. Rev. Geophys. Space Phys. 10:761-797

Imbrie, J., Imbrie, K.P. (1979) Ice ages: solving the mystery. Enslow, Hillside

Kuo, J.T. (1969) Static response of a multilayered medium under inclined surface loads. J. Geophys. Res. 74:3195-3207

Lambeck, K., Nakiboglu, S.M. (1980) Seamount loading and stress in the ocean lithosphere. J. Geophys. Res. 85:6403-6418

Lanczano, P. (1982) Deformations of an elastic Earth. Academic Press, New York

McConnell, R.K. jr. (1965) Isostatic adjustment in a layered Earth. J. Geophys. Res. 70:5171-5188

McConnell, R.K. jr. (1968) Viscosity of the mantle from relaxation time spectra of isostatic adjustment. J. Geophys. Res. 73:7089-7105

Nakiboglu, S.M., Lambeck, K. (1982) A study of the Earth's response to surface loading with application to Lake Bonneville. Geophys. J. R. Astron. Soc. 70:577-620

Parker, R.L. (1972) The rapid calculation of potential anomalies. Geophys. J. R. Astron. Soc. 31:447-455

Parsons, B.E. (1972) Changes in the Earth's shape. Ph.D. thesis, Cambridge University

Peltier, W.R. (1974) The impulse response of a Maxwell Earth. Rev. Geophys. Space Phys. 12:649-669

Peltier, W.R. (1976) Glacial-isostatic adjustment - II. The inverse problem. Geophys. J. R. Astron. Soc. 46:669-705

Peltier, W.R. (1982) Dynamics of the ice age Earth Adv. Geophys. 24:1-146

Peltier, W.R. (1985) The LAGEOS constraint on deep mantle viscosity: results from a new normal mode method for the inversion of viscoelastic relaxation spectra. J. Geophys. Res. (In press)

Peltier, W.R., Andrews, J.T. (1976) Glacial-isostatic adjustment - I. The forward problem. Geophys. J. R. Astron. Soc. 46:605-646

Sclater, J.G., Jaupart, C., Galson, D. (1980) The heat flow through oceanic and continental crust and the heat loss of the Earth. Rev. Geophys. Space Phys. 18:269-311

Tullis, J.A. (1979) High temperature deformation of rocks and minerals. Rev. Geophys. Space Phys. 17:1137-1154

Walcott, R.I. (1980) Rheological models and observational data of glacio-isostatic rebound. In: Morner, N.-A. (Ed.) Earth rheology, isostasy, and eustasy. pp. 3-10. Wiley, New York

Ward, S.N. (1984) A note on lithospheric bending calculations. Geophys. J. R. Astron. Soc. 78:241-253

Weertman, J., Weertman, J.R. (1975) High temperature creep of rock and mantle viscosity. Annu. Rev. Earth Planet. Sci. 3:293-315

Wolf, D. (1984) The relaxation of spherical and flat Maxwell Earth models and effects due to the presence of the lithosphere. J. Geophys. 56:24-33

Wolf, D. (1985a) Thick-plate flexure re-examined. Geophys. J. R. Astron. Soc. 80:265-273

Wolf, D. (1985b) On Boussinesq's problem for Maxwell continua subject to an external gravity field. Geophys. J. R. Astron. Soc. 80:275-279

Wolf, D. (1985c) The normal modes of a uniform, compressible Maxwell half-space. J. Geophys. 56:100-105

Wolf, D. (1985d) An improved estimate of lithospheric thickness based on a reinterpretation of tilt data from Pleistocene Lake Algonquin. Can. J. Earth Sci. 22:768-773

Wu, P., Peltier, W.R. (1982) Viscous gravitational relaxation. Geophys. J. R. Astron. Soc. 70:435-485

Wu, P., Peltier, W.R. (1983) Glacial isostatic adjustment and the free-air gravity anomaly as a constraint on deep mantle viscosity. Geophys. J. R. Astron. Soc. 74:377-449