The relaxation of spherical and flat Maxwell Earth models and effects due to the presence of the lithosphere

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D. Wolf


The radial surface deflection of a spherical Earth model appropriate to time scales characteristic of glacial loading is compared with the associated half-space response. For that purpose the analytical solution for a Maxwell sphere surrounded by a thick elastic shell is derived under the assumption of incompressibility. The half-space approximation is deduced as a special case directly from the spherical solution. Comparison of the response spectra, for different thicknesses of the elastic shell, reveals only minor differences. In the spatial domain, the half-space approximation may, nevertheless, diverge significantly from the spherical solution. For a disk load radius R = 800 km (Fennoscandia), the half-space approximation is adequate, whereas it is usually inappropriate if R = 1600 km (Laurentia). The sensitivity of the response to the thickness of the elastic shell is also investigated. For R = 800 km, the surface deflection in the central region below the load is fairly diagnostic of the shell thickness. If R = 1600 km, the peripheral region is more sensitive to this parameter.

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Wolf, D. (1984). The relaxation of spherical and flat Maxwell Earth models and effects due to the presence of the lithosphere. Journal of Geophysics, 56(1), 24-33. Retrieved from


Brotchie, J.F., Silvester, R. (1969) On crustal flexure. J. Geophys. Res. 74:6240-5252

Bullen, K.E. (1963) An introduction to the theory of seismology, 3rd edn. Cambridge University Press

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

Crittenden, M.D. jr. (1963) Effective viscosity of the Earth derived from isostatic loading of Pleistocene Lake Bonneville. J. Geophys. Res. 68, 5517-5530

Dragoni, M., Yuen, D.A., Boschi, E. (1983) Global postseismic deformation in a stratified viscoelastic Earth: effects on Chandler wobble excitation. J. Geophys. Res. 88, 2240-2250

Haskell, N.A. (1935) The motion of a viscous fluid under a surface load. Physics 6, 265-269

Jeffreys, H. (1976) The Earth, 6th edn. Cambridge University Press, New York

Lebedev, N.N. (1972) Special functions and their applications. Dover, New York

Love, A.E.H. (1911) Some problems of geodynamics. Cambridge University Press

Love, A.E.H. (1927) A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press

McConnell, R.K. (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

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

Peltier, W.R. (1980) Ice sheets, oceans, and the Earth's shape. In: Moerner, N.-A. (Ed.) Earth rheology, isostasy, and eustasy, pp. 45-63. Wiley, New York

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

Peltier, W.R. (1984) The thickness of the continental lithosphere. J. Geophys. Res. (In press)

Stichter, L.B., Caputo, M. (1960) Deformation of an Earth model by surface pressures. J. Geophys. Res. 65, 4151-4156

Sneddon, I.A. (1951) Fourier transforms. McGraw-Hill, New York

Walcott, R.I. (1970a) Flexural rigidity, thickness, and viscosity of the lithosphere. J. Geophys. Res. 75, 3941-3954

Walcott, R.I. (1970b) Isostatic response to loading of the crust in Canada. Can. J. Earth Sci. 7, 716-727

Watson, G.N. (1944) A treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press

Wolf, D. (1984a) Thick plate flexure re-examined. Geophys. J. R. Astron. Soc. (In press)

Wolf, D. (1984) On the relation between two-dimensional and axisymmetric loads in plate flexure problems. J. Geophys. 54, 232-235

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