Viscoelastodynamics of A Stratified, Compressible Planet: Incremental Field Equations and Short- and Long-Time Asymptotes

In recent years a number of studies have investigated the influence of compressibility on geophysical observables such as postglacial rebound deformation rates and the geoid. Some of these studies indicate that long-term signatures such as the geoid might be sensitive to compressibility. As both load relaxation and tidal-effective relaxation of the equatorial bulge are operative in a dependent way, polar wander can potentially be more sensitive to compressible rheologies if the interference between the two relaxation mechanisms is constructive. This has motivated us to study the influence of compressibility on true polar wander by means of spherical, laterally homogeneous, self-gravitating analytical earth models. As we wish to study both short-term rotational changes and polar wander on geological time-scales, we employ a Maxwell viscoelastic model instead of a Newtonian viscous model. The latter is commonly used in geoid modelling. The purpose of this paper is to concentrate on the basic physical aspects of the differences between compressible and incompressible rotational deformation, rather than applying the procedures to fine-graded multi-layered PREM models with realistic forcing functions. An important issue of our method concerns the analytical instead of numerical way of solving the differential equations by the propagator matrix method. Compressible viscoelastic relaxation has usually been treated numerically until now.The results show that homogeneous earth models do not have significant differences on long time-scales between compressible and the corresponding incompressible cases. Compressibility introduces a denumerably infinite set of short-time relaxation modes. The relaxation times of these dilatation modes can be approximated analytically. Twolayer core-mantle models show relatively large differences between incompressible and compressible Maxwell rheologies. Simplified models of true polar wander triggered by Heaviside loads show that differences of several tens of per cent between incompressible and compressible Maxwell rheologies are possible. True polar wander is decreased in the compressible case on both short and long time-scales, which means that smaller viscosities are required to explain polar-wander measurements than in the incompressible case.

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“…The reader is referred to the literature for these basics (rigorous treatises may be found in e.g. Wolf 1991Wolf , 1994.…”

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confidence: 99%

Compressible rotational deformation

Vermeersen

Sabadini

Spada

1996

Geophysical Journal International

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“…In either case, a single mantle mode, M, results, which has been discussed in previous studies of Maxwell earth models (e.g. Wu & Peltier 1982;Wolf 1985aWolf , 1991a. Note that its viscous amplitude is independent of the value of q (Fig.…”

Section: Transfer Function For Displacementmentioning

confidence: 58%

“…Following most previous studies, we use the Burgers viscoelastic fluid (Burgers 1935) to model transient creep in the Earth's interior. In order to simplify the analysis and to emphasize characteristic differences between transient and steady-state rheologies in the uplift signatures, we restrict our analysis to an incompressible, initially hydrostatic half-space model of the Earth subjected to an external gravity field and surface loading (Wolf 1985a(Wolf , 1985b(Wolf , 1991a. The neglect of sphericity and self-gravitation is legitimate in view of the model's application to post-glacial uplift in Fennoscandia, where both features have been shown to be of subordinate importance (Wolf 1984;Amelung & Wolf 1994).…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic relaxation of a Burgers half-space: implications for the interpretation of the Fennoscandian uplift

Rümpker

Wolff

1996

Geophysical Journal International

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We investigate the load-induced response of a Burgers earth model. In particular, using the incremental field equations and interface conditions of viscoelastodynamics, we give closed-form solutions for a two-layer half-space subjected to surface loading. In the special case of homogeneity, the solution shows that the Burgers half-space is characterized by two fundamental normal modes: M, and M,. They correspond to the short-and long-time viscosities, qo and q,, which describe the creep behaviour of the transient Burgers rheology at short and long times after the onset of loading. In the more general case of a Burgers substratum overlain by an elastic layer, the number of normal modes increases to four: M,, Lo, M,, L,. Values of the parameters specifying the Burgers substratum are estimated by predicting the observed post-glacial uplift in Fennoscandia with a simple model of the Pleistocene glaciation history. The calculations return the following results: (1) an upper bound on q, cannot be determined; (2) a comparison with uplift curves for a steady-state Maxwell substratum shows that the marginal and peripheral regions of the Fennoscandian ice sheet are most sensitive to transient creep in the Earth's mantle; and (3) an estimate of qm cannot be obtained without a priori knowledge of the other parameters of Burgers rheology.

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“…In fact, viscous relaxation involves only small perturbations of a hydrostatic equilibrium state, which admits the linearization of the governing field equations (for details see, for example, Peltier, 1982, pp. 38-59, andWolf, 1991). The solutions to the linearized equations for given surface tractions in particular show that the degree of disequilibrium decreases with depth, resulting in subsurface deflections that are far too small to be resolved by current seismological techniques.…”

Section: Detlef Wolfmentioning

confidence: 97%

Glacial isostasy and long-term crustal movements in Fennoscandia with respect to lithospheric and asthenospheric processes and properties—comment

Wolf¹

1991

Tectonophysics

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european geotraverseRecently, Morner discussed his model of glacio-isostatic compensation in the light of new seismological models of the upper mantle below Fennoscandia (Miimer, 1990). He concluded that the P-wave velocity distribution is in "full agreement" with his estimate of the viscosity distribution as inferred from glacio-isostatic relaxation.Whereas the consistency of seismological and geodynamical earth models is a necessary condition for their soundness, the particular type of agreement sought by Momer is not required or expected, nor can his method of attaining such agreement be approved.For easier understanding of my criticism, I briefly recall the type of information provided by the seismological and by the glacio-isostatic evidence:(1) The propagation of high-frequency compressional waves admits an inference of the P-wave velocity distribution, which, in turn, provides basic information on the elastic properties of the earth. from a surface layer of long-term strength to a more ductile region of viscous creep underneath crudely defines the mechanical lithosphereasthenosphere boundary. The mechanical lithosphere can thus be regarded as a manifestation of radial heterogeneity in viscosity.Momer's whole argument rests on the assumption that the seismological and mechanical lithospheres are necessarily coincident.Since the viscosity distribution strongly reflects the temperature distribution, this assumption can obviously be only satisfied if a similar type of temperature dependence applies to the velocity distribution. However, below old shields the velocity distribution may not be thermally controlled at all but be largely due to compositional heterogeneity (e.g. (1) Mijmer formally converts the thickness of the high-velocity lid into the flexural rigidity of the mechanical lithosphere. As an alternative, he also estimates flexural rigidities using signatures of the relaxation process itself (the method applied by him is not without problems, see below).

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Viscoelastodynamics of A Stratified, Compressible Planet: Incremental Field Equations and Short- and Long-Time Asymptotes

Cited by 48 publications

References 23 publications

Compressible rotational deformation

Compressible rotational deformation

Viscoelastic relaxation of a Burgers half-space: implications for the interpretation of the Fennoscandian uplift

Glacial isostasy and long-term crustal movements in Fennoscandia with respect to lithospheric and asthenospheric processes and properties—comment

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