15 Fakultätsübergreifend / Sonstige Einrichtung

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1982 - 1989171990 - 19947

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Author: search.filters.author.Wolf, DetlefSubject: search.filters.subject.550

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    Boussinesq’s problem of viscoelasticity
    (1991) Wolf, Detlef
    We consider an isochemical, isentropic, incompressible fluid half-space and study quasistatic viscoelastic perturbations, induced by two-dimensional (2D) surface loads, of a hydrostatic initial state. In view of the regional or local scale required for deformations of planets to be amenable to the half-space approximation, the model is assumed to be externally gravitating. We derive analytic solutions for the displacement and incremental stress components and study several approximations to the expressions. Particular emphasis is placed on discriminating between the material and local incremental stresses. Based on this distinction, deeper insight is gained into the physical significance of the solution.
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    Glacial isostasy and long-term crustal movements in Fennoscandia with respect to lithospheric and asthenospheric processes and properties : comment
    (1991) Wolf, Detlef
    Recently, Mörner discussed his model of glacio-isostatic compensation in the light of new seismological models of the upper mantle below Fennoscandia. 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 Mörner 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.
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    Inductive coupling between idealized conductors and its significance for the geomagnetic coast effect
    (1982) Wolf, Detlef
    A problem of current interest is the inductive coupling between an ocean, a solid earth conductor and a conductosphere. The anomaly of this configuration is modelled by (i) the inductive response of a two-dimensional system consisting of two thin half sheets and an underlying thin whole sheet or (ii) the superposition of the responses of two related systems, each consisiting of only one of the two half sheets and the whole sheet. The conductivity of these conducting planes is assumed to be perfect, and rigorous solutions for the erived by conformal mapping. induced magnetic fields are a comparison between the anomalies (i) and (ii) permits us to ascertain the degree of inductive coupling between the idealized conductors. This establishes a reference for estimating the inductive coupling between more realistic conductors and may therefore assist in the interpretation of complicated magnetic variation anomalies in coastal regions. Our substitute configurations can also be used directly for the rapid modelling of the inductive response of the earth in the vicinity of coastlines. This is demonstrated by analyzing some field data from the recent literature.
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    Thick plate flexure re-examined : research note
    (1985) Wolf, Detlef
    The flexure of an incompressible, thick elastic plate floating on an inviscid substratum and subject to an external gravity field is re-analysed. The solution is derived from momentum equations which account for the advection of hydrostatic pre-stress. This is contrasted with a recently published thick-plate solution derived from momentum equations without a pre-stress term. It is demonstrated that neglecting pre-stress advection renders the solution singular when the model degenerates into an inviscid half-space. If pre-stress advection is included, the solution remains correct in this limit. A numerical comparison of both types of thick-plate solution with results based on conventional thin-plate theory further shows that, for geophysically relevant models, the difference in the momentum balance entails discrepancies between the thick-plate solutions which are comparable to the errors introduced by the thin-plate approximation.
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    On the relation between two-dimensional and axisymmetric loads in plate flexure problems
    (1984) Wolf, Detlef
    This note has attempted to clarify the relation between straight-edged axisymmetric loads and straight-edged two-dimensional loads by emphasizing the critical role of the elastic plate in this relation. It has been shown that loads of widely varying scale can be approximated by two-dImensional edges, provided that the lithosphere is sufficiently thin. As the distance from the edge of the load increases, the displacement w decreases. This results in enhanced relative discrepancies between the two models in the region of the peripheral bulge. Whether this is significant when modelling data will ultimately depend on the magnitude of the errors associated with the measurements.
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    The changing role of the lithosphere in models of glacial isostasy : a historical review
    (1993) Wolf, Detlef
    During the last 125 years, the role of the lithosphere in models of glacial-isostatic adjustment experienced several changes. Following the postulation of glacial isostasy by Jamieson in 1865, the lithosphere was generally regarded as comparable in importance for the adjustment process to the fluid substratum. This changed with the initiation of quantitative modelling by Van Bemmelen and Berlage and by Haskell in 1935, whereupon effects due to the lithosphere were commonly neglected in interpretations of postglacial uplift for 30 years. After the development of a layered viscous earth model with an elastic surface layer by McConnell in 1965, the lithosphere was eventually reintroduced into models of glacial isostasy. Subsequent studies largely confirmed the original ideas regarding the importance of the lithosphere for the adjustment process, although the effects are pronounced only for short-wavelength deformations. Using this response characteristic of the lithosphere, estimates of its thickness have recently become available for several tectonic provinces.
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    Reply to comments by Robert P. Comer [Letter to the editor]
    (1986) Wolf, Detlef
    In his letter, Comer (1986) addresses three different points which bear on three related publications on load-induced flexure of elastic plates (Comer 1983; Ward 1984; Wolf 1985a). As his first point is primarily an annotation to his own publication on the subject (Comer 1983), I will restrict my reply to the remaining two points.
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    Isostatic compensation and continental lithospheric thickness
    (1984) Wolf, Detlef
    Lateral density inhomogeneities are a general feature of the continental crust and upper mantle. This suggests the generalization of the interpretation of isostatic response functions by introducing internal loads into the conventional model of an elastic plate flexed under a topographic load. With this modification, analyses of continental response functions favour lithospheric thicknesses larger than the average thickness of the crust. These values also conform with independent estimates of the long-term thickness of the continental lithosphere and are therefore more satisfactory than recent estimates of only a few kilometres based on a pure flexure model.
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    Viscoelastic perturbations of the earth : significance of the incremental gravitational force in models of glacial isostasy
    (1994) Amelung, Falk; Wolf, Detlef
    We examine the errors caused by the neglect of the IGF using closed-form solutions of the equations governing surface-load induced perturbations of two types of incompressible, spherical-earth models: (1) Maxwellian-viscoelastic mantle enclosed by elastic lithosphere, and (2) Maxwellian-viscoelastic mantle enclosing inviscid core. Calculations in the Legendre domain of the radial surface displacement for these models show that neglecting the IGF causes enhancement of the elastic response and acceleration of the viscous relaxation. In the space domain, these changes entail corresponding modifications of the calculated land adjustment. The magnitude of the error caused by the neglect of the IGF strongly depends on the deglaciation history and load radius adopted. Assuming a typical deglaciation history, the error reaches a maximum of less than 20m at the end of the deglaciation phase for loads comparable in size to the Canadian or the Fennoscandian ice sheets. We also compare spherical-earth models with IGF and plane-earth models without IGF. Calculations of the radial surface displacement show that the errors due to the neglect of sphericity and the IGF partially compensate each other. Taking the uncertainties of the observational data into account, we conclude that the majority of the Canadian and Fennoscandian glacial-isostatic adjustment data can be modelled with sufficient accuracy using a plane-earth model without IGF.
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    Viscoelastodynamics of a stratified, compressible planet : incremental field equations and short- and long-time asymptotes
    (1991) Wolf, Detlef
    We consider a chemically and entropically stratified, compressible, rotating fluid planet and study gravitational-viscoelastic perturbations of a hydrostatic initial state. Using the Lagrangian formulation, we first derive the incremental field equations and continuity conditions governing the perturbations. Following this, we deduce the asymptotes to the equations for short and long times after the onset of the perturbations, the short-time asymptotic equations are referred to as the incremental field equations and continuity conditions of generalized elastodynamics. They include the equations of conventional elastodynamics as zeroth-order approximations, the long-time asymptotic equations agree with the incremental field equations and continuity conditions of Newtonian-viscous fluid dynamics. In particular, the incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation satisfies the appropriate incremental state equation. Finally, we introduce the generalized incremental incom-pressibility condition. Based on it, we derive approximate incremental field equations for gravitational-viscoelastic perturbations of isochemical, isentropic and compressible regions.