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  • 1
    Electronic Resource
    Electronic Resource
    Mass heterogeneities and convection in the earth's mantle inferred from gravity and core-mantle boundary irregularities (1991)
    Springer
    Pure and applied geophysics 135 (1991), S. 107-123 
    Details
    ISSN: 1420-9136
    Keywords: Gravity anomalies ; core-mantle boundary ; mantle heterogeneities ; mantle convection ; mantle dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Mass heterogeneities in the earth's mantle are retrieved from the gravity data and the topography of the core-mantle boundary as well as the topography of the earth's surface. A mantle circulation induced by the heterogeneities is modelled by solving the Stokes problem for incompressible Newtonian fluid. The derived models of mantle motions correlate well with the plate tectonics and point at a close relation between the surface tectonic activity and the processes in the vicinity of the core-mantle boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00877012
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  • 2
    Electronic Resource
    Electronic Resource
    Initial-value and modal approaches for transient viscoelastic responses with complex viscosity profiles (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 127 (1996), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: An initial-value theory is proposed for studying viscoelastic responses of compressible earth models with complex viscosity profiles. Continuous spectra are caused by both compressibility and the viscosity stratification, and they can cause numerical difficulties for the modal approach. We have studied the different responses for various types of viscosity profiles and found that there are differences in the responses at short wavelengths for viscosity profiles with sharp low-viscosity zones. We found that many modes are required to match the full initial-value solutions in the presence of sharp viscosity stratifications in both the upper and lower mantle. The normal-mode approach is best suited for simple layered models, long wavelengths and timescales greater than several thousand years, while the initial-value approach is indispensable in treating short-timescale problems with sharp low-viscosity zones in the upper mantle and viscosity stratification in the lower mantle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1996.tb04725.x
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  • 3
    Electronic Resource
    Electronic Resource
    Comparison Between Newtonian and Non-Newtonian Flow Driven By Internal Loads (1993)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 112 (1993), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The interpretation of long wavelength geoid and plate motions on the basis of dynamic Earth models has usually been done assuming linear viscous rheologies in the mantle. In this paper, we develop spherical 3-D models of mantle circulation using power-law creep rheologies with an exponent n= 3. We found that the stress-dependent rheologies only modify the amplitude of the topography supported by an internal load, by a small percentage with respect to the linear predictions. the geoid anomalies induced by internal loads can be affected by around 20 per cent. These changes are also occurring at degrees and orders different from those of the mass anomaly itself. As the geoid spectrum is strongly decreasing with degree, the dynamic topography induced at high degrees can be contaminated in a nonnegligible way by the low degree loads. the main contamination occurs at a harmonic triple of that of the most important load. the flow structure is much more dependent on the creep law than are the dynamic topography and the geoid. In contrast to linear rheology, a power-law creep is able to sustain a toroidal velocity field. However, this toroidal component only carries a small percentage of the kinetic energy and thus the non-linear creep with n= 3 cannot by itself explain the observed quasi-equipartition of plate tectonic energy between toroidal and poloidal components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1993.tb01440.x
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  • 4
    Electronic Resource
    Electronic Resource
    Variational principles for the momentum equation of mantle convection with Newtonian and power-law rheologies (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 126 (1996), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Variational principles for the momentum equation with neglected inertial forces are formulated for both Newtonian and power-law rheologies, and their theoretical functional justification is demonstrated. The existence and uniqueness of the solution are proved, and general gradient optimization techniques prior to discretization are studied. Difficulties with the transformation of the non-linear problem to a series of linear problems are outlined. To avoid powers of the nabla operator, which appear when the principles are expressed only in terms of velocities, an alternative hybrid variational principle expressed in terms of velocities and stresses is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1996.tb05286.x
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  • 5
    Electronic Resource
    Electronic Resource
    The thermal field of the lithosphere in the region of mid-ocean ridges modelled on the basis of known surface temperature and heat flows (1984)
    Springer
    Studia geophysica et geodaetica 28 (1984), S. 407-417 
    Details
    ISSN: 1573-1626
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Description / Table of Contents: Summary The possibility of solving the stationary heat equation with the convective term is demonstrated in the case that the velocity field of the continuum, and the temperature and heat flow on the Earth's surface are known, and that an assumption is made about the magnitude of heat flows on another part of the boundary of the two-dimensional region being investigated, whereas no boundary condition is imposed on the remainder of the region's boundary. The problem has been solved numerically for a kinematic model of the lithosphere in the region of mid-ocean ridges, based on the assumption of a broad deflected convective flow moving at a distance of more than about 150 km from the ridge modelled as a plate.
    Notes: Резюме Покaзaнa возможносmь решенuя сmaцuонaрно о урaвненuя nереносa mеnлa в случaе, ко ¶rt;a uзвесmно nоле скоросmеŭ конmuнуумa u нa nоверхносmu Землu uзвесmны mемnерamурa u mеnловоŭ nоmок. Нa ¶rt;ру оŭ чaсmu рaнuцы рaссмamрuвaемоŭ ¶rt;вухмерноŭ облaсmu вво¶rt;umся nре¶rt;nоложенuе о велuчuне mеnлово о nоmокa a нa осmaльноŭ чaсmu рaнuцы крaевое условuе не зa¶rt;aно. Эma nроблемa былa чuсленным меmо¶rt;ом решенa ¶rt;ля кuнемamuческоŭ мо¶rt;елu лumосферы в облaсmu сре¶rt;uнно-океaнuческuх хребmов, основaнноŭ нa nре¶rt;сmaвленuu шuроко сверmывaюще ося конвекmuвно о nоmокa нa рaссmоянuях оm хребma nревышaющuх 150 км ¶rt;вuжуще ося кaк орuзонmaльныŭ nоmок.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01642993
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  • 6
    Electronic Resource
    Electronic Resource
    The inverse gravimetric problem: Existence, uniqueness and stability of the solution (1987)
    Springer
    Studia geophysica et geodaetica 31 (1987), S. 252-257 
    Details
    ISSN: 1573-1626
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Description / Table of Contents: Summary The paper is concerned with the mathematical properties of the density distribution within the Earth obtained by inverting of the external gravity field, provided an Earth's reference density model, used as the initial guess, is available. The method of regularization, which proves the existence, the uniqueness and the stability of the solution, which is nearest the initial guess in the L 2 norm, is described.
    Notes: Резюме Оnuсaн меmо¶rt; ре улярuзaцuu о¶rt;рamноŭ зa¶rt;aчu ¶rt;ля внешне о рaвumaцuонно о nоля Землu счumaя, чmо uзвесmнa нaчaлвнaя оценкa рaсnре¶rt;еленuя nлоmносmu в Земле. Эmоm меmо¶rt; nре¶rt;осmaвum возможносmв нaŭmu решенuе, коmорое о¶rt;нознaчно, усmоŭчuво u вблuзu нaчaльноŭ оценкu.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01624756
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  • 7
    Electronic Resource
    Electronic Resource
    Heating in the D″-layer and the style of mantle convection (1994)
    Springer
    Studia geophysica et geodaetica 38 (1994), S. 286-292 
    Details
    ISSN: 1573-1626
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Notes: Summary We have investigated the influence of heating in the D″-layer on the convection dynamics for the Rayleight number Ra=106. Strong heating, which may represent a local small-scale heat transfer in the D″-layer, results in an increase of lateral heterogeneities near the upper and lower boundaries, the blob-like structure of upwellings and the stabilization of the convection pattern. The influence of the electromagnetic heating was found to be too weak to produce any substantial effect which is in contrast with the idea of Braginskii and Meitlis [1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02296003
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  • 8
    Electronic Resource
    Electronic Resource
    The Problem of Viscoelastic Relaxation of the Earth Solved by a Matrix Eigenvalue Approach Based on Discretization in Grid Space (2000)
    Springer
    Visual geosciences 5 (2000), S. 1-11 
    Details
    ISSN: 1610-2924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Viscoelasticity is a geophysical process which operates over intermediate timescales between a few years to millions of years, depending on the ambient thermal conditions of the self-gravitating spherical planet. Topography undulations with time represent geological signatures to both the internal and external loading processes, such as post-glacial rebound, volcanic eruptions, sedimentary loading, meteoritic impacts and mountain building. The span of relaxation timescales or relaxation spectrum in a viscoelastic spherical body has traditionally been determined by employing the Laplacian transform method and the correspondence principle relating the elastic solution to its viscoelastic counterpart. We have devised a novel approach based on the method of lines in which the equations at each angular order in the spherical harmonic expansion are discretized in the radial co-ordinate. The finite-dimensional space spanned by the discretized points in the radial direction of the planetary model then forms the basis of a matrix Eigenvalue problem. The Eigenvalues can be computed very fast because of the availability of public domain software. We can, for instance, compute the entire range of viscoelastic relaxation with computational times from 0.05 to 50 sec using only 30 to 300 radial grid points. The models can have both realistic density and elastic parameter profiles, derived from seismology. We show results here for complicated viscosity profiles with an asthenosphere in the upper mantle and a viscosity hill in the middle portion of the lower mantle. Because of the rapidity of the code, we may use this new method for exploring non-linear inversion problems by parameter sweeping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10069-000-1008-6
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  • 9
    Electronic Resource
    Electronic Resource
    One thermal model of the young oceanic lithosphere: Direct problem (1986)
    Springer
    Studia geophysica et geodaetica 30 (1986), S. 172-181 
    Details
    ISSN: 1573-1626
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Description / Table of Contents: Summary The two-dimensional solution of the direct plate model of the oceanic lithosphere is computed for t 1/2 dependences of its thickness using the multi-grid technique for the bilinear finite elements. If we assume the dependence of the lithospheric thickness on its age in the form h(t)=6·6t 1/2 +7·5, then this model can roughly approximate the measured heat flow. In this model the horizontal conductive term is not negligible, the heat flow depends both on time and on the velocity of the sea-floor spreading which should be taken into account for the handling of heat flow measurements.
    Notes: Резюме Пре¶rt;ложено рещенuе ¶rt;вухмерноŭ nрямоŭ зa¶rt;aчu ¶rt;ля mермuческоŭ мо¶rt;елu океaнuческоŭ лumосферы с зaвuсuмосmью мощносmu оm t 1/2 . Прuменяеmся mехнuкa мульmuгрu¶rt;a ¶rt;ля бuлuнеŭных конечных элеменmов. Еслu nре¶rt;nоложumь зaвuсuмосmь мощносmu оm временu в вu¶rt;е h(t)=6.6t 1/2 +7.5, mо эma мо¶rt;ель nрuблuзumельно annроксuмuруеm нaблю¶rt;aемыŭ mеnловоŭ nоmок. В эmоŭ мо¶rt;елu нельзя nренебречьгорuзонmaльноŭ сосmaвляющеŭ mеnлоnрово¶rt;носmu; mеnловоŭ nоmок зaвuсum оm временu u оm скоросmu рaсщuренuя океaнuческого ¶rt;нa u, сле¶rt;овamельно, nрu обрaбоmке uзмеренuŭ mеnлового nоmокa нa¶rt;о учumывamь влuянuе скоросmu рaсщuренuя.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01644377
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  • 10
    Electronic Resource
    Electronic Resource
    The optimal shape design method applied to modelling thermal thinning of the oceanic lithosphere near hot spots (1986)
    Springer
    Studia geophysica et geodaetica 30 (1986), S. 356-375 
    Details
    ISSN: 1573-1626
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Description / Table of Contents: Summary Using the optimal shape design method, which is generally described, and von Herzen's et al. measurements of the heat flow, the shape of the lithosphere and its thermal field is computed in the vertical plane parallel to the hot spot source versus the plate velocity at a distance of about 250 km from the axis of the Hawaiian Island chain. The results are compared with the computations based on Crough's idea of thermal rejuvenation of the oceanic lithosphere above a hot spot source. If we assume that the lateral cross-section of the lithospheric bottom is described by the Gaussian curve Δh=Δh0 exp (−y2/2σ2), we obtain Δh0≦35 km and σ≧130 km, where Δh is the value of lithospheric thinning and y the lateral coordinate. We thus obtain the lower limit of the lateral dimension of the Hawaiian anomaly.
    Notes: Резюме Прuменяя меmо¶rt; оnmuмaльного nоuскa облaсmu, коmорыŭ в общuх черmaх оnuсывaеmся, u ¶rt;aнные о mеnловом nоmоке, вычuсленa формa лumосферы u ее mеnловое nоле в верmuкaльноŭ nлоскосmu, naрaллельноŭ скоросmu лumосферы оmносumельно uсmочнuкaгорячеŭ mочкu u у¶rt;aленноŭ nрuблuзumельно 250 км оm лuнuuгaвaŭского aрхunелaгa. Резульmamы срaвнены с вычuсленuямu, основaннымu нa u¶rt;еu Крaфa (Crough), кaсaющuмuся mеnлового уmоненuя океaнuческоŭ лumосферы нa¶rt; uсmочнuкомгорячеŭ mочкu. Еслu nре¶rt;nоложumь, чmо лamерaльное nоnеречное сеченuе лumосферuческого ¶rt;нa оnuсывaеmся крuвоŭ Гaуссa Δh=Δh0 exp (−y2/2σ2), mо nолучumся Δh0 ≦35 кмuσ ≧130 км,г¶rt;е Δh—лumосферuческое уmоненuе u у—лamерaльнaя коор¶rt;uнama. Сле¶rt;овamельно, σ=130 км являеmся нuжным nре¶rt;елом лamерaльного рaзмерaгaвaŭскоŭ aномaлuu.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646380
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