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  • 1
    Publication Date: 2017-04-04
    Description: Tomographical results are commonly presented in the form of color images and not much statistical quantification has been carried out on the derived models. Correlation between different depths can shed important light concerning the dynamics. We have generalized the application of multidimensional wavelets to investigate the products of two field variables, such as the cross-spectrum, which is of paramount importance for quantifying the correlation between two depth levels of seismic tomography with a multiple-scale character. For two multidimensional fields A and B, we calculate the correlation C by projecting this as an Hermitian inner product in physical space with a two-dimensional (2D), fourth derivative of the Gaussian wavelet as the weighting function. The correlation function C becomes now a multi-scaled function, a map cast in terms of both the scale and location of the wavelet transform. Having calculated C, we can delineate the locations and length-scales of the prominent features in the landscape of the correlation function. This wavelet formulation is very general and can be extended to other types of statistical analysis, for example in a Kalman filter system. We have used a high-resolution (finer than 1◦) seismic tomographical model for analyzing the extent of mantle layering under Europe by focussing on the different length-scales in the correlation function involving the 3D seismic anomalies lying between 400 and 600 km depth. Between the depths of 500 and 600 km under Europe, the wavelet correlation analysis shows that an ellipse-shaped object exists with an area of 2000 km × 4000 km having a strong correlation for length-scales of around 400 km, and weaker correlation for shorter length scales of around 150 km. On the other hand, between depths of 400 and 600 km, the correlation deteriorates on the long length scales and becomes even worse at the short length scales. From the wavelet correlation spectra, we can extract an horizontal characteristic length scale of around 100 km, which may be related to the boundary interaction between the slab and the ambient mantle. The correlation results suggest that the thickness of the recumbent fast (cold) material in the transition zone is between 100 and 150 km. This large elliptical pattern of presumably cold material would act to inhibit the vigor of mantle convection locally beneath Europe today.
    Description: Published
    Description: 125–139
    Description: 3.3. Geodinamica e struttura dell'interno della Terra
    Description: JCR Journal
    Description: reserved
    Keywords: wavelets ; correlation ; tomography ; transition zone ; Mediterranean ; 04. Solid Earth::04.07. Tectonophysics::04.07.02. Geodynamics
    Repository Name: Istituto Nazionale di Geofisica e Vulcanologia (INGV)
    Type: article
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  • 2
    ISSN: 1420-9136
    Keywords: Key words: Geodynamics, seismic tomography, spectral analysis, inferences of viscosity from geoid, mantle convection.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract —Recently a high-resolution tomographic model, the P1200, based on P-wave travel times was developed, which allowed for detailed imaging of the top 1200 km of the mantle. This model was used in diverse ways to study mantle viscosity structure and geodynamical processes. In the spatial domain there are lateral variations in the transition zone, suggesting interaction between the lower-mantle plumes and the region from 600 km to 1000 km. Some examples shown here include the continental region underneath Manchuria, Ukraine and South Africa, where horizontal structures lie above or below the 660 km discontinuity. The blockage of upwelling is observed under central Africa and the interaction between the upwelling and the transition zone under the slow Icelandic region appears to be complex. An expansion of the aspherical seismic velocities has been taken out to spherical harmonics of degree 60. For degrees exceeding around 10, the spectra at various depths decay with a power-law like dependence on the degree, with the logarithmic slopes in the asymptotic portion of the spectra containing values between 2 and 2.6. These spectral results may suggest the time-dependent nature of mantle convection. Details of the viscosity structure in the top 1200 km of the mantle have been inferred both from global and regional geoid data and from the high-resolution tomographic model. We have considered only the intermediate degrees (l = 12–25) in the nonlinear inversion with a genetic algorithm approach. Several families of acceptable viscosity profiles are found for both oceanic and global data. The families of solutions for the two data sets have different characteristics. Most of the solutions asociated with the global geoid data show the presence of asthenosphere below the lithosphere. In other families a low viscosity zone between 400 and 600 km depth is found to lie atop a viscosity jump. Other families evidence a viscosity decrease across the 660 km discontinuity. Solutions from oceanic geoid show basically two low viscosity zones one lying right below the lithosphere; the other right under 660-km depth. All of these results bespeak clearly the plausible existence of strong vertical viscosity stratification in the top 1000 km of the mantle. The presence of the second asthenosphere may have important dynamical ramifications on issues pertaining to layered mantle convection. Numerical modelling of mantle convection with two phase transitions and a realistic temperature- and pressure-dependent viscosity demonstrates that a low viscosity region under the endothermic phase transition can indeed be generated self-consistently in time-dependent situations involving a partially layered configuration in an axisymmetric spherical-shell model.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2938-2945 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional direct numerical simulation (using a fully spectral method) of compressible convection of an infinite Prandtl number fluid in a wide box with dimensions 5×5×1 was conducted. Depth-dependent viscosity, thermal expansivity, and thermal conductivity have been included in order to model deep-seated processes in the Earth's mantle. Solutions have been obtained up to a surface Rayleigh number of 4×107. There is a remarkable contrast between the dynamics of the upper and lower boundary layers. Very few cylindrical plumes are developed at the bottom but they merge collectively to form a strong upwelling, which pulses chaotically. Viscous and adiabatic heating are found to become important at high Rayleigh numbers, larger than 107. These results have important implications on the thermal structure of early Earth, where there might have been dramatic effects from intense mechanical heating near the top boundary layer.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 104 (1991), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We investigate the post-glacial relaxation phenomenon of a viscously compressible, non-self-gravitating, spherical-shell model. We have developed analytical solutions to an exponentially depth-dependent viscosity with various types of compressible density models such as those with an exponential dependence of the radius and an algebraic-root dependence of the radius. the solutions of a viscously compressible, multilayered model with constant thermodynamic properties and viscosity are developed by the propagator matrix method. Our results show that inferences of deep mantle viscosity from post-glacial rebound would be hampered by mantle compressibility for long-wavelength harmonics because of the smaller excitation of compressible eigenfunctions in the lower mantle. the relaxation times and velocity fields are more sensitive to higher viscosity contrast for the exponentially varying viscosity than for models with discrete jumps in the viscosity structure. Stress fields associated with deglaciation are extremely sensitive to the underlying mantle viscosity structure. Large stresses, O(102 bar), can still remain at the deglaciated region, if the lower mantle viscosity is O(1023P). the presence of a hard garnet layer in the transition zone will induce a smaller viscosity in the lower mantle in the viscosity trade-off with the standard two-layer model.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2105-2115 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The use of characteristics-based methods for the advection-dominated regimes in thermal convection is investigated. An operator-splitting method applied to the advection–diffusion equation for the very large Péclet (Pe) number regime is presented. In this approach two partial differential equations representing both the purely hyperbolic and the parabolic components must be solved simultaneously. This method has been compared with (1) the Galerkin approximation, (2) the streamwise upwinding Petrov–Galerkin method, and (3) the characteristics-based method using the Lagrangian formulation for the time-derivative operator of the advection–diffusion equation. Solution accuracy of the operator-splitting method improves with larger Pe, while the accuracy of other methods deteriorates with Pe. For the nonlinear problem of two-dimensional thermal convection the Lagrangian method is found to be most computationally efficient. With this Lagrangian method, time-dependent, thermal convection solutions of extremely high Rayleigh number (Ra), up to 3×109, for infinite Prandtl number are obtained. For an aspect ratio of 1.8 the exponent in the scaling of the Nusselt number (Nu) with Ra in time-dependent convection is determined to be 0.301 in the hard turbulent regime and is smaller than in the soft turbulent regime. The behavior of this exponent as a consequence of the transition to hard turbulence agrees with experimental findings. Horizontal Fourier spectra of the thermal fields outside the boundary layers reveal a transition in the high wave-number domain from 1/k to 1/k2 in the transition from soft to hard turbulent regimes. Analysis of the kinetic energy spectra E(k) shows an asymptotic decay of E(k) close to k−2, for large k, spanning over two decades in wave number for strongly time-dependent convection.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Terra nova 5 (1993), S. 0 
    ISSN: 1365-3121
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 351 (1991), S. 53-55 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Estimates of mantle viscosity have been based on postglacial rebound1 and geoid anomalies2. A stratified mantle with a lower-mantle viscosity of ~1022 Pa s is favoured by geoid anomalies2, whereas from global sea-level changes3 a lower-mantle viscosity has been obtained that is slightly higher than ...
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1610-2924
    Keywords: Fractal ; Heterogeneity ; Mantle convection ; Mixing ; Non-Newtonian rheology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract We analyzed and compared the mixing properties of 2-D mantle convection models. Two rheologically different models, Newtonian and non-Newtonian (power-law), were considered with both the line and field methods. The line method is based on monitoring of passive particles joined into lines, while the field method relies on the advection of a passive scalar field. Both visual and quantitative estimates revealed that the efficiency of the Newtonian mixing is greater than the non-Newtonian. A heterogeneity placed in the non-Newtonian convection forms horizontal structures, which may persist for at least 1 Ga on the upper-mantle scale. In addition, the non-Newtonian medium reveals a lesser amount of stretching of the lines than the Newtonian material. The rate of the Newtonian stretching fits well with an exponential dependence with time, while the non-Newtonian rheology shows the stretching rate close to a power-law dependence with time. In the Newtonian medium the heterogeneity is reorganized into two unstable vertical columns, while the non-Newtonian mixing favors horizontal structures. In the latter case, these structures are sufficiently stable in both the temporal and spatial planes to explain the mantle geochemical and geophysical heterogeneities. Due to the non-linear character of power-law rheology, the non-Newtonian medium offers a “natural” scale-dependent resistance to deformation, which prevents efficient mixing at the intermediate length scales.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1610-2924
    Keywords: Geophysics ; Numerical modelling ; Visualization ; Language ; Convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract It was known that deep within numbers and binary data from simulations of geophysical convective flows resided various patterns. Two models of convective fluid flows were being considered. One was a model of two-dimensional (768 × 256) air convection with finite Prandtl number of one and Rayleigh number of 108−1010, and another was a model of three-dimensional (up to 120 × 120 × 90) mantle convection with infinite Prandtl number and Rayleigh number of 106−108. Clearly, phenomena existed which superceded each individual dimensionless computer model to provide a piece of information regarding actual fluid flows. The problem was how to find, prove, and communicate these patterns and phenomena for convection simulations with gigabytes of data. In a search for such an analytical and communicative tool, the alternative of visualization was considered. The need for visualization was recognized and discussed. Then, utilizing both two- and three-dimensional models of high Rayleigh number convection, basic techniques of style and content were developed. Applications of the visualization techniques were designed utilizing IBM’s Data Explorer in order to create communicative images and movies, and after the applications, the problems of data storage and transfer became apparent. Throughout the process though, it became clear how important the language of vision actually could be in the geophysics community. In a field in which words such as plumes and internal waves have in ways replaced mathematics as the basic language for science, there is a need for another resource, another language-the visualization of convective fluid flows.
    Type of Medium: Electronic Resource
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  • 10
    Publication Date: 2007-05-03
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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