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  • 1
    Electronic Resource
    Electronic Resource
    Book review (1988)
    Springer
    Pure and applied geophysics 127 (1988), S. 695-752 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00881752
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fractals in geology and geophysics (1989)
    Springer
    Pure and applied geophysics 131 (1989), S. 171-196 
    Details
    ISSN: 1420-9136
    Keywords: Fractals ; self-similarity ; scale invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The definition of a fractal distribution is that the number of objectsN with a characteristic size greater thanr scales with the relationN∼r −D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. Fractals were originally introduced by Mandelbrot to relate the length of a coastline to the length of the measuring stick. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photographs of many geological features is one indication of the wide applicability of scale invariance to geological problems, scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00874486
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  • 3
    Electronic Resource
    Electronic Resource
    A cellular-automata, slider-block model for earthquakes I. Demonstration of chaotic behaviour for a low-order system (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 111 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We consider a pair of slider blocks connected to each other and to a constant velocity driver by springs. Stick-slip behaviour is obtained using static and dynamic coefficients of friction. With any asymmetry, numerical calculations show that this system can exhibit classical chaotic behaviour. We simplify the behaviour of the system by assuming that the two blocks never slide together. One block may trigger the slip of the other, but its slip is delayed until the first block sticks. The orbits in phase space are periodic in the symmetrical case but the orbit the system evolves to depends on the initial conditions. If the friction coefficients of the blocks are different, we can have chaotic behaviour with positive Lyapunov exponents for some parameter values, and periodic or limit cycles orbits for other values. In some cases we have limit cycle orbits for one interval of initial conditions and chaotic behaviour for others. The Poincarè map for the model is a piecewise linear function and is strongly dependent on the parameters of the model. The behaviour of the simplified single slip model is quite similar to the original multiple slip model. The advantage of the simplified model is that the solution is algebraic and it can form the basis for a cellular-automata model which is completely deterministic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00574.x
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  • 4
    Electronic Resource
    Electronic Resource
    A cellular-automata, slider-block model for earthquakes II. Demonstration of self-organized criticality for a 2-D system (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 111 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: It has been suggested that distributed seismicity is an example of self-organized criticality. If this is the case, the Earth's crust in an active tectonic zone is in a near-critical state and faults can interact over large distances. Observed seismicity and earthquake statistics are consequences of the dynamical interaction of seismic faulting over a wide range of scales. We address this problem by considering a two-dimensional array of slider blocks with static/dynamic friction. The twodimensional system is treated as a cellular automaton such that only one slider block is allowed to slip at a given time and interacts only with its nearest neighbours through connecting springs. Because of this treatment, the amount of slip for each failed block can be obtained analytically, and the system is deterministic with no stochastic inputs or spatial heterogeneities. In many cases, the slip of one block induces the slip of adjacent blocks. The size of an event is specified by the number of blocks that participate in the event. The number of small events with a specified size has a power-law dependence on the size with a power close to -1.36. The distributions of normalized recurrence times for most events are close to a Poisson process, and gradually deviate towards periodicity for large events. The recurrence time statistics are generally insensitive to parameter variations. Large events may occur at stress levels considerably lower than the failure strength of an individual block, and the stress drops associated with large events are generally small. This may provide an explanation for observed low stress levels in tectonically active areas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00575.x
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  • 5
    Electronic Resource
    Electronic Resource
    Fractals, chaos, self-organized criticality and tectonics (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Terra nova 4 (1992), S. 0 
    Details
    ISSN: 1365-3121
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Some geological structures have simple geometrical forms and can be analysed using deterministic equations. Examples include alluvial fans and many sedimentary basins. But most geological structures are complex and appear to defy mathematical analyses. Yet in the complexity there is an order. Complex geological structures generally obey fractal statistics. Examples include topography, distributions of earthquakes and faults, and mineral deposits. An unresolved question is whether the fractal order is simply the result of scale invariance or the result of governing equations that yield deterministic chaos. In order to try to answer this question a variety of slider-block models have been considered. The stick-slip behaviour of slider-block models is a simple analogy to earthquakes. A pair of slider-blocks has been shown to behave chaotically. Models that use many slider-blocks exhibit self-organized criticality and generate fractal statistics similar to the statistics of regional seismicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-3121.1992.tb00444.x
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  • 6
    Electronic Resource
    Electronic Resource
    Implications of a two-component marble-cake mantle (1986)
    [s.l.] : Nature Publishing Group
    Nature 323 (1986), S. 123-127 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] It is suggested that the upper mantle contains elongated strips of subducted oceanic lithosphere. These strips are stretched and thinned by the normal and shear strains in the convecting mantle, and are destroyed by being reprocessed at ocean ridges or, on the centimetre scale, by dissolution ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/323123a0
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Geochemical light on mantle convection (1982)
    [s.l.] : Nature Publishing Group
    Nature 296 (1982), S. 487-488 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] MANTLE convection is generally accepted to be the driving mechanism for continental drift and plate tectonics, but controversy persists about the scale on which the process takes place. Does convection involve the whole mantle, down to the boundary with the core? Or, as Allegre1 has recently ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/296487a0
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  • 8
    Electronic Resource
    Electronic Resource
    Accretional capture of the Moon (1975)
    [s.l.] : Nature Publishing Group
    Nature 258 (1975), S. 219-220 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The primary difficulty with the hypothesis of lunar capture is its inherent improbability. Either collision or escape is much more likely, but capture could take place if sufficient dissipation occurred during a close approach of the Earth and Moon. It is unlikely, however, that tidal dissipation ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/258219a0
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  • 9
    Electronic Resource
    Electronic Resource
    On the structure of Alfvén shocks (1966)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 17 (1966), S. 528-537 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Résumé Nous avons montré que les chocs d'Alfvén en une dimension ne possèdent pas de structure constante dans un fluide incompressible qui est un conducteur d'électricité finie. La structure des chocs d'Alfvén est calculée pour le problème d'un piston uni-dimensionel. En outre, une structure approximative est obtenue pour le choc d'Alfvén oblique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01595987
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Chaotic and self-organized critical behavior of a generalized slider-block model (1992)
    Springer
    Journal of statistical physics 67 (1992), S. 1151-1183 
    Details
    ISSN: 1572-9613
    Keywords: Chaos ; self-organized criticality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The dynamical behavior of two-dimensional arrays of slider blocks is considered. The blocks are pulled across a frictional surface by a constant-velocity driver; the blocks are connected to the driver and to each other by springs. Only one block is allowed to slip at a time and its displacement can be obtained analytically; the system is deterministic with no stochastic inputs. Studies of a pair of slider blocks show that they exibit periodic, limit-cycle, or choatic behavior depending upon parameter values and initial conditions. Studies of large, two-dimensional arrays of blocks show self-organized criticality. Positive Lyapunov exponents are found that depend upon the stiffness and size of the array.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049013
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