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  • 1
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    In:  Proc. R. Soc. London, Basel, Inst. f. Geophys., Ruhr-Univ. Bochum, vol. A. 337, no. 15, pp. 49-71, pp. 1417, (ISSN: 1340-4202)
    Publication Date: 1974
    Keywords: Inversion
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  • 2
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    In:  Pageoph, Amsterdam, Elsevier Scientific Publishing Company, vol. 157, no. 6, pp. 1707-1727, pp. B12308
    Publication Date: 2000
    Keywords: Tsunami(s) ; Crustal deformation (cf. Earthquake precursor: deformation or strain) ; Modelling ; France ; PAG
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 157 (2000), S. 1707-1727 
    ISSN: 1420-9136
    Keywords: Key Words: Numerical modelling, fluid mechanics models, submarine flowslides, water waves, tsunami generation.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract —On the 16th of October 1979, a part of the Nice new harbour extension, close to the Nice international airport (French Riviera), slumped into the Mediterranean Sea during landfilling operations. A submarine slide with initial volume close to seashore of about 10 millions m3, which could have evolved later into an avalanche, was followed by a small tsunami, noticed by several witnesses in the “Baie des Anges.” The maximum tsunami effects were observed 10 km from the slide location near Antibes city, which was inundated. Previous analyses used rough approximate methods and produced models which did not conveniently fit data. In this paper, both the slide and the generated water waves are numerically simulated on the basis of the shallow water approximation. The landslide is assimilated to a heavy Newtonian homogeneous fluid downslope under gravity. Water waves are generated by sea-bottom displacements induced by the landslide. Taking into account a very accurate multibeam bathymetric map, the Nice slide of 10 millions m3 is simulated by this model. The numerical results are generally consistent with the observed hydraulic local effects in front of the Nice airport, however they are not in agreement in the far field. A larger and deeper landslide 2 km off Nice airport is tested to quantitatively study the effects of the landslide volume on water waves generation.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 861-868 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Distorted wave Born series are derived for the impedance equation [A−1(d/dx)A(d/dx)+k2]p=0, where A is a piecewise differentiable function. The first and second orders are given explicitly. They hold for impedances A, which include discontinuities, before and/or after perturbation, so that the problem could not be reduced to the Schrödinger one. The results are used for discussing homogenizations currently practiced in modeling discontinuous media.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4594-4636 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This report contains an exact study of elastic wave propagation and its scattering in discontinuous media where hard reflectors are onionlike sets of surfaces. In order to reformulate the problem as a finite set of boundary integral equations, the wave motion between reflectors is represented by means of elastic potentials which involve vectorial densities on the surfaces. In the external medium, an outgoing asymptotic condition generalizes the Silver–Müller (and the Sommerfeld) condition to the case of coupled waves (S and P waves) moving with different velocities. The uniqueness of the Green's function, which guarantees the uniqueness of the direct problem solution, is proven. For any incident wave and arbitrary number of surfaces, the transmission and scattering problems are studied, with and without the simplification obtained by assuming constant Poisson ratios. According to the parameter ranges, the equations which are obtained are well posed, either as second kind Fredholm equations, or because they reduce to the inverse of the sum of the identity operator and a "small norm'' bounded operator. The results can be used to describe rigorously the three-dimensional scattering of elastic waves in the frequency domain for any kind of incident wave function (P,S,...) as well as the response to a localized source.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4028-4040 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of homogeneous, norm conserving, nonlinear wave equations of the Schrödinger type is studied. It is shown that those equations which derive from a Lagrangian can be linearized, but have no regular confined solutions, whereas the equations which cannot be obtained from a local Lagrangian do admit such confined solutions. The latter however are unstable against small perturbations of the initial data.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2585-2598 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A realistic model for the propagation of scalar waves in a medium must take into account discontinuities of the medium parameters, which may act as "hard'' reflectors; discontinuities of their gradient, which may act as "soft'' reflectors; and continuous variations of parameters. The direct scattering problem is presented here. The "mixed potential–impedance'' equation that characterizes the model depends on two arbitrary parameters: one of them would be the potential if the equation reduces to the Schrödinger equation; the other one would be related to the impedance if the equation describes more "classical'' waves. After the mathematical tools are constructed (Green's functions, etc.), a rigorous three-dimensional scattering theory is described. It encompasses the quantum three-dimensional scattering theory and the theory of acoustical scattering (for instance) by systems of regular surfaces of arbitrary shape. The main integral equations of the quantum scattering theory are generalized. Scattering amplitudes due to reflectors and scattering amplitudes due to diffuse scattering after reflectors have been taken into account are defined and constructed. Born and quadratic approximations are discussed: the explicit formulas corresponding to the scattering by discontinuities and those corresponding to diffuse scattering are not reducible to each other exactly (i.e., unless filtering and errors are allowed). The results can also be used to described rigorously the three-dimensional scattering by the "wave-equation'' in the frequency domain—and in particular the response to an impulsive localized source. Further generalizations are in progress.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and mathematical physics 99 (1994), S. 767-775 
    ISSN: 1573-9333
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 9
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    Hilger
    In:  Bristol, Hilger, vol. 20, no. Publ. No. 12, pp. 81-89, (ISBN 1-4020-1267-5 (hb), ISBN 1-4020-1268-3 (pb))
    Publication Date: 1987
    Keywords: Inversion ; Textbook of mathematics ; Textbook of geophysics
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  • 10
    Publication Date: 1988-04-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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