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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 113 (1993), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: A procedure to evaluate the geometrical properties of the slowness surface for arbitrary anisotropic media is presented. This allows us to use results for computing the displacement field from point sources in general anisotropic media utilizing the Gaussian curvature of the slowness surface of the considered waves. Since the formulae used are based on high frequency asymptotics the procedure gives reliable results as long as no parabolic points of the slowness surface are encountered. Radiation patterns of point sources for models representing rocks in the crust and upper mantle are presented and discussed. The radiation from point sources in anisotropic models is compared with the radiation from point sources in average isotropic models to emphasize the differences. Anisotropy is either caused by aligned cracks (crustal rocks) or by aligned olivine crystals (upper mantle rocks). Considering models of aligned cracks differing only in the physical parameters of the crack material (water or gas) significantly different radiation patterns are obtained. Models with wet cracks exhibit focusing of quasi S-wave energy for some directions whereas this effect is not observed for the corresponding model with dry cracks. The quasi S-wave radiation pattern from explosions are multilobed and the wet crack models exhibit more lobes than the dry crack models. The radiation of single forces in olivine shows strong energy focusing (wave tuning) of quasi S waves, however, for realistic compositions of upper mantle rocks with some 10 per cent of preferentially orientated olivine this wave tuning is less pronounced.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford BSL : Blackwell Science
    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Conventional finite-difference modelling algorithms for seismic forward modelling are based on a time-stepping scheme with a constant (global) time step. Large contrasts in the velocity model or in the spatial sampling rate cause oversampling in time for some regions of the model. The use of locally adjustable time steps can save large amounts of computation time for certain modelling configurations.  The computation of spatial derivatives across the transition zone between regions of the model with different temporal sampling requires the definition of the wavefield at corresponding time levels on both sides of the transition zone. This condition can be obtained by extrapolation in time, which is inaccurate, or by multiple time integration in the transition zone. The error in the latter solution is of the same order as the conventional time-stepping scheme because both methods are based on the same iteration formula. The technique of multiple time integration simply requires the use of different sizes of time step. It is applicable only for certain factors of variation of the time step.
    Type of Medium: Electronic Resource
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