This paper considers propagation of elastodynamic waves in an imperfectly elastic halfspace. Two different excitation modes are investigated : a buried source of compressional waves and a vertically directed area1 load applied to the surface. Numerical integration of the analytical solution of the wave equation allows study of the vertical and horizontal components of displacement and/or particle velocity anywhere in the half-space. One case of particular interest concerns the examination of particle displacement and velocity at the surface in a circular area above the source. In another application seismograms generated by an explosive buried source are contrasted with seismograms generated by the transient application of a vertically directed load to the free surface. Still another application of considerable practical interest concerns the study of the nongeometrical pS-wave, in particular its characteristics as functions of range and depth. Finally, in the last application the behavior of a rarely observed wave (denoted here by the letter U) is studied in both elastic and visco-elastic half-spaces.
A B S T R A C T KUHN, M. and DRACH, V. 1984, On the Possibility of Seismic "Exploration using Surface Torque Source and Related Topics, Geophysical Prospecting 32, In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer.In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques.It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields.In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples.Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at 'wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis.Currently, seismic methods employ source and receiver stations disposed either only horizontally or only vertically. Consequently, the bulk of the collected data consists of either horizontal or vertical profiles.This study concerns the investigation of propagation of horizontally polarized shear waves in field set-ups which are more general than either category. For example, the source may be located anywhere at or near the surface and the sourcegenerated signal recorded at the surface by a string of horizontal geophones oriented perpendicularly to the direction of the profile, or below the surface by a three-component geophone assembly placed at equally spaced intervals against th...
KUHN, M.J. 1987, Evanescent Effects in Acoustical Wave Propagation, Geophysical Prospecting 35, 167-186.The propagation of transient acoustic pressure waves in a layer enclosed between two, not necessarily identical, half-spaces is considered. The source and the receivers are always located in the same half-space and at the same depth. The source excitation function is a narrow causal spike. Several thicknesses of the layer are examined including the case in which the embedded layer vanishes.The phenomena of 'constricted' head waves and wide-angle reflections in the layer are examined in detail using a 'numerical experimentation ' approach. First, a closed-form solution is numerically evaluated. Then this solution is developed in series and each term is evaluated separately using the same numerical techniques. When the contribution of an individual high-order term becomes unimportant, all higher order terms are discarded, and the response is constructed by superposition of the previously computed low-order terms only.Propagation by wide-angle reflections from inside the layer is of interest. When the thickness of the layer is reduced to a fraction of the wavelength, these events consist typically of a low amplitude, high frequency, geometrical acoustics arrival, followed by higher amplitude, low frequency, non-geometrical coda. When all important low-order terms are added, the non-geometrical events tend to interfere destructively, leaving a waveform nearly identical to that obtained by integration of the closed-form solution.When the thickness of the embedded layer is measured in fractions of the dominant wavelength, none of the individual terms of the series development can be duplicated by asymptotic ray tracing. However, because the codas of the various terms interfere destructively, the total response may be well-represented by the addition of a few low-order rays, using asymptotic approximation. This discovery extends the usefulness of Huygens-Kirchhoff ray tracing to modeling of wave propagation in thin layers.
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