Volume 32 Number 2
  • E-ISSN: 1365-2478



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.

The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.


Article metrics loading...

Loading full text...

Full text loading...


  1. Abeles, F.1946, Nouvelles formulas relatives a la lumiere reflechie et transmise par un empilement de lames a faces paralleles, Comptes Rendus de l'Academic des Sciences223, 891–893.
    [Google Scholar]
  2. Brekhovskikh, L. M.1960, Waves in Layered Media, Academic Press, New York , London .
    [Google Scholar]
  3. Kennet, B. L. N.1979, Theoretical reflection seismograms for elastic media, Geophysical Prospecting27, 301–321.
    [Google Scholar]
  4. Kuhn, M. J.1978, The absorptive reflectivity function, SEG Preprint, 48th Annual International SEG Convention.
    [Google Scholar]
  5. Newlands, M.1954, Lamb's problem with internal dissipation: I, Journal of the Acoustical Society of America26, 434–448.
    [Google Scholar]
  6. Pekeris, C. L.1948, Theory of propagation of explosive sound in shallow water, Geological Society of America Memorandum27, 1–116.
    [Google Scholar]
  7. Pekeris, C. L., Alterman, Z. and Abramovici, F.1963, Propagation of an SH‐torque pulse in a layered solid, Bulletin of the Seismological Society of America53, 39–57.
    [Google Scholar]
  8. Tittmann, B. R., Clark, V. A., Richardson, J. and Spencer, T. W.1980, Possible mechanism for seismic attenuation in rocks containing small amounts of volatiles, Journal of Geophysical Research85, 5199–5208.
    [Google Scholar]
  9. White, J. E. and Zechman, R. E.1968, Computed response of an acoustic logging tool, Geophysics33, 302–310.
    [Google Scholar]
  • Article Type: Research Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error