Exact seismograms for a point force using generalized ray theory

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Abstract
Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.

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