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Methods for the calculation of synthetic seismograms along vertical profiles through horizontally layered media are presented; the aim is to simulate numerically the technique of vertical seismic profiling (VSP), which is sometimes used for improved resolution of deep primary reflections. We present the theory for vertically travelling plane waves and for spherical waves, generated by a single force or an explosive point source. The solution is restricted to the acoustic case. The theoretical seismograms are complete, i.e., they contain all surface and internal multiples. Anelastic effects are taken into account with the method of complex velocities. In order to save computing time, seismogram segments are calculated, using the method of complex frequencies. These methods are applied to a layered model of the coal-bearing carboniferous in the Ruhr district of W. Germany. Different assumptions on overburden structure, recording geometry, and anelasticity are made, and the VSP seismograms are compared with seismograms calculated for horizontal profiles at the surface. It is suggested that VSP field surveys be preceeded by similar numerical studies for an estimate of the information that can be obtained by this expensive technique.
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