The computation of synthetic vertical seismic profiles seismograms in the attenuating layered media

The Computation of Synthetic Vertical Seismic Profiles Seismograms in the Attenuating Layered Media For many years, numerical simulations of wave propagation in elastic and anelastic media have became increasingly an important tool in the interpretation of vertical seismic profiles (VSPs). The main purpose of this sort of studies has been to- explain complexity of the VSP data in relation to the Earth' s subsurface. To obtain a reliable the best way is computation of VSP seismograms. In this study, we used the method of discrete wavenumber representation of elastic wave fields to compute of synthetic VSP seismograms that include the effects of attenuation and dispersion. The method is based on a superposition of plane waves propagating in discrete directions from a source. Disretization of elastic waves is results from a periodic arrangement of sources rather than using a single source. In discrete wavenumber solution, seismograms incorporating attenuation and dispersion effects initially computed in the frequency domain, are then Fourier transformed to the time domain. The method can be applied to a large number of layers and a two-dimensional source-receiver's geometry. For propagating of elastic waves in layered media have been used to conventionally propagator matrix formulation. The effects of attenuation and dispersion have been easily included in the calculation of synthetic seismograms by replacing the real elastic velocities with complex frequency and quality factor (Q)-dependent expressions widely used in the current literature. Theoretical seismograms of a medium with flat horizontal layers overlying a half space have been computed for the cases of elastic and anelastic propagation. Effects of quality factor on seismic wavelets and reflection coefficients have been determinated. The complex velocity equation used has been analyzed for causality. VSP seismograms calculated include reflections, multiples, head waves, direct waves, converted waves (from P wave to S wave or its inverse) and Rayleigh surface waves exactly. In addition, the direction of source force has been studied as horizontal and vertical forces. Effects of application direction of source forces on P and S wave fields have been examined by calculating VSP sections for each horizontal and vertical source forces. Key words: Vertical Seismic Profile (VSP), Discrete Wavenumber, Attenuation, Source Forces, Synthetic Seismograms. VI