Near-field seismic effects in a homogeneous medium and their removal in vertical seismic profile attenuation estimates

To better understand (and correct for) the factors affecting the estimation of attenuation (Q), we simulate subsurface wave propagation with the Weyl/Sommerfeld integral. The complete spherical wavefield emanating from a P-wave point source surrounded by a homogeneous, isotropic and attenuative medium is thus computed. In a resulting synthetic vertical seismic profile, we observe near-field and far-field responses and a 90 degrees phase rotation between them. Depth dependence of the magnitude spectra in these two depth regions is distinctly different. The logarithm of the magnitude spectra shows a linear dependence on frequency in the far-field but not in those depth regions where the near-field becomes significant. Near-field effects are one possible explanation for large positive and even negative Q-factors in the shallow section that may be estimated from real vertical seismic profile data when applying the spectral ratio method. We outline a near-field compensation technique that can reduce errors in the resultant Q estimates.