Modelling Near-field Effects in VSP-based Q-estimation

The complete spherical wavefield emanating from a P-wave point source surrounded by a homogeneous isotropic medium is computed with the aid of Sommerfeld/Weyl integrals. In a resulting synthetic VSP, we observe a near-field, a far-field and a 90 degree phase rotation between the two. Depth dependence of magnitude spectra in these two depth regions is distinctly different. Log magnitude spectra show a linear dependence on frequency in the far-field but not in 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 VSP data when applying the spectral ratio method.