Modelling near-field effects in VSP-based Q-estimation

Arnim B. Haase, Robert R. Stewart

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 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.