The AVO-response of two-layer isotropic models for AVO-Classes 1 and 3 is investigated for converted waves. Zoeppritz's reflection coefficients and the Weyl-integral are utilized for the computations. Spherical wave results for R ps and R pp are compared with plane wave reflectivity. Depth dependence of spherical wave AVO is found to be strongest near critical angles of Class 1. There is some similarity between R ps and R pp for Class 1. Normalized Class 3 responses show no depth dependence. There is no similarity between Class 3 R ps and R pp . Attenuation reduces AVO-response magnitudes. R ps appears to be more sensitive to finite Q-factors than is R pp .
A method is presented for efficiently and accurately calculating the spherical-wave generalization of the Zoeppritz P-wave reflection coefficients. The main assumptions are that the wavelet is an exponential form that allows for analytic integration over frequency, and the direction of propagation and arrival time are as dictated by ray theory. These assumptions result in calculations sufficiently rapid to be carried out interactively on the computer. Results for an AVO Class I model show that this method quantitatively reproduces exact spherical-wave reflection coefficients obtained using a Ricker wavelet.
VSP data and well log information from the Ross Lake oilfield, Saskatchewan (owned by Husky Energy Inc.) are used to estimate P-wave and S-wave attenuation (Qfactors). The VSP surveys used both vertical and horizontal vibrators as sources and a downhole five-level, threecomponent receiver. From the spectral ratio method applied to downgoing waves, results are obtained for Q P as well as Q S. We estimate an average Q P , over an interval of 200-1200m, to be 67 from the spectral ratio technique. We also use VSP-sonic drift curves to find a Q p of 40 over the same interval. Q S estimates are 23 from the spectral ratio method and about 37 from "guesstimated" S-wave drift curves over the same interval.
The AVA-response of VTI-models for AVO-Classes 1 to 4 and two special cases is computed utilizing plane-wave reflection coefficients and the Weyl-integral. It is found that below 30° of angle, in most cases, the spherical VTI-response departs more from an isotropic plane-wave comparison than isotropic spherical responses. Depth dependence of isotropic spherical responses is strongest near critical angles, exactly where important information resides. VTI-type anisotropy shifts this point of maximum sensitivity towards larger angles.
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