Spherical wave AVO modeling of converted waves in isotropic media

Abstract

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 .

Experimental verification of spherical-wave effect on the AVO response and implications for three-term inversion

“…On the other hand, a big discrepancy occurs at large angles, especially those close to the critical angle. This is a known effect caused by wavefront curvature ͑Krail and Brysk, 1983;Haase, 2004;Doruelo et al, 2006;van der Baan and Smit, 2006; Physically, this effect can be explained by the fact that the spherical wave ͑or indeed any wave with a curved wavefront͒ can be considered as an infinite sum ͑integral͒ of plane waves with different angles to the vertical. At any given point of the interface, the reflection of the spherical wave involves reflection not of just one plane wave corresponding to the specular ray but a range of plane waves corresponding to the bunch of rays within the ray beam around the central ray.…”

Fundamental parameters of spherical‐wave reflection coefficients

“…It is often assumed that spherical-wave effects are only important in the near surface region. However it has been demonstrated that near critical angles an SWRC can differ significantly from a PWRC even at considerable depth (Haase, 2004). This is illustrated in Figure 1. (Here, as in other figures in this abstract, all spherical divergence effects have been normalized out.)…”

“…The black line represents the plane-wave Zoeppritz curve, and the colored lines represent normalized spherical-wave curves with an Ormsby wavelet. Elastic and wavelet parameters are given in Haase (2004). R PP is the plane wave reflection coefficient and θ i is the angle of incidence.…”

AVO modeling with nonzero‐phase spherical waves

“…As described elsewhere, a code developed by Haase (2004) calculates spherical-wave reflection coefficients by performing a numerical p-integration to obtain the ray-parallel displacement spectrum at several frequency points (cf. Aki and Richards, 1980):…”

“…Previous studies of spherical-wave AVO behavior (Haase, 2004;Ursenbach, Haase and Downton, 2005) have shown the need for spherical-wave modeling near critical points. These studies have employed three different types of wavelet: Ormsby, Ricker, and Rayleigh.…”