Most AVO inversion algorithms are based on plane wave solutions whereas seismic surveys use point sources to generate spherical waves. The plane wave solution is an excellent approximation for spherical waves only when the angle of incidence is well below the critical angle. In the vicinity of the critical angle, however, deviation between plane wave and spherical wave responses is prominent. With the recent advances in seismic acquisition techniques where very long offset data is acquired, it may be important to develop AVO inversion based on spherical wave solution. Here we modify the Greedy Annealing Importance Sampling (GAIS) algorithm so that it uses an analytical approximation for spherical waves as a forward model instead of Fatti’s linearized approximation for plane waves. This algorithm is then applied to resolve Woodford formation in the Cana field, Oklahoma. The improvements are shown by comparing the results with those obtained by a deterministic inversion.


Zoeppritz equations describe the amplitudes of incident, reflected and refracted plane waves at an interface as a function of incidence angle. Because this exact solution is complicated, many linearized approximations have been developed. Most AVO analyses utilize one of these linearized approximations even though spherical waves are generated using a point source in seismic surveys; plane wave solution is an excellent approximation for spherical waves in short offsets. This approximation breaks down in the vicinity of the critical angle (Cervený 1961; Cervený and Ravindra 1971; Krail and Brysk 1983; Winterstein and Hanten 1985; Alhussain et al. 2008; Skopintseva et al., 2009).

Alhussain et al. (2008) shows that AVO inversion for Pwave impedance and S-wave impedance is stable over short angles. Inversion for three parameters (P-wave velocity Vp, S-wave velocity Vs and density ?) is not, however. It depends on the frequency at wide angles. Using critical angle, Downton and Ursenbach (2006) could improve the estimation of density using Zoeppritz equations.

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