Reflectivity Cross Plot of Modified Zoeppritz Equation

Abstract

Beside the complexities and not readily practical applications resulting from the full Zoeppritz equation, the seismic amplitude reflection does not give enough information beyond the critical angle. Consequently, there are breakdown of the Zoeppritz equation approximations at angle of incidence beyond (Shuey’s approximation). More so, the validity is only for slight contrast in elastic parameters across the formations and small angle of incidence is assumed. In an attempt to address these inaccuracies and enhance understanding of seismic reservoir responses and prediction of fluid and lithology, a modified form of the Zoeppritz equation is derived using relations between elastic constants and velocities in terms of Pseudo Poisson’ ratio reflectivity, rigidity reflectivity, density reflectivity in linearized forms devoid of the complexities associated with the original Zoeppritz equation with practical applications in hydrocarbon exploration, exploitation and production. These properties are lithology and fluid discriminators. The modified Zoeppritz equation was analyzed using well data from oil field in a sedimentary basin, onshore of Niger Delta area. Reflectivity crossplot was carried out and comparison with the exact and other approximations was done to validate the derived equation. The results showed that the modified equation can be applied in exploration beyond the critical angle than the shuey’s and Aki & Richards’ approximations especially for deep targets and wide angle acquisition for accurate estimation of intercept and gradient attributes. The modified Zoeppritz equation in this study gives higher accuracy at far offset than the two foremost approximations.