A B S T R A C TMost amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for plane-wave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the far-field, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a plane-wave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the plane-wave response. This approach is sufficiently accurate as long as the angles of incidence are much smaller than the critical angle. Such moderate angles are more than sufficient for the standard estimation of the AVO intercept and gradient. However, when independent estimation of the formation density is required, it may be important to use large incidence angles close to the critical angle, where spherical wave effects become important. For the amplitude of a spherical wave reflected from a plane fluid-fluid interface, an analytical approximation is known, which provides a correction to the plane-wave reflection coefficients for all angles. For the amplitude of a spherical wave reflected from a solid/solid interface, we propose a formula that combines this analytical approximation with the linearized plane-wave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a two-layer three-parameter least-squares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of plane-wave reflection coefficients.

The aim of seismic inversion is to estimate subsurface elastic properties. Deterministic seismic inversion based on local optimization suffers from becoming trapped in a local minimum. Also, the inversion result is generally band limited. Various stochastic inversion algorithms have been introduced to address these issues. Many of them, however, are computationally very expensive or can be trapped in a local minimum if the inversion parameters are not carefully chosen. Quantum Annealing (QA) is a global optimization algorithm that is proven to be faster than the conventional Simulated Annealing (SA) method and is less prone to being trapped in a local minimum. Here, we develop a stochastic inversion algorithm using QA and apply it to a 2D seismic dataset from the Cana field, OK with the primary objective of resolving the Woodford formation. The results are compared with those obtained by a deterministic inversion. Our results clearly demonstrate superior performance of our stochastic QA inversion over standard SA and deterministic inversion of field data. The results show clear delineation of the Woodford formation in the inverted images.

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.

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