Analytical wavefront curvature correction to plane-wave reflection coefficients for a weak-contrast interface
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Most 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.
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