Analytical wavefront curvature correction to planewave reflection coefficients for a weakcontrast interface
Abstract
Most amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for planewave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the farfield, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a planewave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the planewave 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 fluidfluid interface, an analytical approximation is known, which provides a correction to the planewave 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 planewave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a twolayer threeparameter leastsquares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of planewave reflection coefficients.
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