Generalized non-hyperbolic approximation for qP-wave relative geometrical spreading in a layered transversely isotropic medium with a vertical symmetry axis

Compensation for geometrical spreading along the ray-path is important in amplitude variation with offset analysis especially for not strongly attenuative media since it contributes to the seismic amplitude preservation. The P-wave geometrical spreading factor is described by a non-hyperbolic moveout approximation using the traveltime parameters that can be estimated from the velocity analysis. We extend the P-wave relative geometrical spreading approximation from the rational form to the generalized non-hyperbolic form in a transversely isotropic medium with a vertical symmetry axis. The acoustic approximation is used to reduce the number of parameters. The proposed generalized non-hyperbolic approximation is developed with parameters defined by two rays: vertical and a reference rays. For numerical examples, we consider two choices for parameter selection by using two specific orientations for reference ray. We observe from the numerical tests that the proposed generalized non-hyperbolic approximation gives more accurate results in both homogeneous and multi-layered models than the rational counterpart.