Empirically adjusted ray amplitudes in the vicinity of the critical region

an empirical approach for correcting geometrical ray theory p-wave amplitudes in the vicinity of the critical distance xc, is presented. ray theory is well known to produce inaccurate amplitudes. it is found that simply smoothing the amplitudes within the previously defined "critical zone" with a third-degree polynomial provides an excellent match of the avo curves generated by the ray theory with the exact results. the method implicitly takes into account the amplitude variation vs. offset, frequency, source-receiver height above the interface and physical parameters of the geological model.