Prestack AVA synthetic gathers based on the logging elasticity and anisotropy parameters of the reservoir section of a shale gas well: (a) prestack AVA gathers synthesized by the new four-term approximation, (b) prestack AVA gathers synthesized by Rüger's approximation, (c) prestack AVA gathers synthesized by Aki–Richards’ approximation, (d) waveform residuals subtracted from (a) and (b), (e) waveform residuals subtracted from (a) and (c), (f) reflectivity gathers versus the incidence angle θ by Rüger's approximation, (g) reflectivity gathers versus the incidence angle θ by the new four-term approximation, and (h) reflectivity residuals subtracted from (f) and (g)