The formalism for expressing spherical wavefronts as contour integrals over plane waves goes back to Sommerfeld (1909) and Weyl (1919). Brekhovskikh (1960) performed a steepest descent evaluation of the integrals to attain analytic results in the acoustic case. We have extended his approach to elastic waves to obtain spherical-wave Zoeppritz coefficients. We illustrate the impact of the curvature correction parametrically. In particular, we examine conditions appropriate to "bright spot" analysis; expectedly, the situation becomes less simple than in the plane-wave limit. The curvature-corrected Zoeppritz coefficients vary more strongly with the angle of incidence than do the original ones. The determination of velocities and densities from the reflection coefficients is feasible in principle, with exacting prestack processing and interpretation. For orientation, we outline the procedure for the simple case of a separated single source and detector pair over a multilayered horizontal earth.--Modified journal abstract.