We have studied elastic wave scattering and iterative inversion in the context of the Kirchhoff approximation. The approach is more consistent with the weak-contrast reflectivity functions of Zoeppritz equations as compared to the Born approximation. To reduce the computational cost associated with inversion, we demonstrated the use of amplitude-variation-with-offset (AVO) analysis, prestack time migrations (PSTMs), and the corresponding forward modeling in an iterative scheme. Forward modeling and migration/inversion operators are based on the double-square-root (DSR) equations of PSTM and linearized reflectivity functions. All operators involved in the inversion, including the background model for DSR and AVO, are defined in P-to-P traveltime and are updated at each iteration. Our method is practical for real data applications because all operators of the inversion are known to be applicable for standard methods. We have evaluated the inversion on synthetic and real data using the waveform characteristics of P-to-P and P-to-S data.