Obtaining multiparameter elastic depth images is a key step toward seismic reservoir characterization. We develop a prestack depth migration/inversion (m/i) method which produces such images in two steps. The first step involves a ``true amplitude'' Kirchhoff elastic prestack depth migration, which provides migrated depth images of the elastic reflectivity Rpp, and the associated specular reflection angles . The second step involves fitting three elastic parameters to the migrated elastic specular reflectivity by use of the Bortfeld linearized approximation to the nonlinear Zoeppritz relation, which results in three migrated elastic parameter depth images of the target zone. We investigate the m/i in terms of stability and choice of parameterization, and calculate quantitative ``confidence'' images to appraise our results. We find that relative changes in P and S impedances are the most robust parameters for standard surface seismic reflection acquisition geometries, and that little or no unambiguous information regarding density variation is contained in the standard specular illumination range of 0-30. Our method is tested with synthetic and field data examples, the latter to be presented at a later date pending proprietary release.