Long-offset, large-angle reflections have great potential for both both velocity and density inversion. Prestack migration has angle-dependent wavelet stretch effects, which lowers the image resolution at large reflection angles. Current stretch correction filters operate on migrated images. We develop a new stretch-free imaging condition, which does a shrink-and-shift operation on the extracted propagation wavelet after extrapolation, but before the imaging condition is applied. Most existing amplitude versus angle methods do modeling with Zoeppritz approximations, which lose accuracy at large angles. We develop a new inversion method using the "exact" Zoeppritz equation, which is able to invert up to 4 elastic parameters, comparing to the conventional 2- or 3-term inversion. Near- and post-critical reflections have phase shifts as well as amplitude increases. We propose using phase versus angle data (combined with the amplitude data) to do elastic inversion. Phase is less affected than amplitudes by the transmission losses, which makes it more accurate for a target with many overburden layers. The plane-wave reflection coefficients given by the Zoeppritz equation are not applicable near the critical angle in time-space domain, and the modeling of accurate spherical-wave reflection coefficients is expensive. The tau-p transform decomposes spherical waves into plane waves, and thus provides a way of applying the Zoeppritz equation to wide-angle reflections. We test the accuracy of forward modeling and develop a new target-oriented amplitude and phase versus angle inversion algorithm using a tau-p transform and ray tracing, which applies to laterally heterogeneous models. The ray tracing links the reflection angle at the target reflector and the apparent slowness at the receiver, which enables extracting the amplitude and phase versus angle data in the tau-p domain. We suggest using precritical amplitudes and postcritical phases in the tau-p domain for inversion, which uses the Zoeppritz equation to do efficient forward modeling, and can estimate the elastic parameters beneath the target reflector.