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The complexity of transient electromagnetic scattering from objects in free space has been well known for years. Such complexity is mainly due to the high aspect dependency of the early-time response, and the interactions between the various scattering events. Attempts have been made to analytically and numerically study the transient scattering problem using time-frequency (TF) analysis. Using this technique, the occurrences of the scattering events and their frequency content can be revealed, which leads to further information about the actual scattering behavior. For the case of subsurface targets, the entire problem becomes more complicated with the introduction of a dielectric interface. Analytical solutions of such complicated electromagnetic problems are usually not available, and can only be numerically addressed in most cases. In this paper, a systematic study of transient scattering from some subsurface targets is presented. The various interactions between the target and the interface of the half-space can be clearly observed. The findings from this work have opened up some issues that are left for further investigation.