Well-collimated short pulse wave packets, also termed pulsed beams (PB), provide new options for local forward and inverse probing of targets or of a propagation environment. The spatial-temporal resolution achieved under the PB excitation conditions furnishes an unambiguous measure of where the ``physical'' signal resides, in contrast to frequency-domain procedures that must rely on more intricate phase discrimination. In this paper, PB forward and inverse modeling is applied to scattering by three-dimensional weak (Born-type) inhomogeneities with finite support in an otherwise homogeneous background fluid. By performing space--time and wave number--frequency analysis and synthesis in a phase space setting, conventional slant-stack tomography is pushed to its ultimate localization by PB pre- and post-processing. The implications of this scenario with respect to resolution and related issues are discussed. It is shown that this strategy reduces the inversion of the illuminated space-time scattering cell to a pseudo-one-dimensional problem determined by the orientation of the incident and scattered beam axes. Illustrative examples are included.