This paper examines the high-frequency approximations of two integrals associated with the name of Kirchhoff. The first one is known in the geophysical literature as the Kirchhoff-Helmholtz integral. It computes, in the time or frequency domains, the seismic acoustic/elastic response at a receiver, given the locations of a source-receiver pair, a laterally inhomogeneous velocity model and a reflector. The second one is the more recent diffraction-stack integral also known as the Kirchhoff-migration integral. With it, the observed seismic response of an unknown reflector, here formulated for arbitrary source-receiver configurations is transformed (imaged) into the reflector. Both integrals can be understood, both qualitatively and quantitatively, as operations asymptotically inverse to each other. -from Authors33203214