Although some attention has been paid to the idea that seismic migration is equivalent to a type of deconvolution (of the spatial wavelet), less thought has been given to the opposite perspective: that deconvolution (of the earth Q filter) might itself be equivalent to a form of migration. The key point raised in this paper is that a dispersive 1-D backward propagation can form the basis of a number of different algorithms for inverse Q filtering, each of which is akin to a particular migration algorithm. An especially efficient algorithm can be derived by means of a coordinate transformation equivalent to that in the Stolt frequency-wavenumber migration.This fast algorithm, valid for Q constant with depth, can be extended to accommodate depth-variable Q by cascading a series of constant Q compensations, as in cascaded migration. By combining a cascaded phase compensation with a windowed approach to amplitude compensation, we obtain an algorithm that is sufficiently efficient to be used routinely for prestack data processing. Data examples compare the results of conventional processing with the more stable phase treatment that can be obtained by including prestack inverse Q filtering in the processing.