Abstract The central process in wave-equation--based depth migration is inverse wavefield extrapolation. The commonly applied matched filter approach to inverse wavefield extrapolation ignores the angle-dependent amplitude and phase distortions that are related to fine layering. This may result in dispersed images and erroneous amplitude variation with angle of incidence (AVA) effects. "Power reciprocity" formulates a relation between transmitted and reflected wavefields. It provides the basis for a modified matched filter that does account for the aforementioned distortions. The correction term by which the matched filter is modified can be derived directly from the reflection data. With this modified matched filter, prestack depth migration will yield nondispersed images with correct AVA behavior.