Reliable estimates of vertical, inline, and crossline components of apparent displacements in time-lapse seismic images are difficult to obtain for two reasons. First, features in 3D seismic images tend to be locally planar, and components of displacement within the planes of such features are poorly resolved. Second, searching directly for peaks in 3D crosscorrelations is less robust, more complicated, and computationally more costly than searching for peaks of 1D crosscorrelations. I estimate all three components of displacement with a process designed to mitigate these two problems. I address the first problem by computing for each image sample a local phase correlation instead of a local crosscorrelation. I address the second problem with a cyclic sequence of searches for peaks of correlations computed for lags constrained to one of the three image axes.