Correlating transmission wavefields to produce reflection wavefields contains in its rigorous definition the mandate of processing data due to only a single source. If more than one source is contained in the wavefield, crosstalk between the sources will produce a data volume that is not the same as shot gathers with impulsive sources at each receiver location. When attempting to image the subsurface with the truly unknown ambient noisefield, parameterizing the field data by individual sources is impossible.
For truly passive data, the source and time axis are inextricably combined, naturally and by processing. This changes direct migration to something more akin to planewave migration. Since the direct arrival from each source can not be expected to sum together with a common time-delay, the summation manufactures a source wavefront with temporal topography rather than a planewave.
The Fourier transform of field data as a single wavefield provides insight into how sources are summed during correlation. Also, the transform simultaneously stacks away useless waiting periods between useful energy bursts and reduces the data volume. Previously, white, zero-phase source functions were invoked to avoid the summation problem. However, neither assumption is likely in the real environment of a long term experiment.