Partially coherent migration

Abstract Partially coherent migration reduces the spurious details introduced by velocity macro-model imperfections. In a partially coherent migration, instead of summing coherently over the full aperture to achieve maximum lateral resolution, (1) a coherent stack is performed over a limited window width, and then (2) the collection of coherent stacks for different windows along the full aperture are summed incoherently to produce an amplitude value for each output point. Amplitude accuracy of a migration is improved with some sacrifice in spatial (lateral) resolution.A parameter in partially coherent migration is the running coherent window width, which accounts for the spatial correlation of errors in the velocity model. The coherent window width controls the trade-off between signal-to-noise ratio and lateral resolution. Assuming that timing errors introduced by imperfections of a velocity macro-model are from a zero-mean stationary Gaussian process, partially coherent migration is shown to raise the signal-to-noise ratio of the migrated image as compared to a conventional migration. The two competing aspects of signal-to-noise ratio and lateral resolution of the partially coherent migration in the presence of timing errors are analyzed in a stochastic framework. The intuitively attractive idea of limiting the coherent window width to the correlation length of the timing errors is confirmed numerically.