The split-step Fourier method is used to prestack migrate two synthetic borehole-to-surface shot gathers. Model structures in the zone of specular illumination beneath the shot are reconstructed by using the split-step Fourier method both to back-propagate the recorded wavefield and to forward propagate the source wavelet. The overburden is vertically and laterally inhomogeneous. Each depth interval is treated as a homogeneous strip with the mean velocity plus an inhomogeneity correction term. The inhomogeneity correction term is split and spatially multiplied with each spectral component of the wavefield on its entry to and upon its exit from each strip. Propagation through each strip is effected by multiplication in the spatial frequency domain. The split-step Fourier method offers a valuable alternative to finite-difference migration for machines with limited memory.Three imaging methods are compared for two signal-to-noise ratios. They are: image extraction by traveltime, crosscorrelation with source wavelet, and deconvolution with source wavelet. At high signal-to-noise level, the image formed by deconvolution offers better spatial resolution than images formed by crosscorrelation with the source wavelet or by extraction using traveltime. If the signal-to-noise level is low, traveltime imaging deteriorates rapidly, while deconvolution images degrade towards those created by crosscorrelation imaging.

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