Gaussian Beam Migration for Sparse Common-Shot and Common-Receiver Data

We investigate the application of Gaussian beam migration for common-shot and common-receiver seismic data. The inversion of common-shot data is useful for seismic data where the receiver coordinates are well sampled, but the source coordinates are less well sampled. Since Gaussian beam migration uses smoothed, localized windowing of the data, it can provide more stable results for the inversion of sparsely sampled common-shot data. By reciprocity, this approach can also be applied to common-receiver data, such as from an OBS experiment where the source locations are dense but the receiver locations are sparse. In order to test the common-shot Gaussian beam algorithm, a prestack data set was computed using the finite difference method for a slice from the SEG/EAGE salt model which has significant lateral velocity variations. For the generation of the synthetic data, no free surface multiples were included. Prior to the tracing of rays and beams through the model, smoothing of the velocity was performed. The phase times were then corrected using first-order perturbation theory. A receiver spacing of 20 m was used with an offset range of 13,400 m, and the shot spacing was allowed to vary. Comparing the Gaussian beam migration images with the true model, most of the features were well imaged. In particular, most features beneath the salt were imaged including steeply dipping events and a lower flat reflector. The Gaussian beam images also compared well with results from other methods.