The effects of source and receiver motion on seismic data

The effects of source and receiver motion on seismic data are considered using extensions of the standard convolutional model. In particular, receiver motion introduces a time-variant spatial shift into data, while source motion converts the effect of the source signature from a single-channel convolution in time to a multichannel convolution in time and space. These results are consistent with classical Doppler theory and suggest that Doppler shifting can introduce distortions into seismic data even at relatively slow acquisition speeds. It is shown that, while both source and receiver motion are known to be important for marine vibroseis acquisition, receiver motion alone can produce significant artifacts in marine 3D data. Fortunately, the convolutional nature of the distortions renders them amenable to correction using simple deconvolution techniques. Specifically, the effects of receiver motion can be neutralized by applying an appropriate reverse time-variant spatial shift, while those due to source motion can be addressed by introducing time-variant spatial shifts both before and after standard, deterministic, signature deconvolution or correlation.