Deghosting in Depth Image Domain Using a PSF-Trained U-Net

In the marine seismic acquisition, hydrophones are distributed along streamers that are towed under the sea surface, recording both the upgoing primary reflections and the downgoing free-surface reflections. The interferences between them result in notches in the frequency-domain amplitude spectra, causing missing frequencies and destroying the broadband signature. These free-surface reflections, referred to as ghost waves, are usually treated as noises and are supposed to be suppressed or removed before depth migration imaging, namely, the deghosting processing. If the ghost waves are not effectively removed, they will be projected to the subsurface image domain, further causing missing wavenumbers and influencing resolutions. The missing information can hardly be fully compensated through traditional deconvolution-type filters in the data or image domain. Recently, deep-learning-based methods have been introduced to data-domain deghosting. However, generating a sufficiently large number of training samples with and without ghost waves is quite costly, and it is difficult to guarantee the diversity, leading to the limited generalization capability of neural networks trained with these datasets. Therefore, we are motivated to use the point spread function (PSF) to project the near-surface ghost-related parameters to the subsurface local image domain. In this way, large numbers of depth images with and without ghost waves can be constructed efficiently through convolutions between PSFs and local model perturbations. The diversity of training samples can be easily satisfied. Using these paired samples, we train U-nets for deghosting processing in the image domain. Various examples validate the new deep-learning-based method.