Removal of all time-varying sea-surface effects by source deghosting and demultiple

Seismic source deghosting and sea-surface-related demultiple have been long-standing problems in marine seismic data processing. Although the receiver ghost problem may be considered as solved by using collocated measurement of pressure and normal velocity wavefields, the source deghosting and demultiple algorithms are still limited by assumptions related to the sea-surface condition. We have investigated the impact of a time-varying rough sea surface on source deghosting and demultiple. Starting from Rayleigh's reciprocity theorem for time-varying sea surfaces, we uncover a fundamental limitation for source deghosting of time-dependent wavefields, such as marine seismic data that contain a receiver ghost or sea-surface-related multiples. We use simple synthetic examples to study the impact of source deghosting on sea-surface-related multiples. To resolve this limitation, we derive a method for simultaneous source deghosting and sea-surface-related demultiple for time-variant wavefields. Finally, we use the complex geologic model Sigsbee 2B first to illustrate that the source deghosting operation brings significant errors when applied to a data set containing sea-surface multiples. Second, we find that this problem can be resolved by simultaneously performing source deghosting and demultiple operations even in the presence of time-varying sea surfaces.