In marine seismic acquisition, seismic reflections at the sea surface, such as sea-surface ghosts and multiples, affect the accuracy of the retrieved subsurface reflections and reduce the usable frequency bandwidth. These sea-surface effects tend to increase with the increasing roughness of the weather conditions. Consequently, processing techniques that neglect the roughness and time variation of the sea surface induce errors in the data that could compromise the validity of the final images and interpretations. We study the impact of time-varying rough sea surfaces using a modeling method derived from the Rayleigh reciprocity theorem for time-varying surfaces, and we analyze errors in the source-deghosting operation. We show that the source-deghosting limitations are weather dependent for data including sea-surface multiples: For calm sea states (wave heights below 1.25 m), the error made by the source-deghosting process is negligible; however, for rough seas (wave heights above 1.5 m), it becomes significant and blurs the deghosted image at the sea-surface multiple signals. To accurately remove all sea-surface effects from the seismic data, we simultaneously apply source-deghosting and multiple-removal operations to the same up-going wavefield. This procedure is shown to be weather independent based on our theoretical derivation and the synthetic results. Finally, this is tested on a 2D OBC data set. Comparing the proposed inversion to up-down deconvolution, we observe similar features in both wavefields: Source ghosts and sea-surface multiples seem to have been correctly removed from the data, and the inverted result indicates a slightly better resolution for deeper reflections.