Seismic imaging with source deconvolution for marine vibrators with random source signatures

Processes and systems described herein are directed to imaging a subterranean formation from seismic data recorded in a marine survey with moving marine vibrators. The marine vibrators generate random sweeps with random sweep signatures. Processes and systems generate an up-going pressure wavefield from measured pressure and vertical velocity wavefield data recorded in the marine survey and obtain a downgoing vertical acceleration wavefield that records source wavefields, directivity, source ghosts, and random signatures of the random sweeps. The downgoing vertical acceleration wavefield data is deconvolved from the up-going pressure wavefield to obtain a subsurface reflectivity wavefield that is used to generate an image of the subterranean formation with reduced contamination from source wavefields, directivity, source ghosts, and random signatures of the random sweeps.