Methods and systems to separate wavefields using pressure wavefield data

A computer system to generate an image of a subterranean formation, the system comprising:

• one or more processors;
• one or more data-storage devices;
• and
• a routine stored in one or more of data-storage devices that when executed by the one or more processors performs
• computing forward and backward extrapolated gathers based on a pressure wavefield gather for each trial depth of a series of trial depths;
• computing an approximate frozen free-surface profile of the free-surface based on the forward and backward extrapolated gathers;
• computing an approximate vertical particle velocity wavefield gather based on the pressure wavefield gather and the approximate frozen free-surface profile;
• computing one of separate up-going and down-going pressure and vertical particle velocity wavefield gathers based on the pressure wavefield gather and the approximate vertical particle velocity wavefield gather;
• and
• generating an image of the subterranean formation using at least in part the up-going vertical particle wavefield gather, the image revealing subsurface structural information about the subterranean formation.

A non-transitory computer-readable medium having machine-readable instructions encoded thereon for enabling one or more processors of a computer system to perform the operations of

• computing forward and backward extrapolated gathers based on a pressure wavefield gather for each trial depth of a series of trial depths;
• computing an approximate frozen free-surface profile of the free-surface based on the forward and backward extrapolated gathers;
• computing an approximate vertical particle velocity wavefield gather based on the pressure wavefield gather and the approximate frozen free-surface profile;
• computing one of separate up-going and down-going pressure and vertical particle velocity wavefield gathers based on the pressure wavefield gather and the approximate vertical particle velocity wavefield gather;
• and
• generating an image of the subterranean formation using at least in part the up-going vertical particle wavefield gather, the image revealing subsurface structural information about the subterranean formation.