In recent years, the petroleum industry has invested heavily in the development of improved marine survey techniques and seismic data processing methods in order to increase the resolution and accuracy of seismic images of subterranean formations. Marine surveys illuminate a subterranean formation located beneath a body of water with acoustic signals produced by one or more submerged marine sources. One type of marine source often used in marine surveys is composed an array of air guns. An acoustic signal may be generated by simultaneously activating the air guns. The air guns generate separate pressure wavefields that combine to form a total pressure wavefield. This wavefield is an acoustic signal that radiates outward in all directions. A portion of the wavefield travels directly from the source through the body of water and into the subterranean formation, and a portion of the wavefield travels upward to the free surface before being reflected downward from the free surface to the subterranean formation. The reflected portion of the wavefield is called the “source ghost” because the reflected portion is time-delayed and travels behind the direct portion of the wavefield. At each interface between different types of rock or sediment of the subterranean formation a portion of the source wavefield energy is refracted, a portion is transmitted, and a portion is reflected back toward the formation surface and into the body of water. A typical marine survey is carried out with a survey vessel that passes over the illuminated subterranean formation while towing elongated cable-like structures called streamers. The streamers may be equipped with a number of collocated, pressure and particle motion sensors that measure the response of the subterranean formation to the direct and source ghost components of the source wavefield. The pressure sensors generate seismic data that represents the pressure wavefield reflected from the subterranean formation and the particle motion sensors generate seismic data that represents the particle motion, particle velocity, or particle acceleration wavefield reflected from the subterranean formation. The survey vessel receives and records the seismic data generated by the sensors.
The seismic data is processed with seismic data processing techniques that depend on highly accurate estimates of the source wavefield in order to effectively remove source wavefield effects from the seismic data and ultimately generate high-resolution seismic images of the subterranean formation. Any errors in an estimate of the source wavefield lowers the signal to noise ratio and general quality of the seismic images. When the air guns of a source array towed behind a vessel are simultaneously activated, air bubbles created by the air guns in previous activations do not substantially affect estimates of the source wavefield from the current activation, because the air-bubbles remaining in the water from previous activations are behind the current position of the source due to forward motion of the source. On the other hand, when the air guns within a source array towed behind a vessel are activated at different times with short time intervals (e.g., a few seconds or less), the water column surrounding a next to be activated air gun may be filled with air bubbles created by one or more neighboring, previously activated air guns. The air-bubbles create very complex and unpredictable effects on the wavefield emitted by the next to be activated air gun. As a result, an estimate of a source wavefield may not accurately characterize the source wavefield generated by the air guns.