System and methods for hexagonal phase encoding for marine vibrators

A system for arranging two or more seismic sources to separate wavefields generated therefrom, the system comprising:

• a computer processor;
• and
• memory storing instructions that are executable by the computer processor to:
• determine:
• a first seismic source included in the two or more seismic sources that transmits a first signal, and
• a second seismic source included in the two or more seismic sources that transmits a second signal;
• simultaneously transmit, using the first seismic source and the second seismic source:
• the first signal from the first seismic source, and
• the second signal from the second seismic source;
• determine, based on detecting the simultaneously transmitted first signal and second signal, wave number data indicating spatial frequency data that establish a proximal relationship of first plane wave event data associated with the first signal and second plane wave event data associated with the second signal, wherein the spatial frequency data includes:
• first space sampling data associated with a first dimension of a plane wave domain, and
• second space sampling data associated with a second dimension of the plane wave domain;
• designate, based on the wave number data, a position of the first seismic source relative to the second seismic source;
• determine, during a survey and based on the position of the first seismic source relative to the second seismic source, optimal phase modulation of the simultaneously transmitted first signal and second signal that enable deterministic separation of the simultaneously transmitted first signal and second signal in the plane wave domain;
• determine, based on the optimal phase modulation, the first plane wave event data and the second plane wave event data, such that the phase modulation indicates a representation of the first signal and the second signal in the plane wave domain as a hexagon;
• resolve, based on the first plane wave event data and the second plane wave event data, wavefields associated with the first seismic source and the second seismic source and thereby generate resolved plane wave event data;
• and
• arrange, based on the resolved plane wave event data, the first seismic source and the second seismic source to have a distance associated with the position of the first seismic source relative to the second seismic source.

A computer program comprising instructions for arranging two or more seismic sources to separate wavefields generated therefrom, that when executed by a computer processor of a computing device, causes the computing device to:

• determine:
• a first seismic source included in the two or more seismic sources that transmits a first signal, and
• a second seismic source included in the two or more seismic sources that transmits a second signal;
• simultaneously transmit, using the first seismic source and the second seismic source:
• the first signal from the first seismic source, and
• the second signal from the second seismic source;
• determine, based on detecting the simultaneously transmitted first signal and second signal, wave number data indicating spatial frequency data that establish a proximal relationship of first plane wave event data associated with the first signal and second plane wave event data associated with the second signal, wherein the spatial frequency data includes:
• first space sampling data associated with a first dimension of a plane wave domain, and
• second space sampling data associated with a second dimension of the plane wave domain;
• designate, based on the wave number data, a position of the first seismic source relative to the second seismic source;
• determine, during a survey and based on the position of the first seismic source relative to the second seismic source, optimal phase modulation of the simultaneously transmitted first signal and second signal that enable deterministic separation of the simultaneously transmitted first signal and second signal in the plane wave domain;
• determine, based on the optimal phase modulation, the first plane wave event data and the second plane wave event data, such that the phase modulation indicates a representation of the first signal and the second signal in the plane wave domain as a hexagon;
• resolve, based on the first plane wave event data and the second plane wave event data, wavefields associated with the first seismic source and the second seismic source and thereby generate resolved plane wave event data;
• and
• arrange, based on the resolved plane wave event data, the first seismic source and the second seismic source to have a distance associated with the position of the first seismic source relative to the second seismic source.