Method for seismic data acquisition and processing

1. A method for separating sources, comprising:

obtaining, by at least one receiver, wavefield recordings of an underlying continuous wavefield that has conic support in a temporal-spatial frequency-wavenumber domain, based on a synchronous activation of at least two separate sources moved from shotpoint to shotpoint along a first spatial direction, and repeating the activation along two or more activation lines, wherein the two or more activation lines are distributed along a second spatial direction and each activation line comprises separate lines corresponding to the at least two separate sources;

varying at least one parameter between the at least two sources from one activation to a following activation along at least one of the first and second spatial directions, the at least one parameter being at least one of source signal amplitude, source signal spectrum, source activation time, source location at activation time, and source depth, such that the varying causes support of the frequency-wavenumber representation of the obtained wavefield to be a union of at least two shifted replicas of the support of the frequency-wavenumber representation of the continuous wavefield in at least one of the first and second spatial directions, wherein the frequency-wavenumber representation of information contained in the continuous wavefield is distributed, by means of the varying, to the obtained wavefield so that a periodicity of the obtained wavefield is different than a periodicity as determined by the sampling parameters when the varying is omitted;

using knowledge of the varying, at least partially resolving ambiguity present when the varying is omitted, to generate separated contributions of at least one of the at least two sources;

generating subsurface representations of structures or Earth media properties using the separated contributions of the at least one of the at least two sources; and

outputting the generated subsurface representations.

2. The method of claim 1 , further comprising reconstructing the separated contributions of the at least one of the at least two sources up to a temporal frequency that is higher than a corresponding temporal frequency when the varying is omitted.

3. The method of claim 1 , further comprising reconstructing the separated contributions of the at least one of the at least two sources up to a temporal frequency that is higher than a corresponding temporal frequency when considering only data along a single activation line.

4. The method of claim 1 , wherein the varying of the at least one parameter is periodic.

5. The method of claim 4 , wherein the varying of the at least one parameter comprises time shifting by time shifts that are smaller than 100 ms with respect to a firing time of individual sources.

6. The method of claim 1 , wherein the varying of the at least one parameter comprises superposing multiplying at least two varying functions, wherein at least one of the at least two varying functions is periodic.

7. The method of claim 1 , wherein the varying of the at least one parameter is one of random, naturally random by acquisition, pseudo-random, and quasi-random.

8. The method of claim 7 , wherein the varying of the at least one parameter is a time dither greater than 100 ms.

9. The method of claim 1 , further comprising at least one of dealiasing and reconstructing to recover the continuous wavefield beyond the temporal frequency below which the ambiguity has been resolved.

10. The method of claim 9 , wherein the at least one of dealiasing and reconstructing comprises forming an analytic part of recorded wavefield information, extracting a non-aliased representation of a part of the recorded wavefield information, forming a phase factor from a conjugate part of an analytic part of the non-aliased representation, combining the analytic part of the recorded wavefield information with the phase factor to derive an essentially non-aliased function, applying a filtering operation to the non-aliased function, and recombining the filtered non-aliased function with the non-conjugated phase factor to reconstruct a representation of essentially dealiased recorded wavefield information.

11. The method of claim 9 , wherein the at least one of the dealiasing and reconstructing further comprises iteratively forming analytic parts from parts of the at least one of the dealiasing and reconstruction, and using the analytic parts in solvers of linear systems to increase a range of the parts of the at least one of the dealiasing and reconstruction.

12. The method of claim 9 , wherein a quaternion analytic part is used instead of the analytic part.

13. The method of claim 1 , wherein the obtaining step comprises obtaining the wavefield recordings, which are marine seismic data or seabed seismic data, wherein the sources are towed by a same vessel.

14. The method of claim 13 , wherein airguns or marine vibroseis devices are used as seismic sources.

15. The method of claim 1 , wherein the obtaining step comprises obtaining the wavefield recordings, which are marine seismic data or seabed seismic data, and wherein the sources are towed by at least two different vessels.

16. The method of claim 1 , wherein at least one of the at least two sources is towed at a greater depth than other sources such that each source exhibits different notch frequencies to provide a broadband source effect for all of the at least two sources for wavelengths corresponding to and below a certain frequency.

17. The method of claim 1 , wherein the wavefield is obtained at locations corresponding to a Bravais grid.

18. The method of claim 1 , wherein a number of the activation lines is eight or more, and a number of the shot points along an activation line is eight or more.

19. The method of claim 1 , wherein the varying of the at least one parameter between the at least two sources from one activation to a next is source activation time, and

a difference in source activation time between at least two of the sources is smaller than 50 ms to enable constructive interference of an emitted signal of the at least two sources at frequencies below 6 Hz.

20. The method of claim 1 , wherein the at least two sources are located within 750 m from each other to enable constructive interference of an emitted signal of the at least two sources below 4 Hz.