System and method for generating dithering sequences for seismic exploration

1. A method for generating discrete dithering sequences DS i for marine seismic sources S i in a marine acquisition system, the method comprising:

determining ( 1400 ) a number N of the seismic sources S i to be fired;

calculating ( 1402 ) a dithering sequence DS i for each source S i such that when any two consecutive source activation S k and S l , where l=k+1, are selected, a combination DS kl of their dithering sequences DS k and DS l is a uniform random low-discrepancy sequence; and

driving ( 1404 ) each source S i with the corresponding dithering sequence DS i to generate blended seismic data,

wherein uniform random means that any value within a given interval is equally likely or close to equally likely to be drawn, and low-discrepancy means that a proportion of points in the uniform random low-discrepancy sequence falling into an arbitrary set B is close to proportional to a measure of B.

2. The method of claim 1 , wherein the low-discrepancy is obtained by imposing an anti-clustering condition to each element of each dithering sequence DS i .

3. The method of claim 1 , further comprising:

selecting the number of dithering values (nPoints) for each source;

selecting a number of backward values (nBacksteps) to be used for the anti-clustering condition; and

selecting a time range defined by a minimum dither time and a maximum dither time, in seconds, for the elements of the sequence DS i .

4. The method of claim 3 , further comprising:

in a loop, generating new candidate random numbers R for each sequence DS; and

checking if the new random numbers, for each sequence, satisfies the anti-clustering condition.

5. The method of claim 4 , wherein the nBacksteps values in the anti-clustering condition are gradually scaled down in each iteration to ensure that the candidate random numbers are accepted.

6. The method of claim 4 , further comprising:

discarding random numbers that are in excess of a given range.

7. The method of claim 6 , further comprising:

scaling remaining accepted random numbers to fit inside the range in seconds for the elements of the sequence DS i selected by a user.

8. The method of claim 1 , wherein additional checks are performed to also ensure that a combination DS kl of their dithering sequences DS k and DS l from sources S k and S l , where l=k+2, are uniform random or close to being uniform random and low discrepancy.

9. A computing device ( 1700 ) for generating discrete dithering sequences DS i for marine seismic sources S i in a marine acquisition system, the computing device comprising:

an interface ( 1708 ) configured to receive ( 1400 ) a number N of the seismic sources S i to be fired; and

a processor ( 1708 ) connected to the interface and configured to,

calculate ( 1402 ) a dithering sequence DS i for each source S i such that when any two consecutive source activations S k and S l , where l=k+1, are selected, a combination DS kl of their dithering sequences DS k and DS l is a uniform random low-discrepancy sequence; and

drive ( 1404 ) each source S i with the corresponding dithering sequence DS i to generate blended seismic data,

wherein uniform random means that any value within a given interval is equally likely or close to equally likely to be drawn, and low-discrepancy means that a proportion of points in the uniform random low-discrepancy sequence falling into an arbitrary set B is close to proportional to a measure of B.

10. The computing device of claim 9 , wherein the low-discrepancy is obtained by imposing an anti-clustering condition to each element of each dithering sequence DS i .

11. The computing device of claim 9 , wherein the interface also receives:

the number of dithering values (nPoints) for each source;

a number of backward values (nBacksteps) to be used for the anti-clustering condition; and

a time range defined by a minimum dither time and a maximum dither time, in seconds, for the elements of the sequence DS i .

12. The computing device of claim 11 , wherein the processor is configured to:

in a loop, generate new candidate random numbers R for each sequence DS; and

check if the new random numbers, for each sequence, satisfies the anti-clustering condition.

13. The computing device of claim 12 , wherein the processor is further configured to:

discard random numbers that are in excess of a given range.

14. The computing device of claim 13 , wherein the processor is further configured to:

scale remaining accepted random numbers to fit inside the range in seconds for the elements of the sequence DS i selected by a user.

15. The computing device of claim 11 , wherein the nBacksteps values in the anti-clustering condition are gradually scaled down in each iteration to ensure that the candidate random numbers are accepted.

16. The computing device of claim 11 , wherein additional checks are performed to also ensure that a combination DS kl of their dithering sequences DS k and DS l from sources S k and S l , where l=k+2, are uniform random or close to being uniform random and low discrepancy.

17. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for generating discrete dithering sequences DS i for marine seismic sources S i in a marine acquisition system, the instructions comprising:

determining ( 1400 ) a number N of the seismic sources S i to be fired;

calculating ( 1402 ) a dithering sequence DS i for each source S i such that when any two consecutive source activation S k and S l , where l=k+1, are selected, a combination DS kl of their dithering sequences DS k and DS l is a uniform random low-discrepancy sequence; and

driving ( 1404 ) each source S i with the corresponding dithering sequence DS i to generate blended seismic data,

wherein uniform random means that any value within a given interval is equally likely or close to equally likely to be drawn, and low-discrepancy means that a proportion of points in the uniform random low-discrepancy sequence falling into an arbitrary set B is close to proportional to a measure of B.

18. The medium of claim 17 , wherein the low-discrepancy is obtained by imposing an anti-clustering condition to each element of each dithering sequence DS i .

19. The medium of claim 17 , wherein the instructions further cause:

selecting the number of dithering values (nPoints) for each source;

selecting a number of backward values (nBacksteps) to be used for the anti-clustering condition; and

selecting a time range defined by a minimum dither time and a maximum dither time, in seconds, for the elements of the sequence DS i .

20. The medium of claim 17 , wherein additional checks are performed to also ensure that the combined dither from sources S k and S l , where l=k+2, are uniform random or close to being uniform random and low discrepancy.