Systems and methods for reducing noise in a seismic vibratory source

1. A method for reducing noise in a seismic vibratory source, comprising:

generating an initial pilot signal P k (t) for the seismic vibratory source;

receiving a source signature S k (t) corresponding to the initial pilot signal P k (t);

estimating a noise component N k (t) of the source signature S k (t) based on the source signature S k (t) and a target force F target (t);

calculating a noise operator Ω k+1 (t) by deconvolving the noise component N k (t) by the target force F target (t);

generating an anti-noise correction P k+1 corr (t) for the initial pilot signal P k (t) by convolving the noise operator Ω k+1 (t) with the initial pilot signal P k (t); and

computing a modified pilot signal based on the initial pilot signal P k (t) and the anti-noise correction P k+1 corr (t),

wherein a subscript k indicates an iteration of calculations.

2. The method of claim 1 , further comprising

outputting a portion of the modified pilot signal to a seismic source;

receiving a real-time source signature based on the portion of the modified pilot signal; and

calculating a real-time anti-noise correction based on the real-time source signature.

3. The method of claim 1 , further comprising utilizing the modified pilot signal in a seismic survey.

4. The method of claim 1 , further comprising generating an image of a subsurface formation based on the modified pilot signal.

5. The method of claim 1 , further comprising computing the modified pilot signal by subtracting from the initial pilot signal a scalable fraction of the anti-noise correction.

6. The method of claim 1 , wherein the source signature is a combination of one or more measured motions of one or more actuating parts of the seismic source.

7. The method of claim 6 , wherein the combination of one or more measured motions weights each measured motion by the mass of its respective actuating part of the seismic source.

8. The method of claim 1 , wherein the source signature is derived from a near-field measurement.

9. A seismic energy emission system, comprising:

a seismic vibratory source; and

a computing system communicatively coupled to the seismic vibratory source, the computing system comprising:

a processor;

a memory communicatively coupled to the processor; and

instructions stored in the memory that, when executed by the processor, cause the processor to:

generate an initial pilot signal P k (t) for the seismic vibratory source;

receive a source signature S k (t) corresponding to the initial pilot signal P k (t);

estimate a noise component N k (t) of the source signature S k (t) based on the source signature S k (t) and a target force F target (t);

calculate a noise operator Ω k+1 (t) by deconvolving the noise component N k (t) by the target force F target (t);

generate an anti-noise correction P k+1 corr (t) to the initial pilot signal P k (t) by convolving the noise operator Ω k+1 (t) with the initial pilot signal P k (t); and

compute a modified pilot signal based on the initial pilot signal P k (t) and the anti-noise correction P k+1 corr (t),

wherein a subscript k indicates an iteration of calculations.

10. The seismic energy emission system of claim 9 , wherein the instructions, when executed by the processor, further cause the processor to:

output a portion of the modified pilot signal to a seismic source;

receive a real-time source signature based on the portion of the modified pilot signal; and

calculate a real-time anti-noise correction based on the real-time source signature.

11. The seismic energy emission system of claim 9 , wherein the instructions, when executed by the processor, further cause the processor to utilize the modified pilot signal in a seismic survey.

12. A non-transitory computer-readable medium, comprising computer-executable instructions carried on the computer-readable medium, wherein the instructions, when executed by a processor, cause the processor to:

generate an initial pilot signal P k (t) for a seismic vibratory source;

receive a source signature S k (t) corresponding to the initial pilot signal P k (t);

estimate a noise component N k (t) of the source signature S k (t) based on the source signature S k (t) and a target force F target (t);

calculate a noise operator Ω k+1 (t) by deconvolving the noise component N k (t) by the target force F target (t);

generate an anti-noise correction P k+1 corr (t) to the initial pilot signal P k (t) by convolving the noise operator Ω k+1 (t) with the initial pilot signal P k (t); and

compute a modified pilot signal based on the initial pilot signal P k (t) and the anti-noise correction P k+1 corr (t),

wherein a subscript k indicates an iteration of calculations.

13. The non-transitory computer-readable medium of claim 12 , wherein the instructions, when executed by the processor, further cause the processor to

output a portion of the modified pilot signal to a seismic source;

receive a real-time source signature based on the portion of the modified pilot signal; and

calculate a real-time anti-noise correction based on the real-time source signature.

14. The non-transitory computer-readable medium of claim 12 , wherein the instructions, when executed, further cause the processor to utilize the modified pilot signal in a seismic survey.