Seismic source and method for single sweep intermodulation mitigation

1. A method for calculating an intermodulation noise effect generated with one or more land seismic sources, the method comprising:

receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep;

selecting a number of detectors that detect a subset (ga-gf) of the seismic data (g);

estimating earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source, wherein an earth response is indicative of a transmission path response from the one or more land seismic source to a corresponding detector;

calculating plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ); and

removing the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect.

2. The method of claim 1 , wherein the step of estimating comprises:

estimating an earth response (Ha 1 )) in the frequency domain for a given detector; and

applying in inverse Fourier transform on the earth responses (Ha 1 -Hf 1 ) in the frequency domain to obtain the earth responses (ha 1 -hf 1 ) in the time domain.

3. The method of claim 2 , wherein the step of calculating further comprises:

selecting window functions (wa-wf) for windowing strong arrivals;

applying the window functions to remove everything except first break waves and ground roll waves to obtained windowed earth responses (WHa 1 -WHf 1 ) in the frequency domain;

calculating noise transfer functions (NA 1 -NF 1 ) in the frequency domain based on (i) the earth responses (Hal-Hfl) in the frequency domain and (ii) windowed earth responses (WHa 1 -WHf 1 ) in the frequency domain; and

applying an inverse Fourier transform on the noise transfer functions (NA 1 -NF 1 ) to obtain noise transfer functions (na 1 -nf 1 ) in the time domain.

4. The method of claim 3 , further comprising:

removing near zero lag terms from the noise transfer functions (na 1 -nf 1 ) in the time domain to obtain noise terms (a 1 -f 1 ) in the time domain; and

applying a Fourier transform to the noise terms (a 1 -f 1 ) in the time domain to obtain noise terms (A 1 -F 1 ) in the frequency domain.

5. The method of claim 4 , further comprising:

convolving the noise terms (A 1 -F 1 ) in the frequency domain with the ground force (GF) in the frequency domain to obtain plural intermodulation noises (NoiseA 1 -NoiseF 1 ) in the frequency domain.

6. The method of claim 5 , further comprising:

applying an inverse Fourier transform to the plural intermodulation noises (NoiseA 1 -NoiseF 1 ) in the frequency domain to obtain the plural intermodulation noises (noiseA 1 -noiseF 1 ) in the time domain.

7. The method of claim 6 , further comprising:

calculating a combined noise estimate (nAve 1 ) based on the plural intermodulation noises (noiseA 1 -noiseF 1 ) in the time domain.

8. The method of claim 7 , further comprising:

calculating revised earth responses (ha 2 -hf 2 ) based on (i) the subset seismic data (ga-gf), (ii) the ground force (gf) of the one or more land seismic source, and (iii) a product of a constant k and the combined noise estimate (nAve 1 ).

9. The method of claim 8 , wherein the constant k is larger than zero is smaller than or equal to one.

10. A computing device for calculating an intermodulation noise effect generated with one or more land seismic sources, the computing device comprising:

an interface for receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep; and

a processor connected to the interface and configured to,

select a number of detectors that detect a subset (ga-gf) of the seismic data (g),

estimate earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source, wherein an earth response is indicative of a transmission path response from the one or more land seismic source to a corresponding detector,

calculate plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ), and

remove the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect.

11. The device of claim 10 , wherein the processor is further configured to:

estimate an earth response (Ha 1 ) in the frequency domain for a given detector; and

apply in inverse Fourier transform on the earth responses (Ha 1 -Hf 1 ) in the frequency domain to obtain the earth responses (ha 1 -hf 1 ) in the time domain.

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

select window functions (wa-wf) for windowing strong arrivals;

apply the window functions to remove everything except first break waves and ground roll waves to obtained windowed earth responses (WHa 1 -WHf 1 ) in the frequency domain;

calculate noise transfer functions (NA 1 -NF 1 ) in the frequency domain based on (i) the earth responses (Ha 1 -Hf 1 ) in the frequency domain and (ii) windowed earth responses (WHa 1 -WHf 1 ) in the frequency domain; and

apply an inverse Fourier transform on the noise transfer functions (NA 1 -NF 1 ) to obtain noise transfer functions (na 1 -nf 1 ) in the time domain.

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

remove near zero lag terms from the noise transfer functions (na 1 -nf 1 ) in the time domain to obtain noise terms (a 1 -f 1 ) in the time domain; and

apply a Fourier transform to the noise terms (a 1 -f 1 ) in the time domain to obtain noise terms (A 1 -F 1 ) in the frequency domain.

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

convolve the noise terms (Al -F 1 ) in the frequency domain with the ground force (GF) in the frequency domain to obtain plural intermodulation noises (NoiseA 1 -NoiseF 1 ) in the frequency domain.

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

apply an inverse Fourier transform to the plural intermodulation noises (NoiseA 1 -NoiseF 1 ) in the frequency domain to obtain the plural intermodulation noises (noiseA 1 -noiseF 1 ) in the time domain.

16. The device of claim 15 , wherein the processor is further configured to:

calculate a combined noise estimate (nAve 1 ) based on the plural intermodulation noises (noiseA 1 -noiseF 1 ) in the time domain.

17. The device of claim 16 , wherein the processor is further configured to:

calculate revised earth responses (ha 2 -hf 2 ) based on (i) the subset seismic data (ga-gf), (ii) the ground force (gf) of the one or more land seismic source, and (iii) a product of a constant k and the combined noise estimate (nAve 1 ).

18. The device of claim 17 , wherein the constant k is larger than zero is smaller than or equal to one.

19. The device of claim 17 , wherein the processor is further configured to:

calculate refined plural intermodulation noises (noiseA 2 -noiseF 2 ) based on the revised earth responses (ha 2 -hf 2 ).

20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement a method for calculating intermodulation noise generated with one or more land seismic sources, the method comprising:

receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep;

selecting a number of detectors that detect a subset (ga-gf) of the seismic data (g);

estimating earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source, wherein an earth response is indicative of a transmission path response from the one or more land seismic source to a corresponding detector;

calculating plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ); and

removing the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect.