Systems and methods for generating composite non-linear sweeps adapted to vibrator constraints

1. A method for seismic exploration using composite non-linear sweeps adapted to vibrator constraints, the method comprising:

determining a target amplitude function;

determining a constraint set including a constraint;

selecting a scaling constant used to determine a rate of frequency increase;

calculating a low-frequency non-linear sweep based on the constraint set and the scaling constant;

calculating a modified constraint set based on the constrained set and the low-frequency non-linear sweep;

calculating a high-frequency non-linear sweep based on the modified constraint set, the scaling constant, and the low-frequency non-linear sweep;

calculating a composite non-linear sweep by combining the low-frequency non-linear sweep and the high-frequency non-linear sweep; and

operating a vibratory seismic source according to the composite non-linear sweep to inject seismic excitations in an explored subsurface geological structure.

2. The method of claim 1 , further comprising defining a weighting function,

wherein calculating the low-frequency non-linear sweep comprises:

determining a maximum allowable force amplitude at a low frequency based on the constraint set; and

calculating a low-frequency force amplitude at the low frequency by multiplying the value of the weighting function at the low frequency by the maximum allowable force amplitude at the low frequency.

3. The method of claim 1 , wherein the calculating of the high-frequency non-linear sweep comprises:

determining a modified maximum allowable force amplitude at a high frequency based on the modified constraint set; and

calculating a high-frequency force amplitude at the high frequency based on the modified maximum allowable force amplitude at the high-frequency.

4. The method of claim 1 , further comprising:

determining an ending frequency of the high-frequency non-linear sweep;

comparing the ending frequency of the high-frequency non-linear sweep to a desired ending frequency;

in response to determining that the ending frequency of the high-frequency non-linear sweep differs from the desired ending frequency, adjusting the scaling constant; and

repeating the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

5. The method of claim 1 , further comprising:

selecting a weighting function, wherein the low-frequency non-linear sweep is further based on the weighting function;

determining whether the scaling constant can be lowered;

in response to determining that the scaling constant can be lowered, adjusting the weighting function;

selecting a time constant;

determining whether a final frequency spectrum is acceptable;

in response to determining that the final frequency spectrum is not acceptable, adjusting the time constant; and

repeating the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

6. The method of claim 1 wherein the at least one constraint is selected from the group consisting of a hold-down constraint, a rated peak force constraint, an oil-flow constraint, or a maximum displacement constraint.

7. The method of claim 1 , further comprising using the composite non-linear sweep in a seismic survey.

8. A system comprising:

a vibratory seismic energy source;

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

a processor;

a memory communicatively coupled to the processor;

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

determine a target amplitude function;

determine a constraint set including a constraint;

select a scaling constant used to determine a rate of frequency increase;

calculate a low-frequency non-linear sweep based on the constraint set and the scaling constant;

calculate a modified constraint set based on the constrained set and the low-frequency non-linear sweep;

calculate a high-frequency non-linear sweep based on the modified constraint set, the scaling constant, and the low-frequency non-linear sweep;

calculate a composite non-linear sweep by combining the low-frequency non-linear sweep and the high-frequency non-linear sweep; and

transmit the composite non-linear sweep to the vibratory seismic energy source.

9. The system of claim 8 , the instructions, when executed by the processor, further causing the processor to define a weighting function,

wherein causing the processor to calculate the low-frequency non-linear sweep comprises causing the processor to:

determine a maximum allowable force amplitude at a low frequency based on the constraint set; and

calculate a low-frequency force amplitude at the low frequency by multiplying the value of the weighting function at the low frequency by the maximum allowable force amplitude at the low frequency.

10. The system of claim 8 , the instructions, when executed by the processor, further cause the processor to calculate, the high-frequency non-linear sweep by:

determining a modified maximum allowable force amplitude at a high frequency based on the modified constraint set; and

calculating a high-frequency force amplitude at the high frequency based on the modified maximum allowable force amplitude at the high-frequency.

11. The system of claim 8 , the instructions, when executed by the processor, further causing the processor to:

determine an ending frequency of the high-frequency non-linear sweep;

compare the ending frequency of the high-frequency non-linear sweep to a desired ending frequency;

in response to determining that the ending frequency of the high-frequency non-linear sweep differs from the desired ending frequency, adjust the scaling constant; and

repeat the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

12. The system of claim 8 , the instructions, when executed by the processor, further causing the processor to:

select a weighting function, wherein the low-frequency non-linear sweep is further based on the weighting function;

determine whether the scaling constant can be lowered;

in response to determining that the scaling constant can be lowered, adjust the weighting function;

select a time constant;

determine whether a final frequency spectrum is acceptable;

in response to determining that the final frequency spectrum is not acceptable, adjust the time constant; and

repeat the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

13. The system of claim 8 wherein the at least one constraint is selected from the group consisting of a hold-down constraint, a rated peak force constraint, an oil-flow constraint, or a maximum displacement constraint.

14. The system of claim 8 , the instructions, when executed by the processor, further causing the processor to create an image based on the composite non-linear sweep.

15. A non-transitory computer-readable medium, comprising instructions that, when executed by a processor, cause the processor to:

determine a target amplitude function;

determine a constraint set including a constraint;

select a scaling constant used to determine a rate of frequency increase;

calculate a low-frequency non-linear sweep based on the constraint set and the scaling constant;

calculate a modified constraint set based on the constrained set and the low-frequency non-linear sweep;

calculate a high-frequency non-linear sweep based on the modified constraint set, the scaling constant, and the low-frequency non-linear sweep;

calculate a composite non-linear sweep by combining the low-frequency non-linear sweep and the high-frequency non-linear sweep; and

transmitting the composite non-linear sweep to a seismic source that generates seismic excitations injected in an explored subsurface geological structure accordingly.

16. The non-transitory computer-readable medium of claim 15 , the instructions, when executed by the processor, further causing the processor to define a weighting function,

wherein causing the processor to calculate the low-frequency non-linear sweep comprises causing the processor to:

determine a maximum allowable force amplitude at a low frequency based on the constraint set; and

calculate a low-frequency force amplitude at the low frequency by multiplying the value of the weighting function at the low frequency by the maximum allowable force amplitude at the low frequency.

17. The non-transitory computer-readable medium of claim 15 , the instructions, when executed by the processor, wherein causing the processor to generate the high-frequency non-linear sweep comprises causing the processor to:

determine a modified maximum allowable force amplitude at a high frequency based on the modified constraint set; and

calculate a high-frequency force amplitude at the high frequency based on the modified maximum allowable force amplitude at the high-frequency.

18. The non-transitory computer-readable medium of claim 15 , the instructions, when executed by the processor, further causing the processor to:

determine an ending frequency of the high-frequency non-linear sweep;

compare the ending frequency of the high-frequency non-linear sweep to a desired ending frequency;

in response to determining that the ending frequency of the high-frequency non-linear sweep differs from the desired ending frequency, adjust the scaling constant; and

repeat the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

19. The non-transitory computer-readable medium of claim 15 , the instructions, when executed by the processor, further causing the processor to:

select a weighting function, wherein the low-frequency non-linear sweep is further based on the weighting function;

determine whether the scaling constant can be lowered;

in response to determining that the scaling constant can be lowered, adjust the weighting function;

select a time constant;

determine whether a final frequency spectrum is acceptable;

in response to determining that the final frequency spectrum is not acceptable, adjust the time constant; and

repeat the steps of calculating the low-frequency non-linear sweep and calculating the high-frequency non-linear sweep.

20. The non-transitory computer-readable medium of claim 15 wherein the at least one constraint is selected from the group consisting of a hold-down constraint, a rated peak force constraint, an oil-flow constraint, or a maximum displacement constraint.