Instantaneous frequency modulation acquisition scheme for seismic sources
View Patent ↗Computing device, computer software and methods for generating sweep signals corresponding to plural sources that generate seismic waves. The method includes selecting a nominal sweep signal (S 0 ); applying a perturbation (P) to the nominal sweep signal (S 0 ); and calculating the sweep signals (Sn) by varying the perturbation (P), each sweep signal corresponding to a seismic source.
1. A method for generating sweep signals corresponding to plural sources that generate seismic waves, the method comprising:
selecting a nominal sweep signal (S 0 ) whose phase φ(t) is characterized by an instantaneous frequency
F
(
t
)
=
1
2
π
∂
φ
(
t
)
∂
t
;
applying a perturbation (P) to the nominal sweep signal (S 0 ); and
calculating the sweep signals (Sn) by varying the perturbation (P), each sweep signal corresponding to a seismic source,
wherein the perturbation causes a frequency rate change,
d
dt
P
(
t
)
,
that is less than a predetermined fraction, γ, of a nominal sweep's frequency rate
d
dt
F
(
t
)
.
2. The method of claim 1 , wherein the predetermined fraction is less than 0.5.
3. The method of claim 1 , wherein the perturbation (P) is a polynomial function of time.
4. The method of claim 3 , further comprising:
selecting coefficients of the polynomial function.
5. The method of claim 4 , further comprising:
applying constraints to the coefficients, the constraints including at least one of:
maintaining perturbed sweep frequency within a predetermined range; and
having the instantaneous frequency monotonically increasing.
6. The method of claim 5 , further comprising:
calculating candidate sweep signals;
calculating auto- and cross-correlations of the candidate sweep signals;
computing performance statistics associated with the auto- and cross-correlations of the candidate sweep signals;
comparing the performance statistics with reference performing statistics; and
selecting the candidate sweep signals to be the sweep signals (Sn) if a result of the comparing step is positive.
7. The method of claim 1 , wherein the perturbation (P) is a non-linear function of time.
8. The method of claim 1 , wherein the perturbation (P) includes a sine term.
9. The method of claim 1 , further comprising:
downloading in each source a corresponding sweep signal; and
acquiring seismic data with the sweep signals.
10. The method of claim 1 , wherein each one of the sweep signals is unique and when the plural sources operate simultaneously, a cross-correlation among the plural sources is minimized.
11. A computing device for generating sweep signals corresponding to plural sources that generate seismic waves, the computing device comprising:
a processor configured to,
select a nominal sweep signal (S 0 ) whose phase φ(t) is characterized by an instantaneous frequency
F
(
t
)
=
1
2
π
∂
φ
(
t
)
∂
t
;
apply a perturbation (P) to the nominal sweep signal (S 0 ); and
calculate the sweep signals (Sn) by varying the perturbation (P), each sweep signal corresponding to a seismic source,
the perturbation causes a frequency rate change,
d
dt
P
(
t
)
,
that is less than a predetermined fraction, γ, of a nominal sweep's frequency rate
d
dt
F
(
t
)
.
12. The computing device of claim 11 , wherein the predetermined fraction is 0.5.
13. The computing device of claim 11 , wherein the perturbation (P) is a polynomial function of time.
14. The computing device of claim 13 , wherein the processor is further configured to:
select coefficients of the polynomial function.
15. The computing device of claim 14 , wherein the processor is further configured to:
apply constraints to the coefficients, the constraints including at least one of:
maintaining perturbed sweep frequency within a predetermined range; and
having the instantaneous frequency monotonically increasing.
16. The computing device of claim 15 , wherein the processor is further configured to:
calculate candidate sweep signals;
calculate auto- and cross-correlations of the candidate sweep signals;
compute performance statistics associated with the auto- and cross-correlations of the candidate sweep signals;
compare the performance statistics with reference performing statistics; and
select the candidate sweep signals to be the sweep signals (Sn) if a result of the comparing step is positive.
17. The computing device of claim 11 , wherein the perturbation (P) is a non-linear function of time.
18. The computing device of claim 11 , wherein the perturbation (P) includes a sine term.
19. The computing device of claim 11 , wherein each one of the sweep signals is unique and when the plural sources operate simultaneously, a cross-correlation among the plural sources is minimized.
20. A non-volatile computer readable medium including computer executable instructions, wherein the instructions, when executed, implement a method for generating sweep signals corresponding to plural sources that generate seismic waves, the method comprising:
selecting a nominal sweep signal (S 0 ) whose phase φ(t) is characterized by an instantaneous frequency
F
(
t
)
=
1
2
π
∂
φ
(
t
)
∂
t
;
applying a perturbation (P) to the nominal sweep signal (S 0 ); and
calculating the sweep signals (Sn) by varying the perturbation (P), each sweep signal corresponding to a seismic source,
wherein the perturbation causes a frequency rate change,
d
dt
P
(
t
)
,
that is less than a predetermined fraction, γ, of a nominal sweep's frequency rate
d
dt
F
(
t
)
.