Method of summing dual-sensor towed streamer signals using cross-ghosting analysis

• US 8,089,825 B2
• Filed: 08/29/2008
• Issued: 01/03/2012
• Est. Priority Date: 08/29/2008
• Status: Active Grant

• Current Assignee: PGS Geophysical As (PGS ASA)
• Original Assignee: PGS Geophysical As (PGS ASA)
• Inventors: Barr, Frederick James Jr., Tenghamn, Stig Rune Lennart
• Primary Examiner(s): Keith, Jack
• Assistant Examiner(s): Breier, Krystine
• Application Number:
  US12/231,117
• Publication Number:
  US 20100054081A1
• Time in Patent Office: 1,222 Days
• Field of Search: 367 21- 24, 367/38
• US Class Current: 367/24
• CPC Class Codes: G01V 1/3808 Seismic data acquisition, e.g. survey design

Abstract

A merged particle velocity signal is generated by combining a recorded vertical particle velocity signal, scaled in an upper frequency range using a time-dependent arrival angle as determined by cross-ghosting analysis, with a simulated particle velocity signal, calculated in a lower frequency range from a recorded pressure signal using a time-varying filter based on the time-dependent arrival angle. Combined pressure and vertical particle velocity signals are generated from the recorded pressure and merged particle velocity signals.

Claims

1. A method for geophysical prospecting comprising:

disposing a dual-sensor seismic streamer in a body of water;

responsive to signals recorded at sensors in the dual-sensor seismic streamer, calculating pressure and vertical particle velocity traces representing physical pressure and vertical particle velocity wavefields, respectively, traveling in the body of water incident on the sensors;

correcting for low-frequency noise in vertical particle velocity sensors by transforming the seismic traces to produce combined pressure and vertical particle velocity traces representing pressure and vertical particle velocity wavefields, respectively, as they would appear if incident on the sensors with attenuated low-frequency noise, the transforming comprising;

generating merged particle velocity traces by merging recorded vertical particle velocity traces, scaled in an upper frequency range using a time-dependent arrival angle as determined by cross-ghosting analysis, with simulated particle velocity traces, calculated in a lower frequency range from recorded pressure traces using a time-varying filter based on the time-dependent arrival angle;

generating combined pressure and vertical particle velocity traces by combining the recorded pressure and merged particle velocity traces; and

recording the combined pressure and vertical particle velocity traces.

2. The method of claim 1, wherein the vertical particle velocity signals are obtained by using accelerometers to record acceleration signals and determining vertical particle velocity traces from the recorded acceleration signals.

3. The method of claim 1, wherein the vertical particle velocity signals are obtained by using velocity sensors to record velocity signals and determining vertical particle velocity traces from the recorded velocity signals.

4. The method of claim 1, wherein the generating merged particle velocity traces comprises:

recording pressure signals h(t) and vertical particle velocity signals g(t) at a receiver station in the towed streamer;

temporally-transforming the recorded pressure signals h(t) and vertical particle velocity signals g(t) from a time domain to H(ω

) and G(ω

), respectively, in a frequency domain;

selecting a first set of arrival angles {φ

_j};

performing the following for each of the first set of arrival angles {φ

_j};

selecting an arrival angle φ

_j from the selected first set of arrival angles {φ

_j};

calculating particle velocity traces in a lower frequency range from the transformed pressure signal H(ω

) for the selected arrival angle φ

_j from the first set of arrival angles {φ

_j}, thereby generating simulated particle velocity traces G_j^calc(ω

) in the lower frequency range;

scaling the transformed vertical particle velocity traces G(ω

) in an upper frequency range for the selected arrival angle φ

_j from the first set of arrival angles {φ

_j}, thereby generating scaled particle velocity traces G_j^scal(ω

) in the upper frequency range;

merging the simulated particle velocity traces G_j^calc(ω

) from the lower frequency range with the scaled particle velocity traces G_j^scal(ω

) from the upper frequency range to generate merged particle velocity traces G_j^merg(ω

), for the selected arrival angle φ

_j from the first set of arrival angles {φ

_j}; and

inverse-transforming the merged particle velocity traces G_j^merg(ω

) from the frequency domain to g_j^merg(t) in the time domain.

5. The method of claim 4, wherein the temporal transform is a temporal Fourier transform.

6. The method of claim 4, wherein the first set of arrival angles {φ

_j} comprises the set of angles φ

_j=0°

, 1°

, 2°

, . . . , 60°

for j=0, 1, 2, . . . , 60, respectively.

7. The method of claim 4, wherein the scaling the transformed vertical particle velocity traces comprises dividing the transformed vertical particle velocity sensor traces G(ω

) in the upper frequency range by cosine of the selected arrival angle φ

_j from the first set of arrival angles {φ

_j}, generating scaled particle velocity traces G_j^scal(ω

).

8. The method of claim 4,wherein a combination of the lower frequency range and the upper frequency range have substantially the same bandwidth as the bandwidth of the recorded pressure sensor signal h(t).

9. The method of claim 4, wherein the calculating particle velocity traces G_j^calc(ω

) in a low frequency range from a recorded pressure signal H(ω

) for the selected arrival angle φ

_j from the first set of arrival angles {φ

_j} comprises applying the following equation;

10. The method of claim 9, wherein the time delay operator Z_j is given by the equation:

Z_j=exp [−

iω

τ

_j]=cos(ω

τ

_j)−

i sin(ω

τ

_j),

where τ

_j is ghost reflection time delay.

11. The method of claim 10, wherein the ghost reflection time delay τ

is given by;

12. The method of claim 4, further comprising:

extracting a pressure trace and a particle velocity trace from the pressure signal h(t) and vertical particle velocity signal g(t), respectively;

extracting time samples at a recording time t from the pressure and particle velocity traces;

determining an arrival angle φ

_k from a second set of arrival angles {φ

_k} at the recording time t in the time samples from the pressure and particle velocity traces, by cross-ghosting analysis;

determining which arrival angle φ

_j from the first set of arrival angles {φ

_j } is closest to the determined arrival angle φ

_k from the second set of arrival angles {φ

_k}; and

combining a time sample of the recorded pressure signal h(t) with a time sample of the corresponding merged particle velocity traces g_j^merg(t) that corresponds to the closest arrival angle φ

_j from the first set of arrival angles {φ

_j}.

13. The method of claim 12, wherein the determining an arrival angle by cross-ghosting analysis comprises

selecting a second set of arrival angles {φ

_k};

performing the following for each of the second set of arrival angles {φ

_k};

selecting an arrival angle φ

_k from the selected second set of arrival angles {φ

_k};

cross-ghosting the pressure and vertical particle velocity traces for the selected arrival angle φ

_k from the second set of arrival angles {φ

_k}; and

calculating a zero-lag, normalized cross-correlation of the cross-ghosted pressure and vertical particle velocity traces, for the selected arrival angle φ

_k from the second set of arrival angles {φ

_k};

determining which value of the zero-lag, normalized cross-correlations is largest; and

determining the arrival angle φ

_k from the second set of arrival angles {φ

_k} that corresponds to the largest value determined for the zero-lag, normalized cross-correlations.

14. The method of claim 13, wherein the cross-ghosting comprises:

determining a ghost reflection time delay τ

_k that corresponds to the selected arrival angle φ

_k from the second set of arrival angles {φ

_k};

determining a time delay operator Z_k that corresponds to the determined ghost reflection time delay τ

_k; and

cross-ghosting pressure and vertical particle velocity traces using the time delay operator Z_k.

15. The method of claim 14, wherein the determining a ghost reflection time delay τ

_k that corresponds to the selected arrival angle φ

_k from the second set of arrival angles {φ

_k} comprises applying the following equation;

16. The method of claim 15, wherein determining a time delay operator Z_j that corresponds to the determined ghost reflection time delay τ

_k comprises applying the following equation;

Z_j=exp [−

iω

τ

_j]=cos(ω

τ

_j)−

i sin(ω

τ

_j),

where ω

is radial frequency.

17. The method of claim 16, wherein cross-ghosting pressure and vertical particle velocity traces comprises applying the following equations:

P_k(1+Z_k)=β

(1−

Z_k)(1+Z_k)

and

V_k(1−

Z_k)=β

_φ

(1+Z_k)(1−

Z_k),

where β

is the upward traveling wavefield and β

_□

is the upward traveling wavefield modified by the particle velocity sensor'"'"'s directional sensitivity.

18. The method of claim 13, wherein the calculating a zero-lag, normalized cross-correlation XCN_pv(0) of the cross-ghosted pressure and vertical particle velocity traces comprises:

determining time windows for the time samples in the pressure and vertical particle velocity traces;

extracting pressure and vertical particle velocity time sample values {p_n} and {v_n}, respectively, in the time windows in the pressure and vertical particle velocity traces;

calculating two zero-lag auto-correlation factors A_pp(0) and A_vv(0) from the pressure and vertical particle velocity time sample values {p_n} and {v_n}, respectively;

calculating a zero-lag cross-correlation factor C_pv(0) from the pressure and vertical particle velocity time sample values {p_n} and {v_n}, respectively; and

calculating a zero-lag, normalized cross-correlation XCN_pv(0) from the two zero -lag auto-correlation factors A_pp(0) and A_vv(0) and the zero-lag cross-correlation factor C_pv(0).

19. The method of claim 18, wherein the calculating two zero-lag auto-correlation factors A_pp(0) and A_vv(0) comprises applying the following equations:

20. The method of claim 19, wherein the calculating a zero-lag cross-correlation factor C_pv(0) comprises applying the following equation:

21. The method of claim 20, wherein the calculating a zero-lag, normalized cross-correlation XCN_pv(0) comprises applying the following equation: