Method of summing dual-sensor towed streamer signals using seismic reflection velocities

• US 8,811,113 B2
• Filed: 08/01/2008
• Issued: 08/19/2014
• Est. Priority Date: 08/01/2008
• Status: Active Grant

• Current Assignee: PGS Geophysical As (PGS ASA)
• Original Assignee: PGS Geophysical As (PGS ASA)
• Inventors: Barr, Frederick James Jr.
• Primary Examiner(s): BREIER, KRYSTINE E
• Application Number:
  US12/221,255
• Publication Number:
  US 20100027375A1
• Time in Patent Office: 2,209 Days
• Field of Search: 367/15, 367/21
• US Class Current: 367/24
• CPC Class Codes: G01V 1/32 Transforming one recording into another or one representation into another
• CPC Class Codes: G01V 1/364 Seismic filtering G01V1/37 takes precedence
• CPC Class Codes: G01V 1/38 specially adapted for water-covered areas G01V1/28 takes precedence
• CPC Class Codes: G01V 2210/61 Analysis by combining or comparing a seismic data set with other data

Abstract

A merged particle velocity signal is generated by merging a recorded vertical particle velocity signal, scaled in an upper frequency range using a time-dependent arrival angle as determined by velocity 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 time. Combined pressure and vertical particle velocity signals are generated by combining the recorded pressure and merged velocity signals.

Claims

1. A method for combining pressure and vertical particle velocity signals in dual-sensor towed streamers, comprising:

obtaining the pressure and vertical particle velocity signals recorded at a receiver station in the dual-sensor towed streamers, the signals representative of characteristics of subsurface earth formations and acquired by deployment of a plurality of seismic receivers overlying an area of the subsurface earth formations to be evaluated, the seismic receivers generating at least one of an electrical and optical signal in response to seismic energy;

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

generating combined pressure and vertical particle velocity signals, useful for imaging the earth'"'"'s subsurface, by combining the recorded pressure and merged particle velocity signals.

2. The method of claim 1, wherein the generating a merged particle velocity signal 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 set of arrival angles {φ

_j};

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

_j};

selecting an arrival angle φ

_j, from the set of arrival angles {φ

_j};

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

) for the selected arrival angle φ

_j, thereby generating a simulated particle velocity signal G_j^calc(ω

) in the lower frequency range;

scaling the transformed vertical particle velocity signal G(ω

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

_j, thereby generating a scaled vertical particle velocity signal G_j^scal(ω

) in the upper frequency range;

merging the simulated particle velocity signal G_j^calc(ω

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

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

), for the selected arrival angle φ

_j; and

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

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

3. The method of claim 2, wherein the temporal transform is a temporal Fourier transform.

4. The method of claim 2, wherein the set of arrival angles comprises the set of angles φ

_j=0°

, 1°

, 2°

, . . . , 60°

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

5. The method of claim 2, wherein the scaling comprises dividing the transformed vertical particle velocity signal G(ω

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

_j, generating a scaled vertical particle velocity signal G_j^scal(ω

).

6. The method of claim 2, 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 signal (h,t).

7. The method of claim 1, wherein the calculating a particle velocity signal G_j^calc(ω

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

) for the selected arrival angle φ

_j comprises applying the following equation;

8. The method of claim 7, wherein the time delay operator Z₁ is given by the equation:

Z_j=exp[−

iπ

τ

_j]=cos(ω

τ

_j)−

i sin(ω

τ

_j),

for j=0, 1, 2, . . . , 60, where τ

_j is ghost reflection time delay.

9. The method of claim 8, wherein the ghost reflection time delay τ

is given by;

10. The method of claim 2, wherein the generating combined pressure and vertical particle velocity signals comprises:

extracting a seismic trace from the pressure signals h(t) and the vertical particle velocity signals h(t);

extracting a time sample at a recording time t from the seismic trace;

calculating an arrival angle φ

(t) at the recording time t in the time sample from the seismic trace, by velocity analysis;

determining which arrival angle φ

_j of the selected set of arrival angles {φ

_j} is closest to the calculated arrival angle φ

(t); and

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

_j.

11. The method of claim 10, wherein the calculating an arrival angle φ

(t) at the recording time t in the time sample comprises applying the following equation;

12. The method of claim 11, wherein the apparent velocity v_app(t) for the recording time t is calculated from the following equation:

13. The method of claim 11, wherein the recording time t is computed from the following equation:

14. The method of claim 11, wherein the apparent velocity v_app(t) for the recording time t is calculated from the following equation:

15. The method of claim 14, wherein the recording time t is computed from the following equation:

16. The method of claim 15, wherein an arrival angle α

is computed from the following equation;

α

=arccos [cos(ξ

)cos(φ

)].

17. The method of claim 14, wherein the dip angle is determined from another common shot gather velocity analysis in the survey area wherein the line from its shot point location to this receiver location is approximately perpendicular.

18. The method of claim 1, wherein the vertical particle velocity signals are obtained using accelerometers.