Method of wavefield extrapolation for single-station, dual-sensor towed streamer signals

• US 7,929,373 B2
• Filed: 11/19/2008
• Issued: 04/19/2011
• Est. Priority Date: 11/19/2008
• 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): Lobo; Ian J
• Application Number:
  US12/313,317
• Publication Number:
  US 20100124149A1
• Time in Patent Office: 881 Days
• Field of Search: 367/21, 367/24
• US Class Current: 367/24
• CPC Class Codes: G01V 1/364 Seismic filtering G01V1/37 takes precedence
• CPC Class Codes: G01V 1/3808 Seismic data acquisition, e.g. survey design
• CPC Class Codes: G01V 2210/144 with functionally associated receivers, e.g. hydrophone and geophone pairs

Abstract

A time-dependent arrival angle is determined at a single receiver station in a towed streamer. Up-going and down-going pressure wavefields are calculated from pressure and vertical particle velocity wavefields measured at the receiver station. Extrapolated up-going and down-going pressure wavefields are generated from the up-going and down-going pressure wavefields displaced by a time delay based upon the time-dependent arrival angle.

Claims

1. A method for geophysical prospecting, comprising:

disposing a single receiver station in a dual-sensor streamer in a body of water;

responsive to signals recorded at the receiver station, calculating seismic traces representing physical reflected wavefields in the body of water incident on the receiver station at a first depth;

correcting for depth variations of the receiver station over time and for horizontal aliasing by transforming the seismic traces to produce pressure traces representing pressure wavefields as they would appear if incident on the receiver station at a second depth different from the first depth, the transforming comprising;

determining a time-dependent arrival angle of the reflected wavefields;

calculating up-going and down-going pressure traces from pressure and vertical particle velocity traces measured at the receiver station at the first depth;

generating at least one of extrapolated up-going and down-going pressure traces at the second depth from the corresponding up-going and down-going pressure traces displaced by a time delay based upon the time-dependent arrival angle; and

recording the extrapolated up-going or down-going pressure traces.

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

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

4. The method of claim 1, wherein the calculating up-going and down-going pressure traces comprises:

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

correcting the recorded pressure signals h(t) and vertical particle velocity signals g(t) for acquisition effects;

calculating up-going and down-going pressure traces from the corrected pressure signals h(t) and vertical particle velocity signals g(t); and

extrapolating the calculated up-going and down-going pressure traces from receiver depth Z_rto another depth z.

5. The method of claim 4, wherein the correcting the recorded pressure signals h(t) and vertical particle velocity signals g(t) for acquisition effects comprises:

correcting the recorded pressure signals h(t) and vertical particle velocity signals g(t) for impulse response differences between sensors recording the signals;

correcting the previously corrected pressure signals h(t) and vertical particle velocity signals g(t) for effects of non-vertical arrival angles; and

correcting the twice-corrected vertical particle velocity signals g(t) for effects of tow noise.

6. The method of claim 1, wherein the generating extrapolated up-going and down-going pressure traces comprises:

selecting a set of arrival angles {φ

_j};

constructing a set of delay times {τ

_i} from the set of arrival angles {φ

_j};

constructing a set of up-going pressure wavefields {u_j(t)} from the up-going pressure wavefield u(t) and the set of time delays {τ

_i};

constructing a set of down-going pressure wavefields {d_j(t)} from the down-going pressure wavefield d(t) and the set of time delays {τ

_i };

constructing an extrapolated up-going pressure wavefield u_ext(t) from the set of up-going pressure wavefields {u_j(t)}; and

constructing an extrapolated down-going pressure wavefield d_ext(t) from the set of down-going pressure wavefields {d_j(t)}.

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

_j} comprises the set of angles φ

_j=0°

, 1°

, 2°

, . . . , 60°

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

8. The method of claim 6, wherein the set of delay times {τ

_i} is constructed from the set of arrival angles {φ

_j} by applying the following equation;

9. The method of claim 6, wherein the constructing an extrapolated up-going pressure trace u_ext(t) comprises:

selecting a time sample from the up-going pressure trace wavefield u(t);

performing the following for the selected time sample;

determining an arrival angle φ

(t) that corresponds to the selected time sample;

determining a delay time τ

_i in the set of delay times {τ

_i} that corresponds most closely to the determined arrival angle φ

(t);

determining an up-going pressure trace u_j(t) in the set of up-going pressure traces {u_j(t)} that corresponds to the determined delay time τ

_i;

extracting a time sample from the determined up-going pressure trace u_j(t) that corresponds to the selected time sample in the up-going pressure trace u(t); and

adding the extracted time sample to the extrapolated up-going pressure trace u_ext(t).

10. The method of claim 6, wherein the constructing an extrapolated down-going pressure trace u_ext(t) comprises:

selecting a time sample from the down-going pressure trace d(t);

performing the following for the selected time sample;

determining an arrival angle φ

(t) that corresponds to the selected time sample;

determining a delay time τ

_i in the set of delay times {τ

_i} that corresponds most closely to the determined arrival angle φ

(t);

determining a down-going pressure trace d_j(t) in the set of down-going pressure traces {d_j(t)} that corresponds to the determined delay time τ

_i;

extracting a time sample from the determined down-going pressure traces d_j(t) that corresponds to the selected time sample in the down-going pressure trace d(t); and

adding the extracted time sample to the extrapolated down-going pressure trace d_ext(t).