Method for imaging a sea-surface reflector from towed dual-sensor streamer data

• US 20100091610A1
• Filed: 10/14/2008
• Published: 04/15/2010
• Est. Priority Date: 10/14/2008
• Status: Active Grant

• Current Assignee: PGS Geophysical As (PGS ASA)
• Original Assignee: PGS Geophysical As (PGS ASA)
• Inventors: Sollner, Walter
• Granted Patent: US 7,872,942 B2
• Time in Patent Office: Days
• US Class Current: 367/24
• CPC Class Codes: G01V 1/38 specially adapted for water-covered areas G01V1/28 takes precedence

Abstract

A pressure wavefield and a normal velocity wavefield measured on a smoothly shaped acquisition surface by towed dual-sensor marine seismic streamers are decomposed into up-going and down-going pressure and particle velocity components on an observation level between the acquisition surface and a sea surface of undetermined shape. The up-going and down-going pressure and particle velocity components are extrapolated iteratively in steps from the observation level toward the sea surface. An image point and a reflection coefficient of the sea surface at the image point are determined from the iteratively extrapolated up-going and down-going pressure and particle velocity components.

Claims

1. A method for imaging a sea-surface reflector from towed dual-sensor streamer data, comprising:

decomposing a pressure wavefield and a normal velocity wavefield measured on a smoothly shaped acquisition surface by towed dual-sensor marine seismic streamers into up-going and down-going pressure and vertical velocity components on an observation level between the acquisition surface and a sea surface of undetermined shape;

extrapolating the up-going and down-going pressure and vertical velocity components iteratively in steps from the observation level toward the sea surface; and

determining an image point and a reflection coefficient of the sea surface at the image point from the iteratively extrapolated up-going and down-going pressure and vertical velocity components.

2. The method of claim 1, wherein the decomposing a pressure wavefield and a normal velocity wavefield comprises:

transforming the pressure and normal velocity wavefields from space-time domain to space-frequency domain;

performing the following for each frequency;

performing the following for each horizontal wavenumber;

performing the following for each receiver channel;

calculating up-going and down-going pressure and vertical velocity components at the observation level in the horizontal wavenumber-frequency domain from the transformed pressure normal velocity wavefields;

inverse-transforming the calculated up-going pressure wavefield at the observation level and the calculated up-going vertical velocity wavefield at the observation level from the horizontal wavenumber-frequency domain to the space-frequency domain; and

inverse-transforming the inverse-transformed up-going pressure wavefield at the observation level and the inverse-transformed up-going vertical velocity wavefield at the arbitrary observation level from the space-frequency domain to the space-time domain.

3. The method of claim 2, wherein the calculating up-going and down-going pressure and vertical velocity wavefields comprises:

calculating an up-going pressure wavefield in the horizontal wavenumber-frequency domain from the transformed pressure wavefield and the transformed normal velocity wavefield;

calculating an up-going pressure wavefield at the observation level from the calculated up-going pressure wavefield; and

calculating an up-going vertical velocity wavefield at the observation level from the calculated up-going pressure wavefield at the arbitrary observation level;

calculating an down-going pressure wavefield in the horizontal wavenumber-frequency domain from the transformed pressure wavefield and the transformed normal velocity wavefield;

calculating an down-going pressure wavefield at the observation level from the calculated down-going pressure wavefield; and

calculating an down-going vertical velocity wavefield at the observation level from the calculated down-going pressure wavefield at the arbitrary observation level.

4. The method of claim 3, wherein the calculating an up-going pressure wavefield P^up(k_x,z=0,ω

) in the horizontal wavenumber-frequency domain from the transformed pressure wavefield P(x,z^R,ω

) and the transformed normal velocity wavefield V_n(x,z^R,ω

) comprises applying the following equation;

5. The method of claim 4, wherein the calculating an up-going pressure wavefield at an arbitrary observation level comprises applying the following equation:

P^up(k_x,z^obs,ω

)=P^up(k_x,z=0,ω

)exp[jk_zz^obs].

6. The method of claim 5, wherein the calculating an up-going vertical velocity wavefield at an arbitrary observation level comprises applying the following equation:

7. The method of claim 3, wherein the calculating a down-going pressure wavefield P^down(k_x,z=0,ω

) in the horizontal wavenumber-frequency domain from the transformed pressure wavefield P(x,z^R,ω

) and the transformed normal velocity wavefield V_n(x,z^R,ω

) comprises applying the following equation;

8. The method of claim 7, wherein the calculating a down-going pressure wavefield at an arbitrary observation level comprises applying the following equation:

P^down(k_x,z^obs,ω

)=P^down(k_x,z=0, ω

)exp[jk_zz^obs].

9. The method of claim 8, wherein the calculating a down-going vertical velocity wavefield at an arbitrary observation level comprises applying the following equation:

10. The method of claim 1, wherein the extrapolating the up-going and down-going pressure and vertical velocity components comprises:

extrapolating the up-going pressure wavefield component forward in time from the arbitrary observation level upward toward the sea surface;

extrapolating the down-going pressure wavefield component backward in time from the arbitrary observation level upward toward the sea surface;

extrapolating the up-going vertical velocity wavefield component forward in time from the arbitrary observation level upward toward the sea surface; and

extrapolating the down-going vertical velocity wavefield component backward in time from the arbitrary observation level upward toward the sea surface.

11. The method of claim 1, wherein the determining an image and a reflection coefficient of the sea surface comprises:

selecting a sequence of time windows;

calculating a zero-lag value of a cross-correlation of an extrapolated up-going wavefield and an extrapolated down-going wavefield in the sequence of time windows at desired extrapolation depths;

determining a position of an image point on the sea surface as a maximum cross-correlation value of the calculated zero-lag values of cross-correlations of extrapolated up-going and down-going wavefields; and

determining the reflection coefficient at the image point on the sea surface by division of the zero-lag value of the autocorrelation of the extrapolated down-going wavefield by the zero-lag value of the cross-correlation of the extrapolated up-going wavefield and extrapolated down-going wavefield at the image point.