Difference between revisions of "Gaiser’s coupling analysis of geophone data"

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where ''ω'' is the angular frequency, ''I'' is unity, and the nonzero elements ''C<sub>y</sub>, C<sub>z</sub>, V<sub>y</sub>'', and ''V<sub>z</sub>'' describe the coupling response of the geophones.
 
where ''ω'' is the angular frequency, ''I'' is unity, and the nonzero elements ''C<sub>y</sub>, C<sub>z</sub>, V<sub>y</sub>'', and ''V<sub>z</sub>'' describe the coupling response of the geophones.
 
[[file:ch11_fig6-3.png|thumb|{{figure number|11.6-3}} 3-D image volumes associated with (a) ''PP'' data and (b) ''PS'' data as in Figure 11.6-2. (Figure courtesy <ref name=ch11r66>Probert et al., 1999, Probert, T., Hoare, R., Ronen, S., Godfrey, R. J., Pope, D., and Kommedal, J., 1999 (November), Imaging through gas using 4-C 3-D seismic data: a case study from Lomond Field: Petr. Expl. Soc. of Great Britain Newsletter.</ref>, and Schlumberger Geco-Prakla; data courtesy BP-Amoco.)]]
 
  
 
Note from equation ({{EquationNote|66}}) that ''X′''(''ω'') = ''X''(''ω''); this means that we assume that the inline geophone is perfectly coupled. Since the inline geophone is guided by the cable itself, this is considered a valid assumption in practice. Whereas the vertical and crossline geophones are not coupled completely — hence the nonzero elements of the coupling matrix. The imperfect coupling leads to vertical and crossline geophone signals mutually contaminating each other in a manner that can be modeled by equation ({{EquationNote|66}}).
 
Note from equation ({{EquationNote|66}}) that ''X′''(''ω'') = ''X''(''ω''); this means that we assume that the inline geophone is perfectly coupled. Since the inline geophone is guided by the cable itself, this is considered a valid assumption in practice. Whereas the vertical and crossline geophones are not coupled completely — hence the nonzero elements of the coupling matrix. The imperfect coupling leads to vertical and crossline geophone signals mutually contaminating each other in a manner that can be modeled by equation ({{EquationNote|66}}).
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The coupling compensation operators are estimated in a surface-consistent manner <ref name=ch11r81>Taner and Koehler, 1981, Taner, M. T. and Koehler, F., 1981, Surface-consistent corrections: Geophysics, 46, 17–21.</ref> with the constraint that, following the rotation, the energy of the transverse component is minimum.
 
The coupling compensation operators are estimated in a surface-consistent manner <ref name=ch11r81>Taner and Koehler, 1981, Taner, M. T. and Koehler, F., 1981, Surface-consistent corrections: Geophysics, 46, 17–21.</ref> with the constraint that, following the rotation, the energy of the transverse component is minimum.
 
<gallery>file:ch11_fig6-4.png|{{figure number|11.6-4}} An ideal cable layout of a three-component geophone system that can be achieved in land multicomponent surveys. (Figure courtesy > <ref name=ch11r33>Gaiser, 1999b, Gaiser, J. E., 1999b, Applications of vector coordinate systems of 3-D converted-wave data: The Leading Edge, 1290–1300.</ref>, and Baker-Hughes Western Geophysical.)
 
file:ch11_fig6-5.png|{{figure number|11.6-5}} An ocean-bottom cable layout layout of a three-component geophone system. (Figure courtesy <ref name=ch11r33/>, and Baker-Hughes Western Geophysical.)</gallery>
 
  
 
Gaiser <ref name=ch11r31/> reported a coupling experiment to verify the validity of the coupling theory described above. Figure 11.6-12a,b,c show the inline, crossline, and vertical geophone records obtained from an OBC survey. In the same figure, the record associated with the crossline geophone is shown after compenating for coupling (Figure 11.6-12d). To study the validity of the compensation based on equation ({{EquationNote|68}}), a diver firmly planted the receiver unit into the seabed and the recording was repeated. The resulting crossline record is shown in Figure 11.6-12e. If the coupling theory holds, then the records in Figures 11.6-12d,e should look very similar. Differences may be attributed to poor coupling of the planted receiver unit.
 
Gaiser <ref name=ch11r31/> reported a coupling experiment to verify the validity of the coupling theory described above. Figure 11.6-12a,b,c show the inline, crossline, and vertical geophone records obtained from an OBC survey. In the same figure, the record associated with the crossline geophone is shown after compenating for coupling (Figure 11.6-12d). To study the validity of the compensation based on equation ({{EquationNote|68}}), a diver firmly planted the receiver unit into the seabed and the recording was repeated. The resulting crossline record is shown in Figure 11.6-12e. If the coupling theory holds, then the records in Figures 11.6-12d,e should look very similar. Differences may be attributed to poor coupling of the planted receiver unit.
  
 
Figure 11.6-13 shows the result of surface-consistent coupling analysis. To apply the coupling corrections, scale the amplitudes in a given geophone record by the product of the source scalar and the associated component scalar. Figure 11.6-14 shows the common-shot gather as in Figure 11.6-6 after the application of surface-consistent amplitude corrections (Figure 11.6-12). The same shot gather with AGC is shown in Figure 11.6-15. The common-receiver gather as in Figure 11.6-8 after the application of surface-consistent amplitude corrections (Figure 11.6-12) is shown in Figure 11.6-16. The same receiver gather with AGC is shown in Figure 11.6-17. To examine the degree of compensation for differences in geophone coupling, refer to the close-up displays shown in Figures 11.6-18 and 11.6-19.
 
Figure 11.6-13 shows the result of surface-consistent coupling analysis. To apply the coupling corrections, scale the amplitudes in a given geophone record by the product of the source scalar and the associated component scalar. Figure 11.6-14 shows the common-shot gather as in Figure 11.6-6 after the application of surface-consistent amplitude corrections (Figure 11.6-12). The same shot gather with AGC is shown in Figure 11.6-15. The common-receiver gather as in Figure 11.6-8 after the application of surface-consistent amplitude corrections (Figure 11.6-12) is shown in Figure 11.6-16. The same receiver gather with AGC is shown in Figure 11.6-17. To examine the degree of compensation for differences in geophone coupling, refer to the close-up displays shown in Figures 11.6-18 and 11.6-19.
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 +
<gallery>
 +
file:ch11_fig6-12.png|{{figure number|11.6-12}} Common-receiver gathers associated with (a) inline, (b) crossline, and (c) vertical geophones. The gather in (d) is the crossline component (b) after compensating for coupling and (e) is the crossline component recorded by a diver who planted the geophone firmly into the seabed. (Figure courtesy <ref name=ch11r31/>, and Baker-Hughes Western Geophysical.)
 +
file:ch11_fig6-13.png|{{figure number|11.6-13}} Amplitude factors derived from surface-consistent coupling analysis for (a) the source, (b) inline geophone, (c) vertical geophone, and (d) crossline geophone.
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file:ch11_fig6-14.png|{{figure number|11.6-14}} The composite common-shot gather as in Figure 11.6-6 after coupling corrections of Figure 11.6-13, (a) the hydrophone, (b) inline, (c) crossline and (d) vertical geophone components (Data courtesy Chevron.)
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file:ch11_fig6-15.png|{{figure number|11.6-15}} The composite common-shot gather as in Figure 11.6-14, but displayed with with AGC, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components.
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file:ch11_fig6-16.png|{{figure number|11.6-16}} The composite common-receiver gather as in Figure 11.6-8 after coupling corrections of Figure 11.6-13, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components.
 +
file:ch11_fig6-17.png|{{figure number|11.6-17}} The composite common-receiver gather as in Figure 11.6-16, but displayed with with AGC, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components.
 +
file:ch11_fig6-18.png|{{figure number|11.6-18}} A close-up view of the composite common-shot gather after coupling corrections as in Figure 11.6-14, and the spectra of the individual components, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components.
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file:ch11_fig6-6.png|{{figure number|11.6-6}} Individual components of a common-shot gather from a 4-C survey, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components. (Field data related to Figures 11.6-6 through 11.6-29 are courtesy Chevron.)
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file:ch11_fig6-8.png|{{figure number|11.6-8}} Individual components of a common-receiver gather from a 4-C survey, (a) the hydrophone, (b) inline, (c) crossline, and (d) vertical geophone components.
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</gallery>
  
 
==References==
 
==References==

Latest revision as of 09:49, 7 October 2014

Seismic Data Analysis
Seismic-data-analysis.jpg
Series Investigations in Geophysics
Author Öz Yilmaz
DOI http://dx.doi.org/10.1190/1.9781560801580
ISBN ISBN 978-1-56080-094-1
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Variations in geophone coupling contaminate signal amplitudes registered by the geophone components, and need to be compensated for in a surface-consistent manner. Because of coupling problems, what is recorded by each one of the three geophones is not exactly the same as the ground motion at the seabed. A frequency-domain model equation that relates the recorded signal components {X′(ω), Y′(ω), Z′(ω)} by the three geophones in the inline, crossline, and vertical directions (x, y, z), respectively, and the actual ground motions in the three orthogonal directions {X(ω), Y(ω), Z(ω)} is given by [1]


(66)

where ω is the angular frequency, I is unity, and the nonzero elements Cy, Cz, Vy, and Vz describe the coupling response of the geophones.

Note from equation (66) that X′(ω) = X(ω); this means that we assume that the inline geophone is perfectly coupled. Since the inline geophone is guided by the cable itself, this is considered a valid assumption in practice. Whereas the vertical and crossline geophones are not coupled completely — hence the nonzero elements of the coupling matrix. The imperfect coupling leads to vertical and crossline geophone signals mutually contaminating each other in a manner that can be modeled by equation (66).

We wish to estimate the ground motion vector {X(ω), Y(ω), Z(ω)}; this requires inverting equation (66) as given by Gaiser [1]


(67)

where D = VzCy − VyCz and is the determinant of the coupling matrix in equation (66).

From the matrix equation (67), write explicitly the recovered ground motions


(68a)

and


(68b)

The coupling compensation operators are estimated in a surface-consistent manner [2] with the constraint that, following the rotation, the energy of the transverse component is minimum.

Gaiser [1] reported a coupling experiment to verify the validity of the coupling theory described above. Figure 11.6-12a,b,c show the inline, crossline, and vertical geophone records obtained from an OBC survey. In the same figure, the record associated with the crossline geophone is shown after compenating for coupling (Figure 11.6-12d). To study the validity of the compensation based on equation (68), a diver firmly planted the receiver unit into the seabed and the recording was repeated. The resulting crossline record is shown in Figure 11.6-12e. If the coupling theory holds, then the records in Figures 11.6-12d,e should look very similar. Differences may be attributed to poor coupling of the planted receiver unit.

Figure 11.6-13 shows the result of surface-consistent coupling analysis. To apply the coupling corrections, scale the amplitudes in a given geophone record by the product of the source scalar and the associated component scalar. Figure 11.6-14 shows the common-shot gather as in Figure 11.6-6 after the application of surface-consistent amplitude corrections (Figure 11.6-12). The same shot gather with AGC is shown in Figure 11.6-15. The common-receiver gather as in Figure 11.6-8 after the application of surface-consistent amplitude corrections (Figure 11.6-12) is shown in Figure 11.6-16. The same receiver gather with AGC is shown in Figure 11.6-17. To examine the degree of compensation for differences in geophone coupling, refer to the close-up displays shown in Figures 11.6-18 and 11.6-19.

References

  1. 1.0 1.1 1.2 1.3 Gaiser, 1998, Gaiser, J. E., 1998, Compensating OBC data for variations in geophone coupling: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., New Orleans, Expanded Abstracts, 1429–1432.
  2. Taner and Koehler, 1981, Taner, M. T. and Koehler, F., 1981, Surface-consistent corrections: Geophysics, 46, 17–21.

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