Rotation of horizontal geophone components
Return to the OBC geometry shown in Figure 11.6-5. As discussed earlier in the section, by using gimballed geophones, the vertical geophone orientation can be maintained in a true vertical direction. The two horizontal geophones, however, cannot be oriented along the desired inline and crossline directions. Instead, they align themselves in arbitrary orientations from one receiver station to the next. We need to realign the horizontal geophones associated with one common-shot gather to a common orientation. One common orientation that is the source-centered Cartesian coordinates is shown in Figure 11.6-22. This means that the horizontal geophones of all receivers that contribute traces to the shot station with a circle around it are rotated from inline-crossline (x, y) coordinates (the acquisition coordinate system) to radial-transverse (r, t) coordinates relative to the source location (the processing coordinate system). As a result, the radial geophone response will represent the horizontal particle motion in the source-receiver plane and the transverse geophone response will represent the horizontal particle motion perpendicular to the radial response. Following the rotation, a common-shot or a common-receiver gather associated with the radial component will comprise traces with radial responses in the source-receiver azimuthal directions.
Figure 11.6-5 An ocean-bottom cable layout layout of a three-component geophone system. (Figure courtesy Gaiser , and Baker-Hughes Western Geophysical.)
Figure 11.6-22 A source-centered coordinate system applicable to a three-component geophone system after rotation of the inline and crossline components to radial and transverse components. (Figure courtesy Gaiser , and Baker-Hughes Western Geophysical.)
Figure 11.6-23 Coordinate transformation of the horizontal geophone components from field coordinates, inline-crossline (x, y), to processing coordinates, radial-transverse (r, t) as denoted in (c); common-receiver gathers of (a) the inline component and (b) crossline component in (x, y) coordinates; and following rotation, common-receiver gathers of (d) the radial and (e) transverse component in (r, t) coordinates. (Figure courtesy , and Baker-Hughes Western Geophysical.)
Figure 11.6-23 shows a common-receiver gather associated with the inline and crossline geophone components before and after rotation. The equations for coordinate transformation of the particle motions from inline-crossline (x, y) coordinates to radial-transverse (r, t) coordinates are 
where the rotation angle θ is as labeled in Figure 11.6-23c, Y(t) and X(t) are the inline and crossline components as recorded in the field following the compensation for variations in coupling, and R(t) and T(t) are the rotational and transverse components after rotation.
It is generally assumed that most significant signal components — reflections, diffractions, and converted waves, are polarized in the source-receiver direction . This means that, following the rotation of the horizontal geophone components, the radial component would contain most of the PS energy while the transverse component would contain negligible PS energy (Figure 11.6-23). If the transverse component does contain anomalously high level of signal energy, it may be attributable to anisotropy that causes shear-wave splitting in fractured rocks. We shall review this pheonomenon briefly in seismic anisotropy.
Figure 11.6-24 shows the common-shot gather as in Figure 11.6-14 after rotation of the horizontal components. The hydrophone record (first record from left) and the vertical geophone record (fourth record from left) are the same in both figures. The second and third record from the left in Figure 11.6-14 represent the inline and crossline geophone components of the particle motion; whereas, the second and third record from the left in Figure 11.6-24 represent the radial and transverse geophone components of the particle motion. Note from the AGC applied version of the same shot gather in Figure 11.6-25 that the radial component, unlike the inline component shown in Figure 11.6-15, does not exhibit the polarity reversal at zero offset. Also, the transverse component in Figure 11.6-25 contains relatively weak signal energy when compared to the radial component. These observations are also verified in the common-receiver gather shown in Figure 11.6-26. Compare the AGC applied version of the receiver gather before (Figure 11.6-16) and after (Figure 11.6-27) rotation and note the switch in polarity and low signal level in the transverse component. The spectral analysis of the shot and receiver gathers are shown in Figures 11.6-28 and 11.6-29; compare these results with Figures 11.6-18 and 11.6-19.
- Gaiser, 1999b, Gaiser, J. E., 1999b, Applications of vector coordinate systems of 3-D converted-wave data: The Leading Edge, 1290–1300.
- Li and Yuan, 1999, Caldwell, J., 1999, Marine multicomponent seismology: The Leading Edge, 1274–1282.
- 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.
- 4-C seismic method
- Recording of 4-C seismic data
- Gaiser’s coupling analysis of geophone data
- Processing of PP data
- Common-conversion-point binning
- Velocity analysis of PS data
- Dip-moveout correction of PS data
- Migration of PS data