# Common-conversion-point binning

Series | Investigations in Geophysics |
---|---|

Author | Öz Yilmaz |

DOI | http://dx.doi.org/10.1190/1.9781560801580 |

ISBN | ISBN 978-1-56080-094-1 |

Store | SEG Online Store |

We learned in analysis of amplitude variation with offset that an incident *P*-wave is partitioned at a layer boundary into reflected and transmitted *P*- and *S*-wave components. Consider the raypath geometry in Figure 11.6-30a for an incident *P*-wave generated by the source *S*_{1} and a flat reflector. The reflection angle for the *PP*-wave is equal to the angle of incidence; however, the reflection angle for the *PS*-wave is smaller than the angle of incidence. As a result, the *PP* reflection will follow a symmetric raypath and be recorded at receiver location *R*_{2}, while the *PS* reflection will follow an asymmetric raypath and be recorded at receiver location *R*_{1}.

Now consider the common-midpoint (CMP) raypath geometry for a source-receiver pair *S*_{1} — *R*_{1} shown in Figure 11.6-30b. There are two reflection arrivals at the receiver location *R*_{1} associated with the *PP* and *PS* raypaths. The reflection point *B* at which the incident *P*-wave is converted to the *S*-wave is displaced in the lateral direction by some distance *d* away from the reflection point *A* at which the incident *P*-wave is reflected and recorded at the same receiver location *R*_{1} as the converted *S*-wave. This means that, for an earth model with flat layers, the *PP*-wave reflection points coincide with the midpoint location (Figure 11.6-31a); whereas, the *PS* conversion points do not (Figure 11.6-31b). As a direct consequence of this observation, the notion of a CMP gather based on sorting *PP* data from acquisition coordinates — source and receiver, to processing coordinates — midpoint and offset, such that traces in the gather have the same midpoint coordinate, is not applicable to *PS* data. Instead *PS* data need to be sorted into *common-conversion-point* (CCP) gathers such that traces in this gather have the same conversion point coordinate.

An important aspect of CCP sorting is that the asymmetric raypath associated with the *PS* reflection gives rise to a periodic variation in fold of the CCP gathers. As for the conventional *P*-wave data with variations in fold caused by irregular recording geometry, amplitudes of the stacked *PS* data are adversely affected by the variation in the CCP fold ^{[1]} ^{[2]}. Just as one resorts to flexible bin size in the processing of 3-D seismic data to accommodate variations in fold, the same strategy may be applied for the *PS* data processing.

Binning the *PS* data into CCP gathers requires knowledge of the conversion-point coordinate *x _{P}*. Referring to Figure 11.6-31b, note that the conversion-point coordinate follows a trajectory indicated by the broken curve that, in general, depends on the reflector depth

^{[3]}.

**Figure 11.6-32**Geometry of a common-conversion-point (CCP) raypath used to derive the reflection traveltime equation (**74**) for the*PS*-wave.

To derive an expression for *x _{P}*, refer to the geometry of the

*PS*-raypath shown in Figure 11.6-32. By Snell’s law, we know that

**(**)

where *α* and *β* are the *P*-wave and *S*-wave velocities, respectively, and *φ*_{0} is the *P*-wave angle of incidence and *ψ*_{1} is the reflection angle for the converted *S*-wave.

From the geometry of Figure 11.6-32, note that

**(**)

and

**(**)

where *x _{P}* and

*x*are the lateral distances from the CCP to the source and receiver locations, respectively. Substitute equations (

_{S}**71a**,

**71b**) into equation (

**70**), square and rearrange the terms to get

**(**)

Apply some algebraic manipulation to solve equation (**72a**) for *x _{S}*

**(**)

where *γ* = *α*/*β*. Finally, substitute the relation *x _{S}* =

*x − x*, where

_{P}*x*is the source-receiver offset, into equation (

**72b**) to get the desired expression

**(**)

From Figure 11.6-31b, note that the CCP location moves closer to CMP location as the depth of the reflector increases. At infinite depth, the CCP location reaches an asymptotic conversion point (ACP) ^{[4]}. In the limit *z* → ∞, equation (**72c**) gives the ACP coordinate *x _{P}* with respect to the source location

**(**)

Since *β* < *α*, the conversion point is closer to the receiver location than the source location (Figure 11.6-31b). The displacement *d* = *x _{P} − x*/2 of the asymptotic conversion point from the midpoint is, by way of equation (

**73a**),

**(**)

While CCP binning may be performed using the ACP coordinate given by equation (**73a**), more accurate binning techniques account for the depth-dependence of the CCP coordinate *x _{P}* based on a solution to equation (

**72c**)

^{[3]}

^{[5]}. Because of the quartic form of equation (

**72c**) in terms of

*x*, an iterative solution may be preferred in practice

_{P}^{[5]}

^{[6]}

^{[7]}. The iteration may be started by substituting the asymptotic form of

*x*given by equation (

_{P}**73a**) into the right-hand side of equation (

**72c**). The new value of

*x*may then be back substituted into equation (

_{P}**72c**) to continue with the iteration.

Whatever the estimation procedure, note from equation (**72c**) that *x _{P}* depends both on depth to the reflector and the velocity ratio

*γ*=

*α*/

*β*. Unless a value for the velocity ratio is assumed, it follows that CCP binning requires velocity analysis of

*PS*data to determine the velocity ratio

*γ*. Additionally, an accurate CCP binning strictly requires the knowledge of reflector depths; thus, the advocation of an implicit requirement that 4-C seismic data analysis should be done in the depth domain. This requirement may be waivered if we only consider a horizontally layered earth model as in the next subsection.

## References

- ↑ Eaton and Lawton, 1992, Eaton, D. W. S. and Lawton, D. C., 1992,
*P-SV*stacking charts and binning periodicity: Geophysics, 57, 745–748. - ↑ Li and Yuan, 1999, Caldwell, J., 1999, Marine multicomponent seismology: The Leading Edge, 1274–1282.
- ↑
^{3.0}^{3.1}Tessmer and Behle, 1988, Tessmer, G. and Behle, A., 1988, Common reflection point data stacking technique for converted waves: Geophys. Prosp., 36, 671–688. - ↑ Fromm et al., 1985, Fromm, G., Krey, T., and Wiest, B., 1985, Static and dynamic corrections,
*in*Dohr, G., Ed., Seismic Shear Waves: Handbook of Geophysical Exploration, vol. 15a: Geophysical Press, 191–225. - ↑
^{5.0}^{5.1}Zhang and Robinson, 1992, Zhang, Y. and Robinson, E. A., 1992, Stacking*P-SV*converted wave data with raypath velocity: 62nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1214–1217. - ↑ Zhang, 1996, Zhang, Y., 1996, Nonhyperbolic converted wave velocity analysis and normal moveout: 66th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1555–1558.
- ↑ Yuan and Li, 1997, Yuan, J. and Li., X-Y., 1997, Converted-wave CCP binning and velocity analysis:
*in*Processing three-component seafloor seismic data, Edinborough University.

## See also

- 4-C seismic method
- Recording of 4-C seismic data
- Gaiser’s coupling analysis of geophone data
- Processing of PP data
- Rotation of horizontal geophone components
- Velocity analysis of PS data
- Dip-moveout correction of PS data
- Migration of PS data