# NMO for several layers with arbitrary dips

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 |

Figure 3.1-15 shows a 2-D subsurface geometry that is composed of a number of layers, each with an arbitrary dip. We want to compute the traveltime from source location *S* to depth point *D*, then back to receiver location *G*, which is associated with midpoint *M*. Note that the CMP ray from midpoint *M* hits the dipping interface at normal incidence at *D′*, which is not the same as *D*. The zero-offset time is the two-way time along the raypath from *M* to *D′*.

^{[1]} derived the expression for traveltime *t* along *SDG* as

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where the NMO velocity is given by

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The angles *α* and *β* are defined in Figure 3.1-15. For a single dipping layer, equation (**13**) reduces to equation (**8**). Moreover, for a horizontally stratified earth, equation (**13**) reduces to equation (**4**). As long as the dips are gentle and the spread is small, the traveltime equation is approximately represented by a hyperbola (equation **5**), and the velocity required for NMO correction is approximately the rms velocity function (equation **4**).

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## See also

- NMO for a flat reflector
- NMO in a horizontally stratified earth
- Fourth-order moveout
- NMO stretching
- NMO for a dipping reflector
- Moveout velocity versus stacking velocity
- Exercises
- Topics in moveout and statics corrections

## References

- ↑
^{1.0}^{1.1}Hubral and Krey (1980), Hubral, P. and Krey, T., 1980, Interval velocities from seismic reflection time measurements: Soc. Expl. Geophys.