# NMO in a horizontally stratified earth

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 now consider a medium composed of horizontal isovelocity layers (Figure 3.1-6). Each layer has a certain thickness that can be defined in terms of twoway zero-offset time. The layers have interval velocities (*v*_{1}, *v*_{2}, …, *v _{N}*), where

*N*is the number of layers. Consider the raypath from source

*S*to depth point

*D*, back to receiver

*R*, associated with offset

*x*at midpoint location

*M*. Cite error: Closing

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tag that exactly describe wave propagation in a horizontally layered earth model with a given interval velocity function. We now replace the layers above the second shallow event at *t*

_{0}= 0.8 s with a single layer with a velocity equal to the rms velocity down to this reflector — 2264 m/s. The resulting traveltime curve, computed using equation (

**4b**), is shown in Figure 3.1-7b. This procedure is repeated for the deeper events at

*t*

_{0}= 1.2 and 1.6 s as shown in Figures 3.1-7c and d. Note that the traveltime curves in Figures 3.1-7b, c, and d are perfect hyperbolas. How different are the traveltime curves in Figure 3.1-7a from these hyperbolas? After careful examination, note that the traveltimes are slightly different for the shallow events at

*t*

_{0}= 0.8 and 1.2 s only at large offsets, particularly beyond 3 km. By dropping the higher order terms, we approximate the reflection times in a horizontally layered earth with a

*small-spread hyperbola*.

## See also

- NMO for a flat reflector
- Fourth-order moveout
- NMO stretching
- NMO for a dipping reflector
- NMO for several layers with arbitrary dips
- Moveout velocity versus stacking velocity
- Normal moveout
- Exercises
- Topics in moveout and statics corrections

## References