# Effects of normal-moveout (NMO) removal

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 9 |

Pages | 295 - 366 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## Problem 9.32a

Figure 9.32a shows three reflections before and after normal-moveout removal. Explain the broadening of the wavelets produced by the NMO correction.

### Background

A causal wavelet has zero amplitude for negative time, that is, when . A normal-moveout correction is subtracted from the arrival times of a reflection to compensate for the increase of raypath length with offset. The normal-moveout equation (4.1c) has the factor in the denominator and the values of and are the same for all traces and all cycles of the event. However, if the traveltime for each trace and each cycle is used instead of , and if is given as a function of , both and will change: usually increases with traveltime, and the correcton will be smaller than it should be, the error increasing with . This effectively lowers the frequency, an effect called *normal moveout stretch*.

### Solution

The broadening of the wavelet is due to NMO stretch as explained above. The NMO correction calculated for each trace is too small except at , the error increasing with increasing , i.e., as increases along each trace and also as it increases from trace to trace. Consequently, the traveltimes of the early part of the reflection are reduced more than later portions, resulting in broadening, as shown in Figure 9.32a(ii).

## Problem 9.32b

Explain why the reflections in Figure 9.32a do not have straight alignments after NMO correction.

### Solution

If the velocity above a reflector were constant and the normal moveout correct, the corrected reflection would be straight for the entire wavelet. However, because the velocity usually increases with arrival time, different NMO velocities are used to correct different parts of the wavelet. Also, as the offset increases, a wave spends a larger part of its traveltime in the higher-velocity parts of the section so that the average velocity increases with offset, making the reflection appear increasingly early as offset increases. However, NMO programs generally do not allow for the first factor and an empirical velocity value may be used rather than the correct one. Note that the onset of the first reflection is straight because the velocity above it is constant.

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Derivative and integral operators | Weighted least-squares |

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Reflection field methods | Geologic interpretation of reflection data |

## Also in this chapter

- Fourier series
- Space-domain convolution and vibroseis acquisition
- Fourier transforms of the unit impulse and boxcar
- Extension of the sampling theorem
- Alias filters
- The convolutional model
- Water reverberation filter
- Calculating crosscorrelation and autocorrelation
- Digital calculations
- Semblance
- Convolution and correlation calculations
- Properties of minimum-phase wavelets
- Phase of composite wavelets
- Tuning and waveshape
- Making a wavelet minimum-phase
- Zero-phase filtering of a minimum-phase wavelet
- Deconvolution methods
- Calculation of inverse filters
- Inverse filter to remove ghosting and recursive filtering
- Ghosting as a notch filter
- Autocorrelation
- Wiener (least-squares) inverse filters
- Interpreting stacking velocity
- Effect of local high-velocity body
- Apparent-velocity filtering
- Complex-trace analysis
- Kirchhoff migration
- Using an upward-traveling coordinate system
- Finite-difference migration
- Effect of migration on fault interpretation
- Derivative and integral operators
- Effects of normal-moveout (NMO) removal
- Weighted least-squares