Effects of normal-moveout (NMO) removal

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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.

Figure 9.32a.  End-on record of model with four horizontal velocity layers. (i) Before NMO correction; (ii) after NMO correction.

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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