Effect of time picks, NMO stretch, and datum choice on stacking velocity

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Problem 5.21a

Because velocity analysis is not made on the wavelet onset, how will this effect stacking-velocity values?

Background

A causal wavelet has zero amplitude for negative time values, that is, when .

A normal-moveout correction is subtracted from the arrival times of a reflection to compensate for the increase of raypath distance with offset. The normal-moveout equation (4.1c) has the factor in the denominator. While the value of is the same for all traces, it generally cannot be measured and the traveltime is used instead of . Also, the velocity usually increases with traveltime, and hence the correction is smaller than it should be. This effectively lowers the frequency, an effect called normal-moveout stretch.

Because of variable weathering (LVL) and the fact that the source and geophones are at various elevations, seismic traces are usually time shifted to effectively locate them on a horizontal datum surface below which conditions are assumed to be constant; this is called applying static corrections (see problem 8.18).

Solution

Equation (4.1a) gives for the velocity

Because the onset of a wave is not obvious, measured times are slightly larger than those associated with the reflector depths , and the calculated velocities will be slightly smaller.

Problem 5.21b

What will be the effect of NMO stretch?

Solution

All parts of a wavelet should be corrected for the time and velocity that is appropriate for the wavelet onset, but instead they are corrected for a delayed time and the velocity appropriate to it. The undercorrection will increase with offset, making the measured velocity too low.

Problem 5.21c

What will be the effect if the datum is appreciably removed from the surface?

Solution

The objective of corrections to a datum is to be able to treat the data as if the sources and geophones were all located at the same elevation and there are no horizontal velocity changes below the datum. It effectively corrects arrival times, but it does not change horizontal locations to account for the changes in datum depth. Because migration is often done assuming the same vertical velocity at all locations, errors in horizontal location will create errors in the migrated location of events. The datum should be sufficiently deep in the section so that horizontal velocity changes below the datum are so small that they do not affect the results. Note that corrections can be made for depths below the datum level so that deeper corrections do not imply a deep datum. In fact, the datum sometimes is above the ground level.

A datum that is appreciably deeper than the surface makes time measurements too small and calculated velocities too large. The horizontal component of raypaths is usually small near the surface but becomes larger as depths increase. Thus geophones actually located on the datum would involve smaller horizontal components of the distances to features that are not vertically below and thus create errors when the data are migrated.

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