# Factors affecting velocity estimates

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

Velocity estimation from seismic data is limited in accuracy and resolution for the following reasons:

2. Stacking fold,
3. signal-to-noise ratio,
4. Muting,
5. Time gate length,
6. Velocity sampling,
7. Choice of coherency measure,
8. True departures from hyperbolic moveout, and
9. Bandwidth of data.

Figure 3.2-13 shows a synthetic CMP gather with velocity spectra generated by using gradually decreasing spread lengths. Lack of large-offset information means lack of the significant moveout required for velocity discrimination. Note the loss in sharpness of the peaks in the velocity spectra computed from the small-spread portion of the CMP gather. Resolution decreases first in the deeper part of the spectrum where there is little moveout (Table 3-1).

 ΔtNMO, in s ΔtNMO, in s t0, s vNMO, m/s x = 1000 m x = 2000 m 0.25 2000 0.309 0.780 0.5 2500 0.140 0.443 1 3000 0.054 0.201 2 3500 0.020 0.080 4 4000 0.008 0.031

Figure 3.2-14 shows velocity spectra computed from a real data set using spread lengths as indicated. The broadened peaks caused by the use of smaller spreads indicate loss of resolution in the velocity spectrum. This problem may be compounded by the poor signal-to-noise ratio or residual static shifts. An example of residual statics effect is shown in Figure 3.2-15. Velocity spectrum computed from a spread length that includes small offsets (center panel) infers an incorrect velocity function. As the spread length is made smaller (right panel), the velocity trend becomes indistinct.

What if only the far offsets are included when computing the velocity spectrum? Although far-offset data are needed to better resolve the velocity picks, there is a stretching problem in the far-offset region. Therefore, a velocity spectrum computed on the basis of only the far-offset region of a CMP gather suffers from the effects of muting at shallow times. This problem is demonstrated in Figure 3.2-16, where the spread is increasingly confined to the far-offset region of the input CMP gather. Note the loss of coherency peaks from the shallow events because of muting, and the further degradation of the coherency peaks corresponding to deeper events. Thus, adequate resolution in the velocity spectrum can only be obtained with a sufficiently large spread that spans both near and far offsets. This is analogous to the lesson learned in the 1-D Fourier transform on temporal resolution, which requires both low and high frequencies.

Stacking fold plays a significant part in the degree of resolution achieved from velocity spectra. In contemporary seismic data acquisition, it is common to record data with 240 or more channels. For computational savings, high-fold data sometimes are reduced to a low-fold equivalent gather by partial stacking. The idea is to stack a number of traces in a CMP gather from adjacent offsets to produce a CMP gather with lower fold. For example, a reduction of fold from 64 to 16 amounts to producing one output trace for each set of four adjacent input traces. Partial stacking involves differential NMO application to each group of adjacent traces using a reasonable, previously estimated velocity function so that primaries are aligned before stacking. The CMP gather in Figure 3.2-17 was partially stacked down to 32-, 16- and 8-fold gathers. Corresponding velocity spectra also are shown in Figure 3.2-17. No harm was done by reducing the fold to 32. Even the 16-fold data seem to produce accurate picks. However, use of lower fold significantly shifts the peaks in the spectrum. Reducing the fold by partial stacking merely to save computation must not be done at the expense of accuracy.

Noise in seismic data has a direct effect on the quality of a velocity spectrum. Add band-limited random noise to the CMP gather at increasingly higher levels of amplitude (Figure 3.2-18). The corresponding velocity spectra are shown in gated row plot form in Figure 3.2-19 and, for comparison, in contour form in Figure 3.2-20. The velocity spectrum distinguishes signal along hyperbolic paths even with high levels of random noise. (Refer to the velocity spectrum for SNR = 3 in Figure 3.2-19.) This is because of the power of crosscorrelation in measuring coherency. The accuracy of the velocity spectrum is limited when the signal-to-noise ratio is poor. Refer to SNR = 1 in Figures 3.2-19 or 3.2-20. The event at 0.8 s still can be picked, but the others are difficult to distinguish.

As a result of moveout correction, the waveform along a reflection hyperbola is stretched (Normal moveout). Stretching is more severe in the shallow part of the moveout-corrected gather, especially at large offsets. The stretched zone must be muted to prevent degradation of the stacked amplitudes associated with shallow events. However, muting reduces fold in the stacking process for shallow data (Figure 3.1-11c). It also has an adverse effect on the velocity spectrum, for it causes weakening of the peak amplitude that falls within the mute zone, as demonstrated in Figure 3.2-21. These peaks must be corrected for the weakening effect of the muting process. This is done by multiplying stacked amplitudes by a scale factor equal to the ratio of the actual multiplicity to the number of live traces in the mute zone.

The velocity spectrum is computed along hyperbolic search paths for a range of constant velocity values, or constant ΔtNMO (equation 2a). The hyperbolic path spans a two-way time gate specified at zero-offset. Figure 3.2-22 shows velocity spectra computed with four different gate lengths. If the gate length chosen is too coarse, the spectrum suffers especially from lack of temporal resolution. This becomes more evident on the same spectra displayed in contour form in Figure 3.2-23. In practice, the gate length is chosen between one-half and one times the dominant period of the signal, typically 20 to 40 ms. Since the dominant period can be time-variant (small in early and large in late times), the gate length can be specified accordingly.

 ${\displaystyle \Delta t_{NMO}=t-t_{0},}$ (2a)

The velocity range used in the analysis must be chosen carefully; it should span the velocities that correspond to those of primary reflections present in the CMP gather. The velocity increment must not be too coarse, for it can degrade the resolution, especially for high-velocity events.

 Use of Velocity % Error for rms % Error for Interval NMO corrections for conventional stack 2-10 — Structural anomaly detection: 30-m anomaly at 3000-m depth 0.5 — Gross lithologic identification: 300-m interval at 3000-m depth 0.7 10 Stratigraphic detailing: 150-m interval at 3000-m depth 0.1 3

Several options are considered in constructing the velocity spectrum. Partial stacking is one option that already was discussed. Band-pass filtering and automatic gain control (AGC) sometimes can improve the crosscorrelation process, especially when the input gather has poor signal-to-noise ratio.

Another way to improve the quality of a velocity spectrum is to use several neighboring CMP gathers in the analysis. Figure 3.2-24 shows six neighboring CMP gathers. By using the first CMP gather in the group, we get the velocity spectrum in Figure 3.2-25a. There are two ways to analyze these gathers as a group. One way is to sum the gathers and compute the velocity spectrum from the sum. This is shown in Figure 3.2-25b. Another way is to compute the velocity spectra from each individual gather and sum the spectra as shown in Figure 3.2-25c. Clearly, the former is more cost-effective than the latter. In practice, the number of CMP gathers that may be used must be chosen so that there is negligible dip across the gathers under consideration. If the structural dip is significant, then the number of CMP gathers included in the velocity analysis must be kept small. Note that the peak corresponding to the shallow event in Figure 3.2-25b is smaller than its counterpart in Figure 3.2-25c. Look closely at the CMP gathers in Figure 3.2-24 and note the slight difference in travel-times from gather to gather, especially for the shallow event. Summing these gathers distorts the hyperbolic path and causes degradation in the velocity spectrum.

When the input gather has a significant noise level, some smoothing may be done on the velocity spectrum matrix by averaging over velocity or time gates, or by some combination of the two. Another way to suppress small-amplitude correlation peaks that may be related to the ambient noise level in the data is to apply some percentage of bias to the correlation values. Biasing refers to subtracting a constant value from the correlation values over the entire velocity spectrum. Various combinations of averaging and biasing of correlation values also are used in practice. Finally, for computational efficiency, correlation values may be computed within a specified velocity corridor. The corridor must be chosen so that it spans the velocity variations vertically and laterally in the survey area.

Experience in a survey area helps when picking appropriate stacking velocities for primary reflections from velocity spectra. Acceptable velocity errors vary depending on use of the estimated velocities (Table 3-7).