Effect of timing errors on stacking velocity, depth, and dip

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	5
Pages	141 - 180
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 5.17a

Given that the trace spacing in Figure 5.17a is 50 m, determine the stacking velocity, dip, and depth at approximately 0.5, 1.0, 1.5, 2.0, and 2.4 s.

Solution

Using an enlarged version of Figure 5.17a, we measured arrival times on the center traces and on traces symmetrically located left and right of the center, limiting the offsets to where we felt we could pick the events with confidence. The measurements give us $t_{o}$, $\Delta t_{\rm {NMO}}$, and $\Delta t_{d}/\Delta x$ and we must find $z$ and $\xi$; for this we need the velocity ${\bar {V}}$. We can find $V_{s}$ from equation (5.12a) and, since the dip is small, $V_{s}\approx {\bar {V}}$ and we can therefore use equation (4.2b) to get an approximate value of $\xi$. The equations are

Figure 5.17a.  A split-dip record (courtesy Grant Geophysical).

Table 5.17a. Measurements and calculations for five events.

$t_{o}$ (s)	0.533	0.975	1.575	2.008	2.417
offset (m)	575 m	1125	1425	1625	2375
$t_{\rm {left}}$ (s)	0.633	1.150	1.658	2.058	2.533
$t_{\rm {right}}$ (s)	0.608	1.142	1.758	2.150	2.575
$t_{\rm {NMO}}$ (s)	0.0875	0.171	0.133	0.096	0.137
$V_{s}$ (m/s)	1885	1950	2200	2615	2920
$z$ (m)	502	950	1730	2625	3530
$\Delta t_{d}/\Delta x$(ms/m)	0.0435	0.0071	0.0702	0.0566	0.0177
$\sin \xi$	0.0410	0.0070	0.0772	0.0740	0.0258
$\xi$	$2.3^{\circ }$	$0.4^{\circ }$	$4.4^{\circ }$	$4.2^{\circ }$	$1.5^{\circ }$

${\begin{aligned}\Delta t_{\rm {NMO}}=(t_{\rm {left}}+t_{\rm {right}})/2-t_{o}\\V_{s}=x/(2t_{o}\Delta t_{\rm {NMO}})^{1/2},\\\sin \xi =(V_{s}/2)(\Delta t_{d}/\Delta x)\\z=V_{s}t_{o}/2.\end{aligned}}$

The calculated results for five reflections are shown in Table 5.17a.

Problem 5.17b

What problems or ambiguities do you have in picking these events? How much uncertainty is there in your ability to pick times and how much uncertainty does this introduce into the velocity, depth, and dip calculations?

Solution

There are clearly different families of events interfering with each other on this record, which we have not attempted to sort out. The axes of symmetry of some of the data shift to the left with depth, indicating dip to the right. The event at 2.417 s may be a multiple. Clearly many more events could be picked.

We timed the centers of the black peaks, and this involves 5-10 ms $(\approx 0.5-2\%)$ uncertainty in this case. At a work station where a best-fit curve can be used to smooth-out noise, uncertainty can be reduced appreciably, and measurements can be accurate to 1 ms. Measurements of $V_{s}$ and $\xi$ are based on time differences and their errors are probably about 5%. If the offsets had been longer, measured differences would have been larger, giving better accuracy, but then uncertainties in event continuity and interference with other events might have increased the errors. In calculating depths, the onset of reflections should be measured so time measurements are probably 20 ms (1 to 4%) late. This may introduce 1% error in $V_{s}$, but other errors involved in $V_{s}$ are probably more important, including the assumption that it is the correct velocity to use. Dips are almost certainly underestimated by the use of $V_{s}$, which does not allow for the fact that the velocity at the reflector is usually larger than $V_{s}$ because of the usual increase of velocity with depth.

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Also in this chapter

• Maximum porosity versus depth
• Relation between lithology and seismic velocities
• Porosities, velocities, and densities of rocks
• Velocities in limestone and sandstone
• Dependence of velocity-depth curves on geology
• Effect of burial history on velocity
• Determining lithology from well-velocity surveys
• Reflectivity versus water saturation
• Effect of overpressure
• Effects of weathered layer (LVL) and permafrost
• Horizontal component of head waves
• Stacking velocity versus rms and average velocities
• Quick-look velocity analysis and effects of errors
• Well-velocity survey
• Interval velocities
• Finding velocity
• Effect of timing errors on stacking velocity, depth, and dip
• Estimating lithology from stacking velocity
• Velocity versus depth from sonobuoy data
• Influence of direction on velocity analyses
• Effect of time picks, NMO stretch, and datum choice on stacking velocity

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