Vertical depth calculations using velocity functions

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	4
Pages	79 - 140
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 4.14

Assuming flat bedding, calculate depths corresponding to $t_{0}=1.0$, 2.0, 2.1, and 3.1 s using the velocity functions determined in problem 4.13b,c. What depth errors are created?

Solution

The velocity functions determined are

1. average velocity ${\bar {V}}$ versus depth (in problem 4.13b),
2. rms-velocity $V_{\rm {rms}}$ versus depth (in problem 4.13b),
3. the best-fit ${\bar {V}}$ versus depth function (in problem 4.13c),
4. the best-fit $V_{\rm {rms}}$ versus traveltime function (in problem 4.13c).

Using these, we obtain the depths in Table 4.14a.

No depth errors are present in (i) because $t_{0}$ and ${\bar {V}}$ were derived from the the given data. The errors in calculated depths in (ii), (iii), and (iv) are tabulated in Table 4.14b. Using $V_{\rm {rms}}$ gives $z$-values 2–5% too large. The best-fit depth function in (iii) gives the best results overall while the best-fit traveltime function in (iv) has errors of the same order of magnitude as those in (ii).

Table 4.14b. Errors in depth calculations.

		1.00 km	2.50 km	2.80 km	4.80 km
ii)	$V_{\rm {rms}}$	0.0%	2.5%	5.4%	4.6%
iii)	best-fit ${\bar {V}}$	1.0%	1.6%	–2.9%	0.8%
iv)	best-fit $V_{\rm {rms}}$	2.0%	4.8%	0.4%	5.6%

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Table of Contents (book)

Also in this chapter

• Accuracy of normal-moveout calculations
• Dip, cross-dip, and angle of approach
• Relationship for a dipping bed
• Reflector dip in terms of traveltimes squared
• Second approximation for dip moveout
• Calculation of reflector depths and dips
• Plotting raypaths for primary and multiple reflections
• Effect of migration on plotted reflector locations
• Resolution of cross-dip
• Cross-dip
• Variation of reflection point with offset
• Functional fits for velocity-depth data
• Relation between average and rms velocities
• Vertical depth calculations using velocity functions
• Depth and dip calculations using velocity functions
• Weathering corrections and dip/depth calculations
• Using a velocity function linear with depth
• Head waves (refractions) and effect of hidden layer
• Interpretation of sonobuoy data
• Diving waves
• Linear increase in velocity above a refractor
• Time-distance curves for various situations
• Locating the bottom of a borehole
• Two-layer refraction problem

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