Vertical depth calculations using velocity functions
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| 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
- average velocity $ {\bar {V}} $ versus depth (in problem 4.13b),
- rms-velocity $ V_{\rm {rms}} $ versus depth (in problem 4.13b),
- the best-fit $ {\bar {V}} $ versus depth function (in problem 4.13c),
- 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).
| 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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|---|---|
| Relation between average and rms velocities | Depth and dip calculations using velocity functions |
| Previous chapter | Next chapter |
| Partitioning at an interface | Seismic velocity |
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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