Vertical depth calculations using velocity functions

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Problem 4.14

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


The velocity functions determined are

  1. average velocity versus depth (in problem 4.13b),
  2. rms-velocity versus depth (in problem 4.13b),
  3. the best-fit versus depth function (in problem 4.13c),
  4. the best-fit 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 and were derived from the the given data. The errors in calculated depths in (ii), (iii), and (iv) are tabulated in Table 4.14b. Using gives -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) 0.0% 2.5% 5.4% 4.6%
iii) best-fit 1.0% 1.6% –2.9% 0.8%
iv) best-fit 2.0% 4.8% 0.4% 5.6%

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