Parallelism of half-intercept and delay-time curves
 | |
| Series | Geophysical References Series |
|---|---|
| Title | Problems in Exploration Seismology and their Solutions |
| Author | Lloyd P. Geldart and Robert E. Sheriff |
| Chapter | 11 |
| Pages | 415 - 468 |
| DOI | http://dx.doi.org/10.1190/1.9781560801733 |
| ISBN | ISBN 9781560801153 |
| Store | SEG Online Store |
Problem 11.10
Prove that a half-intercept curve is parallel to the curve of the total delay time $ \delta $ (see Figure 11.10a).
Solution
Referring to Figure 11.10a, we can write
$ {\begin{aligned}t_{i}/2=h\left(\cos \theta _{c}/V_{1}\right)\end{aligned}} $
[see equations (11.9b)]. Thus Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): t_{i} /2 is a linear function of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): h with slope Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \left(\cos \theta _{c} /V_{1} \right) . The total delay time is
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \begin{align} \delta=\delta_{s} +\delta_{g}, \end{align}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \delta_{s} being constant. If we substitute Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): N=h\tan \theta _{c} (see Figure 11.9a) in equation (11.8a), we obtain the result
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \begin{align} \delta_{g} =h\left(\cos \theta _{c} /V_{1} \right), \\ \hbox{so}\quad \quad \delta=\delta_{s} +h\left(\cos \theta _{c} /V_{1} \right). \end{align}
Thus the total delay-time curve is parallel to the half-intercept time curve and lies above it the distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \delta_{s} .
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| Barry’s delay-time refraction interpretation method | Wyrobek’s refraction interpretation method |
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| Geologic interpretation of reflection data | 3D methods |
Also in this chapter
- Salt lead time as a function of depth
- Effect of assumptions on refraction interpretation
- Effect of a hidden layer
- Proof of the ABC refraction equation
- Adachi’s method
- Refraction interpretation by stripping
- Proof of a generalized reciprocal method relation
- Delay time
- Barry’s delay-time refraction interpretation method
- Parallelism of half-intercept and delay-time curves
- Wyrobek’s refraction interpretation method
- Properties of a coincident-time curve
- Interpretation by the plus-minus method
- Comparison of refraction interpretation methods
- Feasibility of mapping a horizon using head waves
- Refraction blind spot
- Interpreting marine refraction data
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