Parallelism of half-intercept and delay-time curves

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	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

${\begin{aligned}t_{i}/2=h\left(\cos \theta _{c}/V_{1}\right)\end{aligned}}$

Figure 11.10a.  Delay-time and half-intercept curves.

[see equations (11.9b)]. Thus $t_{i}/2$ is a linear function of $h$ with slope $\left(\cos \theta _{c}/V_{1}\right)$. The total delay time is

${\begin{aligned}\delta =\delta _{s}+\delta _{g},\end{aligned}}$

$\delta _{s}$ being constant. If we substitute $N=h\tan \theta _{c}$ (see Figure 11.9a) in equation (11.8a), we obtain the result

${\begin{aligned}\delta _{g}=h\left(\cos \theta _{c}/V_{1}\right),\\{\hbox{so}}\quad \quad \delta =\delta _{s}+h\left(\cos \theta _{c}/V_{1}\right).\end{aligned}}$

Thus the total delay-time curve is parallel to the half-intercept time curve and lies above it the distance $\delta _{s}$.

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Geologic interpretation of reflection data	3D methods
Table of Contents (book)

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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