Delay time

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 11.8

Show that $NQ$ in Figure 11.8a is given by

${\begin{aligned}NQ=V_{2}\delta _{NQ}\tan ^{2}\theta _{c},\\{\hbox{i.e.,}}\quad \quad \delta _{g}=\delta _{NQ}=NQ/V_{2}\tan ^{2}\theta _{c}.\end{aligned}}$

(11.8a)

Background

The concept of delay time has found wide application in refraction interpretation (see problems 11.9 and 11.11). We define the delay time associated with the refraction path SMNG in Figure 11.8a as the observed traveltime minus the time required to travel from $P$ to $Q$ at the velocity $V_{2}$. $PQ$ is the projection of the path SMNG onto the refractor), Writing $\delta$ for the total delay time, we have

${\begin{aligned}\delta &=t_{SG}-PQ/V_{2}\end{aligned}}$

(11.8b)

${\begin{aligned}&=\left({\frac {SM+NG}{V_{1}}}+{\frac {MN}{V_{2}}}\right)-{\frac {PQ}{V_{2}}}=\left({\frac {SM}{V_{1}}}-{\frac {PM}{V_{2}}}\right)+\left({\frac {NG}{V_{1}}}-{\frac {NQ}{V_{2}}}\right)\end{aligned}}$

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

(11.8c)

${\begin{aligned}{\hbox{where}}\quad \quad \delta _{s}={\hbox{source delay time}}\ =\left({\frac {SM}{V_{1}}}-{\frac {PM}{V_{2}}}\right)\end{aligned}}$

(11.8d)

${\begin{aligned}{\hbox{and}}\quad \quad \delta _{g}={\hbox{geophone delay time}}\ =\left({\frac {NG}{V_{1}}}-{\frac {NQ}{V_{2}}}\right).\end{aligned}}$

(11.8e)

Solution

Referring to Figure 11.8a, we have, by definition,

${\begin{aligned}\delta _{g}&=NG/V_{1}-NQ/V_{2}\\&=NQ\left({\frac {1}{V_{1}\sin \theta _{c}}}-{\frac {1}{V_{2}}}\right)={\frac {NQ}{V_{2}}}\left({\frac {1}{\sin ^{2}\theta _{c}}}-1\right)\\&=NQ/V_{2}\tan ^{2}\theta _{c}.\end{aligned}}$

Continue reading

Previous section	Next section
Proof of a generalized reciprocal method relation	Barry’s delay-time refraction interpretation method
Previous chapter	Next chapter
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

External links

find literature about Delay time