# Traveltime curves for various events

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 6 181 - 220 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 6.14

Draw arrival-time curves for the five events in Figure 6.14a.

Figure 6.14a.  Events involving a mesa.
Figure 6.14b.  Arrival times of events. (i) Geometry; (ii) traveltimes.

### Solution

We have for the depth to the mesa, 1900 m; height of mesa, 900 m. The traveltime curves were obtained graphically. We let ${\displaystyle R}$ stand for receiver locations.

For the reflected diffraction from ${\displaystyle S_{1}}$ (diffracted at A), the virtual source (see problem 4.1) for the event is ${\displaystyle I_{1}}$ in Figure 6.14b(i) (note that traveltime increases upward), so that

{\displaystyle {\begin{aligned}t=(S_{1}A+I_{1}R)/V_{1}=(2.20+I_{1}R)/2.00.\end{aligned}}}

For the reflection from ${\displaystyle S_{2}}$, we use the virtual source ${\displaystyle I_{2}}$. We will also have a diffraction from the ${\displaystyle S_{2}}$ source (paths not shown).

For the reflected refraction from ${\displaystyle S_{3}}$ (reflected at C), we find two traveltimes and then draw a straight line through them.

{\displaystyle {\begin{aligned}{\hbox{At}}\ S_{3},t=2(2.20/2.00+2.20/3.64)=2.80{\hbox{s}}.\\{\hbox{At}}\ S_{4},t=2(2.20/2.00)+1.10/3.64=2.50{\hbox{s}}.\end{aligned}}}

For the diffraction at ${\displaystyle C}$ from ${\displaystyle S_{4}}$,

{\displaystyle {\begin{aligned}t=(S_{4}C+CR)/2.00=(2.20+CR)/2.00.\end{aligned}}}

For the diffracted reflection from ${\displaystyle S_{5}}$ (diffracted at C), we use the image point of ${\displaystyle S_{5}}$ (not shown) so that

{\displaystyle {\begin{aligned}t=(I_{5}C+CR)/2.00,\end{aligned}}}

which gives the same curve as for the diffraction from ${\displaystyle S_{4}}$ except that it is displaced towards increased time by the difference in traveltimes for ${\displaystyle S_{4}C}$ and ${\displaystyle I_{5}C}$.