View source for Traveltime curves for various events

{{publication
 | name    = Problems in Exploration Seismology and their Solutions
 | image   = [[File:897.Def.Lz-cropped.png|frameless|180px|link=Problems in Exploration Seismology and their Solutions]]
 | width   = 120px
 | series  = Geophysical References Series
 | title   = [[Problems in Exploration Seismology and their Solutions]]
 | part    = 
 | chapter = 6
 | pages  = 181 - 220
 | author  = [[Lloyd P. Geldart]] and [[Robert E. Sheriff]]
 | doi     = 10.1190/1.9781560801733
 | pdf     = 
 | store   = https://shop.seg.org/shop/products/detail/897
 | isbn    = ISBN 9781560801153
}}
== Problem 6.14 ==
Draw arrival-time curves for the five events in Figure 6.14a.

[[file:Ch06_fig6-14a.png|thumb|center|{{figure number|6.14a.}} Events involving a mesa.]]

[[file:Ch06_fig6-14b.png|thumb|center|{{figure number|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 <math>R</math> stand for receiver locations.

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

<math>
\begin{align}
t=(S_{1} A+I_{1} R)/V_{1} =(2.20+I_{1} R)/2.00.
\end{align}
</math>

For the reflection from <math>S_{2}</math>, we use the virtual source <math>I_{2}</math>. We will also have a diffraction from the <math>S_{2}</math> source (paths not shown).

For the reflected refraction from <math>S_{3}</math> (reflected at C), we find two traveltimes and then draw a straight line through them.

<math>
\begin{align}
\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{align}
</math>

For the diffraction at <math>C</math> from <math>S_{4}</math>,

<math>
\begin{align}
t=(S_{4} C+CR)/2.00=(2.20+CR)/2.00.
\end{align}
</math>

For the diffracted reflection from <math>S_{5}</math> (diffracted at C), we use the image point of <math>S_{5}</math> (not shown) so that

<math>
\begin{align}
t=(I_{5} C+CR)/2.00,
\end{align}
</math>

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

== Continue reading ==
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| align="center" | [[Identification of events]]
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|-
| align="center" | [[:Category:Geometry of seismic waves| Geometry of seismic waves]]
| align="center" | [[:Category:Characteristics of seismic events|Characteristics of seismic events]]
|-
| align="center" colspan="2" |
[[Problems_in_Exploration_Seismology_and_their_Solutions|Table of Contents (book)]]
|}

== Also in this chapter ==
* [[Characteristics of different types of events and noise]]
* [[Horizontal resolution]]
* [[Reflection and refraction laws and Fermat’s principle]]
* [[Effect of reflector curvature on a plane wave]]
* [[Diffraction traveltime curves]]
* [[Amplitude variation with offset for seafloor multiples]]
* [[Ghost amplitude and energy]]
* [[Directivity of a source plus its ghost]]
* [[Directivity of a harmonic source plus ghost]]
* [[Differential moveout between primary and multiple]]
* [[Suppressing multiples by NMO differences]]
* [[Distinguishing horizontal/vertical discontinuities]]
* [[Identification of events]]
* [[Traveltime curves for various events]]
* [[Reflections/diffractions from refractor terminations]]
* [[Refractions and refraction multiples]]
* [[Destructive and constructive interference for a wedge]]
* [[Dependence of resolvable limit on frequency]]
* [[Vertical resolution solution|Vertical resolution]]
* [[Causes of high-frequency losses]]
* [[Ricker wavelet relations]]
* [[Improvement of signal/noise ratio by stacking]]

== External links ==
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[[Category:Problems and Solutions]]
[[Category:Publications]]
[[Category:Characteristics of seismic events]]