Traveltime curves for various events

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	6
Pages	181 - 220
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	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 $R$ stand for receiver locations.

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

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

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

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

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

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

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

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

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

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

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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
• Causes of high-frequency losses
• Ricker wavelet relations
• Improvement of signal/noise ratio by stacking

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