Appendix B: Exercises

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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
DigitalImaging.png
Series Geophysical References Series
Title Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Author Enders A. Robinson and Sven Treitel
Chapter 2
DOI http://dx.doi.org/10.1190/1.9781560801610
ISBN 9781560801481
Store SEG Online Store

1. Show that (in the case of two dimensions x, y) if the velocity is then the rays are brought to a common focus (both time and distance) with common emergence distance and common emergence time . This exercise represents the traditional case of diving waves.

2. In the case when velocity increases linearly with depth, we first found by integration that . Show that depth y can be found without integration by simply using Snell’s law in the velocity equation .

3. Let the velocity (in the case of two dimensions x,y) be . Show that the equation for the raypath with initial angle to the vertical is

which is a parabola. Find the vertex of the parabola. Show that the ray is progressively bent toward the normal if a is positive and away from the normal if a is negative.

4. Let velocity (in the case of two dimensions x,y) be the exponential . Show that


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Appendix B: Exercises
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