Appendix C: Exercises
- Exercise on tomography. Fill in the numbers in the four squares in Figure C-1.
- The density of the atmosphere of the earth decreases with height. How is the light from a star bent as it passes through the atmosphere? What is the apparent position of the star? In his book Optics, Ptolemy (A.D. c. 100–c. 165) of Alexandria gave a table of the refractions of light when it passes through the atmosphere. This table was used for centuries.
- Consider a homogeneous isotropic medium. Cut a cone by a plane perpendicular to the axis. The resulting circle is the equal-time curve (isochrone) of a zero-offset event. Cut the cone by a plane parallel to the axis. The resulting hyperbola is the time-distance curve of the zero-offset event. Cut the cone by a slanting plane. The resulting ellipse is the equal-time curve for a nonzero-offset event. Is it possible to cut the cone to find the corresponding time-distance curve?
- The combined effects of refraction, dispersion, and internal reflection of sunlight by drops of rain produce a rainbow. In favorable conditions, two bows can be seen. The brighter inner bow is red on the outside and violet on the inside, whereas the outer bow has the colors reversed. How are the bows produced? (At the end of the rainbow lies a pot of gold for the students who can do this exercise).
- If velocity increases with depth in an isotropic medium, show that the wavefronts on the lower side of a ray get ahead of the positions that they would occupy if the entire wavefront traveled at one speed. Thus, the lower end of the wavefront moves faster and bends the ray upward.
- The typical deep-ocean velocity function has a minimum at a depth of about 1000 m. Show that this minimum attracts and channels sound waves to its own level, and thus this phenomenon is known as the sound channel. Sound channels (known to the whales) sometimes extend for distances of 3000 km.
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Also in this chapter
- The seismic reflection method
- Seismic interpretation
- Absorption loss and transmission loss
- The wave equation
- Wave velocity
- Velocity analysis
- Seismic tomography