ABSTRACT
The construction of excellent images of the subsurface is the aim of every geophysicist engaged in seismic exploration. Geophysicists and astronomers make use of tools of remote detection. Planets outside the solar system are such faint light sources that only about 10 have been directly imaged by telescopes. However, hundreds have been detected by the use of the relativistic Doppler effect. Essential to every geophysicist is Huygens construction, which not only gives a geometrical explanation of how waves travel but also gives a means of imaging the data by a process known as seismic migration. Just as the Huygens construction can be used to explain seismic migration, it can also be used to explain the relativistic Doppler effect. A symmetry is a physical or mathematical feature of a system that is preserved under some change. The fact that both seismic migration and the relativistic Doppler effect can each be expressed in terms of the Huygens construction shows that both systems exhibit the same symmetry. In the case of seismic imaging, the symmetry is that observer and observed can be interchanged and still produces the same †nal image. In the case of the relativistic Doppler effect, the symmetry is that the behavior of two objects depends not upon their absolute motion, but only upon their relative motion. Such symmetry is called relativistic symmetry.
