The ray theory belongs to the methods most frequently used in seismology and seismic exploration for forward and inverse modeling of high-frequency seismic body waves. In smoothly varying media with smooth interfaces, it can provide useful approximate solutions of the elastodynamic equation of satisfactory accuracy. Starting from an intuitive description of the propagation of seismic waves along special trajectories -- rays, it has developed into a highly sophisticated method, described briefly in this review paper.
The ray method has its advantages and disadvantages. The basic advantages are its applicability to complex isotropic and anisotropic, laterally varying layered media and its numerical efficiency in such computations. It provides a physical insight into the wave propagation process by separating the wavefield into individual elementary waves and by allowing their identification. In addition, it makes possible to track the paths in the medium along which energy of individual waves propagates, an aspect very important in tomography. The ray method also represents an important basis for other related, more sophisticated methods, such as the paraxial ray method, the Gaussian beam summation method, the Maslov method, the asymptotic diffraction theory, etc. The ray method also has some limitations. As mentioned above, it is approximate. It is applicable only to smooth media with smooth interfaces, in which the characteristic dimensions of inhomogeneities are considerably larger than the prevailing wavelength of the considered waves. The ray method can yield distorted results and may even fail in some special regions called singular regions.
The reprint is available in PDF (893 kB).