Transformation ray method: Controlling high frequency elastic waves (L)

Elastic ray theory is a high frequency asymptotic approximation of solution of elastodynamic equation, and is widely used in seismology. In this paper, the form invariance under a general spatial mapping and high frequency wave control have been examined by transformation method. It is showed that with the constraint of major and minor symmetry of the transformed elastic tensor, the eikonal equation keeps its form under a general mapping, however, the transport equation loses its form except for conformal mapping. Therefore, the elastic ray path can be controlled in an exact manner by a transformation method, whereas energy distribution along the ray is only approximately controlled. An elastic rotator based on ray tracing method is also provided to illustrate the method and to access the approximation.