The problem of inverse ray tracing in a homogeneous anisotropic elastic solid is considered. The wave speeds in the solid are assumed unknown, and must be obtained in the course of the inversion. The specific problem of locating a crack tip in a two-dimensional geometry is investigated. The data are assumed to be in the form of travel times of diffracted ultrasonic signals between transducers positioned on an exterior surface of the solid. Both pulse-echo and pitch-catch data are considered. It is found that travel-time data on the exterior surface suffices to locate the crack tip only if the material is isotropic. If the material is anisotropic, we must be able to move the source and/or receiver in the direction normal to the surface. The same problem is considered with the source and receiver positioned in a surrounding isotropic material, e.g., a water bath. It is shown that the ray inversion is now possible only if the solid is isotropic, the problem being underdetermined for an anisotropic solid. This indicates that the problem of inverse ray tracing, in the context of crack sizing, is not possible in a medium which is both inhomogeneous and anisotropic. Numerical results are presented for a synthetic experiment in which a finite crack is present in some transversely isotropic homogeneous elastic solids. It is demonstrated that an initial presumption of isotropy can lead to very erroneous results.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics