Time Reversal (TR) is a technique that, among other things, allows one to locate a source of wave energy at an unknown position. Cracks are sources of nonlinear harmonic-frequency content when they are dynamically excited. Thus TR may be used to locate cracks since they are sources of the nonlinear frequency content. This paper will describe experiments, conducted over the past several years, to locate surficial cracks, near surficial cracks, and finally buried cracks. The ability to locate and characterize cracks may lead to better design of mechanical parts and may be used to monitor the structural health of solid samples, potentially including rock formations.
Time reversal (TR) is a technique that allows one to localize and characterize an unknown source of wave energy [1-3]. When a crack is elastically excited at sufficient amplitudes, its two opposing surfaces may collide with one another. The collision of crack surfaces results in a rectification of the incident wave energy, resulting in harmonic generation and intermodulation distortion. Thus if a crack is made to vibrate with sufficient amplitude in an otherwise linear medium, then the crack will be the source of “new” frequency content. TR may then be used to locate this source of nonlinear frequency content and hence the crack's location. The first experimental investigation of TR was shown in an underwater acoustic communication application by Parvulescu and Clay [4-6]. Since the 1970s, the basic concept of time reversal invariance of elastic wave propagation in weakly dissipative media has been exploited in different forms by exploration geophysicists for earth subsurface imaging. The basic technique, called Reverse Time Migration [7], has found widespread use only in recent years thanks to the development of high performance computing resources and facilities that are essential for its exploitation. However, the more versatile and general imaging/signal processing principles have been developed in the last twenty years by the group led by Fink at the Institut Langevin, École Supérieure de Physique et Chimie Industrielle (ParisTech). Fink's group focuses on imaging sources and scatterers in fluids with sound/ultrasound waves, while the group led by Kuperman at the Marine Physical Laboratory, Scripps Institute of Oceanography/Univ. of California at San Diego, has expanded the application of TR to underwater/ocean acoustics. The first experimental demonstrations of TR in solid media was done by Draeger et al. in 1998 and 1999 [8- 9]. The idea of locating a crack with TR techniques was first proposed by Guyer in 2001 [10]. The first proof of concept, by a full numerical experiment, of locating a crack was demonstrated by Bou Matar et al. in 2005, though the discussion and results in their paper was quite limited [11]. The first experimental study of TR in a solid sample by Sutin et al. at Los Alamos, without the need to submerge the sample in water, with the transducers directly bonded to the sample, demonstrated linear TR focusing in a doped glass sample and in a sandstone sample [12-13].
