3D Gabor analysis of transient waves propagating along an AT cut quartz disk

Laser detection methods allow the investigation of ultrasonic transient phenomena in both space and time dimensions. Used for the experimental investigation of surface wave propagation along a 2D surface, laser ultrasonic leads to three dimensional (3D) space–time signal collections. The classical high resolution signal processing methods or 3D Fourier Transforms can be used in order to extract the wave propagation information, however these methods are not adapted for identifying where and when the waves are generated. In order to quantify these transient aspects in the space–time–wave number–frequency domains, the 3D Gabor transform is introduced. The 3D Gabor transform properties are presented. The potential of the 3D Gabor for the identification of the local and transient complex wave numbers is illustrated on the propagation of surface waves on a piezoelectric quartz (AT cut, 6 MHz). In this experimental study, the quartz is excited by a voltage pulse and the quartz surface is scanned by a laser vibrometer. The 3D Gabor analysis shows that the circular electrodes borders generate anti-phase surface waves that propagates outside the electrodes, with a strong energy contribution in the low frequency domain (