Time-frequency simulation of ultrasonic longitudinal wave propagation in rocks

Abstract

Ultrasound numerical simulation can be used as a powerful tool to investigate the generation, propagation, and interaction of elastic waves in solid materials for non-destructive evaluation (NDE). It has been widely applied in several domains such as medical, mechanical, construction, and geotechnical engineering, especially for the detection of cracks and defects in structures and for the identification of the characteristics of rock materials. The comprehension of the propagation of the ultrasonic wave in homogeneous and isotropic elastic materials is very important. This paper presents a method for simulating normal incidence ultrasonic waves (Longitudinal waves) propagating in rock structures. A mathematical model of the response of an ultrasonic wave in a submerged rock structure is introduced analytically based on the transfer matrix method (TMM), in which the layer is established in a quadrupole formalism. The simulation results of the ultrasonic response of rock structures are represented in a time–frequency representation. The results have been compared with the experimental data available in the literature and show good agreement. The numerical simulation method established in this work can be proposed as an effective complement to experiments and used for rock characterization by performing the simulation of ultrasonic responses for different thicknesses of rock structures.