Obtaining subsurface profiles from surface−acoustic−wave velocity dispersion

Surface acoustic waves can be used to probe nondestructively subsurface gradients (caused by physical processes) by changing their penetration depth with frequency. A perturbation−theory integral equation that describes the influence of a known gradient on the velocity dispersion is reviewed. The experimental situation requires solution of the ’’inverse problem’’: obtaining the profile from measured velocity data. The inverse problem is solved exactly by the use of Laplace transforms for gradients of the general form F (z). The nature of the solution allows observations about the gradient−dispersion relationship, the physical interpretation of dispersion curves, and the representation and measurement of gradients to be made. Six commonly occurring gradient functions and their dispersion curves are compared by use of an equivalent−area parameter formulation. The solution agrees well with published experimental results for residual stress in an aluminum block and for damaged layers on YZ LiNbO3 substrates. For cases in which the analytic form of neither the dispersion nor the gradient is known, a method is presented for obtaining the gradient from raw data. This technique is applied to published results for quench−hardened−steel cylinders, and the experimental implications of gradient determination are discussed.