Inverse method for determining the depth of nonhomogeneous surface layers in elastic solids from the measurements of the dispersion curves of group velocity of surface SH Waves

Abstract

In this paper, the variational inverse method for determining the depth of nonhomogeneous surface layers in elastic materials, from the measurements of the group velocity of surface shear horizontal (SH) waves, is developed. The direct problem for a given a priori type of profile of the coefficientc44in(x) (e.g. linear, Gaussian, etc.) is solved. The dispersion curves of phase and group velocity of surface SH waves in nonhomogeneous solids are calculated. Experimental verification of the inverse method has been performed for step profiles (structure of Cu on steel). It is stated that the inverse method based on the measurements of group velocity (for step profile) gives a smaller error in the unknown depth of the surface layer than that resulting from the inverse method based on the measurements of phase velocity of surface SH waves.