Estimation of surface-layer structure from Rayleigh-wave dispersion. III. Sparse data case—Interpretation of experimental data

Abstract

Elastic surface waves penetrating into solids to a depth proportional to the wavelength are expected to be dispersive in the presence of gradients in physical properties such as density, chemical composition, internal stress, or metallurgical microstructure. This paper presents the results of studies to use this phenomenon to determine physical property profiles in a nondestructive manner. In a previous paper, a mathematical model was presented giving, for discrete data sets, a probabilistic description of the possible results of measurement, including measurement errors. The model also yields auxiliary measures pertaining to bias, data-vs-model dominance, resolution, and a posteriori variance. Here, the model is applied to actual experimental data consisting of the phase velocities of Rayleigh surface waves measured as a function of frequency for three typical profiles: a thin layer on a thick substrate, a thin layer embedded near the surface of a thick substrate, and a smoothly and monotonically varying profile. The estimated profile is compared with independent (destructive) measurements. As a test, the theory is also applied at a discrete set of frequencies to a set of synthetic data calculated from an assumed profile. The above auxiliary measures giving properties of the estimator are also discussed.