DEDUCING SUBSURFACE PROPERTY GRADIENTS FROM SURFACE WAVE DISPERSION DATA.

Because of the ill-posed nature of the problem, special mathematical techniques must be used to convert surface wave dispersion data into subsurface property measurement. The solution is approached within the framework of estimation theory. This approach starts with a mathematical model giving a probabilistic description of the possible results of measurement and then the optimal estimate is obtained as the most probable value within the constraints imposed by the actual measurements. The theory is applied to actual experimental data consisting of the phase velocities of Rayleigh surface waves in surface-hardened steel at a set of four wavelengths. The estimated profile of hardening is compared with independent destructive measurements. As a test, the theory is also applied at the same set of wavelengths to a set of synthetic data calculated from an assumed profile.