Structure Estimation from Acoustic Reflection Measurements

A preliminary study of a unique approach to the determination of the structure of a medium from noisy normal-incidence acoustic reflection data is carried out. This approach employs a simple equal travel-time layer model for the medium, implemented by a state variable formalism. Structure determination is achieved by maximum-likelihood estimation of the parameters which define the system model, the reflection coefficients. The Cramer-Rao bound on estimation accuracy is derived for the model, and computed for two cases of practical interest. It is shown that physically significant conclusions may be drawn from the behavior of the bound. Monte Carlo tests are used to compare the noise sensitivity of this estimator with that of another estimator, which is based on the Wiener-Hopf integral equation. This latter estimator, although exact in the absence of noise, is found to be unstable when noise is present.