Utilization of prior flaw information in ultrasonic NDE: An analysis of flaw scattering amplitude as a random variable

Probabilistic approaches to flaw detection, classification, or characterization often assume prior knowledge of the flaw distribution. It is implicit that there is a scattering amplitude distribution associated with the flaw distribution. In a number of previously published probabilistic analyses, it has been assumed that scattering amplitude is an uncorrelated, Gaussian random variable with zero mean and known variance. In the work reported here, these assumptions are evaluated for the case of a lognormal distribution of spherical flaws. The correlation, mean, variance, and nature of the scattering amplitude distribution are considered as a function of frequency and as a function of the breadth of the assumed flaw distribution. It is shown for the assumed flaw distributions that scattering amplitude is not uncorrelated and does not have zero mean. It is shown that errors in estimating the flaw distribution variance affect both the scattering amplitude mean and variance. Using both analytical and numerical procedures, the scattering amplitude distribution is shown to be lognormal at long wavelength for a lognormal distribution of spherical scatterers. At high frequency, the distribution is shown to have a bimodal character.