Statistics associated with the scattering of ultrasound from microstructure.

The spatial statistics of an ensemble of waveforms containing ultrasonic scattering from microstructure are investigated. The standard deviation of the waveforms is of primary interest, because it is related to the maximum scattering amplitudes in the extreme value statistics theory. Further statistical measures are employed to define theoretical confidence bounds, which bound the experimentally calculated maximum amplitude when a finite number of waveforms are included in the ensemble. These statistical measures are applied in conjunction with a previously developed ultrasonic backscatter model. It is validated through ultrasonic scattering measurements performed on a stainless-steel pipe sample. These considerations are important for forward models related to the probability of detection (POD) of defects and inverse models used for characterization of polycrystalline microstructures.