Modeling of scattering dominated ultrasonic attenuation using power-law function

In ultrasonic nondestructive microstructure characterization applications, the attenuation information is used as a tool to classify the materials. The scattering coefficient of the attenuation was shown to be 1/f/sup /spl gamma// with respect to frequency f in the previous work when the scatterer sizes have power-law distribution. Since the scaling parameter /spl gamma/ captures the complex interactions between the ultrasonic signals and the scatterers, it was used to characterize the metals such as steel and nickel. The /spl gamma/ parameter was estimated after the scattering coefficient estimation was accomplished. In this paper, we extend the previous work and theoretically establish a power-law relationship between the attenuation of the ultrasonic signals and the scaling parameter /spl gamma/ of the power-law distribution. The proposed model enables the estimation of scaling parameter directly from the received ultrasonic signal, thus eliminating the need to estimate the attenuation coefficient. The theoretical development is verified experimentally using stainless steel data using standard deconvolution and periodogram spectrum estimation technique.