Diffusion of laboratory ultrasonic waves

Multiple scattering of laboratory ultrasonic waves is studied. Seismic coda waves, which are the tail portion of the seismograms, have been proved to be the direct evidence of random heterogeneities in the lithosphere. However, in the frequency range of the order of MHz, the tail portion of laboratory ultrasonic waveform logs are often ignored, which are possibly caused by the difference of scale and the complexity of the ultrasonic waveform. We present three different analytical models to explain the coda of laboratory measurements. The first model is the single isotropic scattering model without regard to multiple scattering. In the second model, seismic energy transport is described as a diffusion process and observed coda data is explained by the diffusion coefficient. In the last model, we use a strongly scattering cylinder model which takes both the multiple scattering and the boundary reflection into account. We discuss the mechanism of stress-associated coda attenuation at the ultrasonic frequencies by these models. Comparisons of coda attenuation of different models show that the strongly scattering cylinder model is more suitable for the coda analysis of laboratory measurement. Finally we investigate the stress-associated coda attenuation quality factors as a function of frequencies and characterize its scale dependence on stress variations in rocks by comparing with the intrinsic attenuation quality factors calculated from ultrasonic measurements.