Measurements of ultrasonic diffusivity and transport speed from coda waves in a resonant multiple scattering medium

Abstract

Frequency-resolved experimental measurements of ultrasonic diffusivity in the MHz range are presented. The samples under study are two-dimensional random arrangements of parallel steel rods immersed in water and exhibit high-order multiple scattering. Their physical characteristics, particularly the density and pair-correlation functions of the scatterers, are well controlled. These synthetic samples are used as phantoms for actual inhomogeneous materials. The resonant nature of the scatterers has a strong effect on diffusivity, which is shown to vary significantly with frequency. This may affect the result of broadband measurements of apparent diffusivity, which can be expected to depend on time and sample thickness, whereas diffusivity is intrinsically an intensive parameter. Moreover, the transport speed is shown to vary drastically with frequency, sometimes by more than 50%, due to a very narrow resonance that slows down transport. Interestingly, this sharp resonance could only be revealed by experiments performed with coda waves, and not with ballistic or coherent waves whose frequency resolution is intrinsically limited from an experimental point of view.

Energy velocity of multiply scattered waves in strongly scattering media

“…Previous experiments using ultrasound [6,7] have also demonstrated the impact of the scattering delay on the energy velocity, but in these cases both the energy and group velocities were reduced and did not exhibit such opposite behavior as is shown in Fig. 11(b) [34].…”

“…Ultrasonic experiments [2,[5][6][7]14] can provide direct observation of the transmitted wave field through strongly scattering media with excellent temporal and spatial resolution, thereby enabling both the average wave and multiply scattered coda waves to be measured. Hence, as shown in this work, a complete set of wave scattering and transport parameters is accessible to experiment, unlike in optics where a similar set of measurements seems to be almost prohibitively challenging [8,18,21,36,37].…”

“…which is the approximate expression for v e used successfully to interpret the data in Refs. [6] and [7]. The interpretation of this expression is more straightforward than Eq.…”

“…Hence the propagation of the average wave field can be described by an effective wave number k. For longer propagation distances, the ballistic wave becomes exponentially small, and the wave field is dominated by waves that have undergone many scattering events, with local directions of propagation that have become randomized. After a linear distance corresponding to several transport mean free paths * , the transport of the waves' energy density can be described by a diffusive process with characteristic diffusivity D [4][5][6][7][8]. The wave diffusion coefficient, D = v e * /3, depends not only on the transport mean free path (the average distance over which the direction of propagation is randomized) but also on the energy velocity v e , which corresponds to the local velocity of energy transport by the diffusive waves.…”

“…Since the theoretical work of van Albada et al [18,19], several studies of classical wave diffusion have focused on the behavior of the energy velocity in both optics [20][21][22] and acoustics [6,7,14], paying particular attention to the resonant scattering regime. While all of these experiments, and the original theoretical predictions, showed significant decreases in the energy velocity due to scattering resonances, differences were found in the link between the group velocity and the energy velocity.…”