Velocity of ultrasound diffusion in strongly heterogeneous media: Further insights

Since the publication of "Velocity of ultrasound diffusion in heterogeneous media and its applications," Ultrasonics 145 (2025): 107476 by the present author, there have been extensive discussions through private communications, regarding the physical implication and validity of treating the diffuse energy velocity as an intrinsic property of the medium, as argued in the original work. These discussions are particularly relevant when the ultrasonic source deviates from an ideal space-time delta function, instead being spatially and temporally finite, as is the case in practical diffuse ultrasonic measurements. Another point of interest is its connection to the energy velocity in the diffusion approximation to the radiative transfer equation (RTE). While different in fundamental physics, recent studies investigate an analogous velocity of magnetic diffusion in the context of pulsed eddy currents. For the benefit of the readership, it might be, therefore, useful to discuss both the physical meaning of the previously defined energy velocity and the influence of finite source characteristics. It is clarified that, in general, the energy velocity defined in the original work depends on the temporal duration and spatial distribution of the excitation source. Nevertheless, under conditions commonly satisfied in ultrasonic diffusion experiments-specifically when observation distances exceed several transport mean free paths-these source-dependent effects become negligible. Therefore, the far-field asymptotic energy velocity remains an intrinsic property of the medium. Finally, an estimation of the energy velocity v_E of the RTE calculated for concrete reveals its equivalence to the far-field asymptotic energy velocity.