Experimental study on the multiscale scattering of high-velocity heterogeneous bodies

There are complex heterogeneous entities in the underground medium, and the heterogeneous scale has a substantial impact on wave propagation. In this study, we used a set of 11 samples of glass beads as high-velocity heterogeneous bodies to evaluate the impact of such heterogeneous bodies on the propagation of P-wave. We vary the heterogeneous scale by changing the diameter of the glass beads from 0.18 to 11 mm while keeping the same volume proportion (10%) of the beads for the set of 11 samples. The pulse transmission method was used to record measurements at the ultrasonic frequencies of 0.34, 0.61, and 0.84 MHz in the homogeneous matrix. The relationship between P-wave field features and heterogeneity scale, P-wave velocity, and the multiple of the wave number and heterogeneous scale (ka) was observed in the laboratory, which has sparked widespread interest and research. Heterogeneous scale affects P-wave propagation, and its wave field changes are complex. The waveform, amplitude, and velocity of the recorded P-waves correlate with the heterogeneous scale. For the forward scattering while large-scale heterogeneities, noticeable direct and diffracted waves are observed in the laboratory, which indicates that the influence of direct and diffracted waves cannot be ignored for large-scale heterogeneities. The relationship between velocity and ka shows frequency dependence; the reason is that the magnitude of change in velocity caused by wave number is different from that caused by heterogeneous scale. According to the change in the recorded waveform, amplitude variation, or the relationship between the velocity measured at different frequencies and the heterogeneous scale, the identified turning points of the ray approximation are all around ka = 10. When ka is less than 1, the velocity changes slowly and gradually approaches the effective medium velocity. The ray velocity measured for heterogeneous media with large velocity perturbations in the laboratory is significantly smaller than the velocity predicted by the perturbation theory.