We have designed transversely isotropic models containing penny-shaped rubber inclusions, with the crack diameters ranging from 2.5 to 6.2 mm to study the influence of fracture size on seismic velocity under controlled conditions. Three pairs of transducers with different frequencies (0.5, 0.25, and 0.1 MHz) are used for P- and S-wave ultrasonic sounding, respectively. The P-wave measurements indicate that the scattering effect is dominant when the waves propagate perpendicular to the fractures. Our experimental results demonstrate that when the wavelength-to-crack-diameter ratio ([Formula: see text]) is larger than 14, the P-wave velocity can be described predominantly by the effective medium theory. Although the ratio is larger than four, the S-wave velocity is close to the equivalent medium results. When [Formula: see text] < 14 or [Formula: see text] is < 4, the elastic velocity is dominated by scattering. The magnitudes of the Thomsen anisotropic parameters [Formula: see text] and [Formula: see text] are scale and frequency dependent on the assumption that the transversely isotropic models are vertical transversely isotropic medium. Furthermore, we compare the experimental velocities with the Hudson theory. The results illustrate that there is a good agreement between the observed P-wave velocity and the Hudson theory when [Formula: see text] > 7 in the directions parallel and perpendicular to the fractures. For small fracture diameters, however, the P-wave velocity perpendicular to the fractures predicted from the Hudson theory is not accurate. When [Formula: see text] < 4, there is good agreement between the experimental fast S-wave velocity and the Hudson theory, whereas the experimental slow S-wave velocity diverges with the Hudson theory. When [Formula: see text] > 4, the deviation of fast and slow S-wave velocities with the Hudson prediction is stable.
Multistage elastic full-waveform inversion for tilted transverse isotropic media