When fractures are vertical, aligned and their dimensions are small relative to the seismic wavelength, the medium can be considered to be an equivalent Horizontal Transverse Isotropic (HTI) medium. However, geophysical data acquired over naturally fractured reservoirs often reveal the presence of multiple fracture sets. We investigate a case where there are two vertical sets of fractures having differing length scales. One fracture set has length scale that is much smaller than the seismic wavelength but the other has length scale that is similar to the seismic wavelength. We use synthetic data to investigate the ability to infer the properties of the small-scale fractures in the presence of the large-scale fracture set. We invert for the Thomsen-type anisotropic coefficients of the small-scale fracture set by using the difference of the P-wave amplitudes at two azimuths, which makes the inversion convex. Then we investigate the influence of the presence of the large-scale fractures on our ability to infer the properties of the small-scale fracture set. Surprisingly, we find that we can reliably infer the fracture density of the small scale fractures even in the presence of large scale fractures having significant compliance values.