Vertical fractures are often embedded into a finely layered medium, which leads to an effective medium with orthorhombic anisotropy. Ten independent parameters are necessary to completely characterize such a medium, including density and excluding rotations. Through wavenumber illumination analysis, it has been shown that only six of these parameters can be reliably inverted from P - P scattered energy. Here, we demonstrate that with the addition of converted waves, nine parameters can principally be recovered. We also demonstrate that the one-dimensional null space is along a linear combination of the shear-wave dimensionless parameters, g1 and g2, or a linear combination of the elastic coefficients C12 and C66 parameters. This null space can be captured by the Thomsen g parameter if it is introduced into the parameterization. Finally and most importantly, there is still a lot of skepticism around the applicability of multiparameter model wavenumber illumination analysis, so we validate the radiation patterns using finite-difference modeling code. We find that theoretical scattering patterns are in good agreement with numerically modeled wavefields scattered from thin layers. The latter is a step towards applications of similar analysis, initially in the framework of time-lapse monitoring of the reservoirs, where the perturbations of parameters are generally small.