Orthorhombic anisotropic model inversion is extra challenging because of the multiple-parameter nature of the inversion problem. The high number of parameters required to describe the medium exerts considerable trade-off as well as additional non-linearity to a full-waveform inversion (FWI) application. Choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem. Using the Born approximation which is the central ingredient of the FWI update process, we derive radiation patterns for the acoustic orthorhombic parametrization. The analysis of the radiation patterns leads us to introduce a new set of parameters for a new orthorhombic parametrization. The new parameters are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature, of any parametrization based on these new parameters, is the azimuthal independency of the modelled data with respect to the vertical transversely isotropic (VTI) parameters, which allows us to propose practical inversion strategies based on our experience with the VTI parameters inversion.