The multi-parameter full waveform inversion is an essential tool to estimate subsurface anisotropic properties in a reservoir that may have complex geological behaviour requiring an elastic orthorhombic medium description. For such elastic orthorhombic media, finding a proper inversion strategy to mitigate parameter trade-off and reduce the Null space is crucial considering the large number of parameters describing the medium. We apply our recently developed strategy for orthorhombic medium inversion on synthetic and real ocean bottom cable data, and find the most efficient inversion strategy. At first, we analyse the trade-off patterns in three elastic orthorhombic parameterizations for a hockey-puck-shaped model. We, then, compare the performance of these orthorhombic parameterizations on a 3D synthetic ocean bottom cable data, which are obtained from a channel-shaped model. By interpreting the inverted models based on analytic radiation patterns of the nine elastic orthorhombic parameters in each parameterization, we observe that parameterizations, which have one P-wave velocity, one S-wave velocity and seven dimensionless parameters, can be optimal to recover subsurface isotropic properties in the early stages of inversion. Then, we show that the choice of three anisotropic parameters and their deviations along the horizontal plane helps us mitigate the complexity of the multi-parameter inversion by decoupling anisotropic features, which have vertical and horizontal symmetric axes, respectively. This decoupling of isotropic and anisotropic properties enables us to perform the multi-parameter anisotropic inversion in a multi-stage manner. In addition, for the marine acquisition, we show that the number of parameters can be reduced from 9 to 4, which makes the multi-parameter inversion more practical. Finally, we apply the elastic orthorhombic inversion to real ocean bottom cable data.