We present the implementation of Thomsen's weak anisotropy approximation for vertical transverse isotropy (VTI) media within TOMO3D, our code for 2-D and 3-D joint refraction and reflection travel-time tomographic inversion. In addition to the inversion of seismic P-wave velocity and reflector depth, the code can now retrieve models of Thomsen's parameters (δ and ε). Here, we test this new implementation following four different strategies on a canonical synthetic experiment in ideal conditions with the purpose of estimating the maximum capabilities and potential weak points of our modeling tool and strategies. First, we study the sensitivity of travel times to the presence of a 25 % anomaly in each of the parameters. Next, we invert for two combinations of parameters (v, δ, ε and v, δ, v⊥), following two inversion strategies, simultaneous and sequential, and compare the results to study their performance and discuss their advantages and disadvantages. Simultaneous inversion is the preferred strategy and the parameter combination (v, δ, ε) produces the best overall results. The only advantage of the parameter combination (v, δ, v⊥) is a better recovery of the magnitude of v. In each case, we derive the fourth parameter from the equation relating ε, v⊥ and v. Recovery of v, ε and v⊥ is satisfactory, whereas δ proves to be impossible to recover even in the most favorable scenario. However, this does not hinder the recovery of the other parameters, and we show that it is still possible to obtain a rough approximation of the δ distribution in the medium by sampling a reasonable range of homogeneous initial δ models and averaging the final δ models that are satisfactory in terms of data fit.