Abstract. We present the implementation of Thomsen's weak anisotropy approximation for VTI media within TOMO3D, our code for 2-D and 3-D joint refraction and reflection traveltime tomographic inversion. In addition to the inversion of seismic P-wave velocity and reflector depth, the code can now retrieve models of the Thomsen's parameters δ and ε. Here we test this new implementation following four different strategies on a canonical synthetic experiment. First, we study the sensitivity of traveltimes 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 performances 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 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.