In this paper, we use the second-generation wavelet transform as multi-scale smooth parameterization technique for history matching of seismic derived models using an ensemble based optimization method (batch-enRML). The construction of the second generation wavelet is presented and their advantages compared to first generation wavelets are discussed. Then, these wavelets are applied to a realistic 3D faulted reservoir model. Their ability to represent correctly this model with a large compression ratio is demonstrated. Finally, using the SGW re-parameterization, we set the basis for a new adaptive multi-scale inversion method, which aims at limiting the increase of the mismatch to seismic data of the seismic-derived realizations by selecting relevant parameters. Efficiency of the method is discussed through a 2D synthetic example.