We discuss an algorithm to regularize elastic waveform inversions using wavelet-based constructive approximations of the data, synthetic and observed, in models that evolve as part of a gradient-based iterative scheme relying on forward and adjoint modeling carried out with a spectral-element method. For an elastic Marmousi model we show how our wavelet-based multiscale waveform inversion proceeds successively from large to small scales in the seismograms, with a progressive increase of the complexity of the resulting model. We explore the sensitivity of surface waves in imaging shallow structure. To circumvent cycle skipping we designed an envelope-misfit function within a wavelet-multiscale framework. We test our approach in a toy model in preparation for inversions at full complexity.