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The full-waveform inversion algorithm using normalised seismic wavefields can avoid potential inversion errors due to source estimation required in conventional full-waveform inversion methods. In this paper, we have modified the inversion scheme to install a weighted smoothness constraint for better resolution, and to implement a staged approach using normalised wavefields in order of increasing frequency instead of inverting all frequency components simultaneously. The newly developed scheme is verified by using a simple two-dimensional fault model. One of the most significant improvements is based on introducing weights in model parameters, which can be derived from integrated sensitivities. The model-parameter weighting matrix is effective in selectively relaxing the smoothness constraint and in reducing artefacts in the reconstructed image. Simultaneous multiplefrequency inversion can almost be replicated by multiple singlefrequency inversions. In particular, consecutively ordered singlefrequency inversion, in which lower frequencies are used first, is useful for computation efficiency.