Full-waveform inversion (FWI) is a technique for determining the optimal model parameters by minimizing the seismic data misfit between observed and modeled data. The objective function may be highly nonlinear if the model is complex and low-frequency data are missing. If a data set mainly contains reflections, this problem particularly prevents the gradient-based methods from recovering the long wavelengths of the velocity model. Several authors observed that nonlinearity could be reduced by progressively introducing higher wavenumbers to the model. We have developed a new inversion workflow to solve this problem by breaking down the FWI gradient formula into four terms after wavefield decomposition and then selecting proper terms to invert for the short- and long-wavelength components of the velocity model alternately. Numerical tests applied on a 2D synthetic model indicate that this method is efficient at recovering the long wavelengths of the velocity model using mainly offset-limited reflection events. The source does not need to contain low frequencies. The initial velocity model may have large errors that would otherwise prevent convergence for conventional FWI.

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