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Full waveform inversion (FWI) is a highly non-linear optimization problem. When there is a lack of low-frequency components in the seismic data and the initial velocity is far from the true velocity, it is easily trapped into local minima. The authors propose a new objective function that combines the normalized cross-correlation of modeled and observed data with the least squares criterion. Cross-correlation emphasizes on phase matching and behaves in a more linear way, thus can mitigate the cycle-skipping issue. By setting a weighting factor, the authors use the cross-correlation norm to update the low-wave number components of the velocity model at the early stage of the inversion, while using the least squares criterion to update high-wave number details of the model. Numerical examples show that FWI based on the new objective function converges quickly toward global minima and does not rely on accurate initial velocity model as well as low-frequency information, it can improve the robustness of the inversion and generate more accurate inversion results than the conventional approach.

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