A Robust Source Wavelet Phase Inversion Method Based on Correlation Norm Waveform Inversion

The source wavelet is the initial condition of wavefield forward modeling, so its accuracy has a direct impact on the quality of full-waveform inversion (FWI) and reverse time migration. At present, the source wavelet estimation method based on wave equation, such as the reverse-time propagation (RTP) algorithm and the L2 norm waveform inversion (L2WI) method, is all affected by the data quality and shallow velocity accuracy. In this letter, a robust source wavelet inversion method based on correlation norm waveform inversion (CNWI) is proposed. The near-offset direct waves are used to construct the cross-correlated objective function. The gradient expression is deduced by taking the source wavelet as the unknown. The proposed method only needs to invert short-time near-offset direct waves, so it has high computational efficiency. The cross correlation objective function is mainly used to invert the phase information of the source wavelet, which is not sensitive to the data amplitude error, so it is more robust than the existing methods. Numerical examples show that the proposed method can still provide reliable source wavelets even when the velocity model is inaccurate, the data contain noise, andthere are bad traces. We also obtain high-quality source function inversion results by applying the proposed method to land deep reflection seismic data.