## 3 Numerical Examples
### Inversion Effects Using Multi-Component Data with Bad Traces  
In this section, we test the inversion effects using data with bad traces. In land seismic exploration, near-offset direct waves are often affected by surface waves, noise, acquisition conditions, and other factors. We used a sinusoidal function to generate bad traces near the source position to simulate these conditions. These bad traces were added to the near-offset position of each shot record. The multi-component observed seismic data of one shot are shown in Figure 9.  
Now, we test the behavior of the objective functions of the L2 EWI and CNEWI methods. The true velocity model and the initial velocity model are shown in Figures 2 and 3, respectively. The true source wavelet is a Ricker wavelet with a dominant frequency of 20 Hz. A series of initial source wavelets was used to calculate the objective function value. The initial source wavelets were calculated by taking phase rotation of the true source wavelet with different degrees. The observed seismic data have near-offset bad  
Figure 8: EFWI results comparison in an ideal case. (**a**) P-wave velocity model using source wavelet estimated by L2 EWI; (**c**) P-wave velocity model using source wavelet estimated by CNEWI; (**d**) S-wave velocity model using source wavelet estimated by CNEWI.  
Figure 9: Seismic data with bad traces. (**a**) Z-component seismic data with bad traces; (**b**) X-component seismic data with bad traces.  
traces, as described above. The behavior of the objective functions is shown in Figure 10. The convergence range of the CNEWI method is obviously wider than that of the L2 EWI method. The minimum of the CNEWI objective function curve corresponds to the true source wavelet. However, the minimum of the L2 EWI objective function curve does not correspond to the true solution, which demonstrates that the L2 EWI method suffers the cycle-skipping problem and it is more sensitive to bad traces than the CNEWI method.  
The L2 EWI method and the CNEWI method were used to perform source wavelet inversion, and the results are shown in Figure 11. As a consequence of the presence of poor-quality traces, the L2 EWI method fails to accurately determine both the amplitude and phase information of the source wavelet. In contrast, the CNEWI method demonstrates an improved accuracy in estimating the source wavelet. The obtained source wavelets were used to conduct elastic full-waveform inversion. Using multi-component seismic data, the elastic full-waveform inversion results are shown in Figure 12. Due to the obvious errors of the source wavelet in the L2 EW  
Figure 12: EFWI results comparison using multi-component seismic data with bad traces. (**a**) P-wave velocity model using source wavelet estimated by L2 EWI; (**b**) S-wave velocity model using source wavelet estimated by L2 EWI; (**c**) P-wave velocity model using source wavelet estimated by CNEWI; (**d**) S-wave velocity model using source wavelet estimated by CNEWI.  
Figure 13: Extracted trace comparison of the inversion results in Figure 12. (**a**) P-wave velocity comparison; (**b**) S-wave velocity comparison. True: true velocity model; Initial: initial velocity model; L2 EWI: inversion result by using the source wavelet estimated by L2 EWI; CNEWI inversion result by using the source wavelet estimated by CNEWI.