**5. Discussion**

We have validated the effectiveness of the proposed AEC-EFWI method in processing OBS 4C data and improving inversion accuracy. This study mainly focuses on reconstructing the high-wavenumber components of elastic parameters from good initial models. Of course, this AEC-EFWI method also suffers from the notorious cycle-skipping and other practical issues. To alleviate this problem, this work should be further considered to combine with the reflection waveform inversion (RWI) [39–43] or the migration velocity analysis (MVA) [44–46]. In these approaches, the most critical step is to compute the PP and PS reflection paths. It can be easily accomplished by the AEC equation instead of performing a complete P/S decomposition on forward/back-propagated wavefields.

In those experiments, the weighting coefficient *ε* is set to be 50%. In fact, this value is determined by the difference of observed pressure and displacement components. Supposing that it reduces to zero, we wonder whether the AEC-EFWI method can still provide reasonable inversions for elastic parameters? Figure 18a shows a simple cartoon of the wave propagation process for this case. The incident P-wave excited from the source location generates both PP and PS transmissions at the seabed, and these transmissions are reflected at the interface of Layer 1. Because the water layer is assumed to be precisely known in advance, the observed PPP and PSP waves can be treated as "pseudo-first-order" reflections excited by virtual mixed sources from the seabed. Note that, this PSP wave path carries more information of subsurface *Vs* distribution, which makes a grea<sup>t</sup> contribution to *Vs* update.

(**a**) OBS case

(**b**) Towed-streamer case

**Figure 18.** Cartoons of the wave propagation for 1C (**a**) ocean bottom seismic (OBS) and (**b**) towed-streamer cases.

We test the method on the Marmousi model (Figure 1), starting from the same initial models (Figure 11) with 1C pressure data. The inverted results are displayed in Figure 19. The extracted vertical profiles and the corresponding wavenumber spectrum are shown in Figures 20 and 21, respectively. Although the inversion accuracy and spatial resolution decrease to some extent, the 1C results can still provide acceptable multiparameter inversions and have a certain consistency with the true ones. It demonstrates that this AEC-EFWI method is feasible to recover elastic parameters using OBS 1C pressure data. Besides, we can find that the high-wavenumber components in the results using 1C pressure data are better reconstructed than the low-wavenumber components (see differences between the green and red lines in Figure 21), which highlights the contribution of pressure component on high-wavenumber reconstruction.

**Figure 19.** Inverted (**a**) *V p* and (**b**) *Vs* results using AEC-EFWI with 1C pressure data.

**Figure 20.** Vertical profiles of *V p* (solid) and *Vs* (dashed) at the horizontal distances of 3.0, 4.5, and 6 km.

**Figure 21.** The 1D wavenumber spectrum of vertical profiles, corresponding to Figure 20. Black lines denote the true model, red lines indicate the results using 4C data, and green lines are the ones using 1C data.

Similarly, this method may be also applied for marine towed-streamer pressure data. As displayed in Figure 18b, the PP-PP and PS-SP wave paths help to reveal subsurface *V p* and *Vs* distributions. Besides, other converted waves, i.e., PP-SP and PS-PP, can further enhance the illumination of *Vs*

model. Of course, it should be further tested with field streamer data. Although some practical problems, i.e., data preprocessing, low-frequency loss, and initial model building, have not been fully considered, the cartoons and the preliminary results can at least inspire us to use 1C pressure data for elastic parameter inversion and eventually provide a flexible method and idea for increasingly complex marine data processing.
