# Vertical Seismic-Profile Data Local Full-Waveform Inversion Based on Marchenko Redatuming
## 4 Discussion  
We demonstrate the feasibility of the proposed VSP-driven local FWI for improving the lateral resolution of inverted results of standard Marchenko local FWI and effectively improving the reconstruction of steep structures. Characterizing reservoirs using traditional full waveform inversion methods is difficult, especially when the reservoir is deeply buried. The benchmark model of the Tarim Basin in the example chapter has a high-velocity layer caused by igneous rocks at a depth of 2.7 km, and the strong reflection caused by the high-velocity layer will repress the signal of the deep target layer, which leads to an inaccurate result of conventional FWI for the deep layer (Figure 12). By comparing Figure 10a with Figure 12, it can be seen that local FWI based on the standard Marchenko method has a very significant improvement compared to full-domain FWI for the same number of iterations. This is due to the fact that local FWI is oriented to local gradients and eliminates the influence of the overburden. However, the lateral resolution in Figure 10a still cannot fully distinguish between the two caves, while the strike-slip fault cannot be accurately reconstructed either due to the aperture limitation. In the present study, our proposed VSP-driven local full-waveform inversion and joint local full-waveform inversion enhance the lateral variation of the gradients by adding lateral observations. Figure 13 shows that the gradient of the VSP-driven local FWI term mainly as a contribution to the lateral variation. The advantage of this method is that the accurate laterally propagating waves can be obtained by Marchenko source-receiver redatuming with VSP data, which results in a higher lateral resolution for the inverted model. In Figure 10b, the lateral resolution of the two caves is improved compared to that in Figure 10a, while the strike-slip faults are also inverted. In particular, this method has great  
Figure 12: The inversion result of conventional full-domain FWI. potential for identifying small-scale stratigraphicable lateral discontinuities and distributed geological objects. As the extension of local FWI based on the Marchenko redatuming method, VSP and Surface data jointed local FWI also has computational efficiency. The computation time of both methods in the inversion process is basically the same, but VSP-driven local FWI needs to retrieve more redatumed subsurface wavefields. It will take more time in the data preparation process (compared to the standard Marchenko receiver redatuming requires the additional process of calculating Equation (16)), but it is still much more efficient than full model domain FWI. However, there are still issues with the proposed method. This paper presents the Marchenko source-receiver redatuming with the requirement that the virtual receiver is above the virtual source [25]. Both the focusing and Green's functions can be calculated at every point. The Green's functions can be calculated between any two points when both input fields are Marchenko estimates [26]. However, the VSP data as actual observations of the receivers in the well lead to the situation that when using the VSP Marchenko source-receiver redatuming method, we can only estimate the Green's function between a virtual source at a location of the VSP receiver to an arbitrary point above it. This limits the application of the VSP-driven local FWI. At the same time, in the case of vertical structures such as faults, a large aperture is required to ensure that the primary amplitude reflected from the vertical structure can be measured at the surface. In other words, to perform VSP Marchenko source-receiver redatuming to obtain the exact Green's function containing the laterally propagating waves also requires certain aperture conditions. We reduce the surface shot records used for the Marchenko redatuming in the example chapter to 105 shots (X: \(-\)1000 m-7400 m) and recalculate the Green's function.