# Vertical Seismic-Profile Data Local Full-Waveform Inversion Based on Marchenko Redatuming
## 3 Example  
To clearly describe the computational process and effectiveness of the method, a 3D model of the strike-slip faulted and fracture-vuggy carbonate reservoir in the Tarim Basin is used as an example. The 3D model of the strike-slip faulted, and fracture-vuggy carbonate reservoir in Tarim Basin is based on the typical characteristics of slip-faulted and karst reservoirs in the field, which is a benchmark model (similar to the Marmousi model). One shot line in the synthesized 3D acquisition record is used for our test. The 2D profile of the benchmark model depth range is 0 to 7900 m, and the X-direction range is 0 to 6600 m (Figure 7a). A total of 281 shots at the surface with an 80 m shot interval is acquired. The source is a Ricker wavelet with a 25 Hz peak frequency. For surface seismic data, each shot corresponds to 241 receivers at the surface with a 40 m receiver interval. There are 35 VSP receivers fixed in the well at 2500 m in the X-direction with a 20 m vertical interval from depths of 6300 m to 7000 m, and the range of local FWI is the area enclosed by the white color rectangle in Figure 7a. The migration velocity model is used as the initial model (Figure 7b). The reverse time migration imaging profile are shown in Figure 7c. Due to the laterally interfering seismic response, there is only one wider \"beam string\" reflection in the imaging profile. The two caves in the lateral direction are completely unidentifiable. Its low lateral resolution causes interpretation uncertainty. Such errors in reservoir identification can pose a significant risk to the design of the trajectories of wells in drilling development. We apply local full waveform inversion to the target region to verify whether the method can accurately restore the fine scale model structure. First, we need to estimate the required Green's functions using the standard Marchenko method. The standard Marchenko receiver redatuming with a virtual receiver array location at \(\mathrm{x_{cr}}\) = (X: 2155-4145 m, Z: 5555 m) corresponding to a surface source at \(\mathrm{x_{s}}\) = (X: 3150 m, Z: 0 m), is tested. The virtual receiver location array is shown by the black solid line in Figure 7d. The wavefield \(P_{all}^{mar}(\mathrm{x_{cr}},\mathrm{x_{s}})\) of the retrieved Green's function \(G_{all}^{mar}(\mathrm{x_{cr}},\mathrm{x_{s}})\) is shown in Figure 8a and can be compared with the wavefield signal (Figure 8b) obtained by waveform modeling with the true velocity model. The comparison in Figure 8 shows that most reflection events are reconstructed relatively well and that the redatumed [PERSON]'s function satisfies the need for inversion. Second, we use the VSP Marchenko source-receiver redatum to retrieve the Green's function \(G_{all}^{matr}\left(\chi_{vr}^{vsp},x_{vsp}\right)\) and its corresponding wavefield. The virtual receiver locations of  
Figure 8: The common source gathers with a row of virtual receivers x\({}_{vr}\) = (X: 2155–4145 m, Z: 5555 m) corresponding to the surface source at 3150 m in X-coordinate from (**a**) the standard Marchenko receiver Redatuming method retrieved wavefield and (**b**) the wavefield obtained by waveform modeling. Figure 7: The 2D profile of the Benchmark model (**a**), the initial model for migration (**b**), the RTM imaging (**c**), and the target zone of the true model (**d**). The black solid line in subfigure (**d**) indicates the setting location of virtual receivers x\({}_{vr}\) in standard Marchenko local FWI. The black dashed lines indicate the setting location of virtual receivers x\({}_{vr}^{vsp}\) in VSP-driven Marchenko local FWI. The black dashed line is the well location. And the white color rectangle is the target region. this method are shown in Figure 7d, where the virtual source (VSP receiver point) is located at x\({}_{\text{vsp}}\) = (X: 2500 m, Z: 6600 m) and the virtual receiver array location at x\({}_{\text{vsp}}^{Sp}\) = (X: 2155 m, Z: 5555-6185 m) is shown by the left black dashed line.