# Least-Squares Reverse Time Migration in Imaging Domain Based on Global Space-Varying Deconvolution
## 5 Field Case  
The target area is a part of the Tarim oil field in Northwest China, which is located in the middle of the North Tarim Uplift Belt to the east of the Halahatang depression. It has a large span, the target layer is deeply buried, the physical properties of the matrix are poor, and the type and scale of fracture caves are seriously affected by karst weathering. From the current development stage, the positioning accuracy of small and medium-sized karst cave cannot meet the requirements of resolution analysis of venting leakage around the well. In this work area, the geophone array recorded 33,000 shots at 5 m depth covering an area of 81 km\({}^{2}\). The main conundrum to be tackled in this work area is high-resolution imaging of Ordovician carbonate fracture-cavity reservoirs, with the depth ranging from 5.5 to 8 km. The migration velocity is built by a 3D travel time tomography as shown in Figure 8. The maximum cut-off frequency of the wavelet is 70 Hz.  
Figure 9 shows the results from RTM and LSM at the inline index of 200. Compared with the RTM results (Figure 9a), the LSM results (Figure 9b) provide higher spatial resolution, finer reflection events, more balanced amplitude, better focus ability, and more accurate fractured-cavity imaging. Figure 10 shows the zoomed region in Figure 9. We can find that the LSM result provides finer descriptions of fractured-cavity imaging and the boundaries between adjacent fractured-cavities, and the fractured-cavity bodies with small sizes in Ordovician carbonate can be presented with higher resolution. Moreover, the deep fracture in the LSM result (Figure 10b) is better retrieved, which demonstrates that the proposed method is effective in fracture description. Figure 11 shows the vertical wave-number spectrum corresponding to the imaging results. The wave-number distribution of the LSM result is much broader, which lifts up at the low and mid-high sides of wave numbers. Besides, LSM can clearly provide information on cavities in the fracture zones, provide a high-quality scientific basis to analyze the development of fracture-controlled fractured-cavities and give guidance to the interpretation of reservoirs. To give an intuitive sight of the caves in Figure 10 denoted by red arrows, we compute the amplitude attributes from the RTM and LSM results and present a regional transverse section at the depth of these caves in Figure 12. We can find that the LSM results can distinguish the adjacent caves and provide better focusing, highlighting the proposed method can provide a high resolution in the horizontal direction and give a great help for reservoir interpretation and development. However, due to the limited observation aperture and shallow desert area, conventional RTM cannot provide correct images. The logging result located at the arrows in Figure 12 can also support the migration results, highlighting the effectiveness of the proposed method.  
Figure 8: Migration velocity for Tarim oil field.  
Figure 10: Locally zoomed-in reservoir sections marked in Figure 9. (**a**) results from RTM; (**b**) results from LSM.  
Figure 9: Comparison between migration results for CDP index of 1198. (**a**) results from RTM; (**b**) results from LSM.