## 2 Background
### Logging Interpretation
#### 2.1.1 Interpretation of Cbl-VDL  
CBL-VDL is a kind of acoustic logging. Its principle is to reflect the cementation quality between cement and casing and between casing and formation by using the attenuation effect of the acoustic impedance of cement and drilling fluid (or water) on the acoustic wave propagating along the casing axis [11]. The schematic diagram of CBL-VDL logging is shown in Figure 1. In the figure, T is the acoustic transmitter, and R1 and R2 are two acoustic receivers. The distance between T and R1 is 3 ft, and the distance between T and R2 is 5 ft. The source distance of CBL is 3 ft. R1 receives the casing wave and records the first wave amplitude of the casing wave. The amplitude of the head wave depends on the degree of cementation between the cement and the casing's outer wall. Therefore, only the quality of the first interface (the interface between the casing and the cement sheath) can be detected, whereas whether the second interface (the interface between the cement sheath and the formation) is well cemented or not cannot be detected. The VDL source spacing is 5 ft, R2 receives the casing wave, cement sheath wave, formation wave, and direct wave, and the recording method is brightness modulation recording, which can check the cementation of the first and second interfaces of the casing well. In order to record the wave train received by the receiver as a continuous record that changes with depth, and to ensure that the wave trains at each depth point do not interfere with each other, variable density logging (VDL) needs to be recorded in the light adjustment mode. VDL light adjustment method: first, the full wave train signal as shown in Figure 2 is clipped to remove the negative half cycle, and the remaining positive half cycle signal is amplified to become a rectangular wave with a consistent width and proportional amplitude. The rectangular wave train is used as the brightness control signal of the light spot of the oscilloscope tube. When the light spot of the oscilloscope tube is scanned from A to B, due to the different amplitude of the rectangular wave, a scanning line with alternating light and dark colors is displayed on the fluorescent screen, and the logging map shows a strip with alternating black (gray) and white colors. The amplitude of the casing wave and formation wave can be analyzed by the brightness and darkness of the black and white strip, and the cementing quality between the casing and cement sheath and between the cement sheath and the formation can be judged. According to the different cementation degrees, the CBL-VDL has the following response characteristics [12]:  
Figure 1: Schematic diagram of CBL-VDL. Figure 2: Waveform chart of full wave train of VDL. Free casing. Above the cement surface, the casing is surrounded by drilling fluid, forming the first acoustic interface between the casing and drilling fluid. On the full wave train oscillogram, because there is no cement outside the casing, the interface wave impedance varies greatly, so the casing wave reflection is very strong, most of the acoustic energy travels along the casing, the energy transmitted to the formation is very low, and the formation wave is weak or absent. Therefore, in the VDL, it shows a strong casing wave signal, with six to eight obvious bands on the left side and a blank formation wave, and the acoustic amplitude curve is the highest value (Figure 3). The first interface and the second interface are well cemented. In the section with good cement and casing formation cementation, the measured value of the amplitude is the lowest. On the full wave train waveform, the casing wave is very weak and the formation wave is very strong. Therefore, on the VDL, the left fringe is blurred or disappeared, and the right fringe is clear (Figure 4). Figure 4: Waveform and CBL-VDL under good cementation of the first and second interface. Figure 3: Waveform and CBL-VDL under the free casing. (5) Poor cementation of the first and second interfaces. This situation is similar to the free casing.