## 5 Small Borehole Array Lateral Logging Forward Modeling
### Formation Thickness and Surrounding Rock Impact  
Previous forward analysis of micro-borehole array lateral logging has primarily focused on models without the influence of surrounding rock, but research on the impact of the surrounding rock presence on logging results remains insufficient. By examining the influence of surrounding rock on micro-borehole array lateral logging results, this section of the study supplements the knowledge in this area, providing a more comprehensive understanding. This is of significant importance for the accurate interpretation of logging data under complex formation conditions [18]. The preliminary study addressed a single-layer structure, with the model parameters as follows: formation thickness, h, was set, respectively, at 0.2 m, 0.5 m, 1 m, 2 m, and 5 m; target layer resistivity, Rt = 20 \(\Omega\)-m; mud resistivity, Rm = 0.1 \(\Omega\)-m; surrounding rock resistivity, Rs = 2 \(\Omega\)-m; invasion zone radius, int = 0.5 m; invasion zone resistivity, Rx0 = 5 \(\Omega\)-m; borehole diameter, d = 8 inches [19]. The corresponding resistivity curves are exhibited in Figure 9. The results indicate that when the target layer thickness was only 0.2 m, due to significant surrounding rock influence, the response of the small borehole array lateral logging was lower than the true resistivity of the formation. However, as the formation thickness increased, the resistivity curves gradually approached the true resistivity of the formation. Figure 9 also demonstrates the potential of the small borehole array lateral logging instrument to excel in resolving changes in thinner formation thicknesses.  
Figure 10 shows the resistivity curves of multi-layer formations under conditions of 0.5 m thickness with various invasion zone resistivities to formation resistivities, as well as curves under the same formation resistivity but with different layer thicknesses [20,21]. Specifically, the parameters for the different formation resistivity models were set as follows: formation resistivities, Rt, of 10 \(\Omega\)-m, 20 \(\Omega\)-m, 30 \(\Omega\)-m, and 20 \(\Omega\)-m; invasion zone resistivities, Rx0, of 5 \(\Omega\)-m, 5 \(\Omega\)-m, 8 \(\Omega\)-m, and 10 \(\Omega\)-m; invasion zone depth, int, at 0.5 m; surrounding rock resistivity, Rs, uniformly at 2 \(\Omega\)-m. The multi-layer formation model parameters for different thicknesses included the following: layer thickness, h, set at 0.5 m, 1 m, 2 m, and 5 m; formation resistivity, Rt, constant at 20 \(\Omega\)-m; other parameters, such as surrounding rock resistivity, Rs, and invasion zone resistivity, Rx0, were as previously  
Figure 8: Negative correlation in resistivity impact due to annular rings.  
set. The analysis of the graph revealed that the formation resistivity, Rt, invasion zone resistivity, Rx0, and the surrounding rock resistivity, Rs, all significantly influenced the response characteristics of the formation's resistivity. Particularly, when the ratios of Rt/Rx0 and Rt/Rs were small, the measurement result tended toward the true resistivity of the target layer. Additionally, the data also indicated that the invasion zones of different resistivities had an impact on the ability of small borehole array lateral logging to identify different formation boundaries [22,23].