## 6 Conclusions  
For array lateral logging instruments under small borehole conditions, a 3D finite element analysis method was utilized to extensively examine the device's lateral response under different borehole sizes, mud properties, invasion effects, annuli, surrounding rock conditions, and formation anisotropy. Simulations were conducted under various borehole diameters, mud characteristics, invasion zones, annular rings, surrounding rocks, and anisotropy of formation, leading to the following conclusions:  
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2. Borehole diameter significantly affected the response of small borehole array lateral logging, but this impact diminished as the investigation depth increased. The resistivity of mud had an insignificant influence on the response when it was lower than the formation resistivity; however, once the mud resistivity increased to the level of formation resistivity, its influence on the logging response escalated rapidly. 3. In the presence of an invasion zone, the resistivity from RLA1 to RLA4 showed sensitivity to the increase in invasion zone width, but this sensitivity decreased progressively with widening invasion. The effect of invasion on the logging response could be further distinguished by the contrast between the invasion zone resistivity and the formation resistivity (low vs. high invasion), where the ratio RLA4/RLA1 varied between 1 to 8 (low invasion) and 0.6 to 0.9 (high invasion), and the degree of separation between RLA4 and RLA1 peaked when the inr value ranged between 0.5 and 0.8 m.
4. The presence of annuli could not be ignored when there was also an invasion zone. In a low-invasion environment with annuli, increasing the annulus resistivity led to a corresponding rise in RLA1 to RLA4. The change in resistivity became notably sharp near the formation interface, indicating dramatic response fluctuations; at the formation center, resistivity trended toward an extreme across all measurement modes, and the degree of separation was maximized. When the resistivity and width of the annulus reach a certain value, there may be unique situations where resistivity curves intersect across different modes. Figure 12: Resistivity variation curves in anisotropic formations with fixed formation thickness according to changes in anisotropy coefficients. * Surrounding rock also plays an important role in the response of small borehole array lateral logging. The impact of surrounding rock on the response is substantial when the formation thickness ranges between 0.2 and 0.5 m; however, when the thickness reached 2 m, it could fully reflect the resistivity information of the target layer. Additionally, simulation studies showed that the instrument continued to demonstrate exceptional vertical layer resolution capabilities both under conditions of the same thickness with different resistivities and multi-layer formations with varying thicknesses but the same resistivity. * In the presence of formation anisotropy, as the anisotropy coefficient increased, the resistivity in different modes generally trended upwards. Deeper investigation modes responded more slowly to variations in formation anisotropy coefficients. The critical point for discernible resistivity changes caused by anisotropy coefficient variations in an anisotropic formation environment simulation was 0.4 m of formation thickness. These conclusions not only validated the performance of micro-borehole array lateral logging instruments under complex formation conditions but also elucidated the influence mechanisms of key parameters on logging responses. The findings of this study deepen our understanding of the response characteristics of micro-borehole logging and provide a theoretical foundation for further optimization of logging techniques and equipment design. Moreover, they offer valuable references for more accurate subsurface formation evaluation and resource development in the future. Z.L., writing--original draft, methodology, conceptualization, supervision.