## 1 Introduction  
In recent years, as oil and gas resource extraction has continually deepened, thin reservoirs have gradually become the main targets for exploitation, making their logging evaluation critically important. In 2008, [PERSON] conducted a study analyzing the numerical response characteristics of array lateral logging instruments under different layer thicknesses and invasion states in a two-dimensional model environment [1]. In 2010, [PERSON] provided significant support for correctly understanding the physical properties of rocks around wells and carrying out inclined well reservoir evaluation through in-depth analysis of invasion characteristics in deviated wells and simulation studies of array lateral logging responses [2]. In 2013, [PERSON] introduced the Preconditioned Conjugate Gradient (PCG) method to solve large linear equation systems formed by finite element computations, which increased the calculation speed of logging responses [3]. In 2017, [PERSON] established a detailed formation simulation model and further researched the sensitivity of horizontal well mud invasion on array lateral logging responses [4]. In 2019, [PERSON] presented a detailed account of numerical simulation results of array lateral logging responses and introduced correction methods for mud filtrate invasion [5]. In 2022, [PERSON] proposed establishing a scaled-down physical model system to validate and calibrate the accuracy of 3D-FEM based on numerical simulation results [6]. In the latest research, in 2023, [PERSON] discussed the response characteristics of array lateral logging instruments in inclined anisotropic formations under small-diameter borehole conditions [7]. The major difficulty in logging interpretation of thin reservoirs lies in the fact that when logging instruments measure near thin reservoirs, they are significantly influenced by factors such as the borehole environment, mud invasion, and surrounding rocks. This makes it challenging to accurately identify thin reservoirs from the logging curve shapes and to reflect the true resistivity of these thin layers, thereby affecting the identification of target layers and the exploration of potential resources. To overcome these challenges, an increasing number of studies are focusing on enhancing the resolution and anti-interference capabilities of logging instruments to improve the accuracy of thin reservoir identification and evaluation. In 2019, [PERSON] et al. primarily researched the amplitude attributes of thin fractured reservoirs and shear-wave splitting. By examining the response of fast and slow S-waves to fractured reservoirs, they predicted the types of fractures within these reservoirs [8]. In 2021, [PERSON] proposed a seismic facies-controlled nonlinear inversion method, a technique that effectively improved the prediction accuracy of thin interbedded reservoirs, providing a reliable basis for reservoir prediction, injection-production connectivity, and well pattern deployment in oil fields [9]. In 2023, [PERSON] employed a hybrid model combining Particle Swarm Optimization (PSO) and Extreme Learning Machine (ELM), enhancing the accuracy of thin interbedded reservoir identification by 10% to 30%. This allowed for more precise characterization of thin interbedded layers with a thickness of approximately 0.3 m, offering technical support for shale oil exploration and development [10]. Despite significant advancements in thin reservoir identification and evaluation, challenges remain in the design and research of array lateralog instruments. To address this issue, this paper proposes an optimized design for an array lateralog instrument intended for small borehole environments to improve logging resolution. This design aims to significantly enhance the performance of distinguishing logging values between surrounding rocks and thin reservoirs in longitudinal measurements, thereby achieving precise identification of thin reservoirs.