## 1 Introduction  
Coal is a solid combustible mineral formed by ancient plants buried underground and undergoing complex biochemical and physicochemical changes, mainly containing elements such as carbon, hydrogen, oxygen, nitrogen, and sulfur. It serves as an important energy source and chemical raw material. In recent years, due to the increasing demand for fossil fuels, the exploration and development of unconventional natural gas have garnered worldwide attention [1]. Unlike conventional reservoirs, coal reservoirs are characterized by complex pore-fracture networks, high heterogeneity, and low porosity and permeability [2]. The adsorption capacity of coal seams largely depends on their nanoporous structure [3]. Therefore, the study of coal seams' microscopic surface properties has become a focal topic in recent years. Current methods for studying pore structures mainly include fluid injection methods [4; 5; 6] (such as mercury injection, nitrogen adsorption, carbon dioxide adsorption, and nuclear magnetic resonance) and scanning methods [6; 7] (including optical microscopy, scanning electron microscopy, CT scanning, and atomic force microscopy or AFM). Scanning methods are applied more extensively due to their reduced sample damage, especially with the application of image segmentation techniques for pore-fracture identification in scanned images [8]. Among these scanning methods, AFM has been widely used in various fields of scientific research, ranging from basic surface morphology characterization to material surface property analysis, from biochemistry [9; 10] to materials science [11; 12]. AFM has gradually evolved into an indispensable tool for nanoscience research. AFM can observe samples in air, vacuum, and liquids, detecting both conductor, semiconductor, and insulator surfaces with a spatial resolution as low as 0.1 nm and a vertical resolution as low as 0.01 nm, thus achieving atomic-scale resolution. Due to AFM's precise characterization capabilities and ultra-high resolution, an increasing number of studies on coal and rock microscopic surface properties using AFM have been published in the last decade [13]. [PERSON] et al. [14] conducted two-dimensional and three-dimensional analyses of high-rank coal through AFM and HRTEM experiments, revealing that during the graphitization process, the matrix morphology tends to become more regular and smooth, with a decrease in the interlayer spacing of the carbon structure. [PERSON] et al. [15] conducted fractal analysis based on surface morphology observations and AFM surface roughness measurements, revealing that the fractal dimension of ultrafine coal powder increases with coal particle size. [PERSON] et al. [16] utilized AFM and SEM to analyze the surface microstructure of coal with varying degrees of tectonic deformation. They found that tectonic activity increases both the fractal dimension of pores on the coal sample surface and the number of pores. [PERSON] et al. [17] observed pore shapes and distributions in coal of different metamorphic grades using nanometer-resolution AFM, revealing that increased coal maturity leads to more regular nanopore morphology. [PERSON] et al. [18] found significant differences in pore parameters among coals of different ranks. AFM can not only measure pore parameters on coal surfaces but also provide in-depth analysis of pore surface roughness. Meanwhile, Gwyddion, a specialized image processing software, is primarily used for surface characterization and statistical analysis of pores and crystals in AFM imaging [19]. When combined, they can obtain nanopore parameters such as pore count, average pore diameter, and facial porosity. In addition, AFM can measure coal's nanoring parameters, which are ring structures within the coal's two-dimensional plane and can be used to assess the uniformity of the material surface. Given the complexity of coal surfaces, traditional Euclidean geometry theory struggles to describe their heterogeneity, while fractal dimension can quantitatively characterize the complexity of pore structures.