# Quaternary Activity and Paleoearthquakes of the Fushan Fault, Shanxi, China
## 2 Materials and Methods
### LiDAR Analysis of Bedrock Fault Scarp Morphology  
The morphology of any fault surface exposed on the Earth's surface results from the combined action of internal forces represented by fault activity and external forces represented by weathering and erosion [27]. Structural activity imparts distinct anisotropic characteristics to the fault surface morphology under the influence of internal forces, leading to significant differences in complexity and roughness between surfaces sliding parallel and perpendicular to the direction of fault movement. Weathering and erosion activities tend to homogenize the morphology of fault surfaces towards isotropy. Thus, a fully exposed bedrock fault surface represents a composite of structural movement, weathering, and erosion information. Currently, there are two main methods for studying the morphological characteristics of bedrock fault surfaces: one-dimensional analysis based on profile lines [28; 29; 30; 31; 32] and two-dimensional analysis based on sliding window techniques. One-dimensional analysis is directional and varies with the orientation of the pulled profile lines and is commonly used to explore the correlation between fault surface morphology and the rupture process [33; 34]. However, for fault surfaces that have been exposed for extended periods and have undergone significant erosion and weathering, such as those in this study, a two-dimensional fractal analysis method, which does not rely on directionality, is required to quantify the variation in erosion and weathering across the surface. This approach can help determine the exposure time and mode of exposure of the fault surface and identify paleoearthquake events through the discontinuous morphological features formed by sudden fault displacements. Along the Fushan Fault, bedrock fault surfaces of varying sizes and scales are developed. Field investigations determined that the Ordovician limestone bedrock fault surface located 200 m east of Qiaojiapo village (see Figure 3) is the most well-exposed, largest, and relatively well-preserved section. We applied terrestrial LiDAR (Trimble GX 3D laser scanner, Trimble Inc., Sunnyvale, CA, USA) to this section to determine the fault scarp morphology. Exposed points (i.e., without vegetation or Quaternary sediment cover) were selected as reference stations, and high-precision LiDAR scanning was used to obtain high-precision, high-density 3D spatial data of the fault surface. The spacing between scanning points was controlled to approximately 2 mm, with an accuracy of 1.5 mm. The collected three-dimensional point cloud data consisted of numerous points with spatial coordinates (X, Y, Z), where (X, Y) denote the positions of points on the fault surface and (Z) represents the elevation. Additionally, the data included true-color information of the objects and laser reflectance intensity information. The point cloud data collected from the fault surface underwent spatial transformation, noise removal, and gridding processes as follows: (1) By maintaining the relative positions of the spatial coordinate points, the point cloud dataset was subjected to a translation and rotation transformation. After the transformation, the \(X\)-axis aligned with the strike line of the fault surface, the \(Y\)-axis corresponded to the dip direction, and the \(Z\)-axis represented the surface relief of the fault. (2) Noise points generated during the data collection process were removed. (3) The leveled point cloud data of the fault surface were gridded to obtain a DEM dataset, with each DEM cell measuring 2 \(\times\) 2 mm, and a rendered image of the bedrock fault surface morphology. The variogram method was employed as the most reliable and accurate approach for determining the surface fractal dimension. The core concept involves calculating the average difference (mean square value of elevation differences) in the elevation field of the DEM as a function of the point pair distance.