*3.2. Buffer Analysis*

Buffer analysis is used to establish a certain distance of a faceted area around a spatial object given a spatial object, the extent of which is determined by the radius R of the area to identify the radiation or influence of the analyzed object on the neighboring objects. Generally, the buffer area for a spatial object B is defined as follows:

$$B = \{ X\_i = \{ X\_i | \mathbf{d}(X\_\prime O) \} \le R \} \tag{1}$$

*B* is the target buffer influence range, *Xi* is the location of any point in the target field (rural settlement point), *O* is the analysis object, d is the minimum Euclidean distance, and *R* is the buffer radius [55]. Different settlement types in the karst trough valley area have different levels of settlement development, and the surrounding land use changes show differences. In this paper, we use the buffer zone analysis method to select different types of settlements as the center point and establish buffer zones (range 50 m, 100 m, 150 m, 200 m, 250 m, 300 m, 350 m, 400 m) according to the center of the settlement; we perform a study on the dynamic variation of surrounding land use under different types of settlements. The buffer zone analysis in this paper was used to establish a polygon land use layer with a certain radius around the settlement as the center point, overlay the established layer with the target layer, and then analyze the results to explore further the evolution and coupling relationship between different types of settlements and their surrounding land use in the trough region.
