Abstract: The quantitative analysis of morphologic characteristics of bedrock fault surface is a useful approach to study faulting history and identify paleo-earthquake. It is an effective complement to trenching technique, specially to identifying paleo-earthquakes in a bedrock area where the trenching technique cannot be applied. This paper focuses on the Luoyunshan piedmont fault, which is an active normal fault extending along the eastern boundary of the Shanxi Graben, China. There are a lot of fault scarps along the fault zone, which supply plentiful samples to be selected to our research, that is, to study faulting history and identify paleo-earthquakes in bedrock area by the quantitative analysis of morphologic characteristics of fault surfaces. In this paper, we calculate the 2D fractal dimension of two bedrock fault surfaces on the Luoyunshan piedmont fault in the Shanxi Graben, China using the isotropic empirical variance function, which is a popular method in fractal geometry. Results indicate that the fractal dimension varies systematically with height above the base of the fault surface exposures, indicating segmentation of the fault surface morphology. The 2D fractal dimension on a fault surface shows a ‘stair-like’ vertical segmentation, which is consistent with the weathering band and suggests that those fault surfaces are outcropped due to periodic faulting earthquakes. However, compared to the results of gneiss obtained by the former researchers, the characteristic fractal value of limestone shows an opposite evolution trend. 1)The paleo-earthquake study of the bedrock fault surface can be used as a supplementary method to study the activity history of faults in specific geomorphological regions. It can be used to fill the gaps in the exploration of the paleo-earthquake method in the bedrock area, and then broaden the study of active faults in space and scope. The quantitative analysis of bedrock fault surface morphology is an effective method to study faulting history and identify paleo-earthquake. The quantitative feature analysis method of the bedrock fault surface is a cost-effective method for the study of paleo-earthquakes in the bedrock fault surface. The number of weathered bands and band height can be identified by the segment number and segment height of the characteristic fractal dimension, and then the paleoearthquake events and the co-seismic displacement can be determined; 2)The exposure of the fault surface of the Luoyunshan bedrock is affected and controlled by both fault activity and erosion. A strong fault activity(ruptured earthquake)forms a segment of fault surface which is equivalent to the vertical co-seismic displacement of the earthquake. After the segment is cropped out, it suffers from the same effect of weathering and erosion, and thus this segment has approximately the same fractal dimension. Multiple severe fault activities(ruptured earthquake)form multiple fault surface topography. The long-term erosion under weak hydrodynamic conditions at the base of the fault cliff between two adjacent fault activities(intermittent period)will form a gradual slow-connect region where the fractal dimension gradually changes with the height of the fault surface. Based on the segmentation of quantitative morphology of the two fault surfaces on the Luoyunshan piedmont fault, we identified four earthquake events. Two sets of co-seismic displacement of about 3m and 1m on the fault are obtained; 3)The relationship between the fault surface morphology parameters and the time is described as follows:The fractal dimension of the limestone area decreases with the increase of the exposure time, which reflects the gradual smoothing characteristics after exposed. The phenomenon is opposite to the evolution of the geological features of gneiss faults acquired by the predecessors on the Huoshan piedmont fault; 4)Lithology plays an important role in morphology evolution of fault surface and the two opposite evolution trends of the characteristic fractal value on limestone and gneiss show that the weathering mechanism of limestone is different from that of the gneiss.

Key words: paleo-earthquake, morphology of bedrock fault surface, isotropic empirical variogram, Luoyunshan piedmont fault

摘要： 以山西地堑系罗云山山前断裂的基岩断层面为例，用陆基LiDAR扫描获取了断层面形貌学数据，采用各向同性变差函数法计算了断层面形貌的分维值。结果显示，断层面形貌在高度上具有显著的分带性，每个分带的特征分维值随断层面高度的增加呈阶跃式变化。分析认为这种形貌特征可能反映了断层面与多次地震相关的间歇式出露方式。分带高度指示了约3m和1m的2组同震倾滑位移量，各分带之间的分维值过渡带是断层面缓慢剥露的结果。与片麻岩区的断层面形貌学研究结果相比，灰岩断层面形貌学分维值随着暴露时间的增加而减小，2种岩性区的断层面分维值D与断层面高度H呈现类似镜像的关系，在气候构造条件大致相同的情况下，考虑为岩性差异的影响。

关键词: 古地震, 基岩断层面形貌, 各向同性变差函数法, 罗云山山前断裂