Research Identification of Paleoearthquakes and Coseismic Slips on a Normal Fault Using High-Precision Quantitative Morphology: Application to the Jiaocheng Fault in the Shanxi Rift, China

The quantitative morphology of bedrock fault surfaces combined with aerial surveys and ﬁ eld identi ﬁ cation is a useful approach to identify paleoearthquakes, obtain coseismic slips, and evaluate the seismogenic capacity of active faults in bedrock areas where traditional trenching methods are not applicable. Here, we report a case study of the Jiaocheng Fault (JCF) in the Shanxi Rift, China. Although several studies have been conducted on the JCF, its coseismic slip history and seismogenic capacity are still unclear. To address these problems, we investigated two bedrock fault surfaces, Sixicun (SXC) and Shanglanzhen (SLZ), on the JCF ’ s northern segment using quantitative morphological analysis together with aerial and ﬁ eld surveys. Quantitative fractal analysis based on the isotropic empirical variogram and moving window shows that both bedrock fault surfaces have the characteristics of vertical segmentation, which is likely due to periodic earthquakes, the coseismic slip of which can be determined by the height of the segments. Three seismic events at SXC, with a coseismic vertical slip of 1.74, 1.65, and 1.99m, and three seismic events at SLZ, with a coseismic vertical slip of 1.32, 2.35, and 1.88m, are identi ﬁ ed. Compared with the previous studies, these three seismic events may occur in the Holocene, but it requires absolute dating ages to support, which is also the focus of our future work. Considering the seismologic capability ( M > 7 : 5 ) and the relationship between the recurrence interval of ~ 2.6kyr and elapsed time of more than 3kyr, the seismic hazard of the northern and middle segments of the JCF requires immediate attention.


Introduction
Full understanding of the behavior and history of an active fault is the key to assessing seismic hazards and reducing the impacts from earthquake disasters [1]. A reasonable seismic hazard assessment mainly depends on the integrity of seismic records [2]. Considering the relative shortness and general absence of historical earthquake records, paleoearthquake research is the most effective way to extend the history of earthquakes and produce more complete seismic records [3]. The main aim of paleoearthquake research is to obtain the information relating to the activity of prehistoric earthquakes, especially the number, timing, and size [4]. The traditional method to study an active fault is based on the analysis of displaced Quaternary sediment through the trenching technique [5,6], which has been widely applied to paleoseismology, becoming a major contributor to paleoseismic studies in continental deformation zones [7][8][9]. For normal faults in terrestrial environments, the number of paleoearthquakes can be relatively easy to acquire by determining the relationship of cutting and coverage between faults and strata in the trench. Meanwhile, ages of paleoearthquakes can be accurately bracketed by dating geomorphic surfaces, displaced deposits, and colluvial wedges [10]. However, since multiple seismic slips often result in complex deformation, the Quaternary stratigraphic markers are not easy to find, and interfaulting sedimentation and erosion are therefore difficult to reconstruct. The accurate coseismic displacement of a single paleoearthquake event is therefore usually difficult to measure via the trench technique [4,11,12]. Therefore, it is necessary to develop a new identification technique to obtain accurate coseismic slips on normal faults.
Absolute and relative age dating methods have been used to obtain the seismic history of bedrock normal scarps. The absolute dating technique mainly refers to in situ cosmogenic nuclide exposure dating, which is most frequently applied to paleoearthquake analysis of normal fault scarps [16, 17, 25-27, 31, 34-36]. Not only can absolute dating obtain the number of individual earthquakes but also it can determine the corresponding age and slip rate by measuring the in situ cosmogenic nuclide concentrations along the fault scarp [18,19,30,[37][38][39][40][41]. The difficulties associated with this technique are that it can be prohibitively expensive, requiring a large amount of time, manpower, and materials to prepare and analyze samples at the sampling intervals required to identify seismic events [22,23,32].
Relative dating techniques assume that the degree of weathering is a function of the exposure time of bedrock fault surfaces and that the time-dependent weathering phenomena are quantifiable [23]. These methods obtain the number and coseismic slips of individual earthquakes by microroughness measurements [15,29], observing discoloration by the naked eye [42], photographic analysis [29], pit depth measurements [43], rebound value tests using a Schmidt hammer [22], lichen size measurements [44], rare earth element analysis [28,35,45], measurements of optically stimulated luminescence residual signals [46], or terrestrial laser scanning (TLS) [47]. In particular, TLS has become a well-established tool for identifying weathering bands and extracting potential paleoearthquake information [20][21][22]48] since it can rapidly obtain three-dimensional morphologic data with high spatial and temporal resolution [49][50][51][52][53][54][55][56]. This method can conveniently determine certain seismic parameters, such as the number of events and coseismic slips, and is suitable for a fault with clear earthquake ages but unclear coseismic slips [32,33,57].
Here, we focus on the JCF, an active normal fault located on the western flank of the Shanxi Rift at the eastern boundary of the Ordos block, which is a stable continental block in northern China (Figures 1(a) and 1(b)). The Taiyuan Basin is mainly controlled by the JCF and is considered the most inactive section of the Shanxi Rift with no historical record of earthquakes of magnitude 7 or greater since 2 kyr [58] ( Figure 1(b)). The greatest earthquakes to hit this area are the Taiyuan M6½ earthquake, which occurred in 1102 CE, and the Pingyao M6½ earthquake, which occurred in 1614 CE [59] (Figure 1(c)). However, this does not mean that the basin is not a strong earthquake hazard, as this depends on the activity of the basin boundary fault over longer time scales. Previous surveys based on the traditional trenching method and knickpoint analysis have shown that the JCF experienced 3 paleoearthquake events during the Holocene [58,60,61], but the accurate coseismic slip of each paleoearthquake event is still not clear due to a lack of stratigraphic markers, a complex deformation history, and signs of strong erosion, making it difficult to estimate the seismic capacity of the fault. The Taiyuan Basin, which is adjacent to the JCF, is one of the most densely populated regions in China, with a total population exceeding 8 million. Therefore, it is urgent to accurately obtain the coseismic slip and calculate the magnitude of each paleoearthquake event if we are to evaluate the potential hazard of regional seismic events to the local populace. The JCF occupies bedrock at a large number of sites, and there are many well-preserved bedrock fault scarps available for study.
In this study, to obtain accurate coseismic slips and the seismic capacity of the JCF, we apply aerial survey, weathering band interpretation, and quantitative morphology analysis. First, aerial survey and field work were conducted on two bedrock fault scarps to ascertain the geomorphological information needed to choose suitable study sites. Second, we scanned two well-preserved bedrock fault surfaces and obtained high-precision 3D morphology data using terrestrial laser scanning (TLS). Third, the fault surface morphologies were quantified as fractal dimensions (D), calculated using the isotropic empirical variogram method and a moving window operation [33], and the morphologic bands were identified using the fractal results. We ascribed the morphologic bands for each fault surface band to individual earthquake events and obtained the coseismic slip and magnitude of each event. Finally, combined with the results of previous paleoseismic studies, we constructed an earthquake history of the JCF, determined the fault rates, and assessed the regional seismic potential.

Geological Setting
The JCF is an active boundary fault in the central Shanxi Rift between the Lvliang Mountain and piedmont Taiyuan Basin,  extending approximately 125 km north from Nitun Town to   2 Lithosphere Fengyang City, with a general strike of NE-SW and dips to the SE at 40°to 80° [62]. The northern end and southern end of the JCF are, respectively, cut off by the Shilingguan uplift and Linshi uplift, which are roughly developing from east to west [61]. The mountain-basin height difference is about 800 m [60]. In the footwall, the Lvliang Mountain is an asymmetrical tight anticline with a core of Paleozoic and Mesozoic limestone and sand-shale covered by Quaternary loess in certain areas. Since the Pliocene, with contin-ued motion along the normal fault dominated by NW-SE extension, this anticline has been tilted to form a block mountain [63]. In the hanging wall, the Taiyuan Basin is filled with sediments that range in age from the Pliocene to the Holocene, where the sedimentary center is inclined to the eastern side of the JCF indicating strong fault activity [64,65] (Figure 1(c)). The JCF is divided into a northern, a middle, and a southern segment according to its geometry and activity:  3 Lithosphere the southern segment is the shortest,~20 km long, with an unclear fault trace; the middle segment is the longest, 70 km long, with the most obvious tectonic landforms; and the northern segment is~35 km long, with an uncontinuous trace [60] (Table 1, Figure 1(c)). The southern segment has no signs of Holocene paleoearthquake activity, while the northern and middle segments are characterized by three paleoearthquake events since the beginning of the Holocene [58,61,64].
The northern segment of the JCF is characterized by a series of well-developed triangular facets and bedrock fault scarps caused by dominant normal-slip faulting. Although the bedrock fault scarps cannot be studied by the traditional trenching method, they remain useful records of previous earthquakes, providing a potential target for obtaining accurate coseismic slips via quantitative morphology analysis.

Field Survey and Fault Surface Morphology Acquisition.
In the field, we conducted an aerial survey, visual interpretation of weathering bands, and morphology acquisition. First, a small unmanned aerial vehicle was used to acquire high-precision, high-resolution topographic data [66][67][68]. In this study, orthophotos of bedrock fault scarps and their surroundings were collected by a Dajiang Inspire sUAV carrying a GPS, an inertial navigation system, and an 8 mm fixed-focus high-definition camera (upper panel in Figure 2(a)). The 3D coordinates of ground control points (GCP) were acquired by GPS differential measurement for point position correlation and correction in the orthophotos (lower panel in Figure 2(a)). Indoor splicing, creating dense point clouds, generating grids, and pasting texture of collected images were conducted by professional image processing software Agisoft Photoscan Professional Edition 1.2.0, which was then used to produce a digital 3D model of the bedrock fault scarps and the surrounding topography. The morphological information of two bedrock fault scarps, e.g., length, continuity, and slope variation, was extracted based on the acquired digital 3D model. Next, the weathering degree of bedrock fault surfaces was estimated by a method of visual interpretation. The visual interpretation was conducted mainly based on structural integrity and surface condition of bedrock fault surfaces, according to the principles derived from Tye and Stahl in 2018 [22]. The structural integrity is classified into three levels, nearly intact, macrofragmented, and blocky, and the surface condition is also classified into three levels, smooth with striae and light-colored, rough associated with deeply colored erosion pits, and crushed with thick vegetation (Figure 2(b)). This provided basic information for target bedrock fault surfaces and a reference for subsequent morphology acquisition.
Next, the surface morphologies of the two fault scarps along the JCF were obtained with the aim of relating variations in surface morphology to paleoseismic activity using terrestrial laser scanning (TLS). The TLS, also known as terrestrial light detection and ranging (t-LiDAR), is a useful survey technique suitable for acquisition of very detailed and precise measurements of slip-surface geometry from well-preserved bedrock fault scarps [47]. As a noncontact measurement system, the t-LiDAR is an effective remote sensing technique for reconstructing, monitoring, and observing geological and geomorphologic phenomena and their related hazards. The fundamental principle of t-LiDAR is to generate a coherent laser beam with little divergence by stimulated emission [57]. In our study, we scanned the two fault surfaces to obtain high-precision and high-resolution morphologies of bedrock fault surfaces using a close-range t-LiDAR (Trimble GX 3-D scanner; Figure 3(a)). The space between two adjacent scan points ranged from 1.6 to 5 mm, with a change in the distance between the scanner and fault surface of 5 to 300 m. The distance between the farthest point and the center of the scanner is less than 15 m, which permits a point cloud with a high resolution of 2 mm. We chose a highquality but time-consuming scanning mode to ensure that the scanner stored the data, and each data point was collected twice to guarantee high data quality. In the field, the wellpreserved fault surface areas without vegetation or deposit cover were selected for scanning to allow complete data acquisition. We obtained high-precision and high-density 3D point clouds (Figure 3(b)) of the two fault surfaces with little divergence. The mean distance between adjacent points was 2 mm across the 3D point clouds. The original scan data were preprocessed by RealWorks Survey Advanced 6.1, Surfer 12, and Global Mapper 17 software packages. First, the point cloud dataset, with space coordinates X, Y, and Z, was moved and rotated to maintain the relative position of the scan points by the RealWorks Survey Advanced 6.1 software (Figure 3(c)).

Lithosphere
The originally inclined fault surface scanning data was levelled, such that after transformation, the x-axis was the strike line of the fault surface, the y-axis was the dip line of the fault surface, and the z-axis was the fluctuation direction of the fault surface. Then, we interpolated the point cloud datasets of the levelled irregular fault surface into DEM datasets with a cell size of 2 mm × 2 mm (Figure 3(d)) using a natural neighbor method in Surfer 12. Finally, the DEM datasets were cut into a rectangle with Global Mapper 17 ( Figure 3(e)).
Here, we selected two well-preserved bedrock fault outcrops on the northern segment for analysis: site 1 at Sixicun (SXC) and site 2 at Shanglanzhen (SLZ) (Figure 1(c)). Both study sites considered here consist of limestone in the footwall of the JCF, roughly 22 km apart. The fault trace is clear and continuous with no branch faults near the two study sites and ground deformation concentrated on the studied fault scarps (Figures 4(a) and 5(a)). Thus, the associated coseismic slips recorded on the fault surface can be treated as representative.
The bedrock fault surface at site 1 lies at the northern end of the northern JCF segment. According to our interpretation of the 3D digital model, the bedrock fault scarp extends for hundreds of meters along an NNE-SSW strike at the foot of the Lvliang Mountain, with the fault surface generally dipping to the SEE at 60°. The scan area was selected to be at a sufficient distance from several small gullies at the foot of the mountain. Furthermore, the chosen site is far from any trace of anthropogenic activity, such as dams or buildings, preventing any interference from these sources (Figure 4(a)). The field survey shows that the footwall of the bedrock fault mainly consists of brecciated limestone and that the bedrock fault scarp in the central segment displays the most complete level of preservation. According to visual interpretation in the field, the bedrock fault displays three weathering bands: (1) the lower part of the fault surface (weathering band 3) where the bedrock fault surface is relatively intact and small fissures are observable at the surface, (2) the middle part of the fault surface (weathering band 2) where the structure of the bedrock fault surface starts to become blocky, with erosion pits and comparatively large fractures on the surface, and (3) the upper part of the bedrock fault surface (weathering band 1) where the bedrock fault surface becomes crushed with thick vegetation (Figure 4(b)). A well-preserved area was scanned using t-LiDAR, and the collected point cloud data was processed to generate a DEM dataset with a cell size of 2 mm × 2 mm (Figure 4(c)).
The bedrock fault surface at site 2 lies in the central part of the northern segment of the JCF. The SLZ fault scarp at site 2 is approximately 10 m high and dips to the SE at 70°. The bedrock fault scarp gradually degrades and retreats 7 Lithosphere upper part of the fault surface (weathering band 1) has a broken bedrock fault surface covered by weathered debris ( Figure 5(b)). Like site 1, a well-preserved area was scanned using t-LiDAR to obtain point cloud data and then DEM datasets with a cell size of 2 mm × 2 mm (Figure 5(c)). The slickenlines ( Figure 5(d)) at the base of the fault surface indicate that the slip direction is approximately vertical, confirming the nearly pure normal faulting exhumation of the JCF.

Fractal Dimension Quantifying the Surface Morphology.
The fault surface buried under the ground has initial morphology [69]. After the surface is exhumed by an earthquake event(s), weathering is the main control over its surface morphology, which may result in vertical segmentation of the morphology along the bedrock fault surface [32,57]. Natural fault surfaces have either a self-similar or selfaffinity morphology features which can be expressed as fractal dimension D [53,70]. Here, we calculated the D value distribution of the fault surfaces by combining the isotropic empirical variogram with the moving window operation.
As an effective method to calculate the fractal dimensions of the DEM field [71,72], the essence of the variogram is to describe how the statistical variation of mean differences rðtÞ varies with the distance, t, between the points: For the surface fractals, the fractal dimension D has the following relationship with the fractal index K [73]: where D reflects the complexity of a natural surface [74,75], and this value ranges between 2 and 3 [76][77][78]. We chose three moving windows with a size of 66 mm × 66 mm, 130 mm × 130 mm, and 258 mm × 258 mm to calculate the fractal dimensions of the bedrock fault surface, according to the principles proposed by Sung et al. in 1998 [79]. The window moves along the whole DEM dataset of the fault surface. After these processes, we obtained a pair of result: a raster image displaying the distribution of fractal dimensions and a scatter plot displaying the average fractal dimensions on each horizontal row. To further determine the weathering bands on the fault surfaces, Student's t-test was applied to identify any morphologic segment along the fault scarp. For more details, please see He et al. [32] and Zou et al. [33].

Defining Morphological Segments and Their Heights.
Identification of weathering bands is a meaningful step as far as the coseismic slip, seismic intensity, and seismic hazard assessment are concerned [18,28]. In the fractal analysis results, the raster images (left panels of  (Tables 2 and 3), which can act as a quantitative indicator of fault surface morphology. The fractal results between SLZ and SXC bedrock fault surfaces are consistent, and both demonstrate three obvious segmentation features on the bedrock fault surfaces. The slight difference lies in the discontinuity between neighboring segments, in that the SLZ fault surface shows a wide transition zone while the SXC fault surface displays a narrow transition zone, indicating that the SLZ bedrock fault surface suffered more from hydrodynamic conditions during the interseismic periods. Furthermore, small fluctuations of the fractal dimension curve were also found in the fractal results ( Figures S1 and  S2). Different from the segmentation features caused by the kyr-scale exposure time difference, these small fluctuations are inside the segments. They have good continuity with the upper and lower data points and cannot be identified as a separate segment by the statistical methods used. Thus, they are not viewed as individual segment boundaries in morphology. Meanwhile, breccia can be observed in certain parts of the fault surface ( Figure 5(c)), which may cause the nonuniformity in rock composition. It is therefore inferred that the small fluctuations observed may reflect the nonuniformity in local rock composition along the fault surface. The above is only one possible explanation, but regardless of the reason, such small discrepancies should not affect the overall segmentation of seismic events.

Determination of Paleoseismic Events, Coseismic Slip, and Magnitude.
Comparing the fractal results of the fault surfaces (Figures 6 and 7) with the possible exposure models [33] allows the exhumation history of the bedrock fault surfaces on the JCF to be defined as follows. A segment of the fault surface is exhumed by a strong fault activity (rupture earthquake), the height of which is equal to the coseismic slip. Then, it suffers from the same weathering processes as before and thus has nearly the same fractal dimension. A series of seismic events may form multiple morphological segments on the bedrock fault surface between two adjacent seismic events, and long-term erosion under weak hydrodynamic conditions at the base of the fault scarp forms a transition zone (gradual change) in the morphology ( Figure S3).
The geological background of the fault surfaces provides strong evidence for this pattern. According to the previous trench studies, there have been three earthquake ruptures  Figure 6 and text for details.  [58,61]. In addition, the JCF is located between the Taiyuan Basin and the Lvliang Mountains. The resistance to erosion is different between the hanging wall, consisting of Paleozoic and Mesozoic limestone, and the footwall, consisting of loose Quaternary deposits, such as loess. The latter is easily influenced by the weak hydrodynamic conditions; therefore, exposure of the fault scarp is likely to be controlled by both seismic activity of the fault and the erosion of loose deposits on the hanging wall. Previous studies indicate that the average sedimentary rate near Shanxi area is 0.078 mm/yr [80] to 0.15 mm/yr. Considering that the average recurrence interval of 3 seismic events of the aimed fault is 2.58 kyr [58,61], the sediment thickness during the interseismic period could be 20-38 cm. The average coseismic slip is about 2 m of the aimed fault in this study, so the sediment thickness during the interseismic period accounts for about 10-20% of the average coseismic slip of the aimed fault. It is important to distinguish erosion processes and seismic events in places where erosion processes may exist, especially in loess areas. Since there is no large gully developed around the study sites (SXC and SLZ) and the scan areas were selected to be at a sufficient distance from small gullies at the foot of the mountain (Figures 4(a) and 5(a)), the two bedrock fault scarps could not be affected by strong erosion. Accordingly, we can exclude the existence possibility of intermittent strong erosion which is easily confused with the effect of seismic events. Since the weak hydrodynamic erosion is usually a continuous process, the segmentation could not be produced by such a process. When the statistical method was used to divide the segments, some gradual changes in the fractal curve were observed ( Figures S1 and S2), confirming that the transition zones between adjacent segments are caused by the gradual erosion of loess during the interseismic period, dominated by weak hydrodynamics.
In a model where the morphological segments of the fault scarp are mainly the result of repeated seismic events, the three morphological segments of the SLZ and SXC fault scarps would represent seismic events, and the coseismic slips can be estimated by the heights of these segments. The length of surface rupture (L) and the displacement (D) on continental faults are the most commonly used parameters for estimating the magnitude of paleoearthquakes [4,81]. However, the length of surface rupture for a prehistoric earthquake is usually not easy to obtain. The coseismic displacement not only reflects the seismic energy release but also is positively correlated with the magnitude of the earthquake [81]. Therefore, in this study, the coseismic displacements obtained by the morphological analysis of bedrock fault surfaces can be used to estimate magnitude. Based on the results from the fractal analysis method, the three segments, segment 1, segment 2, and segment 3, on the SXC bedrock fault surface are considered to represent three earthquakes, E1, E2, and E3, with respective coseismic slips of 2 m, 1.9 m, and 2.3 m in the dip direction. The corresponding magnitudes, calculated by the empirical formulas between magnitude (M) and displacement (D) for normal faults in North China, as proposed by Liu and Wang in 1996 [82], are estimated to be M S 7:5, M S 7:5, and M S 7:6, respectively (Figure 8 In the profile of the SLZ fault scarp, there is an obvious slope break at 7 m, and the surface of the fault scarp starts to degrade and retreat above this height, which may indicate earlier event(s); however, they have not been obtained in this study (Figure 8(b)).
The southern segment is inactive since the late Pleistocene [64], and the northern and middle segments have the characteristics of synchronous seismic activity [58,60]. To show the seismic capacity of the whole aimed fault, the coseismic displacement (D) and total length (L,~105 km) of the northern and middle segments are comprehensively considered to estimate the magnitude. The magnitudes of earthquakes E1, E2, and E3 identified on the SXC fault surface, calculated by the empirical formulas between magnitude (M) and length multiplied by displacement (LD) for normal faults in North China, as proposed by Liu and Wang in 1996 [82], are estimated to be M S 7:8, M S 7:8, and M S 7:9, respectively (Figure 8(a)). Similarly, the corresponding magnitudes of earthquakes E1, E2, and E3 identified on the SLZ fault surface are estimated to be M S 7:7, M S 7:9, and M S 7:8, respectively, by the empirical formula M − LD (Figure 8(b)). Previous studies indicate that the northern and middle segments of the JCF have a seismogenic capacity of M > 7 based on the estimated coseismic slips from the trenching method [58,62]. This study suggests that the northern and middle segments are able to produce earthquakes together with magnitudes greater than 7.5, which is basically consistent with the previous studies.
The distance between the two study sites SXC and SLZ is about 22 km, and the minor difference in coseismic slips and magnitudes obtained from the two study sites may reflect

Paleoearthquake History and Slip
Rate of the JCF. Due to the lack of direct dating (e.g., exposure ages) of the fault surfaces studied here, we compared the results of this study with previous research to establish a more complete paleoearthquake history of the JCF (Figure 9). The northern and middle segments of the JCF were active in the Holocene, while the southern segment remained inactive since the late Pleistocene [64]. Previous studies have determined ages for paleoearthquakes recorded in the JCF. Xie et al. [61] defined three paleoearthquakes on the northern and middle segments through the excavation of four trenches in 2008 (XZ, ZY, SGY, and XM1 in Figure 9(a)). According to thermoluminescence dating, the corresponding earthquake ages are estimated to be 3.06-3.53, 5.32-6.14, and~8.36 kyr (Figure 9(b)). A similar study carried out by Guo et al. in 2012 [58] also revealed three paleoearthquakes on the northern and middle segments through the excavation of three trenches (LWG, XM2, and WY in Figure 9(a)). The corresponding earthquake ages determined by radiocarbon dating are 3.06-3.74,~5.91, and 8.53-8.56 kyr (Figure 9(b)). Regarding the number of paleoseismic events, both the studies conducted by Xie et al. in 2008 [61] and Guo et al. in 2012 [58] suggest that the northern and middle segments of the fault experienced three paleoseismic events, which is in good agreement with the morphologic results of the bedrock fault scarps in this study. In terms of the activity time, the paleoearthquake ages obtained by radiocarbon dating [58] are highly consistent with the ages derived from thermoluminescence dating [61], indicating that the northern and middle segments are characterized by Holocene seismic activity. Following event window analysis [83,84] of the above dates, the ages of three paleoseismic events are corrected to 8.36-8.56 kyr, 5.32-6.14 kyr, and 3.06-3.53 kyr, with a recurrence interval of~2.6 kyr and an elapsed time (since the last earthquake) of~3 kyr (Figure 9(b)).
Although the paleoearthquake history of the JCF has been well-established in terms of ages of the seismic events by previous studies [58,61], the accurate coseismic slip of each seismic event is still unclear. The coseismic slip based on the traditional trenching method is 1.5-4.7 m, showing a large uncertainty range [58]. Due to lack of stratigraphic markers, this value is mainly estimated by the strata depth of the hanging wall and therefore has a large error range. The coseismic slips of the 3 seismic events estimated from the average height of each level knickpoint are 2.8 m, 3 m, and 2.6 m, respectively [60]. It should be noted that these values are not directly measured on the fault, which was severely destroyed by strong erosion. The coseismic slips in this study are directly obtained from the two bedrock fault surfaces, which are more accurate and reliable.
The previous trench and knickpoint studies indicate that the northern and middle segments experienced 3 ruptured events (8.36-8.56 kyr, 5.32-6.14 kyr, and 3.06-3.53 kyr) and have the characteristics of synchronous seismic activity since the beginning of the Holocene [58,61,64]. This study also reveals 3 ruptured events and their corresponding coseismic slips. In the absence of measured age constraints on the fault scarps studied here, it is necessary to make a good    (Table 3), and previous studies [58,61]. 11 Lithosphere correlation between the seismic event sequence obtained in this study and previous studies. Besides the same number of seismic events found in this study and previous research, there are other three important pieces of evidence to support a correlation. The first is the scale of displacement for each event. Previous trench studies reveal that the magnitudes of the 3 earthquake events are greater than 7 [58], which is consistent with the results of this study (Figure 8). This indicates that 3 seismic events of similar magnitude are recorded both in trenches and on bedrock scarps. The second is that for each of the two bedrock fault outcrops, there is an excavated trench nearby, and the bedrock fault site and corresponding trench are close to each other (within 2 km) (Figures 1(b) and 9(a) and Figure S4). More importantly, the two bedrock fault sites and the excavated trenches nearby are on the same fault segment while there is no evidence of branch faults nearby (Figure 1(b) and Figure S4). The conditions above ensure that the latest three seismic events (in the Holocene) can be recorded both in the trenches and on the bedrock scarps. As for the seismic information prior to the Holocene, it may remain in certain study sites such as SLZ fault scarp (Figure 8(b)), but it is difficult to recognize and analyze. Thus, it is feasible to combine this study result with previous researches to obtain more complete paleoearthquake information of the JCF in the Holocene and make a more reasonable seismic risk assessment. Considering a recurrence interval of 2.6 kyr, an elapsed time of more than 3 kyr, and the capacity of producing earthquakes with a coseismic slip greater than 2 m and magnitude greater than 7.5, the seismic hazard on the northern and middle segments of the JCF requires immediate attention.
The fault slip rate is another key parameter concerning fault activity. Based on the cumulative slip of 6.2 m from the SXC fault surface and a corresponding age of 8.36-8.56 kyr, the dip slip rate is estimated to be 0.72-0.74 mm/ yr. A dip angle of 60°for the SXC fault surface leads to a vertical slip rate of 0.63-0.64 mm/yr on the northern segment of the JCF. Similarly, for the SLZ fault surface, based on the cumulative slip of 5.9 m and a corresponding age of 8.36-8.56 kyr, a dip slip rate of 0.69-0.71 mm/yr is estimated. Again, considering there is a dip angle of 70°, the corresponding vertical slip rate becomes 0.64-0.67 mm/yr. We provided a systematic summary about the slip rate of the JCF, which can be used as a reference frame ( Figure S5). Previous studies show that the slip rate of the JCF is 0.58-0.86 mm/yr in the northern segment [64], which is in good agreement with the above two survey sites. It indirectly reflects the accuracy of the coseismic slip we obtained and the rationality of event matching.
It should be pointed out however that the prerequisite for the event match and the slip rate estimate is that the two bedrock fault scarps are produced by the 3 Holocene seismic events identified in previous research. Although we have provided more evidence and conducted further discussion to support seismic event match, it still lacks the absolute age constraints. Ideally, an absolute dating would be robust evidence to constrain the age of the bedrock fault outcrop, which has been applied to a number of case studies of bedrock normal faults [16,27,31,34]. However, it needs a large amount of time and labor. As a result, we are unable to carry out this work soon. In the future, it is better to be supported by this robust method. Zou

Lithosphere
Rift by combining the morphology results with the absolute ages [33], providing a feasible workflow. In future work, a series of 36 Cl rock samples should be collected from the bedrock fault surfaces of the JCF and measured by Accelerator Mass Spectrometry (AMS) to determine the ages of each event interpreted from the morphology analysis.

4.4.
Significance of Paleoearthquake Studies within the Bedrock Area. Typically, the normal faults at a basinmountain boundary zone spatially separate two areas along a strike: the bedrock areas and the sedimentary areas ( Figure 10(a)). The traditional method to study an active fault is based on analyzing displaced Quaternary deposits via the trenching technique [5][6][7][8]10]. Therefore, its focused objects are the fault segments spreading into sedimentary areas with attention paid to Quaternary stratigraphic markers. The paleoearthquake study of bedrock fault surfaces focuses on fault scarps spreading into bedrock areas, increasing the number of sites available for study both spatially and temporally, providing a more complete understanding of the fault behavior. Trenching in sedimentary areas is an effective method for extracting the number and ages of earthquakes and establishing a paleoearthquake history. In comparison, the advantages of bedrock fault surface morphology analysis lie in the ability to rapidly identify seismic events and accurately measure coseismic slips. This helps to obtain the frequency of seismic events and evaluate the seismic capacity of a fault, as shown in this study. The combination of these two methods allows for the extraction of more faulting information, the synthesis of a more complete paleoearthquake reconstruction, and a better assessment of seismic hazards (Figure 10(b)).

Conclusions
The study of bedrock fault surfaces using a combination of aerial survey, field identification of weathering bands, and quantitative high-resolution morphology analysis can provide theoretical and methodological support for the research of active faults in bedrock areas. It is an effective method for efficiently identifying the number of paleoearthquakes, accurately obtaining the coseismic slip of individual paleoearthquakes, reasonably evaluating the seismic capacity of faulting in bedrock areas, and greatly expanding the number of study sites, thereby broadening the spatial and temporal understanding of events. Fractal analyses of the SXC and SLZ bedrock fault surfaces on the JCF show that both surfaces have the characteristics of vertical segmentation. This kind of segmentation feature indicates that the fault surfaces are exposed intermittently, likely due to periodic earthquakes. Thus, earthquake events can be identified by determining morphological segments, and the corresponding coseismic slip can be determined by the height of the identified segments. These kinds of studies complement the traditional trenching method in sedimentary areas, allowing for the extraction of more paleoseismic information and a fuller understanding of the activity behavior of the whole fault. 13 Lithosphere This study is also meaningful for seismic hazard assessment in the densely populated Taiyuan Basin. Based on high-precision quantitative morphology analysis of the bedrock fault surface, three paleoearthquake events are identified on both the SXC and SLZ bedrock fault scarps, which is consistent with the previous trenching results in sedimentary areas. The results suggest that the JCF is dominated by stick slip behavior and has the ability to produce earthquakes with magnitudes greater than 7.5. Considering the high slip rate, the capacity of producing M S > 7:5 earthquakes, a recurrence interval of~2.6 kyr, and an elapsed time of more than 3 kyr since the last earthquake, full attention needs to be paid to potential seismic hazards on the northern and middle segments of the JCF. Since the absolute dating work has not been carried out on the bedrock fault outcrops, the lack of chronological evidence is the limitation of this study. In situ cosmogenic nuclide dating such as 36 Cl should be carried out on the bedrock fault outcrops to provide a robust age constraint, which is also the focus of our future work.

Data Availability
The authors confirm that the data supporting the findings of this study are available within the article.

Conflicts of Interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. Figure S1: morphologic segment and segment height determination for the SXC bedrock fault surface by Student's ttest. Figure S2: morphologic segment and segment height determination for the SLZ bedrock fault surface by Student's t-test. Figure S3: schematic diagram of the bedrock fault scarp exhumation and the corresponding fractal curve. Figure S4: locations of the bedrock fault surfaces and nearby trenches. Figure S5: summary of the vertical slip rates for the JCF [64,65,85,86]. (Supplementary Materials)