The results show that at least 12 817 landslides were triggered by the 2014 Ludian earthquake. A nearly circular area of 603 km2 is framed according to the distribution of these landslides. The total occupation area of these landslides is 16.33 km2, the area of the smallest landslide is 12 m2, and the largest one covers about 345 000 m2. Among them, 4 landslides are larger than 100 000 m2, 215 landslides are between 100 000 and 10 000 m2, 2 929 landslides are between 10 000 and 1 000 m2, and 8 836 landslides are between 1 000 and 100 m2. The distribution of these landslides is an ellipse with a long axis trending northwest-southeast, consistent with the inferred seismogenic structure. Most of these landslides occurred southeast of the epicenter, a few in the northwest, the majority of which were concentrated along the valleys with large topographic relief (Fig. 4).
Figure 4. (a) The distribution of coseismic landslides triggered by the 2014 Ludian earthquake (red patches) and seismic intensity isolines (dark green circles). BXF. Baogunao-Xiaohe fault. 1. Hongshiyan landslide; 2. Miaozhaizi landslide. (b) Enlarged view of the bright green box in (a).
The volume of a landslide is usually estimated by using a landslide area-volume law from statistics (Xu et al., 2016b, 2014e; Larsen et al., 2010; Guzzetti et al., 2009). For example, for the 2008 Wenchuan earthquake, the area-volume formula (Xu et al., 2016b) is
where A is the area of a single landslide, and V is its volume. The volume of each landslide triggered by the Ludian earthquake is calculated by using this formula. Then the total volume of the landslides triggered by the Ludian earthquake is calculated to be 132 million m3. According to the number, total area, total volume, and elliptic area of landslide distribution, the landslide number density is 12 817/603 km2=21.25 km-2, landslide area density is (16.33 km2/603 km2)×100%=2.71%, and landslide volume density is 132 million m3/603 km2=0.219 m.
Figure 5 shows the frequency-area curve of the coseismic landslides on log axes, which represents the relationship between the cumulative landslide number (N) whose area is larger than or equal to the landslide area (A). This relationship is expressed as
Figure 5. Frequency-area curve of landslides triggered by the 2014 Ludian earthquake. Updated from Wu and Xu (2018).
where a and b are constants. The landslide number data is shown as a line in a logarithmic coordinate system. Inventories of earthquake-triggered landslides often have omission of some small- or medium-scale landslides. Therefore, this line shows a significant tendency to bend down corresponding to the small-scale landslides. This phenomenon can be found in many previous case studies (Xu et al., 2015, 2014b; Guzzetti et al., 2002). It can be seen from Fig. 5 that the area of the landslides triggered by the earthquake began to obviously bend in the values of 200–300 m2. It indicates that there is almost no omission for the landslides with an area larger than these values. Some of those landslides with smaller area may have been omitted due to difficulty in delineation on satellite images. Therefore, the curve can be used to determine the integrity of the inventory of coseismic landslides.
The largest landslide triggered by the 2014 Ludian earthquake occurred at a place named Hongshiyan, 8.2 km southwest to the epicenter (27.038°N, 103.400 1°E, Fig. 4). The maximum elevation of its slip cliff is about 1 770 m, and the minimum elevation of the landslide accumulation area is 1 135 m. The main substance of the landslide slid in the S30°W direction, dominated by dolomite and limestone. The landslide area is about 3.45×105 m2, and the collapse volume is about 12 million m3. The landslide slid down the slope and blocked the Niulan River, where deposits formed a dam with a height of about 100 m and a dammed lake with a storage capacity more than 2 billion m3 (Fig. 6). This site became the most dangerous after the earthquake, because the dammed lake threatens the safety of nearly 10 000 people who live in downstream of the river (Shi et al., 2017; Xu et al., 2014d).
Figure 6. The Hongshiyan landslide triggered by the 2014 Ludian earthquake. (a) 3D Google Earth post-quake image taken on 20 August 2014 with resolution about 0.5 m, view to northeast. (b) Post-quake aerial orthophoto taken on 7 August, 2014 with resolution 0.2 m.
Another big one, the Miaozhaizi landslide is located on the right bank of the Shaba River, which is a tributary of the right bank of the Niulan River (27.068 9°N, 103.380 8°E, Fig. 4). More than 50 people in 28 homes in the Miaozhaizi Village were buried by the slope failure. The landslide also destroyed the Ganjiazhai segment of the Zhaotong-Qiaojia Road (Fig. 7). The elevation of its slip cliff is 1 510 m, the elevation of the landslide lip is 1 210 m, with a southwestward direction of sliding. The landslide area is 16×104 m2 and the volume is about 1.3 million m3. Landslide material is mainly composed of rock masses, broken stones, and cohesive soil. Locally vegetation integrity remained good after the quake, indicating the damage is not particularly serious. The reason may be the movement of this landslide is rather coherent (Xu et al. 2014d).
Earthquake-triggered landslides are affected by many factors, such as topography, geology, and seismology (Tian et al., 2016; Xu et al, 2014a; Gorum et al., 2011). This study selects the most important and common factors for statistical analysis. Slope gradient is undoubtedly one of the most important factors affecting earthquake-triggered landslides, because the greater the gradient, the stronger the gravity and more susceptible to landsliding. The slope aspect affects the occurrence of earthquake- triggered landslides through two ways: (1) slopes with different aspects may have different rainfall, temperature, sunshine, and vegetation coverage (Kamp et al., 2008), and (2) the different combinations of the slope aspect and the direction of seismic wave propagation or the sudden movement direction of the blocks have different effects (Xu et al., 2015, 2014a). Although the elevation is also a factor in landsliding, the ways it affects earthquake-triggered landslides also include rainfall, temperature, sunshine and vegetation coverage, which are similar to slope aspect. Therefore, this study does not consider the elevation factor. This study selects lithology as a major geological factor because it is easy to obtain and determines the rock-soil mechanical strength of slopes, thus strongly affecting the occurrence of landslides. PGA and epicentral distance are undoubtedly two of the most important controls for coseismic landslides (Xu et al., 2014a; Gorum et al., 2011). Therefore, we employ slope gradient, slope aspect, lithology, PGA and epicentraldistance as the influence factors to analyze the spatial distribution of the landslides triggered by the Ludian earthquake.
Taking slope gradient and slope aspect as topographic factors, we first examine their correlations with the spatial distribution of the coseismic landslides by a statistic analysis (Fig. 8). Results show that the range of the slope gradients in the study area is 0°–81°. The number and area of landslides increase and then decrease with slope gradients. The gradient range of 20°–30° corresponds to the largest landslide number 3 925; the largest landslide area occurs in the gradient range of 30°–40°, which is 4.81 km2. The LND and LAD generally increase with the growing gradient. It is only the abnormal point of LND value in the gradient range of 50°–60° (Fig. 8a) with the LND of 27.40 km-2. The LAD value corresponding to the gradient range of 60°–81° is only 18.09 km-2. This gradient range has a maximum LAD value of 8.1% (Fig. 8b) possibly because the gradient range of 60°–81° hosts some large landslides with less number and larger area. On the whole, landslides tend to occur in the gradient range of 10°–40°, and the susceptibility increases with the growing gradient. Due to the less area coverage, the number and area of landslides on high slopes are few, similar to the expressions in other earthquakes (Xu et al., 2015, 2014a; Wang et al., 2007).
Figure 8. Changes of landslide number and LND (a) and landslide area and LAD (b) with slope gradient.
The slope aspect (or the facing direction of a slope) in the study area is divided into nine categories: flat, north, northeast, east, southeast, south, southwest, west and northwest. Figure 9 shows the statistical results of landslide number, landslide area, LND and LAD in each category. It is noted that a large number of landslides occurs in east, southeast, and west that has 2 155, 1 824 and 1 914 landslides, covering 2.68, 2.23 and 2.84 km2, respectively. The slope aspect of the east has the larger landslide number density and landslide area density, with LND and LAD values 24.83 km-2 and 3.09%, respectively. It indicates that the most susceptive slope aspects are east and southeast. This is probably due to the direction of earthquake rupture is from northwest to southeast, which exerted a significant influence on the occurrence of landslides. The slope aspect consistent with the direction of seismic energy transmission is more prone to slide, while that of the opposite aspect is not. This phenomenon has also been noted in other earthquakes (Shen et al., 2016; Xu et al., 2015, 2014a), which is a significant feature of earthquake-triggered landslides different from those induced by rainfall.
The lithology of a slope can exert an important influence on the occurrence of coseismic landslides because it determines the slope's strength to a large extent. In this work, the lithologic distribution in the study area is obtained from a 1 : 200 000 geological map. It is divided into 11 categories based on the geological ages (Table 1). The landslide number, landslide area, LND and LAD values of each category are statistically analyzed (Fig. 10). The results show that there are significant differences of landslide occurrence in different strata. Permian P2 strata have the largest landslide number 3 269; the maximum value of LND is in Permian P1 strata which is 28.22 km-2. The maximum area of landslides is in P1 strata, 3.75 km2 and the LAD value of Sinian Z1 strata is the highest which is 4.68%. In addition, the landslide number density is the largest in P1 strata, while the highest landslide area density is in Z1 strata. It is noted that a lot of large-scale landslides occurred in Z1 strata. The differences of landslide number density and landslide area density in different strata indicate that the lithology plays an important role in the occurrence of landslides triggered by earthquakes.
No. Stratum Lithology description 1 T Triassic System. Siltstone, argillaceous siltstone with fine sandstone 2 P2 Upper Permian System. Mudstone, porphyritic basalt, volcanic breccia 3 P1 Lower Permian System. Siltstone, shale, limestone 4 D Devonian System. Quartz sandstone, siltstone, dolomite 5 S Silurian System. Shale, carbonatite, clastic rocks 6 O2–3, O2 Upper–Middle Ordovician System. Dolomite, sandstone with shale and argillaceous limestone 7 O1 Lower Ordovician System. Fine sandstone, dolomite, mica siltstone 8 Є2, Є3 Cambrian Upper and Middle Cambrian System. Gray dolomite, shale with siltstone, clastic rock, argillaceous limestone 9 Є1 Lower Cambrian System. Sandstone, shale, dolomite, argillaceous limestone 10 Z2 Upper Sinian System. Dolomite, dolomite limestone, dolomitic shale 11 Z1 Lower Sinian System. Basal conglomerate, pebbly sandstone, sandstone, quartz sandstone, silty mudstone
Table 1. Descriptions of categorized lithology in the study area
The PGA represents the intensity of ground shaking during an earthquake. In general, the vulnerability of the slope increases with the PGA. More landslides can be triggered by a major earthquake at a site with larger PGA and other similar conditions (Xu et al., 2015, 2014a). From data available, the PGA of the study area ranges 0.08g–0.36g, which is divided into 8 classes using an interval of 0.4g. The relationship between PGA and landslides is calculated on a GIS platform (Fig. 11). The results show that both landslide number and LND value increase first with the PGA and then decrease. The landslide number reaches the maximum when PGA is 0.2g, which is 3 085, and then begins to decrease. The LND value peaks at the PGA 0.28g that is 31.36 km-2, and then decreases. Both landslide area and LAD value increase at first and then decrease with the rise of the PGA, both of which reach the maximums when PGA is 0.2g, the values of which are 5.37 km2 and 6.16%, respectively. Landslide area and LAD value reduce after the PGA exceeds 0.2g. Obviously, the relationship between landslide and PGA for this event is different from other earthquakes. It is an obvious bias in the core area of coseismic landslide distribution (the center is roughly located at 27.074°N, 103.373°E) and maximum area of PGA distribution (the center is roughly located in 27.189°N, 103.409°E) when we overlay coseismic landslides and the PGA diagram from the USGS. Their difference in space is about 15 km. The area of landslide distribution is only about 600 km2 with a radius less than 14 km if we regard it as a circle. It may cause a large error because that the seismic stations used by USGS to locate the epicenter are relatively sparse. Therefore, the PGA distribution map obtained by simulation does not match the coseismic landslides. The mismatch between PGA and coseismic landslides should not be explained as an abnormal phenomenon which is different from previous earthquakes. The more reasonable explanation may be the error of the PGA data or the coseismic landslides are also affected by local topography and geological conditions.
Apparently seismic factors, such as the epicenter and seismogenic fault, can exert significant effects on the occurrence of the earthquake-triggered landslides. The statistical relationships between these factors and earthquake-triggered landslides were often analyzed in previous work (e.g., Shao et al., 2019b; Rao et al., 2017; Xu et al., 2014a; Gorum et al., 2011; Keefer 1984). As the magnitude of the 2014 Ludian earthquake is only Mw 6.2, and the surface rupture is only exposed for about 2 km at the southeastern end of the inferred seismogenic fault (Xu X W et al., 2015), it is difficult to clarify the relationship between earthquake-triggered landslides and the seismogenic fault. Therefore, in this study, the distance to the epicenter is used to examine the relationship between earthquake-triggered landslides and the seismic source. According to the China Earthquake Network Center, the epicenter of the Ludian earthquake is at 27.099 4°N, 103.34°E. The buffers of 2 km interval around the epicenter are established on the GIS platform and the whole study area is divided into 9 intervals according to the distance from the epicenter, i.e., 2–4, 4–6, 6–8, 8–10, 10–12, 12–14, 14–16, and 16–18 km. Then, relationships between landslide distribution and the distances from the epicenter are calculated (Fig. 12). In general, the landslide number and landslide area increase first and then decrease. The reason for this is that the buffer area of the same buffer distance rises gradually with the distance from the epicenter, thus landslide number and area increase. This is probably because fewer landslides occurred when the distance from the epicenter exceeds a certain value and the outer area is smaller because of cutting by the boundary of the study area. Landslide number and area peak at 8–10 and 4–6 km away from the epicenter, i.e., 2 597 landslides and 4.68 km2, respectively. In general, LND and LAD decrease with increasing distance from the epicenter. However, the maximum values of both are not located in the buffer 0–2 km far from the epicenter, instead of 2–4 and 4–6 km to the epicenter, which are 47.58 km-2 and 7.44%, respectively. On the whole, the farther from the epicenter, the lower susceptibility of landslides. This is likely because that seismic shaking reduced with the increase of distance from the epicenter, thus leading to fewer landslides. This is common in other cases (Xu et al., 2015, 2014a). Besides, the lower landslide density in 0–4 km distance from the epicenter is probably associated with the error in epicenter location or lower gradients in this area or unfavorable geological conditions for landsliding.
3.1. Inventory of Coseismic Landslides
3.2. Typical Landslides
3.3. Spatial Distribution of Landslides with Respect to Control Factors
3.3.4. Distance to the epicenter
After the 2014 Ludian earthquake, quite a few inventories of coseismic landslides were completed by some research teams, which differs from each other to some extent. Compared with these data, the resultant inventory of this study is more complete, detailed and objective. For example, the number of coseismic landslides is much greater than those in previous work. The reasons for this may include the quality, resolution, and coverage of remote sensing images used, as well as the landslide interpretation methods. Here we make a comparison of them in the following five aspects: types and resolution of remote sensing images, landslide number, landslide area, landslide distribution area and integrity of post-quake images (Table 2). Zhou S H et al. (2016) obtained 19.12 km2 of the landslide area that is the largest in previous results. Their work is based on pre- and post-quake Landsat-8 images (15-m resolution), combining with ultrahigh-resolution aerial photographs (0.2-m resolution) covering part the affected area (Fig. 13a). Apparently, such a low resolution of the satellite images can lead to commission and omission errors, i.e., missing a large number of small- and medium-landslides. Because ground objects identified are not clear, the landslides existing before the earthquake, residential areas and lakes might be recognized as coseismic landslides, leading to the low quality of the landslide inventory. For instance, as shown in Fig. 13b, a quarry and exposed slope have been interpreted as a fairly large coseismic landslide. Meanwhile, the whole township named Huodehong was depicted into several large-scale coseismic landslides (Fig. 13c). These are obviously severe commission errors in the work of Zhou S H et al. (2016).
No. Source and resolution of images Landslide number Landslide area (km2) Landslide distribution area (km2) Integrity of images References 1 SJ9A (Pan: 2.5 m; MSS: 10 m), 1 024 5.19 250 Yes Xu et al. (2014d) TH01-02 (Pan: 2 m) 2 Aerial image (0.2 m) 1 053 2.36 44.13 No Tian et al. (2017b) 3 Landsat-8 (Pan: 15 m; MSS: 30 m) 1 826 19.12 735 Yes Zhou S H et al. (2016) Aerial image (0.2 m) 4 Not availible 114 4.2 368.2 Yes Chen et al. (2015) 5 Google Earth (~0.5 m) 10 559 14.975 357 Yes Wu and Xu (2018) 6 Google Earth (~0.5 m) 12 817 16.33 603 Yes This study
Table 2. Comparison of landslide inventories of the 2014 Ludian earthquake
Figure 13. Erroneous interpretation to seismic landslides by Zhou S H et al. (2016). (a) Distribution of coseismic landslides triggered by the Ludian earthquake (Zhou S H et al., 2016). (b) Quarry and exposed slope misjudged as coseismic landslides, image taken on February 17, 2015. Central coordinates: 27.067 4°N, 103.467 3°E; (c) Huodehong Township was misjudged as coseismic landslide, image taken on August 14, 2014, central coordinates: 27.040 1°N, 103.466 4°E.
Xu et al. (2014d) established that the Ludian earthquake triggered at least 2014 individual landslides with a total distribution area of 5.19 km2. For comparison, we choose a rectangle 850 m×930 m with central coordinates 27.105 9°N, 103.311 2°E, where 81 landslides were interpreted by this study and 16 landslides were delineated by the study from Xu et al. (2014d), as shown in Fig. 14. Xu et al. (2014d) used the high-resolution satellite images that cover the whole region, with resolution 2.5 m that was fused with multi-spectrum images with 10 m resolution and a panchromatic image with 2.5 m resolution. In addition, the spectral difference between landslide regions and non-landslide regions is not so obvious that a number of small-scale landslides were unrecognized. Therefore, the results of Xu et al. (2014d) are notably different from this study.
Figure 14. Comparison between the work of Xu et al. (2014d) and this study. (a) Landslides interpreted by this study and pre-quake image from Google Earth (taken on December 6, 2011); (b) landslides interpreted by this study and post-quake image from Google Earth (taken on August 20, 2014); (c) landslides interpreted by Xu et al. (2014d) and pre-quake image taken by SJ9A; (d) landslides interpreted by Xu et al. (2014d), by this work and post-quake image of SJ9A. Modified after Wu and Xu (2018).
Tian et al. (2017b) delineated the Ludian earthquake- triggered landslides on both sides of the Niulan River using ultrahigh-resolution aerial images. As their study area does not cover the whole affected area, hence the resulting landslide number in the inventory is less than the actual one. Nevertheless, landslide number and area density from their work are 1 053/44.13 km2=23.86 km-2 and 2.36 km2/44.13 km2×100%= 5.35%, close to those of this study which are 12 817/603 km2=21.25 km-2 and 16.33 km2/603 km2×100%=2.71%, respectively. Probably Tian et al. (2017b) adopted ultrahigh- resolution aerial photographs which have equivalent resolution of satellite images from Google Earth platform used in this study. On the other hand, the study area of Tian et al. (2017b) covers both sides of the Niulan River where slopes are highly prone to landsliding. Therefore the landslide density of Tian et al. (2017b) is higher than that in the whole range of this study. Besides, the study of Chen et al. (2015) did not mention the source of remote sensing images used; and they have delineated 114 landslides greater than 1 000 m2 and used them to analyze the special distribution of the coseismic landslides. Their study ignores a large number of small and medium-scale landslides triggered by the earthquake.
Also based on visual interpretation of high-resolution satellite images from Google Earth, Wu and Xu (2018) constructed an inventory quite similar to this study, which determined 10 559 coseismic landslides with a total area of 14.975 km2 and a spatial distribution area of 357 km2. This study makes a new landslide inventory in a nearly circular area with the radius about 3 km larger than that of the study area in Wu and Xu (2018), and finds that there are still quite a few small landslides outside this area. Although the number of landslides in the area far from the epicenter is less and their scale is small, the new landslide distribution area in this study reaches 603 km2, which is 1.7 times the study area of Wu and Xu (2018). While the landslide number and distribution area of our new results are 12 817 pieces and 16.33 km2, respectively, which are only 1.2 and 1.1 times the results of Wu and Xu (2018).
In this study, the landslide number is much greater than most of the previous work, because our work is strictly in compliance with the principles of establishing inventories of coseismic landslides (Xu, 2015; Guzzetti et al., 2012; Harp et al., 2011). Meanwhile, the coverage of pre- and post-quake satellite images that overlaps the whole affected area ensures the integrity of the inventory. Using post-quake high-resolution satellite images on Google Earth platform (resolution is about 0.5 m) permits landslides interpreted as many as possible, including small ones. Besides, in this work pre-quake satellite images are used to eliminate landslides that existed before the earthquake, avoiding the commission error when delineating coseismic landslides, and ensuring the accuracy of the inventory. We adopt artificial visual interpretation, in which coalescing landslides are divided into individual landslides according to the principle of interpretation (Xu, 2015), rather than complex landslides framed as individual ones, so that the resulting coseismic landslide number is objective. This is why the inventory of the landslides obtained in this study is relatively more complete and accurate. Comparing with the inventories of landslides triggered by other earthquakes can also explain why the inventory of this study is objective. For instance, the Minxian Mw 5.9 earthquake of June 22, 2013 triggered at least 6 478 landslides (Tian et al., 2016; Xu et al., 2014c). The Northridge Mw 6.7 earthquake in 1994 triggered more than 11 000 landslides in an area about 1 000 km2 (Harp and Jibson, 1996, 1995). The average gradient in the Ludian quake-affected area is larger than those of the Minxian and Northridge earthquake areas. Besides, Ludian is located in a subtropical region and the earthquake occurred in summer. Before the 2014 Ludian earthquake, continuous precipitation could have lowered the slope stability, thus more prone to landsliding. Hence, referring to the number of landslides triggered by the Minxian and Northridge earthquakes, it is unreasonable that the Ludian earthquake only triggered more than 1 000 major landslides as suggested by previous studies (Chen 2015; Xu et al., 2014d).