A landslide inventory is essential for assessing landslide hazard or risk on a regional scale (Pellicani and Spilotro, 2015). The Jiuzhaigou earthquake triggered numerous landslides in the study area. To derive a landslide inventory containing detailed and reliable information on landslide distribution, location, etc., Sentinel-2A images on 29 July, 13 August and 7 September 2017 were used to recognize and locate the earthquake-triggered landslides. The Sentinel-2A image has 13 spectral bands (from blue to shortwave infrared) with the spatial resolution of 10, 20 and 60 m, respectively. In this study, three visible bands (red, green, blue) with the spatial resolution of 10 m were adopted to analyse the image characteristics of earthquake-triggered landslides. With the aid of ArcGIS and ENVI tools, the landslide information of the study area was extracted using on-screen visual interpretation on pre- and post-earthquake Sentinel-2A images. In order to ensure the quality of visual interpretation, GF-1 images with spatial resolution of 2 m on 15 January 2017 and GF-2 images with spatial resolution of 1 m on 9 August 2017 were used to verify the results. Consequently, a total number of 842 earthquake-triggered landslides were recognized and positioned. Smaller landslides with total pixels fewer than 20 were not included as they were not clear enough in visual features. It is worthwhile mentioning that most of the interpreted landslides were triggered by the Jiuzhaigou earthquake, and unless otherwise specified, in this article the earthquake-triggered landslide refers to the co-seismic landslide. We assumed that the distribution of the earthquake-triggered landslides was reasonably accurate and complete at a regional scale in order to make the problem tractable. For earthquake-triggered-landslide susceptibility mapping, the landslide inventory dataset was randomly split into two groups, among which 80 % (673 landslides) of the recognized landslides were used for training the integrated weighted index model and the remaining 20 % (169 landslides) for validation.

The occurrence of landslides is a consequence of geological, meteorological, anthropogenic and triggering factors, commonly referred to as landslide controlling factors (Bai et al., 2010). Standard guidelines for choosing the optimal landslide controlling factors are unavailable, but the scale of analysis, the nature of the study area, the data availability, and the quasi-empirical and statistical criterions in literature can be referenced (Romer and Ferentinou, 2016; Zhou et al., 2016). In this study, slope, aspect, elevation, lithology, distance from faults, distance from rivers, land use–land cover (LULC), normalized difference vegetation index (NDVI), and peak ground acceleration (PGA) were selected as the landslide controlling factors, as shown in Fig. 3.

Among all landslide controlling factors, slope, aspect and elevation have been recognized as the most important topographic factors closely related to landslides (Ayalew and Yamagishi, 2005; Chalkias et al., 2016). Slope directly affects the velocity of both surface and subsurface flows (Su et al., 2015). Landslides become more possible once the slope gradient is higher than 15∘ (Lee and Min, 2001). In the study area, the slopes were generally steep, with an average slope angle of about 30∘. Aspect, referring to the direction of slope faces, is related to soil moisture, surface runoff and vegetation, which indirectly affects landslide development (Zhang et al., 2016). The elevation, as the measure of the land surface height, is a key factor determining gravitational potential energy of terrain and is often considered in relevant studies (Conforti et al., 2014; Peng et al., 2014). Topographic factors can be calculated with DEM. The DEM from the SRTM database was used to extract slope (0–78∘), aspect and elevation (1624–4855 m) in the study area.

Lithology is directly related to the slope stability, which plays an important role as a landslide controlling factors (Guo et al., 2015; Saha et al., 2002). A total of 10 geological formation units including Quaternary (Q, Qh), Triassic (T1, T2, T3), Permian (P, P2), Carboniferous (C) and Devonian (D) outcrop in the study area (Wang et al., 2018a). During the Jiuzhaigou earthquake, most landslides in the study area occurred in the Carboniferous formation, which is mainly composed of metamorphic quartzite sandstones, limestone and slate (Fan et al., 2018). In addition, the Permian limestone and Triassic sandstone also exhibited a large number of landslides. In this study, the lithological data were obtained from the geological map at 1:500000 scale and were digitized in ArcGIS for further analysis. The distance of a slope from faults as well as from the river channels is also an important factor in terms of slope stability (Kanungo et al., 2006). In addition, earthquake-triggered landslides are usually found in the vicinity of active faults. Hence, the distances of a slope from a geological tectonic zone were often taken into account in slope stability analysis. Fan et al. (2018) had revealed that this earthquake occurred along a previously unknown blind fault probably belonging to a south branch of the Tazang fault or north part of the Huya fault. However, due to its great uncertainty, this blind fault was not taken into account in the study area. In this study, the faults were digitized from the geological map at a 1:500000 scale, and the river channels were interpreted from remote sensing images. Furthermore, the LULC map is one of controlling factors that pose direct impact on the occurrence of landslides (Song et al., 2012; Mansouri Daneshvar, 2014). In this study, the LULC map was downloaded from the Geographical Information Monitoring Cloud Platform.

Vegetation coverage affects soil water erosion, which indirectly affects the occurrence of landslides. NDVI, as the measure of vegetation coverage, is usually adopted in landslide susceptibility analysis (Siqueira et al., 2015). The NDVI is calculated from these individual measurements as follows: 1NDVI=DNNIR-DNRDNNIR+DNR, where DNNIR stands for the spectral reflectance derived from the measured radiances in the near-infrared regions (NIR), and DNR stands for the spectral reflectance derived from the measured radiances in the visible (red) regions.

In this study, the NDVI map was generated from the Landsat 8 image acquired on 8 April 2017 over the study area.

Earthquakes as an important dynamic factor often trigger slope failures (Xu et al., 2012a). Usually, the impact of earthquakes on landslides is measured and quantified by recording the absolute maximum amplitude of ground acceleration (PGA) (Chalkias et al., 2016). In this study, the PGA map of the study area was downloaded from the USGS website (https://www.usgs.gov, last access: 14 August 2019).

To ensure the consistency and easy process of these data, all factor layers were converted into raster data format (GeoTIFF) with an identical spatial projection (WGS84 datum) and resampled to a resolution of 30 m by ENVI 5.3 and ArcGIS 10.2.

The AHP method, developed by Saaty (Saaty, 1977), is an important multiple-criteria decision-making method (Vaidya and Kumar, 2006), which has been applied for landslide susceptibility assessment for many years (Akgun, 2012; Barredo et al., 2000; Kayastha et al., 2013; Komac, 2006; Pourghasemi et al., 2012; Yalcin, 2008).

In the AHP, a complex non-structural problem is first broken down into several component factors. Then, based on the expert's prior experience and knowledge, a pair-wise comparison matrix can be constructed through comparing the relative importance of each factor (Vargas, 1990). An underlying nine-point recording scale is used to rate the relative importance of factors (Mansouri Daneshvar, 2014). Specifically, when a factor is more important than another, the score varies between 1 and 9. Conversely, the score varies between 1/2 and 1/9. The higher the score, the greater the importance of the factor. With the help of a pair-wise comparison matrix, the contribution of factors can be converted into numerical values. Note that a consistency check of comparison matrix needs to be carried out, and a consistency ratio (CR) of less than 0.1 is generally accepted.

In this study, the relative importance of landslide controlling factors was determined from the prior experience and knowledge of experts. Since the knowledge source varies from person to person, the best judgement always comes from an individual who has good expertise (Ayalew et al., 2004). To find the appropriate correlation between controlling factors, we investigated some related literature (Shahabi and Hashim, 2015; Xu et al., 2012b; Zhang et al., 2016) and consulted with some professional experts. Finally, the pair-wise comparison matrix was determined by means of discussion (Table 2) and a general consensus achieved by experts. Weights of factors were determined in the process of a pair-wise comparison matrix using Python software, as shown in Table 2. The consistency ratio (CR) for this study was 0.017, which showed that the pair-wise comparison matrix satisfied the consistency requirement.

The FR method is one of the most widely used approaches to assess the landslide susceptibility at a regional scale (Guo et al., 2015; Li et al., 2017; Mohammady et al., 2012), which is based on the observed spatial relationship between landslide locations and controlling factors (Lee and Pradhan, 2007; Poudyal et al., 2010). The assumption behind the FR is that future landslides will occur under similar environmental conditions as historical landslides (Guzzetti et al., 1999; Pourghasemi and Rahmati, 2018), and the susceptibility can be evaluated from the relationship between the controlling factors and the landslide occurrence locations (Zhu et al., 2014). The definition of FR is the ratio of the probability of occurrence to non-occurrence for given properties (Lee and Talib, 2005). The spatial relationship between landslides and controlling factors can be investigated by using the FR method. Therefore, the FR values of each controlling factor category were calculated from their relationship with landslide occurrence locations as illustrated in Table 3. The average value of FR is 1 so that a value larger than 1 represents a higher correlation and those less than 1 a lower correlation (Romer and Ferentinou, 2016).

The FR value can be calculated as follows (Ghobadi et al., 2017): 2FRi=NcellSiNcellNi∑NcellSi∑NcellNi, where Ncell(Si) represents number of grid cells recognized as landslides in class i, and Ncell(Ni) represents total number of grid cells belonging to class i in the whole area. ∑Ncell(Si) stands for the total number of grid cells recognized as landslides in the whole area, and ∑Ncell(Ni) represents total number of grid cells in the whole area.

The integrated weighted index is considered to measure the probability of slope failures. By combining the FR and AHP methods, the integrated weighted model can assess the correlation between the controlling factors and also the influence of each landslide controlling factor on landslide occurrence.

The integrated weighted index can be calculated as follows: 3I=∑imWi×FRi, where m stands for number of controlling factors, Wi is the weight of each controlling factor calculated by the AHP method and FRi is the FR value of the controlling factor calculated by the FR method.

In this study, the values of Wi and FRi were used to obtain the integrated weighted index of each grid cell in the study area, and the final landslide susceptibility map was generated by using the Weighted Overlay analysis tool of ArcGIS.

The AHP method was used to assign the weights for each controlling factor. The higher the weight was, the more impacts on landslide occurrence could be expected. As shown in Table 2, the weight of slope was highest, implying the most significant influence of slope on the landslide occurrence, and the weights of aspect and NDVI were the lowest, which indicated that these two factors played the least role in the landslide occurrence.

The FR values of each controlling factor category were calculated by using the Eq. (2) (as shown in Table 3). Table 3 clearly shows the relationship between each controlling factor and the landslide occurrence. In terms of the relationship between landslide occurrence and slope, landslides mostly occurred in the slope ranging from 40 to 60∘. For the elevation, landslides mostly occurred below the elevation of 3400 m, which implied that the probability of landslide occurrence was higher in moderately steep mountainous regions. In terms of the aspect, the FR value was very high for the classes of E, N, SE and NE, and it was lowest for the class of flat. For the lithology, the highest FR value was achieved for the Permian system, which influenced the landslide occurrence. For the factor of distance from faults, the highest FR value belonged to the area higher than 2000 m. The distance from rivers with the highest FR value for frequent landslide occurrence was usually found between 0 and 600 m, and landslides mostly occurred in the region with low vegetation cover with a lower NDVI value. In the case of PGA, the value of 0.26 g had the highest FR value, which indicated the significant influence of the earthquake on the landslide occurrence. In general, our results were basically consistent with the previous study (Fan et al., 2018), which found that most of the landslides mainly occurred in close proximity to rivers and the epicentre, with an elevation of 2600 to 3200 m and a slope of 35 to 55∘.

Finally, the landslide susceptibility map of the study area was generated by using the Weighted Overlay analysis tool of ArcGIS, and the study area was classified into seven categories of landslide susceptibility levels as presented in Fig. 5: very high, high, relatively high, moderate, relatively low, low and very low by using the natural breaks (Jenks) method with ArcGIS, respectively.

According to the landslide susceptibility map, the location close to the epicentre and rivers was classified as the most susceptible area for landslides, and the areas with high and very high landslide susceptibility were mostly located in the middle central mountainous region. The low- and very low-susceptibility areas were far from the epicentre and less affected by the earthquake, mainly distributed in the north and southwest parts of the study area. Table 4 presented the distribution of seven landslide susceptibility levels. As indicated in Table 4, the very low-susceptibility area covered 9.72 % of the whole area, whereas low, relatively low, moderate, relatively highly, highly and very highly susceptible areas covered 25.34 %, 22.92 %, 17.76 %, 13.27 %, 7.97 % and 3.02 % of the whole area, respectively. A total of 61.76 % of the landslides were observed in the high- and very high-susceptibility areas, and only 3.08 % of the landslides were observed in the low- and very low-susceptibility areas. For the landslide density, the values for very low, low, relatively low, moderate, relatively high, high and very high were 0.03, 0.06, 0.11, 0.37, 0.96, 3.03 and 4.79, respectively. The landslide density for the very highly susceptible area was significantly larger than for the other susceptible areas.

For landslide susceptibility mapping, validation of the modelled results is essential. A simple procedure of validation can make a comprehensive and reasonable interpretation of the future landslide hazard (Chung and Fabbri, 2003).

In this study, the operating characteristics curve (ROC) approach (Brenning, 2005; Bui et al., 2016) was adopted to evaluate the performance of the integrated weighted index model, including the degree of model fit and model predictive capability. The ROC was obtained by calculating the area under the curve (AUC) and the AUC value varied from 0.5 to 1.0 (Umar et al., 2014). The AUC value of 1.0 implied a perfect performance of the model, whereas a value close to 0.5 indicated that the model performed not so well. To assess the fitting performance of the integrated weighted index model, five sub-datasets containing 20 %, 40 %, 60 %, 80 % and 100 % of a training dataset (i.e. 673 landslides) were used to obtain the fitting curves. These fitting curves can be generated by comparing resultant maps with the existing training dataset. Figure 6a shows a quantitative measure of the ability of the integrated weighted index model to describe the known distribution of landslides. The AUC values of five sub-datasets were 82.57 %, 84.52 %, 84.99 %, 86.08 % and 85.65 %, which suggested the effective fitting capability of the integrated weighted index model developed in this study.

To investigate the prediction performance of the integrated weighted index model, we also adopted five sub-datasets containing 20 %, 40 %, 60 %, 80 % and 100 % of the validation dataset (i.e. 169 landslides), to estimate the prediction rates. The prediction rates can be calculated by comparing resultant maps with the unknown validation dataset. Note that the validation dataset (i.e. 20 % of the landslide inventory dataset) was not used in the training process. The AUC values of five sub-datasets, as presented in Fig. 6b, were 78.71 %, 81.66 %, 84.27 %, 86.09 % and 87.16 %. With the increase in input data, the performance of the integrated weighted index model was significantly improved, which indicated a reliable predicting capability of the integrated weighted index model adopted in this study.

In addition, the landslide density distribution of each susceptibility level was computed by associating landslides with the classified landslide susceptibility map (as shown in Table 4). There was a clear trend that the increase in the level of landslide susceptibility was highly correlated with the density of landslides. The high- and very high-susceptibility levels had significantly high landslide density values, while the low-susceptibility categories were just the opposite, which also implied the effectiveness of the generated landslide susceptibility map of the study area.

Landslide susceptibility is defined as the likelihood of landslides occurring in an area under local environmental conditions (Fell et al., 2008; Reichenbach et al., 2018). There are numerous methods that have been proposed to evaluate the susceptibility. The main purpose of this study is to assess the spatial probability of landslide occurrences by using an integrated weighted index model in association with the utilization of FR and AHP approaches. The FR is a data-driven statistical approach which can derive the spatial relationship between landslide locations and controlling factors. However, the FR method does not consider the mutual relationships between controlling factors. The AHP method is an important multiple criteria decision-making method, which can overcome this shortcoming. To some extent, the integrated method preserves the advantages of FR and AHP methods and restrains their weak points. Some similar studies have also pointed out this fact (Reichenbach et al., 2018; Youssef et al., 2015; Zhou et al., 2016).

The implementation of the integrated weighted index model revealed that landslide susceptibility levels were basically consistent with the distribution of earthquake-triggered landslides. The high-susceptibility areas were concentrated in the central mountainous region close to the epicentre of the earthquake of the study area, which indicated the significant influence of the Jiuzhaigou earthquake on the landslide occurrence. From the landslide susceptibility map (as shown in Fig. 5 and Table 4), the very high- and high-susceptibility areas covered 10.99 % of the whole area, and most of the Jiuzhaigou National Nature Reserve was classified as the most-landslide-susceptible areas.

However, some limitations still existed in the proposed method. Firstly, the accuracy of the FR method is highly dependent on the quality of the dataset, especially the landslide inventory (Zhou et al., 2016). Nevertheless, the landslide inventory is generally incomplete (Fell et al., 2008), and is affected by many factors, such as the quality and scale of remote sensing images, the tectonic setting complexity of the study area, and the expertise of the interpreter involved (Malamud et al., 2004). In this study, we mainly focused on the interpretation of earthquake-triggered landslides (i.e. co-seismic landslides). We did not accurately identify the landslides before the Jiuzhaigou earthquake due to the limitations of historical images. Since the remote sensing images we used were very close to the time of earthquake, we have reason to believe that most of the landslides we interpreted were triggered by the Jiuzhaigou earthquake. In addition, interpretation results were basically consistent with the previous studies (Fan et al., 2018; Wang et al., 2018a, b), and smaller landslides were also not completely identified. Future work should focus on the preparation of more detailed landslide inventories, and field work should be carried out in time. Secondly, in this study, as the proposed method was applied to medium-scale datasets, the results may not be suitable for specific analysis on a large or detailed scale. At large or detailed scales, a more detailed landslide inventory dataset and controlling factor layers are required. Additionally, the assumption behind much of the landslide susceptibility mapping is that future landslides will occur under similar environmental conditions as historical landslides (Guzzetti et al., 1999; Pourghasemi and Rahmati, 2018). Although most landslide susceptibility mapping studies are based on this assumption, results obtained in the past environmental conditions are not a guarantee for the future (Guzzetti et al., 2005). In this study, we used a weighted index model by integrating the AHP and FR approaches to map the earthquake-triggered-landslide susceptibility and the generated susceptibility map of the study area was made for the present situation. The susceptibility results need to be adapted as soon as environmental conditions or their causal relationships obviously change in the future. However, for earthquake emergency and safe planning, a reliable landslide susceptibility map can provide rapid assessment for reconstruction of tourism facilities, regional disaster management, etc. Therefore, to some extent, the integrated method can serve engineers and decision makers involved in hazard mitigation.