Analysis of the spatial distribution of the landslides triggered by the 1923 Great Kanto Earthquake, Japan

Abstract

The Great Kanto Earthquake that occurred in the southern part of Kanto district, Japan, on September 1, 1923, was reported to have triggered numerous landslides (over 89,080 slope failures over an area of 86.32 km²). This study investigated the relationship between the landslide occurrence caused by this earthquake and geomorphology, geology, soil, seismic ground motion, and coseismic deformation. We found that a higher landslide density was mainly related to a larger absolute curvature and a higher slope angle, as well as to several geological units (Neogene plutonic rock, accretionary prism, and metamorphic rocks). Moreover, we performed decision tree analyses, which showed that slope angle, geology, and coseismic deformation were correlated to landslide density in that order. However, no clear correlation was found between landslide density and seismic ground motion. These results suggest that landslide density was greater in areas of large slope angle or fragile geology in the area with strong shaking enough to trigger landslides.

1. Introduction

On September 1, 1923, a magnitude (M) 7.9 earthquake¹⁾ called the Great Kanto Earthquake struck the southern Kanto district of Japan (Fig. 1). Many houses in urban areas were destroyed by the strong shaking of this earthquake and the resulting fires, and as many as 105,000 people were dead or missing.²⁾ The earthquake also caused landslides in mountainous areas, especially in Kanagawa Prefecture,³⁾ where detailed slope failure surveys were conducted. The earthquake triggered 89,080 slope failures over an area of 86.32 km² in the prefecture, which is equivalent to 7% of the forested area of the prefecture, making this incident one of the largest slope failure disasters in Japan.⁴⁾

Figure 1.

Location, topography, and epicenter of the Great Kanto Earthquake.

Many studies on coseismic landslides have indicated that the spatial distribution of coseismic landslides is related to seismic motion, fault distance, geology, topography, soil, hydrology, land cover, and so on.^5–8) Seismic motion is a triggering factor, and peak ground acceleration (PGA) and peak ground velocity (PGV) have been commonly used for coseismic landslide analysis as indicators of seismic ground motion. Further, the effect of coseismic deformation on landslides has been noted.^9–13) Kamiyama et al.¹²⁾ argued that although earthquake damage results from the dynamic effects of oscillating strains during earthquakes, static strains may be useful for detecting the structural damage potential of an earthquake as static strains are proportional to the absolute peaks of oscillating strains.¹⁴⁾ Kamiyama et al.¹¹⁾ concluded that coseismic deformation is more closely related to landslides than seismic intensity from the 2016 Kumamoto earthquake. In addition, Sakai et al.¹³⁾ claimed that the interrelated influences of seismic ground motion and topography may become clearer by utilizing high-resolution ground surface displacement using synthetic aperture radar (SAR) satellite data.

Some studies have examined the characteristics of the coseismic landslides triggered by the 1923 Kanto Earthquake by focusing on topography, geology, and hydrology.^15,16) The Public Works Research Institute, Ministry of Construction,¹⁶⁾ showed that the landslide area ratio is over 10% in the drainage with an average slope of 30° and over 20% in that with an average slope of more than 45°. Furthermore, between the Tanzawa Mountains, where Neogene rocks are mainly distributed, and Hakone volcano, where volcanic rocks are the predominant rock type, the coseismic landslide area ratio was found to be larger in the Tanzawa Mountains than in Hakone volcano, indicating that geology is more influential than topography when comparing these two areas. Prior rainfall was also considered. However, as there was no rainfall observation point in the mountainous areas, it was estimated that several tens of millimeters of rain had fallen between the day before and that of the earthquake using observation records from the plains.

Thus, geomorphology, geology, and rainfall distribution have been considered proxies that influence coseismic landslides. However, others such as soil, vegetation, seismic ground motion, and their interrelationships are insufficiently considered. Therefore, in the present study, we discuss the characteristics of the areal distribution of landslides and examine the relationship between landslides and proxies, including geomorphology, geology, soil, seismic ground motion, and coseismic deformation, in the Great Kanto Earthquake. In addition, we estimate the order of influence of the proxies on coseismic landslides using data mining with the decision tree technique. Vegetation was excluded in this study because the oldest available vegetation map was created in 1975,¹⁷⁾ and the effects of changes over time cannot be ignored. Similarly, a hydrological proxy was excluded because of lack of detailed data.

2. Study area

The target study areas were the Tanzawa Mountains, Hakone volcano, and the surrounding areas of western Kanagawa Prefecture in eastern Japan (Fig. 1). Many landslides were triggered in the areas by the 1923 Kanto Earthquake, and these landslides were mapped by Kanagawa Prefecture.^18–24)

The strata of the Tanzawa Group are distributed over a wide area from the northern to eastern Tanzawa Mountains. According to the Kanagawa Prefectural Museum of Natural History,²⁵⁾ the Tanzawa Group is classified as an accretionary complex formed by the thick sedimentation and solidification of lava and volcanic ejecta from submarine volcanoes active on the seafloor of the Pacific Ocean in the Neogene period. Plutonic, metamorphic, and sedimentary rocks are distributed in the western and southern areas of the Tanzawa Mountains. Plutonic rocks are intrusive rocks that intrude from the underground and solidify into dome shapes. Metamorphic rocks were formed by compression from plate motion and magma heat during magma intrusion into the Tanzawa Group. Sedimentary rocks were formed from trough-filling sediments deposited between the Honshu Arc and the Izu Peninsula prior to their collision.

Hakone volcano is located in the southern part of the study area. Hakone volcano began erupting approximately 400,000 years ago, and it is composed of a central crater–hill complex surrounded by new and old outer volcanoes. The surface geology consists of quaternary volcanic rocks.²⁶⁾

3. Data and methodology

3.1. Data unit.

For data analysis, we used approximately 250-m quarter grid square (divided grid square) data (7.5 arcsec in latitude and 11.25 arcsec in longitude), referred to as the “250-m grid”, which is the basic unit used in many Japanese Government Statistics.²⁷⁾ QGIS (QGIS Development Team) and ArcGIS (ESRI) were used for subsequent analyses.

3.2. Datasets.

3.2.1. Landslide data.

We mainly used 1:50,000 natural disaster history maps.^18–24) These maps show the locations of the landslides during the Kanto Earthquake as revealed by field surveys. We scanned and digitized these maps and created landslide geographic information system (GIS) data (Fig. 2(a)). In some areas, GIS data had already been created for Kanagawa Prefecture, and we edited and compiled the data.

Figure 2.

Distribution of—landslides (a); geology (b); geomorphology: slope gradient (c) and absolute curvature (d); soil type (e); and seismic ground motion: PGA (f), PGV (g), and seismic intensity (h).

We converted landslide inventory data to the 250-m grid data using the method described by Iwahashi et al.²⁸⁾ Briefly, random points were generated in a landslide. The number of random points in the polygon is calculated by dividing the polygon area by 2,500 m² (rounded down to the nearest whole number). We calculated the landslide density (pt/km²) for each 250-m grid based on the number of data points in the grid (Fig. 3).

Figure 3.

Flow of creating 250-m grid data from landslide polygon data (modified from the report of Iwahashi et al.).²⁵⁾

3.2.2. Geomorphological data.

We used a 250-m grid slope angle and absolute curvature data^29,30) as indicators of topography (Fig. 2(b) and (c)). These data were obtained by interpolating a 10-m digital elevation model (DEM) of the Fundamental Geospatial Data published by the Geospatial Information Authority of Japan. The 10-m DEM was created by digitizing the contour lines on 1:25,000 topographic maps. Therefore, it should be noted that the elevations were not from the 1923 earthquake but from the time of the creation of the contour lines, that is, the 1960s and 1970s. However, changes in topography were considered negligible because of the lack of large-scale cuttings. It is unlikely that erosion would occur during the few decades between 1923 and the 1960s/1970s to the extent that even a 250-m grid resolution would be clear. However, we excluded four lake areas where the reservoirs were constructed between 1923 and the 1960s/1970s (Fig. 1).

Slope data were obtained by calculating the local slope gradient in 3 × 3 cells using the 10-m DEM and by averaging them within a 250-m grid. Absolute curvature data were obtained by calculating the composite curvature of the vertical and horizontal curvatures in 3 × 3 cells using a 10-m DEM and by averaging their absolute values within a 250-m grid.

3.2.3. Geological data.

We used a seamless digital geological map of Japan V2.³¹⁾ Figure 2(d) shows the geological units used in this study. Because the geological data are polygon data, they were converted to 250-m grid data.

3.2.4. Soil data.

We used soil map data from the Japanese Soil Inventory.³²⁾ Figure 2(e) shows the soil category used in this study. As these data are also polygon data, they were converted to 250-m grid data.

3.2.5. Seismic ground motion data.

Seismic observations have been collected before 1923 in Japan. However, many records did not qualify for analysis because the seismograph needles had swung out of alignment or the records from this earthquake were unclear.³³⁾ Therefore, we used the estimated PGA and PGV data from USGS ShakeMap³⁴⁾ (Fig. 2(f) and (g)). In addition, we used estimated seismic intensity data from Moroi and Takemura³⁵⁾ (Fig. 2(h)).

3.2.6. Coseismic deformation data.

The Military Land Survey has been conducting nationwide triangulation surveys in Japan since 1883 and immediately after the earthquake in Kanto district. The distribution of the triangulation points used in this study is shown in Fig. 4(a). The Military Land Survey calculated coseismic deformation using the first-order triangulation results before and after the earthquake.³⁶⁾ However, the calculation method and results were debatable, so the results have been re-examined by other studies.^37–39)

Figure 4.

(a) Targeted triangulation points in 1923, (b) horizontal displacement vector at first- and second-order triangulation points, as reported by Nakane,³⁹⁾ (c) vertical displacement, as reported by Military Land Survey,³⁶⁾ (d) first- and second-order triangulation net, (e) areal shear strain, (f) maximum shear strain, and (g) landslide distribution.

In this study, horizontal and vertical displacements, area, and maximum shear strain were obtained or calculated using triangulation data. Horizontal displacement was acquired following Nakane,³⁹⁾ who recalculated the results of the first and second triangulation surveys (Fig. 4(b)). Vertical displacement was acquired from “the Map showing the Depression and Upheaval of the Ground Produced at Kwanto Districts after the Great Earthquake of Sept. 1st. 1923”,³⁶⁾ which shows the results of indirect leveling at first-, second-, and third-order triangulations and leveling (Fig. 4(c)). For calculating the strain, Delaunay triangulations⁴⁰⁾ were generated (Fig. 4(d)). Subsequently, the strain of each triangle was calculated using horizontal deformation, and the gravity center of each triangle was considered to correspond to that strain. Figure 4(e) and (f) show the area and maximum shear strain, respectively.

3.3. Decision tree technique.

To assess the extent of the contribution of each factor to landslides, we performed decision tree analyses, which can elucidate the importance of explanatory variables and can visualize the rules of conditional branching.⁴¹⁾ Because various analyses have been proposed, each with different characteristics, we used the three algorithms shown in Sections 3.3.1–3.3.3. We used the R software ver. 4.1.2 (R Foundation for Statistical Computing, Vienna, Austria) for all analyses.

We used the following explanatory variables: slope angle, absolute curvature, PGV, PGA, horizontal and vertical displacements, geological era (Quaternary, Neogene, Paleogene, and Late Cretaceous), geological classification (sedimentary rock, volcanic rock, plutonic rock, metamorphic rock, accretionary prism, and others), soil, area strain, and maximum shear strain. Three classes of landslide density (pt/km²) (high: >50, low: >0 and <50, and none: 0) were used as explained variables.

3.3.1. Classification and regression tree (CART).

The CART algorithm was characterized using an evaluation function called the Gini index to set the threshold value for branching. The Gini index L(t) was calculated as follows:

$$L(t)=1-\sum _{i=1}^{n}p(i|t{)}^2,$$ [1]

where p(i|t) is the probability that a sample branching to node t belongs to class i.

Divisions were made such that the reduction in the Gini index ΔL(t) was maximized:

$$\Delta L(t)=L(t)-(p_{L}L(t_L)+p_{R}L(t_R)),$$ [2]

where p_L and p_R are probabilities. Furthermore, k-fold cross-validation was used for this analysis. k was determined using the following Sturges’ formula⁴²⁾:

$$k=1+{\log }_{10}(n/2),$$ [3]

where n is the data amount. In this study, n was 14,586 and k was set to 15. We used the rpart package of the R software.

3.3.2. C5.0.

The C5.0 algorithm^43,44) was characterized using entropy for measuring purity. Entropy was calculated as follows:

$$\mathit{\text{Entropy}}(S)=-\sum _{j=1}^k{p}_j{\log }_2(p_j),$$ [4]

where p_j is the probability of a sample belonging to class j.

The divisions were made in a condition that the information gain IG was maximized.

$$\mathit{I}\mathit{G}=\mathit{\text{Entropy}}(S_1)-\sum _{i=1}^n\frac{|T_i|}{T}\times \mathit{\text{Entropy}}(S_i).$$ [5]

The first half of Eq. [5] shows the entropy before the branching, and the second half shows the total entropy after the branching. We used the C50 package of the R software. Minimum cases of parent branches were set to 5% of the data amount (723) to avoid overfitting.

3.3.3. Conditional inference tree (CIT).

The CIT algorithm⁴⁵⁾ was characterized using a combined framework of recursive binary partitioning and permutation tests. At first, CIT use involved selecting a covariance most strongly associated with the response after the global null hypothesis was rejected of independence between covariates and response. Subsequently, using the permutation test, the division was made at the covariate by dividing the data with the smallest p-value. We used the partykit package of R software. The maximum depth of the tree was set to two to avoid overfitting.

4. Results

4.1. Characteristics of the distribution of coseismic landslides.

4.1.1. Geomorphology.

The relationship between landslide density and geomorphology is shown in Fig. 5. The absolute curvature (Fig. 5(a)) of the grid where landslides occurred was in the range of almost 5–19 [m⁻¹], and the highest number of grids where landslides occurred was 10–14 [m⁻¹]. For landslide density, the larger the absolute curvature was, the larger was the landslide density, except in a few cases (n = 12) where the curvature was greater than 20 [m⁻¹]. The correlation coefficient (R) between the absolute curvature and landslide density was 0.35.

Figure 5.

Relationship between landslide density and geomorphology: absolute curvature (a) and slope angle (b).

By contrast, the slope angle (Fig. 5(b)) of the grid where landslides occurred was in the range of approximately 10°–49°, and the highest number of grids where landslides occurred was 30°–39°. The steeper the slope was, the larger was the landslide density, except in a few cases (n = 2) where the slope angle was greater than 50°. The R value between the slope angle and landslide density was 0.48.

4.1.2. Geology.

The relationship between landslide density and the geological units is shown in Fig. 6. The number of grids with landslides was higher for the Neogene accretionary prism, Quaternary volcanic rocks, and Quaternary sedimentary rocks. In addition, significant differences were observed in the landslide densities among geological eras, with Neogene having the highest landslide density, followed by Quaternary and Paleogene. In particular, landslide density was highest in the Neogene plutonic rock, accretionary prism, and metamorphic rocks.

Figure 6.

Relationship between landslide density and geology.

4.1.3. Soil.

As shown in Figs. 2(e) and 7, Regosolic and Allophanic Andosol was primarily distributed in the study area. Landslide density was highest for Lithosols, Regosolic Andosol, Allophanic Andosol, and Brown Forest soils in that order.

Figure 7.

Relationship between landslide density and soil type.

4.1.4. Seismic ground motion.

Figures 8 show the relationship between landslide density and seismic ground motion. PGA was estimated to range from 350 to 700 gal in the study area. The peak of landslide density was found in the 400–450 gal range, and the larger or smaller the PGA was, the smaller the landslide densities tended to be above that range. By contrast, PGV was estimated to range from 20 to 100 cm/s. There were two peaks of landslide density: 40–50 and 60–70 cm/s. The correlation coefficients between landslide density and PGA and PGV were −0.03 and −0.17, respectively. For seismic intensity, the peak of landslide density was found at 6 lower.

Figure 8.

Relationship between landslide density and seismic ground motion: PGA (a), PGV (b), and seismic intensity (c).

4.1.5. Coseismic deformation.

Figure 9 shows the relationship between landslide density and coseismic deformation. In the grids where landslides occurred, horizontal displacement was most frequent at 1.5–2 m (Fig. 9(a)). Landslide density was also most frequent for horizontal displacement at 1.5–2 m, followed by 2–2.5 m. Overall, the larger the horizontal displacement was, the larger was the landslide density. By contrast, the number of grids where landslides occurred was predominant in the range of −1–0 m for the vertical displacement (Fig. 9(b)). Finally, the landslide density was higher in settled areas than in uplifted areas. In addition, the larger the settlement was, the larger the landslide density tended to be. The R values between landslide density and horizontal and vertical deformations were 0.08 and −0.23, respectively.

Figure 9.

Relationship between landslide density and crustal deformation: horizontal displacement (a) and vertical displacement (b).

Figures 10(a) and (b) show the relationship between landslide density and crustal strain. The number of grids where landslides occurred was predominant in the area strain frequency range of −1.0–0.5 × 10⁻⁴. For landslide density, two peaks of greater density were found in the range of −0.5–0 × 10⁻⁴ and −2.0–−1.5 × 10⁻⁴. Overall, the tensile region had a slight tendency to exhibit a higher density. For the maximum shear strain (Fig. 10(b)), the strain of the grid where landslides occurred was approximately 0.5–1.5 × 10⁻⁴ and the highest number of grids where landslides occurred was for the strain of 0.5–1.0 × 10⁻⁴. The landslide density peaked at the maximum shear strain in the range of 1.0–1.5 × 10⁻⁴ and above 3.5 × 10⁻⁴. The R values between landslide density and area and maximum shear strain were −0.04 and −0.03, respectively.

Figure 10.

Relationship between landslide density and crustal strain: area strain (a) and maximum shear strain (b).

4.2. Decision tree.

4.2.1. CART.

According to the method described in Section 3.3, the CART analysis produced four groups and slope angle, maximum shear strain, and geological era emerged as factors in this order of importance (Fig. 11). At the first split, the percentage of grids with the landslide density class “none” was highest when the slope angle was smaller than 26.5° and that with the “high” landslide density was highest when the slope angle was larger than 26.5°. At the second split, the percentage of grids with “none” landslide density was highest when the maximum shear strain was smaller than 8.61 × 10⁻⁵ and that with the “high” landslide density was highest when the maximum shear strain was smaller than 8.61 × 10⁻⁵. At the final split, the percentage of grids with “none” landslide density was highest when the slope angle was smaller than 32.5° and that with the “high” landslide density was highest when the slope angle was larger than 32.5°. In short, the higher the slope angle was, the larger was the maximum shear strain associated with a higher density of landslides.

Figure 11.

Results of the CART analysis.

4.2.2. C5.0.

The C5.0 analysis is shown in Fig. 12. The conditions to classify the landslide class “high” (node 8) were a larger slope angle at the first split (>26°), a larger horizontal displacement at the second split (>1.514 m), the geology at the third split (accretionary prism, metamorphic rock, and plutonic rock), and the geological age at the fourth split (Late Cretaceous and Neogene). Subsequently, the landslide class “low” (node 6) was related to the geology at the third split (sedimentary and volcanic rocks). Finally, other terminal nodes (2, 4, and 9) were classified as the landslide class “none”.

Figure 12.

Results of the C5.0 analysis. Se: Sedimentary rock; Vo: Volcanic rock; Ac: Accretionary prism; Me: Metamorphic rock; Pl: Plutonic rock; LaC: Late Cretaceous; Ne: Neogene; Pa: Paleogene; and Qu: Quaternary.

4.2.3. CIT.

The CIT analysis is shown in Fig. 13. The conditions to classify the landslide class “high” were a larger slope angle (>26°) and geological age of Neogene or Quaternary. Although other terminal nodes were classified as the landslide class “none”, the percentage of grids where the landslide density class was “none” was higher in a case where the slope angle was <18° (nodes 3 and 4).

Figure 13.

Results of the CIT analysis. LaC: Late Cretaceous; Pa: Paleogene; Ne: Neogene; and Qu: Quaternary.

5. Discussion

5.1. Relationship between coseismic landslides and each factor.

We summarized the contributing proxies to coseismic landslides in Table 1 based on the relationships between each proxy and landslide density and the decision tree analyses.

Table 1.

Relationship between proxies and landslide density. P: positive correlation, N: negative correlation, H: high landslide density, M: moderate landslide density, +: positive contribution. The values in column “R” indicate the correlation coefficient between each proxy and the landslide density

Proxy	Subclass	1 vs. 1	R	CART	C5.0	CIT
Slope angle		P	0.48	+	+	+
Absolute curvature		P	0.35
Geological age	Quaternary	M				+
	Neogene	H			+	+
	Paleogene
	Late Cretaceous				+
Geology	Sedimentary
	Volcanic rock	M
	Plutonic rock	H			+
	Accretionary prism	H			+
	Metamorphic rock	H			+
Soil	Regosolic Andosol	H
	Wet Andosol
	Fulvic Andosol
	Non-allophanic Andosol
	Allophanic Andosol	M
	Gley Lowland soils
	Gray Lowland soils
	Brown Lowland soils
	Red-Yellow soils
	Brown Forest soils	M
	Sandy Regosols
	Lithosols	H
	City/Water/Others
Horizontal displacement			0.08		+
Vertical displacement		N	−0.23
Maximum shear strain			−0.03	+
Area strain			−0.04
Seismic ground motion	PGA		−0.03
	PGV		−0.17
	Seismic intensity

First, in terms of geomorphology, landslide density increases as the absolute slope curvature or slope angle increases (R = 0.35 for the absolute slope curvature and 0.48 for the slope angle). The tendency of landslide density to increase as the slope angle increases has also been observed in previous studies.^46–48) Because this is also consistent with all of the decision tree analysis results and the slope angle was selected as the primary parameter, it was inferred that the slope angle was the most significant contributor to the occurrence of landslides in the Kanto Earthquake. Conversely, although the absolute curvature was the second largest correlation, it was not selected in the decision tree analyses. This is believed to be because the slope angle and absolute slope curvature are correlated (R = 0.75) and only using a slope angle that correlates more with landslide density was sufficient to branch in the analyses.

Second, geological proxies seem to be correlated with landslide density. Regarding geological age, landslide density was particularly high in the Neogene plutonic and metamorphic rocks and accretionary prism of the Tanzawa Mountains. The Public Works Research Institute, Ministry of Construction,¹⁶⁾ has pointed out that the major reason for the higher landslide density in the Tanzawa Mountains than in Hakone volcano was the substantial weathering caused by the many faults and cracks in the Neogene Tanzawa Group (accretionary prism) or quartz diorite (plutonic rocks) as a result of the uplifting of the Tanzawa Mountains in Neogene. These are consistent with the characteristics of the distribution of coseismic landslides in geomorphology (Fig. 5) and geology (Fig. 6). The same explanation can be provided for the result that the landslide density in the Neogene accretionary prism was greater than that in the Late Cretaceous and Paleogene accretionary prism to the north. These results are also consistent with the results of the CART and CIT analyses, in which geological era was selected. In other words, the aforementioned geological conditions for dense landslides may be unique to the study area.

Regarding soil, landslide density was higher in the order Lithosols, Regosolic Andosol, Allophanic Andosol, and Brown Forest soils, but soil was not selected as a proxy in the decision tree analyses. The Lithosol area with the highest landslide density is characterized by shallow soil layers distributed on the slopes of heavily eroded mountainous or hilly terrain.³²⁾ Thus, Lithosol is primarily in the plutonic rock and accretionary prism area (Fig. 2). Therefore, it can be estimated that erosion-prone geological condition cause a higher landslide density. Conversely, Regosolic and Allophanic Andosols cover most of the study area, including the lowland areas with few landslides. Hence, soil was unselected in the decision tree analyses.

In this study, neither PGA, PGV, nor seismic intensity was correlated with landslide density (R = −0.03 for PGA and −0.17 for PGV) and was not selected in the decision tree analyses. Several studies have reported that the correlation between PGA and landslides is not clear.^49–52) Wartman et al.⁴⁹⁾ mentioned that PGA does not represent other potentially important characteristics such as frequency content, duration, or multiple phases of shaking recorded at some locations. Further, Xu and Xu⁵⁰⁾ highlighted that “the entire area experienced ground shaking above the intensity required to trigger slope failure and that factors other than ground shaking (such as geological unit, slope gradient, and active fault) controlled the distribution of the landslides in the area near the seismogenic fault”. In our study area, the PGA ranged from approximately 350 to 700 gal. According to Xu and Xu,⁵⁰⁾ all this PGA range may be sufficient to trigger landslides in this study area.

In terms of horizontal and vertical displacements, they were not correlated with landslide density (R = 0.08 and −0.23, respectively) and horizontal displacement was selected in the C5.0 analysis. Focusing on the horizontal displacement (Figs. 4(b) and 9(a)), most of the study area was displaced by 1.5–2 m, and because the area covers Tanzawa Mountains and the northern part of Hakone volcano, an area of high landslide density, it is likely that frequency and landslide density reached their maximum at 1.5–2 m displacement and the displacement threshold determined by the C5.0 was 1.514 m. By contrast, the trend of vertical displacement was reversed, with subsidence in the northern part of the study area and uplift in the southern part. As the Tanzawa Mountains with higher landslide densities tend to settle, landslide density becomes higher in larger subsidence areas. It is believed that subsidence itself does not cause landslides but it is due to the overlap of the subsidence area with the fragile geology.

Regarding area strain, it was not correlated with landslide density (R = −0.04) and was not selected in the decision tree analyses. Then, focusing on the relationship with topography, the compressive area is at a relatively low elevation in the northeastern part of Hakone volcano. The tensile area is almost the entire study area, and the degree of strain is locally large in the western part of Hakone volcano. This may explain why the landslide density was lower in the compressive area and higher in the tensile area. In addition, the density distribution in the tensile area is likely to be more variable. In contrast, dense landslides were observed in areas with a larger maximum shear strain according to the CART analysis. This result is consistent with the case of the 2016 Kumamoto earthquake.¹¹⁾ The strain threshold determined by the CART analysis was 8.61 × 10⁻⁵. Kamiyama et al.¹¹⁾ estimated that approximately 90% of the landslides occurred in areas with strains greater than 10^−4.5 (approximately 3 × 10⁻⁵) and approximately 94% of the landslides occurred in areas with strains greater than 10^−4.3 (approximately 5 × 10⁻⁵) in the 2016 Kumamoto earthquake. In our study area, the grid where landslides occurred with the maximum shear strain greater than 8.61 × 10⁻⁵ was approximately 93%. Conversely, there was no clear correlation between the maximum shear strain and landslide density (R = −0.03). This result may suggest that landslides may occur in the region of maximum shear strain above a certain level, and the threshold of the maximum shear strain at which landslides occur is generally consistent with the value estimated by Kamiyama et al.¹¹⁾

5.2. Influence of aftershocks on landslides.

Several aftershocks occurred after the main shock of the Kanto Earthquake.⁵³⁾ The locations of the major aftershocks (M ≥ 6) that occurred at an epicenter of 100 km are shown in Fig. 14. Moroto⁵⁴⁾ inspected the affected area in October 1923 and observed numerous landslides. Because the maximum magnitude of the aftershocks was 7.3 and most aftershocks occurred in September 1923, some of the landslides identified by Moroto were likely caused by aftershocks. Here, we focused on the relationship between earthquake magnitude (M) and total landslide area (A_T) [km²] by Malamud et al.⁵⁵⁾:

$$\begin{array}{rl}& \mathit{\text{mLS}}=1.29M-5.65,\\ & A_T=3.73\times {10}^{-3}\times {10}^{\mathit{\text{mLS}}}.\end{array}$$

Figure 14.

Epicenters of the main shock and aftershocks.

The estimated A_T values for the mainshock and aftershocks are shown in Fig. 15. The A_T of the mainshock was approximately 107 km², and that of aftershocks ranged approximately 0.4–18 km². Adding all A_T in aftershocks gives 63.2 km². However, as aftershocks occurred outside the study area, except one aftershock, the landslide area of aftershocks in the study area was assumed to be significantly <63.2 km². Therefore, the impact of the aftershocks may be limited. The largest aftershock, M 7.3, occurred on January 15, 1924, its epicenter was inside the study area, and its A_T was approximately 18 km². Because we could not find detailed information regarding the landslide investigation by Kanagawa Prefecture, concluding whether the landslides triggered by the aftershock were mapped in Kanagawa Prefecture is complicated. However, if they were, the impact was possibly approximately a dozen percent on an area basis. It is hoped that more detailed documents of landslide investigations will be found in the future.

Figure 15.

Estimated A_T of the mainshock and aftershocks.

5.3. Classification results of the decision tree analyses and the proxies contributing to coseismic landslides.

As discussed in Section 5.1, the slope angle was almost certainly the most significant contributing proxy, but the second proxies selected differed for each decision tree. We created landslide distribution maps classified according to the results of the decision trees and a proxy related to landslides (Fig. 16).

Figure 16.

Landslide distribution maps and related proxies: Actual map (a); map based on the CART (b), C5.0 (c), and CIT (d); slope angle (e); geology (f); horizontal displacement (g); and maximum shear strain (h).

Figure 16(b), (c), and (d) indicate that the landslide density showed a generally similar trend for all decision trees. Focusing on the second proxies selected in the decision tree analyses, there was a wide overlap in the study area between areas with a maximum shear strain of >8.61 × 10⁻⁵, areas with a maximum displacement of >1.514 m, and areas with a geological age of Neogene or Quaternary, which may explain the differences in the proxies selected in the decision tree analyses. Xu and Xu⁵⁰⁾ argued that factors other than seismic ground motion contribute to coseismic landslides if the seismic motion is above a certain level. Similarly, it can be inferred that seismic ground motion should affect landslides. Therefore, they suggest that seismic ground motion proxies, which were not used in this study, or coseismic deformation may be a critical triggering proxy, and the geological proxy is the second predisposition. As we could not discuss this subject further owing to limited information on seismic ground motion, the relationship between these indicators and landslides is not well known, making it a subject for future studies.

Hence, it is considered that coseismic deformation or seismic ground motion above a certain scale that can trigger landslides was distributed over a wide area in the study area during the Kanto Earthquake. Thus, under these trigger conditions, landslides were most likely to occur in the Tanzawa Mountains, which have a large slope angle and fragile geology, followed by Hakone volcano, where the landslide density was greater.

6. Conclusions

This study examined the characteristics of the landslide distribution triggered by the 1923 Great Kanto Earthquake in terms of geomorphology, geology, soil, seismic ground motion, and coseismic deformation using decision tree analyses. The following factors were found to be related to a higher landslide density: a larger absolute curvature, a higher slope angle, and a geological unit of Neogene plutonic rock, accretionary prism, and metamorphic rocks.

In addition, the results of the decision tree analyses indicated that a higher landslide density was influenced by a higher slope angle, geology, and coseismic deformation. However, no correlation was found between landslide density and seismic ground motion (neither PGA, PGV, nor seismic intensity), and soil.

These results may suggest that the coseismic deformation or seismic ground motion above a certain scale that can trigger landslides was distributed all over the study area during the Kanto Earthquake. Thus, under these trigger conditions, landslides were most likely to occur in the Tanzawa Mountains, which have a large slope angle and fragile geology, followed by Hakone volcano, where the landslide density was greater. For assessing damage from similar types of earthquakes that may occur in the Kanto region in the future, further studies are needed.

Non-standard abbreviation list

CART

classification and regression tree

CIT

conditional inference tree

DEM

digital elevation model

GIS

geographic information system

M

magnitude

PGA

peak ground acceleration

PGV

peak ground velocity

SAR

synthetic aperture radar

USGS

United States Geological Survey