1. Statistical Approach to Model Spatial and Temporal Variability of
The Next Generation of Research on Earthquake-induced Landslides
Statistical Approach to Model Spatial and Temporal Variability of
Earthquake-Induced Landslides
Chyi-Tyi Lee
Institute of Applied Geology, National Central University, Taiwan
International Conference in Commemoration of 10th Anniversary
of the Chi-Chi Earthquake, September 21~26, 2009

2. INTRODUCTION

3. INTRODUCTION
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◆ The study of earthquake-induced landslide susceptibility on a regional scale commonly requires the employment of an analytical slope-stability method and the infinite-slope model (Wilson and Keefer, 1985; Jibson and Keefer, 1993; Harp and Wilson, 1995; Jibson et al., 1998, 2000; Liao, 2004). This method requires calculation to determine the limit-equilibrium of the slope stability given the strength parameters, failure depth, and groundwater conditions for every calculation point in the study area. This requirement causes immense problems in terms of data acquisition and control of spatial variability of the variables (Hutchinson, 1995; Guzzetti et al., 1999).

4. INTRODUCTION
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◆ In traditional landslide susceptibility analysis, it is most common to use a statistical approach where landslide inventories and causative factors are utilized to build a susceptibility model for the prediction of future landslides. Many different methods and techniques for assessing landslide hazards have been proposed and tested. These have already been systematically compared and their advantages and limitations outlined (Carrara, 1983; Varnes, 1984; Carrara et al., 1995; Hutchinson, 1995; Chung and Fabbri, 1999; Guzzetti et al., 1999; Chung, 2006; van Western et al., 2006). Most of these approaches require multi-temporal landslide inventories so that the susceptibility model can predict landslide occurrence over a given time period (Guzzetti et al., 1999).

5. INTRODUCTION
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◆ In the study of earthquake-induced landslides, the landslide inventory is naturally event-based; it is not possible to use a multi-temporal landslide inventory. Therefore, the temporal significance of a susceptibility model should incorporate the use of a triggering factor, like that used in the deterministic method.
◆ Lee et al. (2008) introduced a new approach using statistical method in building an earthquake-induced landslide prediction model. In this study, I demonstrate the new method using an example form the Yinlin quadrangle with two earthquake events, and the results are then cross-validated.

6. Geology of Taiwan
Taiwan orogeny started at Late Miocene and is presently active.
The Central Range consists of metamorphic complex and a Paleogene slate belt.
Bordering the Central Range is the Western Foothills, consisting of Neogene sedimentary formations, and the Eastern Coastal Range, which is also made of Neogene sedimentary strata.
The Longitudinal Valley located between the Central Range and the Eastern Coastal Range is the suture zone between two plates.

7. Terrain Division & The Study Area
For the purpose of producing a set of landslide susceptibility quadrangle maps for Taiwan. We classified whole Taiwan into 13 geomorphological and geological homogeneous zones for further study.
Study Area

8. Topography of the Study Area
The study area is divided into two homogeneous region for training the susceptibility model.
Hilly Terrain
Mountainous Terrain

9. Geology of the Study Area

10. METHODOLOGY
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◆ Since multi-temporal landslide inventories are not available for earthquake-induced landslides, I consider using an event-based landslide inventory and an event-based landslide susceptibility analysis (EB-LSA) which was proposed by Lee et al., (2008).
◆ In EB-LSA, an event-based landslide inventory must be constructed firstly. In parallel with this, the causative factors of the landslides are processed and the triggering factors determined. These factors are then statistically tested, and the effective factors selected for susceptibility analysis. Each selected factor is rated, and their weighting analyzed.

11. METHODOLOGY
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◆ Discriminant analysis allows us to determine the maximum difference for each factor between the landslide group and the non-landslide group, as well as the apparent weights of the factors.
◆ A linear weighted summation of all factors is used to calculate the landslide susceptibility index (LSI) for each grid point. The LSIs are used to establish a landslide ratio to LSI curve and determine the spatial probability of landslide at each grid point. The spatial probability of landslides is then used for landslide susceptibility mapping. For a more detailed description of EB-LSA, please refer to Lee et al. (2008).

12. Data Sources
Multi-spectral (XS) and panchromatic (PAN) SPOT2 images from Satellite Receiving Station of Center for Space and Remote Sensing Research, National Central University.
Digital terrain model (DEM) of 40x40m resolution from Aerial Survey Office, Forestry Bureau, Council of Agriculture, Taiwan.
Geological map of 1 to 50,000 scaled from Central Geological Survey, Taiwan.
Strong-motion data from the Seismological Center, Central Weather Bureau, Taiwan.
Road map digitized from 1 to 5,000 scaled topographic maps.

13. Data Processing
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Both XS and PAN SPOT images were used. They were fused into a higher resolution (6.25m x 6.25m) false-color image for landslide interpretation.
XS images taken prior to Jueili and Chi-Chi earthquakes were used for calculation of normalized differential vegetation index (NDVI).
Digital terrain model (DEM) of 40x40m resolution was corrected for erroneous data and filtered for noises, and then the DEMs were interpolated to grid cells of 20x20m resolution using cubic spline interpolation.
Slope gradient, slope aspect, slope height, etc. which are derived from DEM are also in 20x20m grid data format.
Geological map, NDVI, etc. are transferred into 20x20m grid data for further use.

14. Data Processing
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Strong-motion seismograms in and around the study area were collected by base-line correction and filtered for removing noises according to the standard procedure suggested by the Pacific Earthquake Engineering Research Center (PEER).
The Arias intensity was then calculated from each corrected seismogram. The arithmetical mean of the Arias intensities of the N-S and E-W components were used to represent the earthquake intensity for a strong-motion station site. These values were interpolated on each grid point in the study area using the ordinary Kriging method.
Tools used are MapInfo vector GIS and ERDAS Imagine raster GIS.

15. Event-based Landslide Inventory
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Prior to Jueili
After Jueili
Landslides triggered by the Jueili earthquake
（Blue color indicates cloud or
shade in SPOT image）

16. Event-based Landslide Inventory
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Prior to Chi-Chi
After Chi-Chi
Landslides triggered by the Chi-Chi earthquake
（Blue color indicates cloud or
shade in SPOT image）

17. Preliminary Selection of Factors
Lithology
Slope gradient
Slope aspect
NDVI
Terrain roughness
Slope roughness
Total curvature
Slope height
Total slope height
Topographic wetness index
Distance to road
Distance to fault
Distance to river bend
Distance to river head
Peak ground acceleration (PGA)
Peak ground velocity (PGV)
Arias intensity (AI)

18. Selection of Effective Factors
Success Rate Curve
Non-landslide
Probability of Failure Curve
Portion of Landslide
P-P Plot
Exp. Cum. Prob.
Prob. of Failure
Frequency
Landslide
AUC=0.767
D=0.790
Slope, %
Obs. Cum. Prob.
Slpoe, %
Portion of Area
Visual inspection of frequency distribution of the two groups, and calculation of discriminator D.
Test of normal distribution of the factor.
Examination of probability of failure curve to see if landslide probability increases with the factor value.
Examination of success rate curve to check the ability of interpreting landslides of the factor.
Discriminator Dj :
, where, j A
is average of landslide group, j B
is average of
non-landslide group, Pj S
is pooled standard deviation of two groups, j indicates j th factor.

19. Effective Factors Selected
► The following factors are tested to be effective in interpreting landslides:
Lithology
Slope gradient
Slope aspect
Terrain roughness
Slope roughness
Total curvature
Arias intensity (AI) (triggering factor)

20. Processing of Landslide Causative Factors
SLOPE GRADIENT
(Chi-Chi for example)
Mountainous
Terrain
Hilly
Terrain %
Frequency %
524.55 % %
Landslide ratio %
Hilly terrain
Mountainous terrain
Thick line: Landslide group
Thin line: Non-landslide group %

21. Processing of Landslide Causative Factors
SLOPE ASPECT
(Chi-Chi for example)
Hilly Terrain
Mountainous Terrain
Frequency %
360 o o
Landslide ratio %
Hilly terrain
Mountainous terrain
Thick line: Landslide group
Thin line: Non-landslide group o

22. Processing of Landslide Causative Factors
TERRAIN ROUGHNESS
(Chi-Chi for example)
40%
Hilly Terrain
Mountainous
Terrain m
Frequency %
13.84 m m
Landslide ratio %
Hilly terrain
Mountainous terrain
Thick line: Landslide group
Thin line: Non-landslide group m

23. Processing of Landslide Causative Factors
SLOPE ROUGHNESS
(Chi-Chi for example)
Hilly Terrain
Mountainous
Terrain m
162.61
Frequency % m m
Landslide ratio %
Hilly terrain
Mountainous terrain
Thick line: Landslide group
Thin line: Non-landslide group m

24. Processing of Landslide Causative Factors
TOTAL CURVATURE
(Chi-Chi for example)
Hilly Terrain
Mountainous Terrain
Frequency %
Log(radius/m)
-0.65
Log(radius/m)
Log(radius/m)
Landslide ratio %
-6.00
Hilly terrain
Mountainous terrain
Thick line: Landslide group
Thin line: Non-landslide group
Log(radius/m)

25. Processing of Landslide Causative Factors
LITHOLOGIC UNIT
(Chi-Chi for example)
Hilly Terrain
Mountainous Terrain 10
Frequency % 1
Lithologic Unit
Lithologic Unit
Landslide ratio %
Hilly terrain
Mountainous terrain
1 Alluvium & Terrace Deposites
2 Lateritic Terrace Deposites
3 Toukoshan Formation (Conglomerate)
4 Toukoshan Formation (Sandstone & Mudstone)
5 Cholan Formation
6 Chinshui Shale
7 Kueichulin Formation (Tawo Sandstone)
8 Kueichulin Formation (Shih Liufen Shale)
9 Kueichulin Formation (Kantaoshan Sandstone)
10 Nanchung Formation
Lithologic Unit

26. Topographic Correction of Arias Intensity
Get amplification factor of Ia by using the ratio of Ia from strong-motion data recorded at stations on ridge top and other stations.
Establish the relationship between amplification factor and a topographic factor : (Lin and Lee, 2003)
where F is amplification factor, h is relative height to riverbed, and Ia’ is Arias intensity after correction.

27. + Chi-Chi Earthquake Arias Intensity Original
Relative height to riverbed +
Frequency %
Landslide Ratio %
m/s m
Chi-Chi Earthquake

28. Arias Intensity Chi-Chi Earthquake ( After correction) Frequency %
m/s
Frequency %
Landslide Ratio %
Chi-Chi Earthquake

29. Arias Intensity Jueili Earthquake ( After correction) Frequency %
m/s
Landslide Ratio %
m/s
m/s

30. Result of the Discriminant Analysis

31. Landslide Susceptibility Maps
(Jueili)
Susceptibility map trained from the Jueili earthquake-induced landslides
Susceptibility map with no-triggering factor

32. Landslide Susceptibility Maps
(Chi-Chi)
Susceptibility map trained from the Chi-Chi earthquake-induced landslides
Susceptibility map with no-triggering factor

33. RESULTS a b c d e f
Event-based landslide susceptibility maps at Yinlin quadrangle. (a) Landslides triggered by 1997 Jueili earthquake, (b) event-based landslide susceptibility map trained by Jueili data set, (c) background landslide susceptibility map for Jueili event. (d) Landslides triggered by 1999 CHI-CHI earthquake, (e) event-based landslide susceptibility map trained by Chi-Chi data set, (f) background landslide susceptibility map for CHI-CHI event.

34. RESULTS Success rate curve Predict rate curve
Hilly Terrain
Mountain Terrain
Jueili AUC= Chi-Chi AUC=0.9099
Jueili AUC= Chi-Chi AUC=0.8177
Jueili Earthquake Chi-Chi Earthquake
Hilly Terrain
Mountain Terrain
Predict rate curve
Jueili AUC= Chi-Chi AUC=0.8661
Jueili AUC= Chi-Chi AUC=0.7264
Success rate curve and Predict rate curve in the Yinlin quadrangle

35. Arias Intensity Hazard Map for Taiwan
475-year
Arias Intensity Hazard Map for Taiwan
44 earthquakes and 5109 records are used.
Mw=7.0
Mw=7.6

36. Modeling Spatial Probability
Hilly Terrain
Mountainous
Terrain
(Chi-Chi event) 36

37. Landslide Hazard Map
An example of 475-year earthquake-induced landslide hazard map for the Yinlin Quadrangle

38. DISCUSSION AND CONCLUSIONS
An event-based landslide susceptibility map reflects landslide distribution for a certain triggering event based on which the susceptibility model was trained. Therefore, there may have many different event-based landslide susceptibility maps for a given region.
Spatial probability of landslides can be modeled by a landslide ratio curve, and temporal probability of landslides can be achieved via a probabilistic seismic hazard analysis. And a landslide hazard map may be constructed; similar to those have been done by Jibson et al
The advantage of this landslide hazard models is capable of predicting shallow landslides induced during an earthquake scenario with similar range of ground shaking, without requiring the use of geotechnical, groundwater or failure depth data.

39. Thanks for your attention!謝謝