Interaction among landslides, seismicity and climate in New Zealand 

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The New Zealand 1996-2004 landslide catalogue

GNS Science Ltd has compiled a landslide catalogue (http://www.geonet.org.nz) of 2100 events for the 1996-2004 period. Data in the catalogue were obtained from a variety of sources, such as media reports, aerial surveys and ground inspection. For each landslide, the available parameters include: date, location, type of material, type of movement, trigger mechanism, size, impact and references. Time accuracy varies from one day to one year, with a mean value of 1.77±0.95 day for the whole catalogue. Landslide location accuracy ranges from a few metres for GPS-located landslides to a few kilometres for events remotely located using news reports, e.g. the distance to the nearest village. Volumes were roughly estimated from aerial photographs or from visual ground surveys, without any quantifying tool. Information on the trigger of a given landslide is provided for more than 90% of the landslides. The trigger mechanism relates to any nearby triggering event (intense rainfall, >M4 earthquake, etc), on the basis of a one to two days correlation in time with the landslide occurrence.
By imposing known location and time accuracy within two days, we extract 1943 landslides from the catalogue (Fig. 2.1a). Landslide volumes are given for 12% of the 1943 landslides, the largest event being Vmax = 24 ∗ 106 m3. 98% of the 1943 landslide volumes are sorted in three volume classes (1 to 3) corresponding to 1) V < 103 m3, 2) 103m3 < V < 106 m3 and 3) V > 106 m3. The 3 classes containing 1775, 118 and 26 landslides respectively. The material type and the landslide type are unknown for 58% and 91% of events, respectively. 65% of the landslides are reported as rainfall-triggered on 142 different days, 30% were earthquake-triggered on 4 different days, 7% had no reported trigger on 105 different days and 2% were triggered by other mechanisms (flooding, anthropic works, etc.) on 19 different days. In the first instance, we use all the 1943 landslides from the catalogue, independently of their reported trigger, for an overview of landslide behaviour in New Zealand. Then, we check how the a priori classification for triggered landslides may influence the results.
The landslide catalogue can be split into two different periods, before and after July 2001, for which the sampling methods and accuracies were different. July 2001 corresponds to the first use of more sensitive data sampling techniques which resulted in an increase of the average daily rate in the July 2001-2004 period compared to the 1996-June 2001 period.
Figure 2.1: a) 1943 New Zealand landslides with known time and location which occurred in the 1996-2004 period, red dots. b) 1943 largest earthquakes, from 1996 to 2004 (green dots: 4 < M < 5, yellow dots: 5 < M < 6, orange dots: 6 < M < 7, red dots: M > 7).
Key for color shading on the map is elevation; ranging from green, 0 m elevation above sea level, to dark brown, 4000 m elevation a.s.l..
For this study, we analyse the 1943 New Zealand landslide catalogue and different subcatalogues, to test the robustness of the results. The sub-catalogues were selected over i) space (North and South Island sub-catalogues), ii) time (1996 to June 2001 and July 2001 to 2004 sub-catalogues), iii) volume and iv) rate dynamics (binary sub-catalogue where the daily rate is set to 1 if at least one event occurred on that day or to 0 if no event was recorded on that day).

Methods

We test landslide time-series data in order to characterize any departure from randomness and the thresholds from which a given distribution emerges, if any. To accept or reject the null hypothesis of randomness i.e. independent events, we test the time and volume data for exponential (i.e. the time distribution of random processes) or power-law distributions, which often emerge for natural processes.
To test and quantify for randomness, we use the reduced chi-square 2 r test (e.g. Dussauge et al., 2003, for application to rock-fall volumes) and the test (e.g. Marzocchi and Zaccarelli, 2006). The 2 value is a measure of the difference between the observed histogram and a histogram obtained by sampling the hypothesized distribution function (e.g. Press et al., 1992) and the 2 r value is a normalised value of the 2 value (e.g. Dussauge et al., 2003). A 2 r >> 1 rejects the tested distribution as a possible description of the observed data. The = /μ ratio, where μ and are the average and standard deviation of the inter-event times, respectively, allows us to characterize any clustering against random processes. For a Poisson process (i.e. random distribution) = 1, while > 1 characterizes statistical distributions more clustered than an exponential one, and < 1 is typical for more “regular” time occurrences (see e.g. Marzocchi and Zaccarelli, 2006 for an application to volcano processes).
Power-law tests were performed using the Kolmogorov-Smirnoff (KS) test (e.g. Press et al., 1992) associated with the Maximum Likelihood Method (Aki, 1965) which allows an estimate of the exponent b of the power-law. The KS test consists of minimizing the distance between the empirical data and the synthetic power-law (e.g. Press et al., 1992).
Estimations of the power-law parameters and power-law goodness of fit are worked through using the algorithm proposed by Clauset et al. (2009) and are as follows: 1) setting series of lower cut-off and exponent b (via the Maximum Likelihood method) combinations of power-law models which describe the distribution; 2) selecting the combination giving the best power-law fit, using the Kolmogorov-Smirnoff statistic; 3) estimating the standard deviation of the lower cut-off and exponent b via a non-parametric bootstrap method. It consists in generating 2500 synthetic datasets with a similar distribution to the original one by randomly drawing a new sequence of points from the original data. Then, estimation of the best exponent b and lower cut-off pair for each of the 2500 datasets is performed. The standard deviation of both the 2500 exponent b and lower cut-off values gives the standard deviation of the estimated parameters of the power-law describing the empirical data.
The validity of the power-law to describe the frequency-volume distribution is tested using a goodness-of-fit test. It consists of generating 2500 power-law distributed synthetic datasets with the exponent b and lower cut-off equal to those of the distribution that best fits the observed data. Then a fit of each synthetic dataset is performed and the KS statistics are computed for each synthetic distribution relative to its own model. The fraction of times where the resulting statistic is larger than the value obtained from the empirical data is the p-value. Following Clauset et al. (2009) we take p > 0.1 for the power-law to be accepted.

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Landslide catalogue completeness

Catalogues for natural phenomena are always incomplete at the smallest event sizes.
Due to the resolution of the measurement technique, not all events below a given size (V0) can be recorded. V0 depends on the space and time sampling accuracies, which are notably influenced by population distribution, official awareness of landslide hazard (e.g. Glade, 1998, Stark and Hovius, 2001, Dussauge et al., 2003, Malamud et al., 2004) and also on surface morphology (Guzzetti et al., 2002).
To estimate V0, one usually measures the minimum volume for which the landslide volume distribution follows a power-law (e.g. Dussauge et al., 2003). For volumes smaller than V0 there is a “roll-over” which is due to a lack of reporting of small events as discussed above. Following Clauset et al. (2009), we compute the probability p that the distribution follows a power-law with corresponding values of b exponent and lower cut-off V0 (see section 2.3.2 above).
For the New Zealand landslide volume distribution, we found V0 = 45 ± 2, 700 m3, b = 1.36±0.06 and p=0 (Table 2.1, Fig. 2.2); the power-law is therefore rejected. It is also rejected for the North and South Island sub-catalogues. It is accepted for the 1996-June2001 and July 2001-2004 sub-catalogues, with b = 1.76 ± 0.68, V0 = 8, 000 ± 4, 000 m3 , and b = 1.36 ± 0.04, V0 = 150 ± 1, 400 m3, respectively (Table 2.1, Fig. 2.2). V0 standard deviations show large variations, perhaps because less than 15% of the landslides from the catalogue were associated with a volume, which was generally roughly estimated. The exponent values of the volume distributions are of the same order of magnitude as the exponent values found for rock-fall volumes on sub-vertical cliffs (1.5±0.2), and are smaller than the 2.2 ± 0.3 value reported for mixed landslide types (see references of Table 3 of Dussauge et al., 2003).

Table of contents :

General introduction
1 Landslide triggering 
1.1 Triggering of landslides by increase of slope angle
1.2 Triggering of landslides by increase of load applied to the slope
1.3 Triggering of landslides by rise in groundwater level and pore water pressure
1.4 Triggering of landslides by frost weathering processes
1.5 Triggering of landslides by earthquake loading
2 Interaction among landslides, seismicity and climate in New Zealand 
2.1 Abstract
2.2 Introduction
2.3 Data and methods
2.3.1 The New Zealand 1996-2004 landslide catalogue
2.3.2 Methods
2.3.3 Landslide catalogue completeness
2.3.4 Earthquake and weather catalogues
2.4 Correlation between landslide occurrences
2.4.1 Landslide daily patterns
2.4.2 Distributions of landslide waiting (inter-event) times
2.4.3 Distribution of landslide daily rate
2.5 Possible processes for landslide clustering in time
2.5.1 Earthquake-landslide interaction
2.5.2 Landslide-landslide interaction
2.5.3 Climate-landslide interaction
2.5.4 Discussion
2.5.5 Conclusion
3 Characterization and comparison of landslide dynamics in different tectonic and climatic settings 
3.1 Abstract
3.2 Introduction
3.3 Databases
3.3.1 Landslide databases
3.3.2 Earthquake databases and tectonic settings
3.3.3 Weather databases and climatic settings
3.4 Correlation between landslide occurrences
3.4.1 Evidences for complex inter-relationship between landslide patterns, and rainfall and seismicity forcings
3.4.2 Landslide daily patterns
3.4.3 Distribution of landslide times and waiting times
3.4.4 Distribution of landslide daily rates
3.4.5 Distribution of landslide inter-event distances
3.5 Analysis of the possible processes for landslide triggering
3.5.1 Landslide – landslide interactions
3.5.2 Earthquake – landslide interactions
3.5.3 Climate – landslide interactions
3.6 Discussion and Conclusions
4 Unified picture for aftershocks and earthquake-triggered landslides 
4.1 Introduction
4.2 Data and Methods
4.3 Characteristics of the 5 sequences
4.4 Results
4.4.1 Landslide and aftershock distance distributions
4.4.2 Ground motions and triggered landslide and aftershock space distributions
4.5 Discussion
Conclusions and perspectives
Appendices

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