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| Titel |
The Statistical Distributions of Landslide Length to Width Ratios |
| VerfasserIn |
F. E. Taylor, B. D. Malamud |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250058699
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| Zusammenfassung |
| There has been considerable effort in analysis of the frequency-size statistics of landslide
areas and volumes, yet less attention to the statistics of landslide shape. Here, we use two
substantially complete triggered event landslide area inventories to quantify how length (L)
to width (W) ratios vary as a function of landslide area. The first inventory is 11,111
landslides triggered by the 17 January 1994 Northridge earthquake in California and the
second inventory is 9594 landslides triggered by heavy rainfall from Hurricane Mitch in
Guatemala in late October and early November 1998. We assume that all landslide
shapes can be abstracted to a rectangle L Ã W , and find that the ratio of the
long side (L) to the short side (W) of this shape varies with landslide area. The
length-to-width ratio, L/W , is calculated by two methods which are considered
separately: (i) from a quadratic equation using the given inventory landslide area
and perimeter; (ii) applying a ‘bounding box’ where L is the longest linear axis
of the landslide and W perpendicular to this. For each of the two methods, the
statistical distribution using Maximum likelihood estimation of L/W values were then
considered for eight landslide area categories (bins) increasing logarithmically: AL =
100–199, 200–399, 400–799, 800–1599, 1600–3199, 3200–6399, 6400–12,799,
12,800–25,600 m2. We find that for each landslide area bin considered, the probability
density function of L/W follows reasonably well a three-parameter inverse gamma
distribution; this distribution has a power-law decay with exponent (Ï + 1) for medium
and large landslide areas and an exponential rollover for small areas. There is a
relatively low probability of landslides where L/W = 1 (i.e. a square), with the
maximum probability of occurrence for L/W = 1.8 to 2.2 for landside areas in
categories 100–199, -¦, 3200–6399 m2, and L/W = 3 and 7 for the two largest landslide
area categories. For the three landslide area categories between 100–800 m2, the
inverse gamma distributions are broadly similar. For the next five categories, 800 to
25,600 m2, as the landslide area category gets larger, the gradient of the left hand tail
(smaller length-to-width ratios) decreases and the right hand tail (larger ratios) is a
little more variable: first a decreasing gradient but then it increases again. In this
paper we have found that the statistics of length-to-width ratios, when considered
for different landslide area ranges, follow inverse-gamma distributions, similar to
that found in the literature for the statistics of landslide areas themselves. This
work will aid in analytic and computer landslides modelling, where the models
need as an input a general statistical distribution of length-to-width landslide ratios. |
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