IEEE Geoscience and Remote Sensing Magazine - March 2020 - 106

the conditional probability P ^ $ h for a randomly selected
building at risk to be in, or exceed, a certain damage level
^ D i h when the intensity parameter ^ D h equals a given
value, is computed as
P ^Damage level $ D i | ∆ h = U ;

1
D
ln r mE with i = 1, f5,
b cD
i
(10)
where U 6 $ @ is the standard normal cumulative distribution
function and ∆r i (median value of the intensity parameter)
and b (standard deviation of the natural logarithm of the
intensity parameter) are the fragility parameters.
Following the generation of fragility curves, a single vulnerability curve representative of the expected mean level of
damage for a building, considering a given value of the intensity parameter, is derived. For this purpose, the expected
mean level of damage n D ^D h is computed for a fixed intensity parameter ^D h using (11), adapted from [139], [140]:
	

n D ^D h = / Pi d i, (11)
5

i=1

where Pi is the discrete probability associated with a damage severity level D i (extracted from the generated fragility
curves) for a numerical index
d i (taken for this application
as 1, 2, 3, 4, and 5 for D1, D2,
THE NUMERICAL INDEX di
D3, D4, and D5, respectively).
IS A CONVENIENT MEASURE
The numerical index di is a
FOR QUANTIFYING THE
convenient measure for quanAVERAGE STRUCTURAL
tifying the average structural
LOSSES AND ASSESSING
losses and assessing the vulTHE VULNERABILITY OF THE
nerability of the building at
BUILDING AT RISK.
risk. Finally, the empirical vulnerability curve that allows
forecasting, for a randomly selected building at risk, of the expected mean level of damage
n D for a certain value of the intensity parameter ^D h is derived by fitting the n D ^ D h data obtained from (11), using the
tangent hyperbolic function as the regression model [141]:
	

n D = a 6b + tanh ^c∆ + d h@, (12)

where a, b, c, and d are four coefficients that must be estimated based on the observed n D ^D h in (11) from the analyzed sample of buildings.
AN APPLICATION EXAMPLE
In this section, the potential use of remote-sensing DInSAR
data for different aspects of slow-moving landslide risk analysis, concerning landslide characterization and analysis of the
vulnerability of exposed buildings shown in the procedure
sketched in Figure 5, is applied to a representative case study.
LUNGRO CASE STUDY
The selected study area corresponds to the well-documented urban area of the Lungro municipality, located at
106

650 m above sea level in the southern Italian Apennines
(Calabria region). As described in [50] and [142], the geological context mainly consists of Middle Pliocene-Pleistocene sediments [Figure 6(a)]. The urban area is affected
by several slow-moving landslides-with either active or
dormant activity states based on geomorphological criteria [Figure 6(b)]-of different types, including slides,
complex slide/flows [126], and landslide zones [143],
[144]. The landslide zones are areas where the clustering of mass movements (slides, complex slide/flows) is
so tight that it is impossible to distinguish the different bodies, but sometimes landslide phenomena can be
mapped inside the area [50]. The urban area consists of
the historic center with low-rise (2 or 3 floors) masonry
buildings on shallow foundations, mainly made with
pebbles or erratic/irregular stones; two subzones (Carmine and Lafcantino) with both masonry and RC buildings; and the San Leonardo area, where RC buildings up
to 5 or 6 floors were built in the early 1950s-1960s.
Over the Lungro area, surface and deep-displacement
monitoring data [50] are available [Figure 6(b)] deriving
from, respectively, 12 vertical inclinometers (measurements collected from 2006 to 2011 between depths of 25
and 80 m) and nine GPS points (monitored from June 2006
to May 2011).
The SAR data set consists of 35 Envisat images (ascending
orbits from 2003 to 2010) and 39 COSMO-SkyMed images
(ascending orbits from 2012 to 2014) processed according
to SAR tomographic analysis [104]. The DInSAR velocity
distributions over the Lungro area are shown for the Envisat
and COSMO-SkyMed radar sensors in Figure 7(a) and (b),
respectively, where the significantly larger density of measurement points achieved by processing VHR COSMOSkyMed data can be appreciated.
DERIVATION OF FRAGILITY AND
VULNERABILITY CURVES
According to phase 1 in Figure 5, based on the aPosIn procedure, slow-moving landslides [Figure 6(b]) affecting the
Lungro urban area could be described by six categories
(Figure 8), the main features of which are summarized in
Table 3 [50]. In phase 2, the buildings exposed to landslide
risk were identified by intersecting the inventory map of
typified landslides with the map of the built-up area (Figure 8). In the Lungro municipality, the results of an extensive building damage survey (on 540 total buildings, dated
October 2015) are available (Figure 9). The figure shows
111 buildings interacting with the categorized landslides
and the distribution of different levels of recorded damage
severity [38], [39].
The present analysis (phase 3) considered 49 exposed
buildings (12 of RC and 37 of masonry structure) of the 111
total buildings interacting with a slow-moving landslide
for which an in situ damage survey was performed, with
shallow foundations and covered by at least two DInSAR
benchmarks in both the Envisat and COSMO-SkyMed data
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2020
IEEE Geoscience and Remote Sensing Magazine - March 2020

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