Strategies for rapid global earthquake impact estimation: the Prompt Assessment of Global Earthquakes for Response (PAGER) system - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 844

exploring the potential of incorporating high-resolution subnational GDP
dataset, in order to better characterize the spatial variation of economic
exposure within a given country.
Following the formulation as described in Eq. 31.3, the total expected
economic loss following an earthquake i could be estimated by summing
the product of total economic exposure and loss ratio at each shaking
intensity level j using the following equation:

∑

() ()

Er s = Ps [31.7]

i i j i j

j

The loss ratio function r ( s ) is defi ned in terms of a two-parameter log-
normal cumulative distribution function of shaking intensity s as shown in
Eq. 31.2. If we suppose that O i is the recorded economic loss (in millions
of US dollars, USD, taken from the Munich Re catalog as shown in Table
31.1) for an earthquake i , and there are N such earthquakes for that country,
then we can determine the parameters of the loss ratio function by minimiz-
ing the total error between expected loss E ( L ) (also termed as model-

estimated loss, abbreviated as E i ) and reported or observed loss O i . This is
analogous to the fatality rate estimation approach defi ned in the previous
section.
Figure 31.3 illustrates recorded versus model-estimated losses for histori-
cal earthquakes in Turkey and Italy. Each symbol on the top portion of the
plot represents one earthquake for which losses are estimated using the
population exposure, GDP, the correction factor, and the loss ratio function
shown in the bottom portion of the country-specifi c plot. We mapped 62
earthquakes in Turkey (1980-2008) with the EXPO-CAT catalog for which
population exposure and economic loss estimates were available. Among
these, the August 17, 1999, Izmit earthquake caused $12 billion of direct
economic loss according to the Munich Re catalog. Using a nonlinear opti-
mization procedure, we determine the loss ratio function parameters

ε

θ and

β that best predict both high and low economic loss events. In the case of

Table 31.1 Snapshot of Munich Re economic loss data for selected events

Direct overall
loss (USD mil.,
original values)

Insured
loss (USD
mil.)

Deaths
(total) MR number Country

MR199401A043 Northridge CA USA 44 000 15 300 61

MR199501A046 Kobe, Japan 100 000 3000 6430

MR199909A017 Chi Chi Taiwan 14 000 750 2368

MR200805A004 Sichuan China 85 000 300 69 227

Source: NatCat Service (2008).