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Working Paper C
Characterization of Earthquake
Hazards for Loss Studies
Technically, earthquake hazard or seismic hazard refers to the di
rect impact of an earthquake on the earth, including ground shaking,
ground failures (liquefaction, surface faulting, landslides, and settle
ment), and the waterrelated phenomena of tsunamis and seiches.
In this usage, the characterization of earthquake or seismic hazard
does not include effects on the humanly constructed environment.
Thus, threats such as collapsing buildings, overturning shelving, or
breaking gas lines which in common language are often caned earth
quake hazards, or which are encompassed in the National Earthquake
Hazards Reduction Program, are not topics in this working paper.
This paper describes earthquake hazards and how they can be
quantified, reviews current practice in the specification of hazards
for loss studies, and describes a range of hazard specifications that
might be used ~ future loss studies.
TYPES OF EARTHQUAKE HAZARDS
The primary and most pervasive hazard associated with earth
quakes is the shaking of the ground. This causes direct damage to
structures as well as physical phenomena (seiches, liquefaction, and
landslides) that can result in significant damage and loss. Ground
shaking is generally caused by the release of crustal energy by rup
ture along a fault surface. Sometimes the rupture reaches the earth's
113
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114
surface and is evident after the event, but often the rupture is buried
beneath surficial sediments and rocks. Voicanic earthquakes are less
common, tend to be limited to moderate magnitudes, and are pri
mariTy caused by thermal rather than mechanical action.
The energy released by a rupture propagates in the form of com
pressional waves and shear waves. The character of ground motion
from these waves is a function of the source characteristics of energy
release, the attenuation (clamping) characteristics of the earth's crust
along the wave travel path, the nearsurface geologic characteristics
that may modify the frequency content of the motion (amplifying
certain frequencies and damping others), and the interaction of the
body waves with the earth's surface to form surface waves.
Collateral earthquake hazards caused by ground shaking include
seiches, liquefaction, and landslides. These hazards can lead to com
plete destruction of structures. For example, the Niigata earthquake
of 1964 led to the liquefaction of soil in a large area, causing the loss
of foundation strength for many apartment buildings. As a result,
buildings tilted by as much as 70 degrees. A recent report of the
National Research Council (1986) summarizes the state of the art
of estimating the hazard from liquefaction. Landslides constitute
a similar, shakinginduced hazard. In the 1964 Alaska earthquake,
landslides in Anchorage caused the destruction and total loss of many
residences and buildings. Landslides into bodies of water, or on the
bottom of harbors and bays, can produce water waves that may cause
very serious losses.
Another hazard associated with earthquakes is rupture of the
earth's surface caused by displacement of a fault. In the United States
this phenomenon is generally observed only in the western states and
Alaska. The fault movements associated with great earthquakes may
be on the order of 510 meters. Such deformations are difficult or
impossible to design for, and the best policy may be to avoid fault
locations entirely.
For some civil engineering works (e.g., pipelines, transmission
lines, highways, railroacis, and aqueducts) it is not possible to avoid
fault crossings. In these cases the hazard to the facility can be
identified and quantified, and the eject on the system's function can
be evaluated. If the system damage and its probability of occurrence
are not acceptable, alternative system designs are usually possible
to alleviate damage to components crossing faults (e.g., designing
redundant links in the system, designing the fault crossing to be easily
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115
repairable, or devising an earthquake response plan that reduces the
functional loss).
Still another earthquake hazard is a tsunami, which is a wave
generated in the open ocean as a result of tectonic movement of the
floor of the ocean. Where such waves come ashore, they can rise to
significant heights and cause considerable damage. Tsunamis are a
potentially severe problem for Alaska, and tsunamis generated by
Alaskan earthquakes have also caused damage to the West Coast
states. Tsunamis generated both in Alaska and Chile have caused
great destruction and fatalities in Hawaii. Apparently tsunamis are
not a problem along the Atlantic and Gulf coasts, but may be a
threat in Puerto Rico and the Virgin Islands.
SCOPE OF EARTHQUAKE HAZARD ASSESSMENT
The purpose of assessing earthquake hazards is to identify and
quantify the severity of the various hazards in the geographic area
of interest for the loss estimation study, given a scenario earthquake.
In most cases an estimate of the frequency in tune (or probability of
occurrence over a given period of time) of the hazard is also necessary.
The results of the hazard assessment are combined with the ground
motion and damage relationships and the inventory of facilities in
the study region to produce estimates of losses.
Assessing earthquake hazards and specifying the other inputs
to a loss study are related but independent activities that can be
undertaken by different investigators at different times. One advan
tage of this independence is that various parts of the analysis can be
updated (e.g., more recent data from a U.S. census can be incorpo
rated) without having to reinvestigate other inputs to the analysis.
Also, studies of facility inventories and vulnerability relations can be
locally or regionally undertaken, while nationally developed seismic
hazard data (e.g., studies by the U.S. Geological Survey) can be pro
duced separately. The converse division of labor is also possible, as
when national inventory data (e.g., census data on housing) is com
bined with seisrn~c hazard studies locally undertaken by state or local
government geological agencies or local geotechnical consultants.
Earthquake hazards and other inputs to loss estimation are re
lated in that the hazard must be specified in terms that are meaning
ful to the vulnerability analysis. For example, if the seismic hazard
is specified in terms of the peak acceleration during the earthquake,
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116
the vulnerability functions cannot be given using a qualitative inten
sity scale such as MMI. If either the hazard or vulnerability analyses
must be translated to make it compatible with the other, care must
be taken in the translation, and the conversions used must be fully
documented.
Simple empirical correlations based on observed statistics often
lead to incorrect results in particular applications. Simple repre
sentations of the shaking hazard, for example, those using peak
acceleration or Modified Mercalli Intensity (MMI), are attractive be
cause hazard analyses are frequently available for these parameters,
and vulnerability functions are available to estimate losses for them
for many types of structures. The price for this simplicity is a wide
range of uncertainty in the damage and loss, because simple rep
resentations of seismic shaking or earthquakecaused ground failure
cannot capture the details of the underlying phenomena.
More complex representations of ground shaking, for example,
through a filtered "effective peak motion, a singledegreeoffreedom
linear response spectrum, a nonlinear spectrum, a time history of
motion, and the duration of strong shaking, have the ability to be
more accurate predictors of damage and loss. There is less agreement,
however, on how to estimate these functions for a future earthquake,
how to quantify the single or multidimensional hazard associated
with them, and how to derive an accurate predictor of damage from
them.
CHARACTERIZATION OF GROUND SHAKING
For historical and pragmatic reasons, MMI has been used as the
groundshaking measure in most earthquake loss studies conducted in
the past, and likely will remam the standard for studies in the near
future. This procedure was popular in early loss studies because
multiple, instrumental records of ground shaking were not available
to correlate motion levels to damage. Even today, records of strong
shaking at the site of buildings damaged during earthquakes are rare,
whereas assessments of the MMI level at that site can always be made
by an experienced investigator. The MM! assessment denotes the
severity of earthquake shaking at a particular location in terms of the
effects on people, on construction, and on the earth's natural features.
The MMI level depends on seismic, geologic, engineering, and human
factors. The assigned MM! value for a particular earthquake and
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location is a qualitative measure of the integrated response of the
natural and manmade environments to earthquake energy.
As Richter (1958) also notes, at the higher intensity levels (MMI
_ X, XT, XIT) the scale refers primarily to ground failure rather than
directly to ground vibration. The primary fault trace phenomena
and secondary ground effects depend on the type of faulting motion
(vertical versus horizontals, the duration of the faulting movement,
and the nature of the ground in the immediate vicinity of the fault.
Ground failures such as liquefaction, faulting, and landslides are not
good measures of ground shaking since they can occur at low as well
as high levels and durations of ground motion.
Contrary to conventional seismological practice and to previous
applications in the loss estunation field (e.g., ATC13), it is desirable
to use MMI intensity as follows: First, ground failure phenomena
should be treated separately from ground shaking, and second, only
intensities below MMI X! should be used to describe the severity of
ground vibration. This does not unply that quantitative measures
of ground vibration (e.g., peak ground acceleration or velocity) are
limited to a maximum value that would correspond, according to
one of the various MMIacceleration or MMIvelocity relationships
proposed, to MM! X. In other words, MMI X is not necessarily the
maximum severity of ground shaking that could occur on earth. As
a general rule, the estimation of MM} can rarely be refined beyond a
1unit range.
When making loss estimates, the ejects of soil conditions on
intensity of shaking must be considered. One means of accomplishing
this, if ground motion is used as an intermediate variable to estimate
losses, is to modify the estimates of ground motion (e.g., MMI) to
reflect the expected effects of soils at locations in the region from the
hypothesized earthquakes. Table C1 presents one set of correction
factors that has been proposed for southern California and that
attempts to account for both the type of rock that might underlie
a site, ~d the depth to the water table (Evernden and Thomson,
1985~. Other correlations may have equal or greater justification,
depending on the data base and the region of study.
The use of MMI in loss estimates is a gross simplification that is
justifiable only if more precise methods are not available. It is known,
for example, that modifications of earthquake ground motions by
soils are frequency dependent. Therefore, an accurate modification
of ground motion should consider the frequency characteristics of the
structures for which losses are to be estunated. Similarly, explicit
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118
TABLE C1 GroundMotion Correction Factors for Southern
California
Geologic Condition
Change in Intensity
Quaternary alluvium
(water table > 100 ft)
Quaternary alluvium
(water table 30100 ft)
Quaternary alluvium
(water table < 30 ft)
Sedimentry rock
Volcanic, granitic, and
metamorphic rock
0.0
+1.0
+1.5
0.0 to 1.6
1.7 to 2.0
SOURCE: E,rernden and Thomson (1985~.
quantification of the effects of earthquake magnitude, distance, and
duration are ignored when MMI is used. For example, an MMI VII
observed at the epicenter of a magnitude 5 earthquake does not unply
the same ground motion as an MMI VII observed (for the same soil
conditions) 100 km from a magnitude 7 (Murphy and O'Brien, 1977~.
For these reasons, use of MMI (and similar intensity scales) should be
recognized as a lessthanperfect representation of earthquake ground
shaking to be used only until more precise parameters and methods
are available.
HAZARD AND LOSS ESTIMATION PROCEDURES
Scenario earthquakes have been deterrn~ned following rationales
that in different ways express the need to compromise between the
likelihood or credibility of the event and its destructive potential.
Once the scenario event has been selected, all existing largescale loss
estunation procedures use deterministic relationships to calculate the
level of ground motion at each site, the resulting damage, and the
losses.
Occasionally, some of the relationships (most notably the rela
tionship between groundmotion intensity and damage) include un
certainty, but in no study has uncertainty been propagated through
the analysis to produce probabilistic estimates of loss. For the treat
ment of uncertainty, one can therefore regard all previous largescale,
generalpurpose loss est~rnation methods as Deterministic proce
dures under scenario earthquakes. This type of analysis reflects
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119
TABLE C2 Applications of Loss Estimation Methods
Applications
Appropriate Methods
Advocacy
Response planning
Preparedness planning
Mitigation strategies
Relocation/reco~rery
Risk evaluation
Economic impact analysis
Insurance
National security
A,B
A,B,D
A,8
A,B,C
B,C
B
A,B,C,D,E
B,C,D
. KEY: Current practice: A = extrapolation from
historical data; and B = scenario analyses and accuracy
estimates. Emerging methods: C = losefrequency
analysis; and D = simulation of actual events with
variability. E = cumulative over time.
the heritage of early loss estimation efforts. Resistance to change
has resulted from the difficulty of more complete representations of
uncertainty and by computational constraints.
Deterministic scenariotype analyses are easy to interpret and
will likely remain the basic type of earthquake loss calculation in the
near future. However, they are not ideal for all purposes because they
are not capable of fully representing uncertainty and because of the
lack of a clear rationale for selecting scenario earthquakes. For cer
tain uses, deterministic scenario analyses are actuaby inappropriate,
and alternative methods, not yet fully available, must be developed.
A listing and brief description of loss estunation procedures (some
existing, others in need of development) and an indication of their
potential uses follow. Appropriate applications of each are shown in
Table C2.
Extrapolation from Historic Losses
Loss information from historical events in the region of inter
est can be adjusted to reflect recent changes in the inventory and
differences between characteristics of the scenario earthquakes and
those of the historic events. This analysis is simple and inexpensive,
but typically less accurate and less general than analyses based on
models of ground motion, damage, and loss. Such a technique is
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120
appropriate when a historic event, not much different from the sce
nario earthquake of interest, has occurred in the recent past, as in
the case of the largest of the six scenario earthquakes used in the
National Oceanic and Atmospheric Adm~nistration's San Francisco
study (AIgermissen et al., 1972~. This condition, however, seldom
applies.
Selecting a historic event as the basis for a loss stiffly does not
avoid the problem of uncertainty, although the nontechnical audience
is less likely to bring up the issue of uncertainty because of the
intuitively convincing nature of events that have happened before.
Results of analyses of this type are illustrated in Figure Cla.
Scenario Analysis with a Statement of Accuracy
This type of analysis is most often used today, although often
without the accompanying statement of accuracy. One or more earth
quakes are selected, based on criteria reviewed earlier herein, and
singlevalue estimates of the resulting losses are produced. Accom
panying these estimates with even sunple but objective statements
of certainty would prove useful to the users. For example, one might
use sensitivity analysis: each major input parameter or relationship
is modified in turn and the analysis is repeated to calculate the effect
of the change on the calculated losses. The amount by which each
input parameter is modified should reflect the degree of uncertainty
on that parameter. The results of such an analysis are similar to the
"type A" seismic hazard analysis (Figure Cla), but a description of
uncertainty in the estimates for the scenario event may be included.
Historic Maximum E:arthqu~ce
Historic earthquakes, when judged to be suitable and perhaps
with adjusted magnitude, intensity distribution, or location, can be
used in loss estimation studies. These earthquakes are convincing to
both the users and the general public.
Recurrence Bate Earthquake
This can be an appropriate selection technique when a known
seismic source zone or fault dominates the problem at hand, for ex
ample, the Was atch Fault at Salt Lake City, Utah. In such a case, an
earthquake magnitude may be selected on the basis of its recurrence
rate, that is, from the magnitudefrequency law flog N = a  bM). N
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121
L = Best estimate loss
(a) HISTORIC LOSSES OR SCENARIO EARTHQUAKE
100%
,'_
m
Cl:
m
o
a:
J ~
m LL' 1
~ ~ 10
m an
O ~
a: Cal
Q ~
102
~ X
Z
1 03
0%
L = Loss
(b) PROBABILISTIC
1W
_ ~
,.
\ Existing Hazard

With Hazard ~
Reduction
L= Loss
(c) LOSSFREQUENCY ANALYSIS
FIGURE C1 Form of results of different loss estimation techniques.
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122
is the number per unit tune of earthquakes exceeding magnitude M,
and a and b are coefficients typically estimated by statistical analy
sis. For example, the magnitude of earthquake expected to occur on
the average once in every 100 or perhaps 500 years or more Knight be
selected. The location of the earthquake can be defined to maximize
damage or loss. This method is more difficult to apply In an area of
diffuse seismicity in that the locationts) of the seismogenic tectonic
structures are not well constrained, as in much of the eastern United
States. However, even in those areas, it is possible that the recurrence
rate method could be a viable approach for some problems.
Geologically Defined Characteristics
This method is also most applicable to regions where the tec
tonic regime and the seismogenic tectonic structures are well known.
Earthquake magnitude and location are determined on the basis of
geologic and seismologic parameters that have been specifically asso
ciated with a given fault or area, for example, slip rate, stress drop,
and typical fracture directions and lengths. Locations where this
criterion might be applied are Pallet Creek and Anza, California,
because of the ability of geologists to define the characteristic fault
behavior at these places.
Forecasting
Based on past seism~city as well as relevant physical premonitory
considerations, specific earthquake forecasts can sometimes be made.
Such forecasted events (earthquake predictions) might then be used
as scenario earthquakes. Regions of the United States where earth
quake prediction efforts are under way include the Aleutian Islands
and central California (Parkfield).
Maximum Credible Earthquake
This and similar undefined criteria have sometimes been used in
the past, but such concepts are vague and should be avoided in favor
of more objective criteria.
[os~Erequency Analysis
This Toss estimation procedure is very different from the previous
two methods (extrapolation of historical losses and scenario analysis).
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123
Its objective is not to estimate earthquake losses under a single
postulated event, but to calculate the frequency with which various
levels of loss are exceeded in the region of study. It is important to
realize that a particular loss may result from earthquakes of different
characteristics, for example, from a nearby earthquake of moderate
size or from a distant earthquake of larger magnitude. This procedure
sums up the contributions to the frequency with which any given loss
is exceeded from all possible earthquakes, large and small, near and
far away. The final result is a plot of the annual probability of
exceedance versus loss (Iossfrequency curve), as shown in Figure
Clc.
From an operational point of view, the analysis proceeds as
follows: discrete ranges of possible magnitudes and locations are se
lected and a frequency of occurrence is assigned to each magnitude
location combination. The loss produced by each combination is
then estimated using a procedure signaler to scenarioearthquake
analysis and the results of all such loss calculations are summa
rized through the lossfrequency curve. (A mathematical formu
lation of this method is given later.) The major departure from
existing scenariotype analyses is that, in lossfrequency calculation,
one would typically regard the loss from a given magnitudeIocation
combination as a random variable, due to the uncertainties of pre
dicting groundmotion intensity, physical damage, and economic and
human losses.
The mathematical procedure for this type of analysis follows
closely the method of probabilistic seismic hazard analysis described
in a report authored by the Committee on Seismology, National
Research Council (1987~. Described here is the specific application
of these probabilistic concepts to derive estimates of losses and their
frequencies of occurrence for a region or metropolitan area.
Procedures are well established for estimating the probabilities of
seismic ground motion at a point. Three types of input are required:
(~) a designation of faults or sources that generate earthquakes and
the distribution of earthquake locations on the faults or sources, (2) a
description of the distributions of earthquake sizes (magnitude*) and
tones of occurrence for each fault or source, and (3) a function that
estimates the intensity of ground motion at the site, for earthquakes
of specified magnitudes and locations on the faults or sources. With
*It is essential to be clear as to which magnitude scale is used.
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these three inputs, probabilities that a specified amplitude of ground
motion a wiD be exceeded at the site per unit time can be calculated.
The total probability theorem is used for this calculation:
PI`A > a)`Gime ~ As, Hi / ~ PtA > Am, is fM,Rtm, r`J&m~r. (~)
~ m r
in equation 1, Pt.] indicates probability, the vertical bar (~)
indicates conditions, f(.) is probability density, the summation is
over all sources, i, that might produce ground motions affecting
the site, pi represents the expected number of earthquakes per unit
time in source i, and m and r are general descriptors of earthquake
size (e.g., magnitude) and location tenth respect to the site (e.g.,
distance). The approximation in equation ~ results from using the
expected number of earthquakes rather than calculating probabilities
of multiple occurrences and from neglecting the effects of multiple
exceedances of amplitude a. For the usual annual probabilities of
interest this approximation is very accurate. The formulation of
seismic hazard considers (and integrates over) all earthquakes that
can affect the site. The resulting annual probability is calculated, in
effect, by weighting all these earthquakes by the ground motion that
they may produce at the site.
Practical applications of seismic hazard analysis are accom
plished in several steps, which lead to the calculation of equation
1. An illustration ~ given in Figure C2. First, earthquake faults
or zones of seismicity must be delineated; from these, the distribu
tion of distance fR(r) between earthquakes and the site is obtained.
Next the probability distribution of earthquake magnitudes fat (m) is
derived for each source or fault, often by analysis of historical earth
quakes that are spatially associated with that feature. The product
of these two distributions is fM,R(m,r) in equation 1.
The third specification concerns the ground motion occurring at
a site, which is a distribution of groundmotion levels conditional on
earthquake magnitude, distance, and local geology. This distribution
allows calculation of the probability PEA > a~m,r] in equation I. The
equation that calculates a mean or median groundmotion level as a
function of m and ~ is often termed an attenuation equation. The
final step in the process consists of integrating over all earthquake
magnitudes and distances, in the manner of equation 1, to calculate
hazard results for various groundmotion amplitudes, as illustrated
in Figure C2d by a typical hazard curve.
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A. Seismic Source i
(Earthquake locations in space
lead to a distribution of
epicentral distances fR (rl m)

/
fR(r~ m)
,' RuDture
_,_
Site
a
L. I
Distance r
C. Ground motion estimation:
Alm,r~
cut
cut
c'
a,
a

Fault i
m =~\
GAm,r(
Distance
(log scale)
125
B. Magnitude distribution and rate
of occurrence for Source i:
f M (m), Hi
f M (m)
Lo,
mO mmax
Magnitude m
D. Probability analysis:
P[ A ~ a in time t] /t ~
Zi V! !GA~mr(a*)
f M (m) f R (r ~ m) dmdr

a,
c'
0
ce a,
0
_
CL At_ ,
ok\
\
Ground Motion Level a.
(log scale)
FIGURE C2 Graphs indicating probabilistic seismic hazard analysis steps.
Source: McGuire (1987~.
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126
A similar procedure can be applied to calculate annual prob
abilities of earthquake losses from earthquake ground shaking in a
region, but additional information is needed. First, a scalar variable
needs to be chosen to represent the potential losses (e.g., dollar loss
or number of deaths). Second, the correlation of ground motion at
different sites must be taken into account. This correlation results
because separate sites may be affected simultaneously by the same
earthquake, by similar focusing effects of the source, by similar travel
paths, and by similar geologic conditions at the site. Just as the un
certainty in ground motion is important in site hazard calculations,
PtA > a~m,r] in equation 1, correlation of ground motion at multiple
sites is important to regional risk estunates. The estimation of an
nual probability of exceeding a loss $' for the region can then proceed
by an enumeration of all earthquakes that might affect the region:
P[$ > $ ~ ~ Eui / ,/ Pt$ > $'m' r] fM,R(m, r`)dmdr, {~2~)
m r
which is similar to equation 1 except that the summation is over all
earthquakes that may affect the region of interest, and R represents
earthquake location (without reference to a particular site). The
conditional probability in equation 2 is evaluated as:
P[$ > $' ~ m,r] = Pt(~$j~xj,yj)) > $' ~ m,r), (3)
.j
where $j (I, y, ) is the loss at location I, yj and the summation is over
all locations in the region. The correlation of ground motion enters
into this calculation of total loss over all locations in the region for
an earthquake of specified size and location. In practice the region
is divided into convenient units (e.g., census tracts, statistical areas,
or blocks) for this enumeration. The available format for the facility
inventory or census information obviously plays a role in choosing
the appropriate size of subdivisions for estimating total losses.
Several simplifying assumptions are usually made in applying
equation 2 to estimate earthquake losses. Often the uncertainty
in earthquake losses during a hypothesized earthquake is ignored,
leading to a great simplification of equation 3. These uncertainties
may result from variabilities in the ground motion generated at the
site (whether or not this is used as an intermediate variable), the
effect of local geology on ground motion, the loss that might be
generated in specified facilities for a given ground motion, and the
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127
number and type of facilities at a given location (e.g., uncertainty
in the facility inventory). Ignoring these uncertainties constitutes
a simplification that may be justified if, for example, only a best
estimate of losses versus annual probability Is desired, but in this
case the statistical mean of all relations (rather than, for example,
the median) should be usecI. Even then the results only approximate
the mean loss, and they are likely to underestimate it, perhaps
substantially.
Other sunplifying approximations are appropriate under certain
conditions. If the region considered for the loss estunate Is rather
small (several tens of square kilometers), the integration over loca
tions in the region can be avoided by assuming that the entire region
is subjected to the same ground motion. Then, an accurate hazard
analysis can be performed for one point (e.g., the geographical center
of the region), and the seismic hazard results can be translated to
loss estimates. In effect, this assumes that the region Is small enough
that the same ground motion occurs over its entirety.
In some parts of the United States, the earthquake hazard re
sults from specific fault zones or sources that are small relative to
the size of the area that could be affected, for example, the New
Madrid fault zone. In these cases the earthquakes occur in an area
that is small relative to the region that may be examined for loss
calculations, for example, the Mississippi Valley. The loss (more
specifically, the range of losses) calculated for a specific magnitude
earthquake occurring in the fault zone can then be associated with
the annual probability of that event, using the recurrence relation
for earthquake magnitudes in that source. In erect, one avoids the
integration over location in equation 2; the 1,000~year earthquake
is used to estimate the 1,00~year loss. Note that this circumstance
does not by itself justify ignoring uncertainty in the resulting losses;
as a minimum, mean values (rather than medians) should be used in
aD relations to calculate the resulting losses.
Simulation of Actual Events
In this typical analysis, all of the uncertain input parameters, ex
cept possibly for earthquake magnitude and location, are numerically
simulated. Hence, for each given earthquake magnitude and location,
different loss scenarios are generated in different simulations. The
results are patterns of damage and Toss, which are more realistic
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128
than those produced by bes~estimate scenario analysis. Figure Clb
illustrates results of this type.
Cumulative [ose Over Time
For applications that depend on the total loss that may be ex
pected in a certain geographical region over a given time period, one
should sum losses due to future earthquake occurrences in the region.
One use of this result would be to compare earthquake risks with risks
from other natural phenomena. For certain uses, one may need only
the expected (actualized) cumulative loss, whereas for others it may
be important to calculate the entire probability distribution of the
cumulative loss.
SU~RY
This description of loss estimation methods is neither exhaus
tive nor exclusive, meaning that certain applications may require the
development of specialized procedures not included in the present
list or the combined use of several methods. Generally speaking,
deterministic scenario analyses can be made at a level of detail and
spatial resolution that is ~rnpractical in probabilistic risk calcula
tions, because of the large number of calculations required by the
latter methods. Hence, deterministic analyses (methods A and B
as described in Table C2) might be ideal tools for use in disaster
exercises and for the detailed evaluation and improvement of loss
reduction strategies. On the other hand, public safety policies (such
as the selection of suitable building code provisions) and economic
decisions would be best made considering the integrated results of
risk studies (method C).
The usefulness of scenario type analyses may vary geographically.
For example, in regions where events of size close to the magnum
possible magnitude occur frequently, a singleevent analysis using
one such event may be all one needs to make informed decisions.
By contrast, in regions where seismicity is low and the maximum
earthquake size is unknown, the earthquake threat may be dominated
by events in an intermediate magnitude range. ~ the latter case,
one should make decisions based on the projected loss from a variety
of earthquakes, considering the frequency with which each type of
event occurs in the area.
For many uses, a fully probabilistic risk calculation by method C
is the ideal type of analysis. For example, knowledge of the risk curve
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would allow quantitative assessments of public safety with respect
to earthquakes and comparisons with other risk sources. Insurance
and financial institutions would find risk curves appropriate for the
evaluation of expected (Iongterm average) profits as well as for the
evaluation of the frequency of catastrophic losses. Another example
is the comparison of risk reduction options: different risk reduction
or preventive actions might have different effects depending on the
earthquake size and the amount of damage. The effectiveness of each
proposed action could then be represented in terms of the downward
shift that a particular action produces on the original risk function,
as shown by the dotted curve of Figure CIc. Method D (repeated
simulation) is perhaps most appropriate to plan emergency response,
when one needs to evaluate the adequacy of response strategies in
the context of certain damage and loss scenarios.