Evaluation of earthquake Hazard
Naturgefahren – Erdbebenrisiko
Nachdiplomkurs in angewandten Erdwissenschaft 15-19 Mai 2000
Seismische Gefährdungsanalyse
-------------------------------------------
Evaluation of earthquake hazard
Souad Sellami
SED, Institute of Geophysics, ETH-Hoenggerberg, CH-8093 Zurich,
[email protected]
Keyword: seismic hazard, probabilistic methods, sources zones, attenuation, frequency-magnitude
distribution, return period, probability of exceedance.
Introduction: Seismic Hazard Objective
The general theme of this course is earthquake risk. The concept of risk includes hazard and vulnerability.
The first part has dealt with earthquakes, where when they occur, how big they are and why they happen. The
second part is about the effects.
Hazard assessment is to evaluate, for a certain place, how frequent and how strong earthquake will be felt,
in order to take measure to reduce the possible damages. In other terms, it is to qualify and quantify the level
of ground motion in a site due to the earthquake. Seismic hazard maps depict the levels of chosen ground motions
that likely will, or will not, be exceeded in specified exposure times. The ground motion can be the intensity of
the earthquake, displacement, velocity or acceleration of the seismic wave at the site.
Seismic hazard is determined by the following three factors:
●
●
●
The distribution in time, space and size of the regional seismicity
The attenuation of seismic waves at increasing distances from the location of the earthquake
The action of the shallow geology in the distortion of the seismic signal
The hazard can be estimated using deterministic or probabilistic methods. The probabilistic method (Cornell
1968), broadly applied, will be first described. Alternative methods will be presented in the discussion paragraph.
The three major elements of the probabilistic method are: 1) the characterisation of seismic sources; 2)
the characterisation of attenuation of ground motion; and 3) the actual calculation of probabilities.
Probabilistic method basic principles
The objective of an earthquake-hazard analysis is to evaluate the probability of exceeding a particular level of
ground motion (such as a certain value of peak acceleration) at a site during a specific time interval (such
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (1 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
as 50 years).
The different steps of the probabilistic (Cornell) method are
outlined on the sketch (figure 1.) below (Ruettener 95):
Figure 1.
1. the characterisation of seismic sources is usually achieved by
●
●
●
compilation of an earthquake catalogue (a)
delineation of the seismic sources (b)
magnitudes-frequency distribution (c)
1. the characterisation of attenuation of ground motion is described by attenuation functions (d)
2. computation of the probability analysis (c)
An earthquake-hazard analysis must incorporate the inherent uncertainty of the size, location, and time of
occurrence of future earthquakes, and the attenuation of seismic waves as they propagate from all
possible sources in the region to all possible sites.
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (2 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Probability functions are required, they include the probability density function for the magnitude probability FM
(m), for the distance FR(r) to earthquake, and for the probability that the ground motion exceed a certain value
at a site given m and r.
Characterisation of seismic sources
The first element of seismic hazard assessment, the characterisation of seismic sources,
involves obtaining ‘robust’ answers to three questions, which have been addressed in the first part of this
course:
●
●
●
Where do earthquakes occur?
How often do earthquakes occur?
How big can we expect these earthquakes to be?
In practice three physical parameters of a potential seismic source must be quantified in a seismic-hazard analysis:
1. geometry of the source (or fault), (where)
2. rate of earthquake recurrence (how often) and
3. maximum magnitude, (how big).
Seismicity catalogues are the fundamental data base used to determine where, how often, and how
big earthquakes are likely to be. However and seismicity statistics are based on geologically short catalogues.
For magnitude above 6, the completeness is less than 1000 year in Switzerland (one of the best case) and
less than 200 years in California). Therefore other deformation data are examined. The results from
seismic monitoring, the historic record, geodetic monitoring, and the geologic record are combined to
characterise seismic sources. These data, when available, are used to interpret seismic source zones.
Because many interpretations of the input data are possible, large uncertainties are associated with
source characterisation.
Geometry of the source
The identification of the seismogemic sources in the region is very important. In theory earthquake sources are
faults. In most of the places, the earthquake distribution does not coincide with known fault visible at the
earth surface. So in practice, the shape of a source can be a fault, but they are surfaces (area zones) when
active fault can not be recognised, which is the most common case (for example in Switzerland), The Figure 2
(Rutenner 1995) shows the historical seismicicity map (time span 1300-1994 and earthquake intensity V
and above) together with the geographic distribution of the seismic sources (Sägesser and Mayer-Rosa, 1978).
The shape of the source zone depends strongly on the earthquake distribution ‘per extenso’ on the catalogue. Their
design is subject to a part of subjectivity or expert judgement (Schenk 1996). This is illustrated, for example,
by the source zoning of the Ibero-maghreb region (Jimenez et al 1999) shown on Figure 3.
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (3 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Figure
2. Seismicicity (1300-1994) and sources zones (Ruettener 1995)
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (4 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Figure
3. source delimitations in the Ibero-maghreb region (Jimenez et al 1999)
Rate of earthquake recurrence
The frequency-magnitude occurrence relationship help to characterise the activity of each source. The rate
of recurrence of earthquakes on a seismic source is assumed to follow the Gutenberg-Richter relation
log10 n(M) = a-bM
where n(M) is the number of events per year having magnitudes greater than M. a and b are constants defined
by regression analysis. The slope of the magnitude-frequency Gutenberg-Richter defines the "b value" parameter.
Maximum magnitudes
For a single source, the modified (double truncated) Gutenberg-Richter relation is
N(M)= an)[1 - (1-e-b'(M-Mlow)) /(1-e-b'(Mupp-Mlow))]
an is N(Mlow), b' is the exponential form of the b value. Mupp and Mlow are the upper and lower bound
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (5 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
magnitude on the source. Mlow, is the magnitude below which no engineering-significant damage is expected
and Mupp represents the maximum expected magnitude.The maximum magnitude is related to the tectonic
setting, geometry, and type of the seismic source.
Although no standard method exists for assigning a maximum magnitude to a given fault, empirical correlation
of the fault,
are used based on the length of rupture
the total length
of the fault trace or the area
of the fault
rupture zone. In most cases, faults cannot be clearly recognised, maximum magnitude are than deduced
either from the earthquake catalogue, from the recurrence rate (extrapolating the Gutemberg-Richter
relationship) or from paleoseismicity studies.
To characterise each source zone, the following parameters are evaluated:
●
●
●
●
Mupp and Mlow, the upper and lower bound magnitude on the source,
the Gutenberg-Richter earthquake recurrence parameter (b-value),
the activity rate an the number of event per year having magnitudes equal to or greater than Mlow on the
source, and
additionally, the average hypocentral depth.
Characterisation of attenuation of ground motion
State-of-the-art estimates of expected ground motion at a given distance from an earthquake of a given magnitude
are the second element of earthquake hazard assessments. These estimates are usually equations, called
attenuation relationships, which express ground motion as a function of magnitude and distance (and
occasionally other variables, such as type of faulting). Commonly assessed ground motions are maximum
intensity, peak ground acceleration (PGA), peak ground velocity (PGV), and several spectral accelerations
(SA). Each ground motion mapped corresponds to a portion of the bandwidth of energy radiated from
an earthquake. PGA and 0.2s SA correspond to short-period energy that will have the greatest effect on
short-period structures (one-to two story). PGA values are directly related to the lateral forces that damage
short period. Longer-period SA (1.0s, 2.0s, etc.) depict the level of shaking that will have the greatest effect on
longer-period structures (10+ story buildings, bridges, etc.). Ground motion attenuation relationships may
be determined in two different ways: empirically, using previously recorded ground motions, or theoretically, using
seismological models to generate synthetic ground motions which account for the source, site, and path
effects. There is overlap in these approaches, however, since empirical approaches fit the data to a functional
form suggested by theory and theoretical approaches often use empirical data to determine some parameters.
The ground motion at a site, for example Peak Ground Acceleration depends on the earthquake source, the seismic
wave propagation and the site response. Earthquake source signifies the earthquake magnitude, the depth and
the focal mechanism, the propagation depends mainly on the distance to the site. The site response deals with
the local geology (site classification); it is the subject of microzonation.
The basic functional (logarithmic) form for ground motion attenuation relationship is defined as (Reiter 1990)
ln Y = lnb1 + lnf1(M) + lnf2(R) + lnf3(M,R) + lnf4(P) + ln ε
●
●
●
Y is the strong motion parameter to be estimated (dependant variable), it is lognormal distributed.
f1(M) is a function of the independent variable M, earthquake source size generally magnitude. In that case
moment magnitude (M) is the preferred magnitude measure, because it is directly related to the seismic
moment of the earthquake and does not saturate. But it can also be the epicentral intensity.
f2(R) depends on the variable R, the seismogenic area source to site distance,
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (6 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
●
●
●
f3(M,R) is a possible joint function between M and R. For example for an earthquake with big magnitude the
seismogenic area is large and the source to site distance may be different.
f4(Pi) are functions representing possible source and site effects. For example different style of faulting in the
near field may generate different ground motions values Abrahamson and Shedlock (1997).
ε is an error term representing the uncertainty in Y
These relationship are for a specific site classification (hard rock, soft rock, etc.). Hazard values calculated for
rock/stiff soil sites (the most common site classifications) are lower than hazard values calculated for soil sites. A
comprehensive review and application for Switzerland can be found in Smit (1996).
Example of different attenuation functions used in the different countries of the Ibero-maghreb region are
shown on table 1 and figure 4 (Jimenez et al. 1999).
Table 1
Country
Algeria
Morocco
Portugal
Spain
Attenuation law
PGA = (190.67
e 0.823 M
+0.864 e
log PGA = -1.02 +
0.25 M - 0.00255
2 +7.3
(R
(R
) / (R
0.463 M
2
2
)
1.561
+7.3
)
1/2
2
- log
)
1/2
I = 6.8 + 1.13 M 1.68 ln (R+14)
I=I
0
+ 12.55 -
3.53 ln (R+25)
Tunisia
PGA = (5600 e
M ) / (R+40)
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (7 of 16) [05.11.2007 15:10:24]
0.8
2
Evaluation of earthquake Hazard
Figure
4. Attenuation function used in the Ibero-Maghreb (Jimenez et al. 1999).
For the calculation of the seismic hazard map of the whole region, only one attenuation law was considered
Joyner and Boore (1981). This relationship is represented on the figure 4 with one standard deviation in log PGA.
It could roughly represent an average of the different laws used in the region.
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (8 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Figure 5. Isoseismal map of the 1356 Basel event (Mayer-Rosa and Cadiot, 1979)
To adjust the parameters of the attenuation function for intensities (ex. Portugal and Spain in table
1), macroseismic data are needed. For example the isoseismal map of the 1356 Basel earthquake (after
Mayer-Rosa and Cadiot, 1979) shown on figure 5.
Figure 6. Intensity distribution (13/03/64) and
attenuation low (Ruettener 1995)
The figure 6 depict the observed intensity distribution of an event (13 March 1964 in Central Switzerland)
together with the attenuation law, for subalpine region (Ruettener1995). It shows a significant scattering of
data around the attenuation function. This scattering depends not only on physical effect like the directivity of
the radiated energy or the local geology but also on the quality of intensity data.
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (9 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Calculation of probabilities
The third element of hazard assessment, the actual calculation of expected ground motion values,
involves determining an annual frequency of exceedance of the ground motion parameter of interest,
then summing over the time period of interest.
The probability tool used is a poissonian model. The occurrence of a ground-motion parameter at a site in
excess of a specified level is poisson
process if the occurrence of earthquakes is
poissonian
. This means that any event is independent
occurrence of all other events. In theory, the catalogue has to be declustered, the foreschoks and
afterschoks should be removed
of the
Probability of Exceedance
The annual mean number of events in which GM exceeds the specified ground motion level Z is calculated
by summing up the incremental contributions of the N sources, taking into account:
●
the annual mean rate of recurrence of earthquakes of magnitude Mi on each source
●
given the occurrence of an earthquake of magnitude Mi, the distance from the rupture surface to the site,
●
given the occurrence of an earthquake of magnitude Mi at a distance of rj, the probability that the value of
ground motion at the site exceeds a specified level.
The probability (ex 10%) of exceeding a specified level of ground motion (such as a certain value of
peak acceleration) at a selected site within the time interval of interest (such as 50 years) is calculated by:
1/ combining the three probability functions,
2/ integrating over all possible earthquake, location, magnitude for a source
3/ integrating over all the sources
The probability of exceedance, in a specific time interval, that ground motion amplitude a* is exceeded can
be expressed as follows (McGuire, 1993)
where n
i
is the mean annual rate of occurence in source i, G is the probability that an earthquake given m
and r exceeds ground motion a* at a specific site.
for magnitude,
is the probability density function
and is the probability distribution function for distance.
Probability terms
Two equivalent results are typically calculated:
1/ The ground motion corresponding to a certain probability of exceedance in a specific interval of time (exposure
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (10 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
time) (see hazard for Brig, Ruettener, 1995 in Figure 7.a), or
2/ The ground motion having a specific average return period (id. Figure 7.b).
Figure 7.a and b. Hazard outputs of the historical
method for Brig (Ruettener 1995)
Return period = -T
p(Zz)
/ ln(1-P(Zz)
desired probability of exceedance during the time T
)
(exposure time)
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (11 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Probability of exccedance in a
given exposure time
Probability of non-exceedance
in a given exposure time
approximate average return
period in years
20 % in 10 years
80% in 10 years
50 years
10% in 10 years
90% in 10 years
100 years
10% in 50 years
90% in 50 years
500 years
10% in 250 years
90% in 250 years
2500 years
1% in 100 years
99% in 100 years
10 000 years
The probability of non-exceedance of 90% in 50 years corresponds to a return period of 475 years. It is
frequently used to represent seismic hazard maps because 50 years is the average life span of a building. Note
that it is also the level required for European building codes EC8. Longer return periods are chosen when
dealing with critical lifeline systems like dams etc..(see next contributions).
Incorporation of Uncertainties
The uncertainties of the basic input data must be taken into account. Uncertainties are introduced either by lack
of data or/and lack of knowledge. There are random uncertainties which could be incorporated in the hazard
curve calculation. There are also systematic or modelling uncertainties for example for the choice of
maximum magnitude, the correct ground motion model. These uncertainties are taken into account by
developing alternative strategies and models in the interpretation of those input data for which
significant uncertainties are known to exist. For example, multiple source zone models may be defined.
Hazard calculations from each model are then combined using various schemes that produce a weighted mean
(or median) hazard value. It is the logic tree analysis (Frankel 1995).
Applications, alternative techniques and limits of earthquake hazard assessment
The probabilistc method, based on a poissonian model, does not depict a possible variation of the seismicity
in time, because of the hypothesis of stationarity of the model. Some research is developing in this direction.
Seismic hazard assessment in low seismicity areas is much more subject to large errors than in areas with
high earthquake activity. This is specifically the case if the time span of the available data catalogue is
considerably smaller than the mean return interval of large events, for which the hazard data has to be calculated.
Alternative techniques of the probabilistic method are mainly to avoid the delimitation of source zone. The historical
method for example, applied in Switzerland by Ruettener (1995) estimates the ground motion at a site from each
event of the historical catalogue. The probability distribution of the historic occurrences of earthquake is
calculated from the earthquake rate.
The deterministic approach evaluates the maximum expected ground motion at a site, resulting from the
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (12 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
strongest potential earthquake at the nearer possible distance. Deterministic approaches are often used to
evaluate the hazard for a selected site. They are in general more conservative. But they do not take into
account uncertainties nor an estimate of frequency of occurrence which is needed by decision makers for planning
purposes.
The probabilistic method allows to take uncertainties into account and is easily applied. However, as the quality
of the output depends strongly on the quality of the input parameters (earthquake catalogues, strong motion
relationships), and it might be that there is little transparency on the quality and the integration of the data. On the
other hand the output reflects the state of the data and is subject to improvement.
Probabilistic approach can be applied to mapping the hazard for different probabilities and exposure time and
for different area sizes (local / regional (Figure 8) / global).
Global seismic hazard assessment maps: The variations in each element of the seismic hazard assessment lead
to differences in the estimated hazard along the national borders. Some research programs (DACH
GSHAP, SESAME) have been launched in order to homogenise this hazard (Figure 9).
Figure 8.
Earthquake hazard map of the Ibero-Maghreb region. PGA [m/s2] with 90% probability of non-exceedance in
50 years.
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (13 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Figure 9. Horizontal peak ground acceleration seismic hazard map representing stiff site conditions for
an exceedance or occurrence rate of 10% within 50 years (Gruenthal et al. 1999).
Links
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (14 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
Non commercial computer programs for hazard analysis:
●
SeisriskIII ( Bender and Perkins)
http://geohazards.cr.usgs.gov/eq/html/swmain.html
●
Wizmap (Musson) BSGS
http://www.gsrg.nmh.ac.uk/~phoh/wizmap.htm
●
CRISIS (Ordaz) Bergen, Norway In SEISAN package
http://www.ifjf.uib.no/Seismologi/software/seisan/seisan.html
Application projects:
●
USGS national seismic hazard mapping
http://geohazards.cr.usgs.gov/eq/index.html
●
Global Seismic Hazard Program
http://seismo.ethz.ch/GSHAP/
BSGS World seismic hazard service
http://www.gsrg.nmh.ac.uk/hazard/hazard2.htm
●
●
A short guide to seismic hazard; a brief paper on the subject.
Seismic hazard in the UK; a guide to UK seismicity, with examples.
Lexicon (partly based on Hays 1980)
●
●
●
Attenuation / Abminderung Daempfung / attenuation: decrease of the seismic ground motion with
the distance.
b-value / b-Werte/ - : from the Gutenberg-Richter relationship, this parameter indicates the relative
frequency of earthquake of different sizes (magnitude) derived from the historical seismicity.
Catalogue / Katalog / catalogue: record of historical earthquake. It can be used for the time span of
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (15 of 16) [05.11.2007 15:10:24]
Evaluation of earthquake Hazard
●
●
●
●
●
●
●
●
●
completness for different magnitudes.
Exceedance probability / Ueberschreitenswahrscheinlichkeit / probabilite de dépasser ou
d'exceder: the probability over some exposure time that an earthquake will generate a value of ground
shaking greater than a specific level.
Exposure time / - / - : The period of time (period of interest ex 50 years) that a structure or a facility is
exposed to hazard. Linked to the design lifetime of the structure.
Ground motion / Bodenbewegung / mouvement du sol: Parameter (acceleration, velocity or
displacement) which is evaluated by the hazard study can be also intensities or acceleration at different
frequencies (Spectral acceleration).
Hazard / Gefaehrdung/ danger ou aléa: the phenomena accompagning the earthquake which may
cause the damage or loss in that case ground shaking
Return period / Wiederkehrperiode / periode de retour: average period of time between events
causing ground motion that exceed a particular level at a site. It is the inverse of annual probability of
exceedance. Also mentioned as the reccurence interval
Risk / Risiko/ risque: it is the possible probability of lost. It is a function of hazard * vulnerability *
(exposure)*(value)
Seismic activity/ Aktivität/ activité sismique: (of a source) it is described with the frequency/
magnitude relationship ( Häufigkeitverteilung) characterise by the b-value.
Source / Quelle / source: the source of energy release causing an earthquake. For computing purpose,
they can be areas, faults or points the source is characterise by its activity and the maximal an minimal
magnitudes
Vulnerability/ Verletzbarkeit/ vulnerabilité: value of the structure exposed to the hazard
file:///M|/undervisning/geo4100/extradocuments/Evaluation of earthquake Hazard.htm (16 of 16) [05.11.2007 15:10:24]