Jee Bommer 2002 Dsha vs Psha

8/12/2019 Jee Bommer 2002 Dsha vs Psha

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Journal of Earthquake Engineering, Vol. 6, Special Issue 1 (2002) 4373c Imperial College Press

DETERMINISTIC VS. PROBABILISTIC SEISMIC HAZARD

ASSESSMENT: AN EXAGGERATED AND

OBSTRUCTIVE DICHOTOMY

JULIAN J. BOMMER

Department of Civil and Environmental Engineering,

Imperial College, London SW7 2BU, UK

Deterministic and probabilistic seismic hazard assessment are frequently representedas irreconcilably different approaches to the problem of calculating earthquake groundmotions for design, each method fervently defended by its proponents. This situationoften gives the impression that the selection of either a deterministic or a probabilisticapproach is the most fundamental choice in performing a seismic hazard assessment.The dichotomy between the two approaches is not as pronounced as often implied andthere are many examples of hazard assessments combining elements of both methods.Insistence on the fundamental division between the deterministic and probabilistic ap-proaches is an obstacle to the development of the most appropriate method of assessmentin a particular case. It is neither possible nor useful to establish an approach to seismic

hazard assessment that will be the ideal tool for all situations. The approach in eachstudy should be chosen according to the nature of the project and also be calibratedto the seismicity of the region under study, including the quantity and quality of thedata available to characterise the seismicity. Seismic hazard assessment should continueto evolve, unfettered by almost ideological allegiance to particular approaches, with theunderstanding of earthquake processes.

Keywords: Seismic hazard; probabilistic seismic hazard assessment; deterministic seismichazard assessment; seismic risk.

1. Introduction

Seismic hazard could be defined, in the most general sense, as the possibility of

potentially destructive earthquake effects occurring at a particular location. With

the exception of surface fault rupture and tsunami, all the destructive effects of

earthquakes are directly related to the ground shaking induced by the passage

of seismic waves. Textbooks that present guidance on how to assess the hazard of

strong ground-motions invariably present the fundamental choice facing the analyst

as that between adopting a deterministic or probabilistic approach [e.g. Reiter,

1990; Krinitzsky et al., 1993; Kramer, 1996]. Statements made by proponents of

the two approaches often imply very serious differences between deterministic andprobabilistic seismic hazard assessment and reinforce the idea that the choice be-

tween them is one of the most important steps in the process of hazard assessment.

This paper aims to show that this apparently diametric split between the two ap-

proaches is misleading and, more importantly, that it is not helpful to those faced

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44 J. J. Bommer

with the problem of assessing the hazard presented by earthquake ground motions

at a site.

2. DSHA VS. PSHA: An Exaggerated Dichotomy

Probabilistic seismic hazard assessment (PSHA) was introduced a little over

30 years ago in the landmark paper by Cornell [1968] and has become the most

widely used approach to the problem of determining the characteristics of strong

ground-motion for engineering design. Some, however, have challenged the approach

and put up vociferous defence of deterministic seismic hazard assessment (DSHA),

in turn soliciting firm responses from those favouring PSHA. The division between

the two camps has been expressed in the scientific and technical literature, some-

times in terms reminiscent of political debate.a In some situations the division

has become public as for example when in October 2000 US newspapers reported

the disagreements between Caltrans and the US Army Corps of Engineers regard-

ing the choice of PSHA or DSHA in assessing design loads for the new eastern

span of the Bay Bridge in San Francisco Bay. Hanks and Cornell [2001] have pre-

dicted a similar showdown around the seismic hazard assessment for the Yucca

Mountains nuclear waste repository [Stepp et al., 2001]. All of this points to a

seemingly irreconcilable split between DSHA and PSHA, which warrants closer

examination.

2.1. Determinism and probability in seismic hazard assessment

Reiter [1990] and Kramer [1996], currently the most widely consulted textbooks on

seismic hazard analysis, describe DSHA in the same way. The basis of DSHA is to

develop earthquake scenarios, defined by location and magnitude, which could affect

the site under consideration. The resulting ground motions at the site, from which

the controlling event is determined, are then calculated using attenuation relations;

in some cases, there may be more than one controlling event to be considered indesign.

The mechanics of PSHA are far less obvious than those of DSHA, with the result

that there is often misunderstanding of many of the basic features. The excellent

recent papers by Abrahamson [2000] and by Hanks and Cornell [2001] provide very

useful clarification of many issues that have created confusion regarding PSHA.

The essence of PSHA is to identify all possible earthquakes that could affect a site,

including all feasible combinations of magnitude and distance, and to characterise

the frequency of occurrence of different size earthquakes through a recurrence rela-

tionship. Attenuation equations are then employed to calculate the ground-motionparameters that would result at the site due to each of these earthquakes and hence

aThe reader is referred, for example, to the acknowledgements in the paper by Krinitzsky [1998]and the response by Hanks and Cornell [2001].


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Deterministic vs. Probabilistic Seismic Hazard Assessment 45

the rate at which different levels of ground motion occur at the site is calculated.

The design values of motion are then those having a particular annual frequency of

occurrence.Common to both approaches is the very fundamental, and highly problematic,

issue of identifying potential sources of earthquakes. Another common feature is

the modelling of the ground motion through the use of attenuation relationships,

more correctly called ground-motion prediction equations [D. M. Boore, written

communication]. The principle difference in the two procedures, as described above,

resides in those steps of PSHA that are related to characterising the rate at which

earthquakes and particular levels of ground motion occur. Hanks and Cornell [2001]

point out that the two approaches have far more in common than they do in

differences and that in fact the only difference is that a PSHA has units of timeand DSHA does not. This is indeed a very fundamental distinction between the

two approaches as currently practised: in a DSHA the hazard will be defined as

the ground motion at the site resulting from the controlling earthquake, whereas

in PSHA the hazard is defined as the mean rate of exceedance of some chosen

ground-motion amplitude [Hanks and Cornell, 2001]. At this point it is useful to

briefly define the different terms used to characterise probabilistic seismic hazard:

the return period of a particular ground motion, Tr(Y), is simply the reciprocal

of the annual rate of exceedance. For a specified design life, L, of a project, the

probability of exceedance of the level of ground motion (assuming that a Poissonmodel is adopted) is given by:

q= 1 eL

Tr . (1)

Once a mean rate of exceedance or probability of exceedance or return period is

selected as the basis for design, the output of PSHA is then expressed in terms of

a specified ground motion, in the same way as DSHA.

Another important difference between the two approaches, which is discussed

further in Sec. 3, is related to the treatment of hazard due to different sources of

earthquakes. In PSHA, the hazard contributions of different seismogenic sources arecombined into a single frequency of exceedance of the ground-motion parameter;

in DSHA, each seismogenic source is considered separately, the design motions

corresponding to a single scenario in a single source.

Regarding differences and similarities between the two methods, it is often

pointed out that probabilities are at least implicitly present in DSHA in so far

as the probability of a particular earthquake scenario occurring during the de-

sign life of the engineering project is effectively assigned as unity. An alterna-

tive interpretation is that within a framework of spatially distributed seismicity,

the probability of occurrence of a deterministic scenario is, mathematically, zero[Hanks and Cornell, 2001] but in general the implied probability of one is a valid

interpretation of the scenarios defined in DSHA. As regards the resulting ground

motions, however, the probability depends upon the treatment of the scatter in the

strong-motion prediction equation: if the median plus one standard deviation is


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46 J. J. Bommer

used, this will correspond to a motion with a 16-percent probability of exceedance,

for the particular earthquake specified in the scenario. The probabilistic nature of

ground-motion levels obtained from scaling relationships is reflected in the fact thatin Japan probabilistic usually refers to ground motions obtained in this way from

a particular scenario, as opposed to deterministic ground motions obtained by

modelling of the fault rupture and wave propagation [Abrahamson, 2000].

It can equally be pointed out that any PSHA includes many deterministic

elements in so much that the definition of nearly all of the input requires the

application of judgements to select from a range of possibilities. This applies in

particular to the definition of the geographical limits of the seismic sources zones

and the selection of the maximum magnitude. The deterministic nature of defining

seismic source zones and the consequently great differences that can arise amongstthe interpretations of different experts are well known [e.g. Barbano et al., 1989;

Reiter, 1990].

In addition to the various parameters that define the physical model that is the

basis for any PSHA, it could also be argued that another parameter, which has a

pronounced influence on the input to engineering design, is also defined determin-

istically: the design probability of exceedance. This issue, which is of fundamen-

tal importance to the raison detreof probabilistic seismic hazard assessment, is

explored in Sec. 4.

2.2. From Cornell to kernel boldemdash which PSHA?

The nature of the conflict between proponents of PSHA and DSHA was previously

likened to that between opposing political or religious ideologies, in which each

side claims exclusive ownership of the truth. However, scratching the surface of

opposing sides in ideological conflicts nearly always reveals the division to be far

less clear, with divisions within each camp being often almost as pronounced as

the fundamental ideological split itself. One only needs to look at the history of

the Left in international politics, in which internal conflicts have often taken ona ferocity at least as great as that shown in the confrontation with the Right, for

a clear example of an apparent dichotomy concealing a multitude of opinions and

philosophies.b In this sense, the analogy remains useful for the split between the

proponents of DSHA and PSHA: the defendants of PSHA often ignore the fact

that there are many different methods of analysis that fall under the heading of

probabilistic and the proponents of each of these methods argue their case by

pointing out shortcomings in the others.

The formal beginning of PSHA, as mentioned before, can be traced back to the

classic paper by Cornell [1968]. Important developments included the developmentof the software EQRISK by McGuire [1976], with the result that the method is fre-

bHence the joke that if there are three Trotskyists gathered in a room there will be four politicalparties.


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quently referred to by the name CornellMcGuire. A significant difference between

EQRISK and the original formulation of Cornell [1968] was the inclusion of the

influence of the uncertainty or scatter in the strong-motion prediction equation,subsequently explored by Bender [1984].

Two fundamental features of the CornellMcGuire method are definition of

seismogenic source zones, as areas or lines, with spatially uniform activity and the

assumption of a Poisson process to represent the seismicity, both of which have been

challenged by different researchers who have proposed alternatives. For example,

the use of Markov renewal chains has been proposed as an alternative probabilistic

model for subduction zones with identified seismic gaps, to develop either slip-

dependent [Kiremidjian and Anagnos, 1984] or time-dependent [Kiremdjian and

Suzuki, 1987] estimates of hazard. There have also been numerous studies publishedgiving short-term hazard estimates based on non-Poissonian seismicity, such as the

forecast by Parsons et al. [2000] for hazard in the Sea of Marmara area following

the 1999 Kocaeli and Duzce earthquakes.

Many alternatives to uniformly distributed seismicity within sources defined by

polygons have been put forward, such as Bender and Perkins [1982, 1987] who

proposed sources with smoothed boundaries, obtained by defining a standard error

on earthquake locations. In an earlier study Peek et al. [1980] used fuzzy set theory

to smooth the transitions between source boundaries.

There have also been proposals to do away with source zones altogether and usethe seismic catalogue itself to represent the possible locations of earthquakes, an

approach that may have been used before 1968. Such historic approaches can be

non-parametric [Venezianoet al., 1984] or parametric [Shepherdet al., 1993; Kijko

and Graham, 1998]; Makropoulos and Burton [1986] developed an approach using

the earthquake catalogue to represent sources and Gumbel distributions. Recent

adaptation of these zone-free methods include the approach based on spatially-

smoothed historical seismicity of Frankel [1995] and the kernel method of Woo

[1996], who alludes to misgivings over zonation and, consequently, with the edifice

of hazard computation built on zonation, the cornerstone of the CornellMcGuiremethod. In these most recent methods, earthquake epicentres in the catalogue are

smoothed, according to criteria related to their magnitude and recurrence interval,

to form seismic sources.

The differences amongst these different approaches to PSHA are not simply aca-

demic: Bommer et al. [1998] produced hazard maps for upper-crustal seismicity in

El Salvador determined using the CornellMcGuire approach, two zone-free meth-

ods and the kernel method. The four hazard maps, prepared using exactly the same

input, show very significant differences in the resulting spatial distribution of the

hazard and the maximum values of PGA vary amongst the four maps by a factorof more than two. Similarly divergent results obtained using the CornellMcGuire

and the Frankel [1995] approach have been presented by Wahlstrom and Grunthal

[2000] for Fennoscandanavia.


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48 J. J. Bommer

2.3. . . . and which DSHA?

Just there are many different approaches to PSHA, developed since the publica-tion of Cornell [1968], there is not a single, established and universally accepted

approach to DSHA, in part precisely because of the absence of a classic point of

reference. Arguably, the recent paper by Krinitzsky [2001], could become the stan-

dard reference for DSHA that is currently missing from the technical literature.

One important difference between DSHA as proposed by Krinitzsky [2001] and

DSHA as described by Reiter [1990] and Kramer [1996], is that whereas the latter

imply that the ground motions for each scenario should be calculated using median

(50-percentile) values from strong-motion scaling relationships, Krinizsky [2001]

proposes the use of the median-plus-one-standard deviation (84-percentile) values.

Confusion regarding the meaning of DSHA is created by the use of the word

deterministic to describe scenarios obtained by deaggregation of PSHA, a sub-

ject discussed in Sec. 3. Romeo and Prestininizi [2000] obtain design earthquake

scenarios by manipulation of magnitude-distance pairs found from deaggregation

and refer to these as deterministic reference events; to add to the confusion, the

paper also uses the term in the sense defined in Sec. 2.1, assigning the maximum

magnitude earthquake to an active fault.

It is sometimes thought that DSHA is mainly applicable to site-specific hazard

assessments, but there are examples of deterministic seismic hazard maps, such

as those produced by the California Division of Mines and Geology for Caltrans

[Mualchin, 1996]. The map is prepared by assigning the maximum credible earth-

quake (MCE) to each known active or potentially active fault, calculating the re-

sulting ground motions, and mapping contours of the highest values of the chosen

ground-motion parameter. Anderson [1997] argues for supplementing probabilistic

maps with such deterministic scenario maps to provide insight to what might

happen if particular faults actually rupture during the design life of a project.

The hazard mapping method developed by Costa et al. [1993] for Italy, and sub-

sequently applied to many other countries [e.g. Alvarez et al., 1999; Aoudia et al.,

2000; Panza et al., 1996; Radulian et al., 1996] has also been called deterministic,

although it is significantly different from DSHA as described in Sec. 2.1. The method

is based on the generation of synthetic accelerograms at the nodes of a grid, from

which contours of the peak motions are drawn. One notable feature of the approach

is that the choice of grid size results in an arbitrary minimum source-to-site distance

of about 15 km, which is hardly a worst-case scenario.

2.4. Combined DSHA and PSHA

The apparently irreconcilable contradiction between PSHA and DSHA has not beensufficient to prevent their combined use in some recent applications. In common with

most seismic design codes, the 1997 edition of the Uniform Building Code (UBC97)

defines the design earthquake actions on the basis of a zonation map corresponding

to a 475-year return period, used to anchor a response spectrum. Within Zone 4,


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for any site within 15 km of an identified active fault capable of producing an

earthquake ofM6.5 or greater, the near source factors Na and Nv are applied to

increase the spectral ordinates for the effects of rupture directivity [e.g. Somervilleet al., 1997]. Arguably there is a probabilistic element in this procedure since the

slip rate is used in addition to the maximum magnitude to classify the fault and

thus determine the values of the factors. However, the application ofNa and Nv is

essentially deterministic: the implicit assumption is that if there is an active fault

within 15 km of the site, it will rupture during the design life of the structure and

furthermore it will rupture in such a way as to produce forward directivity effects

at the site.

A more explicit combination of DSHA and PSHA has been used in the prepa-

ration of the maximum considered earthquake (for which the acronym MCE is,confusingly, also used) maps for the 1997 NEHRP Recommended Provisions for

Seismic Regulations for New Buildings [Leyendecker et al., 2000]. Before continu-

ing, it is important to note here that in this context MCE has a different meaning

from that within DSHA mentioned above. Most importantly and this is a source

for much potential confusion in the DSHA context, the earthquake refers to

an event defined by magnitude and location, whereas in PSHA earthquake now

refers to the ground motion at the site. Two maps are produced, giving contours of

spectral ordinates at 0.2 and 1.0 s, one using PSHA for a probability of exceedance

of 2% in 50 years, the other deterministic, using active fault locations and activi-ties combined with median values from strong-motion scaling relations multiplied

by a factor of 1.5. Areas are defined on the probabilistic map where the ordinates

exceed 1.5gand 0.6gfor periods of 0.2 and 1.0 s respectively; within these plateaus,

the values from the deterministic map are used instead wherever these are lower

than those from the probabilistic map. This process effectively uses DSHA to cap

the results of PSHA by not allowing motions higher than those corresponding to

a deterministic scenario. Wherever the deterministic values are higher than those

from the probabilistic map, the latter are retained; hence, the conclusion is that

the probabilistic estimates should not exceed the deterministic estimates, which areeffectively considered therefore as an upper bound. The validity of this assumption

is questionable, however, in part due to the possibility that a significant active fault

has not been recognised, but more importantly because of the very different treat-

ment of uncertainty in the preparation of the two maps, a subject explored further

in the next section.

3. Earthquakes, Seismic Actions and Seismic Hazard

One of the most fundamental differences between DHSA and PSHA is the trans-parency or otherwise of the underlying features of the earthquake processes and in

the treatment of the uncertainties associated with current models of these processes.

In this section, the two methods are considered with respect to their treatment of

uncertainty and their relationship with real earthquake processes.


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50 J. J. Bommer

3.1. Earthquake scenarios and seismic actions

The first and most fundamental output from a PSHA is a hazard curve, a plotof the values of the annual rate of exceedance, return period or the probability

of exceedance within a particular design life against a selected ground-motion or

response parameter (Fig. 1).

The values on a hazard curve convey whether the area is of low, moderate

or high seismic hazard and its slope may indicate if the larger earthquakes have

relatively short or long recurrence intervals. Beyond this, a hazard curve for a sin-

gle ground-motion parameter tells one almost nothing about the nature of earth-

quakes likely to affect the site. For a given exceedance probability, the curves imply

that the corresponding level of ground motion increases smoothly and continuously

with the period of exposure. This is the inevitable result of calculations based on

random spatial distribution of earthquakes and a continuous magnitude-frequency

relationship. In passing it is worth noting that the validity of the GutenbergRichter

recurrence relationship, which forms the backbone of PSHA, has been questioned by

several researchers [Krinitzsky, 1993; Speidel and Mattson, 1995; Hofmann, 1996].

Several centuries from now, when some accelerograph stations have been operating

for thousands of years, it will be possible to plot the actual variation of aver-

age ground-motion parameters with time to observe how well our hazard curves

are modelling what actually may happen at any given site. The results will of

course be a series of step functions rather than a smooth curve, but if the hazard

Fig. 1. Seismic hazard curves obtained for San Salvador (El Salvador) using the median valuesfrom the attenuation relationship and including the integration across the scatter [Bommer et al.,2000].


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Fig. 2. Relationship between magnitude and recurrence intervals for earthquakes of M 7.1 andgreater in the Mexican subduction zone [Hong and Rosenblueth, 1988].

Fig. 3. Contours of MMI > VII for upper-crustal earthquakes in and around San Salvador duringthe last three centuries [Harlowet al., 1993].


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52 J. J. Bommer

curve provided a good fit to the recorded values this would vindicate PSHA. In

the meantime, it is not actually possible to validate the results of a probabilistic

seismic hazard assessment.The characteristic earthquake model, in which major faults produce large earth-

quakes of similar characteristics at more or less constant intervals, is clearly not

consistent with the idea that hazard varies gradually with time. The model was

originally proposed by Singh et al. [1983] for major events in the Mexican subduc-

tion zone, where earthquakes of magnitude above 8 occur quasi-periodically and

there is an absence of activity in the magnitude range 7.4 to 8.0 (Fig. 2). The con-

cept of characteristic earthquakes has been subsequently applied to major crustal

faults and reinforced by paleoseismology [Schwartz and Coppersmith, 1984]. For a

given site affected by a single source with a characteristic earthquake, the groundmotion expected at the site will clearly jump by a certain increment when the

characteristic earthquake occurs.

The concept of characteristic earthquakes may not be limited, however, to large

events on plate boundaries and major faults. Main [1987] identified characteristic

earthquakes of magnitude about 4.6 in the sequence preceding the 1980 eruption

of Mount St. Helens. Another example may be the upper-crustal seismicity along

the Central American volcanic chain [White and Harlow, 1993]. These destructive

events occur at irregular intervals, often in clusters, around the main volcanic cen-

tres (Fig. 3). Recurrence relationships derived for the entire volcanic chain clearlyindicate a bilinear behaviour, reminiscent of the characteristic model (Fig. 4). The

recurrence of these destructive events, sometimes with almost identical locations

and characteristics [Ambraseys et al., 2001], obviously suggests itself for a deter-

ministic treatment, as has been done for example in the microzonation study of San

Salvador [Faccioli et al., 1988].

Fig. 4. Magnitude-frequency relationships for the Central American volcanic chain using theseismic catalogue for different periods: clockwise from top left 18981994, 19311994 and19641994 [Bommer et al., 1998].


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3.2. Seismic hazard from multiple sources of seismicity

In the simple descriptions of DSHA and PSHA given in Sec. 2.1, apart from thefundamental difference related to the units of time, the most important distinc-

tion between the two approaches is in the way the hazard from different sources of

seismicity are treated. DSHA treats each seismogenic source separately and their

influence on the final outcome is entirely transparent. PSHA combines the contri-

butions from all relevant sources into a single rate for each level of a particular

ground-motion parameter. The consequence is that if the hazard is calculated in

terms of a range of parameters, such as spectral ordinates at several periods, the

final results will generally not be compatible with any physically feasible earth-

quake scenario. In recent years, many deaggregation techniques have been devel-

oped to identify the earthquake scenarios that contribute most significantly to the

design motions obtained from PSHA [McGuire, 1995; Chapman, 1995, 1999; Baz-

zurro and Cornell, 1999; Musson, 1999]. The output of these techniques is often

that more than one scenario must be defined in order to match different por-

tions of the uniform hazard spectrum (UHS). This is the reason that Romeo and

Prestininzi [2000] needed to use an adjusted design earthquake, altering the sce-

nario found by deaggregation, in order for the resulting spectrum not to fall below

the UHS.

If such manipulation of the scenarios found from deaggregation is required or if

different scenarios from different sources are to be used, this begs the question of

why should the influence of different seismogenic sources be combined in the first

place. The answer would appear to lie in the primordial importance that PSHA

attaches to the rateof exceedance of ground-motion levels. The total probability

theorem requires that all earthquakes contributing to the rate of exceedance of a

given ground-motion level be considered simultaneously and therein PSHA creates

for itself considerable physical problems for the sake of mathematical rigour.

For now let us assume that there is a sound and rigorous basis for the selection

of the design probabilities, an assumption that will be revisited later. If many

earthquake sources affect a site, and consequently a wide range ofM-Rscenarios are

possible, selecting the design seismic actions at a particular annual frequency may

be a rational approach. If, however, characteristic earthquakes are identified, what

is the result of this approach? The answer will depend on the relation between the

characteristic recurrence interval and the design return period; for large magnitude

earthquakes on plate boundaries the result could lie somewhere in the no-mans

land above the ground-motion levels from the background seismicity and below

the ground motions due to the occurrence of the characteristic event.

Let us return to the case of San Salvador (Fig. 4); the historical record over

three centuries reveals recurrence intervals of between 2 and 65 years for localdestructive earthquakes, with an average of about 22 years [Harlow et al., 1993].

What then is the result of selecting ground motions corresponding to a 475-year

return period? Unlike characteristic events on major faults or subduction zones,

there is evidently a degree of uncertainty associated with the location of future


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54 J. J. Bommer

events, hence a probabilistic approach may help to select an appropriate source-

to-site distance (although it cannot guarantee that the distance for any site in the

next earthquake will not actually be shorter). The source-to-site distance of thehazard-consistent scenario has indeed been found to decrease as the return period

grows, but the main effect of going to lower and lower probabilities of exceedance

is just to add more and more increments of standard deviation to the expected

motions from a typical earthquake scenario [Bommer et al., 2000].

3.3. The issue of uncertainty

All seismic hazard assessment, based on our current knowledge of earthquake pro-

cesses and strong-motion generation, must inevitably deal with very considerableuncertainties. Fundamental amongst these uncertainties are the location and mag-

nitude of future earthquakes: PSHA integrates all possible combinations of these

parameters while DSHA assumes the most unfavourable combinations.

Another very important element of the uncertainty is that associated with the

scatter inherent to strong-motion scaling relationships, which again is treated dif-

ferently in the two methods. PSHA generally now includes integration across the

scatter in the attenuation relationship as part of the calculations, although this has

not always been the case: the US hazard study by Algermissenet al. [1982] is based

on median values. In DSHA, as noted previously, the scatter is either ignored, byusing median values, or accounted for by the addition of one standard deviation to

the median values of ground motion. Both approaches have shortcomings, discussed

in the next section and also in Sec. 5.3, but it is also important to note here that

the different treatments of scatter in the two methods questions the validity of the

comparisons that are sometimes made between the two. In particular, the use of

the deterministic map to cap the ground motions calculated probabilistically in the

NEHRP MCE maps, discussed in Sec. 2.4, ignores completely the fact that the de-

terministic motions are based on median values while the probabilistic values may,

for a 2475-year return period, may be related to values more than 1.5 standarddeviations above the median [Bommer et al., 2000]. Like is not being compared

with like.

An important development in the understanding of the nature of uncertainty in

strong-motion scaling relationships is the distinction between epistemic and aleatory

uncertainty. In very simple terms, the epistemic uncertainty is due to incomplete

data and knowledge regarding the earthquake process and the aleatory uncertainty

is related to the unpredictable nature of future earthquakes [e.g. Anderson and

Brune, 1999]; a more complete definition of epistemic and aleatory uncertainty is

provided by Toro et al. [1997]. A major component of the uncertainty is due to allof the parameters that are currently not included in simple strong-motion scaling

relationships, whose inclusion would reduce the scatter. Consider equations for du-

ration based on magnitude, distance and site classification: additional parameters

that could be included to reduce the scatter are those related to the directivity


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[Somervilleet al., 1997] and velocity of rupture, and degree to which the rupture is

unilateral or bilateral [Bommer and Martinez-Pereira, 1999]. This would reduce the

scatter in the regressions to determine the equations, but it would not necessarilyreduce the uncertainty associated with estimates of future ground motions because

the point of rupture initiation, and the direction and speed of its propagation, are

currently almost impossible to estimate for future events. The reduction of the

uncertainty in the strong-motion scaling relationship has simply transferred it to

the uncertainty in the other parameters of the hazard model. PSHA would then

handle this by considering more and more scenarios to cover all of the possible vari-

ations of each feature, whereas DSHA would simply assume their least favourable

combination.

3.4. Acceleration time-history representation of seismic hazard

The most complete representation of the ground-shaking hazard is an acceleration

time-history. The specifications for selecting or generating accelerograms in current

seismic design codes are generally unworkable, largely because of the representation

of the basic design seismic actions in terms of probabilistic maps and uniform hazard

spectra [Bommer and Ruggeri, 2002].

The requirement of dynamic analysis for critical, irregular and high ductility

structures and the need to define appropriate input has been one of the main mo-tivations for the development of deaggregation techniques such as Kameda and

Nojima [1988], Hwang and Huo [1994], Chapman [1995] and McGuire [1995], the

last of which has been widely adopted into practice. Since the PSHA calculations

include integration across all possible combinations of magnitude (M) and distance

(R) andalso across the scatter in the strong-motion relationships, the deaggrega-

tion must define the earthquake scenario in terms ofM, R and , the number of

standard deviations above the median. Bommer et al. [2000] have shown that if a

single seismogenic source is considered, it is possible to define the hazard-consistent

scenario almost exactly rather than as bins ofM, R and values. Performingthe deaggregations of hazard determined with and without integration across the

scatter reveals interesting features of the way PSHA treats the uncertainty: for a

100 000-year return period, the scenario without scatter is an earthquake ofMs 6.6

at 2 km from the site; with scatter, the scenario becomes an Ms 6.3 earthquake

at 6 km, together with 2.7 standard deviations above the median. The implica-

tions of this for hazard assessment in general are discussed in Sec. 5.4 but here the

interest is to consider the implications for the selection of hazard-consistent real

accelerograms for engineering design. In the first case, records could be searched

that approximately match the M-Rpair of 6.6 and 2 km; if sufficient number of ac-celerograms were found, the uncertainty would be represented by their own scatter,

whereas if only few records were found they could be scaled to account for the un-

certainty. That the scatter is inherent in selected suites of accelerograms is reflected

by specifications such as those in the 1999 AASHTO Guidelines for Base-Isolated


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56 J. J. Bommer

Bridges: if three records are used in dynamic analysis, the maximum response val-

ues are used for design, whereas if more than seven are employed, it is permitted

to use the average response. In the case of the second earthquake scenario, one isfaced with the almost impossible task of finding records that approximately match

theM-Rpair of 6.3 and 6 km, for which allground-motion parameters aresimulta-

neouslyalmost three standard deviations above the median for this M-Rscenario.

This problem can be overcome by carrying out the hazard assessment considering

the joint probabilities of different strong-motion parameters [Bazzurro, 1998] but

such techniques are some way from being adopted into general practice.

4. Seismic Hazard and Seismic RiskSeismic hazard outside of the context of seismic risk is little more than an academic

amusement. The development of better practice is not always well served by papers

that present local, regional or even global hazard studies whose intended purpose

is never stated or those that propound the virtues of one particular approach or

method as the best for all applications.

4.1. Hazard assessment as an element of risk mitigation

The seismic risk in the existing built environment may be calculated in order todesign financial (insurance and reinsurance) or physical (retrofit and upgrading)

mitigation measures. For planned construction, hazard estimates are required so

that appropriate measures can be taken to control the consequent levels of risk

through relocation (exposure) or earthquake-resistant design (vulnerability).

In the case of financial loss estimation for the purposes of insurance, the prob-

ability associated with different levels of risk is a vital part of the information

required to fix premiums and to guide the purchase of reinsurance. In the case of

seismic design, of new or existing structures, the target is an acceptable level of

risk, for which probability may be needed. In the PSHA approach, once the designprobability of exceedance is chosen, it is assumed that design for the corresponding

level of ground motion will provide an acceptable level of risk.

The important issue is always what is at stake since what matters is the

possibility of loss of function due to an earthquake, whether that be to safely

house people, to provide rapid transportation, emergency medical care or a constant

energy supply, or to contain radioactive material. Krinitzsky [2001] proposes that

any project for which the consequences of failure are intolerable, to the owner and/or

the users, should be considered critical. There are strong arguments for using a de-

terministic approach for critical facilities [e.g. Krinitzsky, 1995b] although currentDSHA procedures may warrant improvement (Sec. 5.4).

The definition of intolerable is, of course, subjective, although it is unlikely that

anyone would contend the adjective being applied to the failure of a nuclear power

plant. In this context, let us consider the seismicity of Great Britain, which by


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Fig. 5. British earthquakes during the over a period of more than seven centuries. Magnitudes:a: M = 5.5, b: 5.5 > M > 5.0, c: 5.0 > M > 4.5, d: 4.5 > M > 4.0. [Ambraseys and Jackson,1985].


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58 J. J. Bommer

anyones standards is low. Ambraseys and Jackson [1985] review several centuries

of seismicity in Britain (Fig. 5) and find no earthquake larger than Ms 5.5 with the

additional blessings that these events are very infrequent recurrence intervalsnationally of at least 300 years and that focal depths tend to increase with

magnitude. Accounts of losses of life or property due to British earthquakes are

hard to come across. This lack of significant activity and of any consensus on the

principles for zoning this seismotectonically inhomogeneous territory [Woo, 1996]

has not prevented PSHA being performed. The probabilistic study by Musson and

Winter [1997] found 10 000-year PGA values below 0.10gin most of the country but

nudging past 0.25g at isolated locations, no doubt in part because of their use of

rather high values of maximum magnitude from 6.2 to 7.0. An earlier study by Ove

Arup and Partners [1993] found similar results at selected locations and also carriedout a probabilistic risk assessment. It was found that annual earthquake losses were

only 10% of those due to meteorological hazards, although this was largely the

result of the unlikely but still credible scenario of a magnitude 6 earthquake directly

under a city [Booth and Pappin, 1995]. A useful, but complex and lengthy, study

would compare these probabilistic losses with the cost of incorporating earthquake-

resistant design into UK construction, and actually perform an iterative analysis to

determine the reduction in risk from different levels of investment in earthquake-

resistant design and construction. This would allow an informed decision regarding

the benefit of the investment compared to the loss that may be prevented, takinginto account competing demands on the same resources.

The issue of seismic safety definitely cannot be dismissed for nuclear power

plants built in the UK, for which elaborate probabilistic hazard assessments have

been carried out to define the 10 000-year design ground motions. The real hazard is

posed by moderate magnitude [M 5] earthquakes, whose association with tectonic

structures is tenuous, that could produce damaging ground motions over a radius

of about 510 km. In the authors opinion, unless there is good scientific reasons

to exclude it as unfeasible, the only rational design basis for seismic safety in such

a setting is a DSHA based on an earthquake of about Ms 5.5, which would requirerupture on a fault that could very easily escape detection, occurring close to or even

below the power station. This approach could be classified as one of conservatism.

In their treatise on the philosophy of seismic hazard assessment for nuclear power

plants in the UK, Mallard and Woo [1993] argue against the use conservatism

and in favour of a systematic methodology for quantifying uncertainty. The tool

proposed for this procedure is the logic-tree, a device that has become part of the

stock-in-trade of PSHA enthusiasts. As applied to seismic hazard assessment, the

etymology of the second part of its name is obvious from its dendritic structure,

but the logic is sometimes harder to detect.

4.2. The use and abuse of probability

At this point, three principles for seismic hazard assessment can be stated:


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(1) Seismic hazard can only be rationally interpreted in relation to the mitigation

of the attendant risk.

(2) If determinism is taken to mean the assignment of values by judgement, it is im-possible to perform a seismic hazard assessment, by any method, without many

deterministic elements. These should be based, as far as possible, exclusively

on the best scientific data available.

(3) Probability, at least in a relative sense, is essential to the evaluation of riskc

(but not necessarily to its calculation).

The application of logic-trees to seismic hazard assessment is a mechanism for

handling those epistemic uncertainties that cannot, unlike the aleatory scatter in

strong-motion scaling relationships, be statistically measured. The different optionsat each step are considered and each is assigned a subjective weight that reflects the

confidence in each particular value or choice. The results allow the determination of

confidence bands on the mean hazard curve, which as Reiter [1990] rightly points

out, places an uneasy burden on those who have to use the results. Krinitzsky

[1995a] presents powerful arguments against the use of logic-tree for hazard assess-

ment, while illustrating how without the contentious application of weights it

Fig. 6. Contours of 475-year PGA levels for El Salvador produced by independent seismic hazardstudies [Bommer et al., 1997].

cFor critical structures, any finite probability of failure may be considered intolerable.


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60 J. J. Bommer

can be a useful tool for comparing risk scenarios. In the context of this study, and

in terms of the three principles outlined above, the logic-tree for hazard assessment

appears to be upside down: deterministic judgementsd are turned into numbersand treated together with observational data to calculate probabilities that then

fix the design ground motions. Returning to the point made in Sec. 3.2, this again

points to PSHA having a degree of confidence in its probabilities, which, to the

author, does not seem justified. Reiter [1990] notes that different studies may

conflict over whether the likelihood of exceeding 0.3g at site X is 103 or 104

and whether the likelihood of exceeding the same acceleration at location Y is104

or 105. Given how PSHA is actually applied, this means that for a specified

annual rate of exceedance estimates of PGA can vary by factors of two or more

(Fig. 6). It is important to note that a degree of this divergence in results canbe removed through application of the procedures proposed by the Senior Seismic

Hazard Analysis Committee [SSHAC, 1997]. However, the available earthquake

and ground-motion data for most parts of the world is such that any estimate

of the ground motion for a prescribed rate of exceedance will inevitably carry an

appreciable degree of uncertainty.

So the big question is, how are the probabilities fixed? Hanks and Cornell [2001]

explain that the starting point is a performance target expressed as a probability

of failure, Pf, which is set by life safety concerns or perhaps political fiat. This

probability is defined by the integral:

Pf =

0

H(a) F(a) da (2)

whereH(a) describes the hazard curve (annual rate of exceedance of different levels

of acceleration, a), and F(a) is the derivative of the fragility function (the proba-

bility of failure given a particular level of acceleration). This is fine if an iterative

process is carried out in order determine the appropriate fragility curve, which

would then define the design criteria, to give the desired level ofPf. If the fragility

curve is sufficiently steep, once it has been determined Hanks and Cornell [2001]show how Eq. (2) can be approximated to determine the level ofH(a) to be used as

the basis of design, although this begins to get complicated because to obtain F(a)

the design must already have been carried out. However, this is not how the design

levels used in current practice have been fixed or else it is quite remarkable that

nearly every country in the world, from New Zealand to Ethiopia, regardless of

seismicity, building types or construction standards, all came up with 0.002 as the

design annual rate of exceedance!

In fact, the almost universal use of the 475-year return period in codes can be

traced back to the hazard study for the USA produced by Algermissen and Perkins[1976], which was based on an exposure period of 50 years (a typical design life)

dKrinitzsky [1995a] describes these as degrees of belief that are no more quantifiable than loveor taste.


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and a probability of 10% of exceedance, whose selection has not been explained.

Every code and regulation since has either followed suit or else adopted its own

return periods: Whitman [1989] reports proposals by the Structural Engineers As-sociation of Northern California to use a 2000-year return period, chosen because

the committee believed it reflected a probability or risk comparable to other risks that

the public accepts in regard to life safety. If one considers that in most structural

codes the importance factor increases the design ground motions by a constant

factor, this means that the actual return period of the design accelerations will be

different from 475 years and will probably vary throughout a country. In the devel-

opment of the NEHRP Guidelines, this is actually been done intentionally in order

to provide a uniform margin against collapse, resulting in design for motions cor-

responding to 10% in 50 years in San Francisco and 5% in 50 years in Central andEastern US [Leyendeckeret al., 2000]. A review of seismic design regulations around

the world reveals a host of design return periods, the origin of which is rarely if

ever explained. The AASHTO Guidelines specify 500 years for essential bridges,

2500 years for critical bridges.e In the Vision 2000 proposal for a framework

for performance-based seismic design, return periods of 72, 244, 475 and 974 years

have been specified as the basis for fixing demand for different performance levels

[SEAOC, 1995]. It is hard not to feel that some of these values have been almost

pulled from a hat, all the more so for the 10 000-year return periods specified for

safety-critical structures such as nuclear power plants.

5. The Best of Both Worlds

The three principles stated in Sec. 4.2 imply that it is not possible to perform useful

seismic hazard assessment that is free from determinism or probability, since both

are essential ingredients. Hence it is logical to look for ways that make best use of

both these components.

5.1. Hybrid approaches

Hanks and Cornell [2001] assert that the main difference between deterministic and

probabilistic approaches is that PSHA has units of time and DHSA does not. This

is true in the brief descriptions of the two methods presented at the beginning of

the paper but it does not mean that time and probabilities cannot be attached

to deterministic scenarios. Orozova and Suhadolc [1999] assign recurrence rates

to earthquakes of particular magnitude in order to adapt the method of Costa

et al. [1993] discussed in Sec. 2.3 to create a deterministic-probabilistic

approach. Furthermore, it is common in loss estimation to model the hazard as aseries of earthquake scenarios, each of which is assigned an average rate from the

eA wonderful example occurred in a recent project the design return period was finally fixedby the engineer at 2000 years because the bridge was judged to be almost critical!


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62 J. J. Bommer

recurrence relationships [e.g. Frankel and Safak, 1998; Kiremidjian, 1999; Bommer

et al., 2002].

It has in fact already become well recognised that there is not a mutually exclu-sive dichotomy between DSHA and PSHA, opening up the possibility of exploring

combined methods. Reiter [1990] says that in many situations the choice has been

rephrased so that the issue is notwhetherbut ratherto what extenta particular

approach should be used. McGuire [2001] asserts that determinism vs. probabil-

ism is not a bivariate choice but a continuum in which both analyses are conducted,

but more emphasis is given to one over the other. It is, however, interesting to

note that both Reiter [1990] and McGuire [2001], who make positive contributions

to moving away from the dichotomy, point towards deaggregation of PSHA as an

important tool in hybrid approaches.

5.2. Against orthodoxiesf

How should the method for seismic hazard assessment be chosen? Reiter [1990]

rightly argues that the analysis must fit the needs. Nonetheless, there is a ten-

dency amongst many in the field of earthquake engineering who would argue for

the superiority of one approach or the other as the ideal, a panacea for all situ-

ations. Such arguments carry the danger of establishing orthodoxies, with all their

attendant perils and limitations. Hazard assessment should be chosen and adapted

not only to the required output and objectives of the risk study of which it forms

part, it should also be adapted to the characteristics of the area where it is being

applied and the level and quality of the data available. There is no need to establish

standard approaches that may be well suited to some settings and not to others, or

which may be appropriate now and yet not be in a few years time as understanding

of the earthquake process advances. Every major earthquake that is well recorded

by accelerographs throws up new answers and poses new questions, leading to rapid

evolution. The near-field directivity factors proposed by Somervilleet al. [1997], for

example, have had to be revised not only numerically but also conceptually fol-

lowing the 1999 earthquakes in Turkey and Taiwan, a mere two years after their

publication. The ability to locate and identify active geological faults in continental

areas has also advanced by leaps and bounds over recent years, and continues to

do so [e.g. Jackson, 2001].

What are the bases for the orthodoxies of PSHA and DSHA? For the PSHA

church, the cornerstone of its creed seems to be the overriding importance of the

probability of exceedance of particular levels of ground motion, despite the fact

that teams of experts working with the same data can easily come up with answers

fIn the period 182 to 188 A.D., at a time when the early Christian church had gone beyondonly having enemies outside its camp, St. Irenaeus of Lyons penned a multi-tome treatise entitledAdversus Haereses Against Heresies. The effects of such rigid insistence on a particular, narrowphilosophy in stifling religious and scientific thought in later centuries are known only toowell.


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that differ by an order of magnitude. For the DSHA temple, the sacred cow is

the worst-case scenario, even though this is not what they actually produce, as

discussed in the Sec. 5.4. The fact is that one cannot get away from the fact thatwith current levels of knowledge of earthquake processes a major component of

seismic hazard assessment is judgement and risk decisions are governed not only

by scientific and technical data but also by opinion. The word orthodoxy, from

the Greek, has exactly that paradoxical and unscientific meaning: correct (ortho)

opinion (doxa). The Oxford Dictionary goes on to define the word also to mean

not independent-minded and unoriginal.

5.3. Alternative approaches to seismic hazard mappingOne area in which PSHA currently enjoys almost total domination is in seismic

hazard mapping, particularly for seismic design codes. The difference between de-

terministic and probabilistic hazard maps highlights one extremely important dif-

ference between current practice of the two methods, quite apart from the debat-

able issue of whether or not units of time are included. Probabilistic maps combine

the influence and effects of different sources of seismicity, often into a single map

showing contours of PGA that are then used to anchor spectral shapes that relate

only to the site conditions and which somehow try to cover all possible earthquake

scenarios.Donovan [1993] states that the ground motion portion of codes represents an

attempt to produce a best estimate of what ground motions might occur at a site

during a future earthquake. Current code descriptions of earthquake actions clearly

do not fulfil this objective for many reasons, particularly because of the practice of

combining the hazard from various sources of seismicity. Here it is hard to justify

this by insisting on the importance of the total probability when codes are generally

based on the arbitrary level of the 475-year return period and, even more impor-

tantly, a return period which holds only for the zero period spectral ordinate. In

fact, because of the use of discrete zones to represent continuously varying hazardover geographical areas, the actual return period will often not correspond to the

475-year level even at the spectral anchor point. The uniform hazard spectra of

seismic codes do not represent motions that might occur during a plausible future

earthquake, whence the difficulties of codes to specify acceleration time-histories.

In certain regions, particularly those affected by both small, local earthquakes and

larger, distant earthquakes, the application of spectral modal analysis using the

code spectrum can amount to designing a long-period structure for two different

types of earthquake occurring simultaneously. It is important to note here that

several codes, and in particular the NEHRP provisions [FEMA, 1997], use two pa-rameters to define the spectrum, hence the spectral shape does vary with hazard

level, but the above comments still apply to some extent.

If it is accepted that the total probability theorem is not an inviolable principle

in defining earthquake actions, especially when the calculation of that probability


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64 J. J. Bommer

is subject to such uncertainty and presented so approximately, more imaginative

procedures can be used. The hazard resulting from different sources of seismicity

can be treated individually and their resulting spectra defined separately. Thisis, in fact, already done: the seismic design codes of both China and Portugal

define one spectrum for local events and another for more distant large magnitude

earthquakes. Once different types of seismicity are separated, it will usually be found

that at most sites one source dominates. One possibility is then to deaggregate the

hazard associated with the dominant source for each site and hence characterise the

hazard in terms of actual M-Rscenarios. The hazard could then be represented by

maps showing contours ofM and R for different types of seismicity. The problem

still remains as to how to select an appropriate return period at which to perform

the deaggregation, but in many cases it will be possible to define the M-R pairsdeterministically [Bommer and White, 2001]. This would differ from the maps of

magnitude and distance presented by Harmsen et al. [1999] because a single pair

of maps would cover all strong-motion parameters rather than just the spectral

ordinate at a single response period.

Another issue is how to incorporate rationally the uncertainty without going

to very complex representations of hazard in terms ofM-R- contours [Bazzurro

et al., 1998]. The important point is that once the hazard is characterised by pairs of

magnitude and distance, every required parameter of the ground motion, including

ordinates of spectral acceleration and displacement in both the vertical and hori-zontal directions, and duration, can be computed directly and the required criteria

for selecting or generating acceleration time-histories are provided [Bommer, 2000].

Within the framework of performance-based seismic design it is already envisaged

that several levels of earthquake action will be considered in structural design. If

the objective is to obtain improved control over earthquake response to expected

seismic actions, then it is surely a step in the right direction to begin by separating

different types of earthquake action.

5.4. Upper bounds: the missing piece

In 1971, the San Fernando earthquake more than doubled number of strong-motion

accelerograms available, marking the dawn of the age of curve fitting to clouds of

data to find scaling relationships. It is curious that the curves fitted severely under-

estimated the most significant ground-motion recorded in the earthquake (Fig. 7).

The scatter in these relationships is generally assumed to be lognormal and is

invariably large: for spectral ordinates, the 84-percentile values are typically 80

100% higher than the median. This scatter creates difficulties for both DSHA and

PSHA. In PSHA the untruncated lognormal scatter results in the probable maxi-mum ground motion at a particular site increasingly indefinitely as the time window

of the PSHA increases, due to the increasing influence of the tail of the Gaussian

distribution on the probabilistic values [Anderson and Brune, 1999]. This has given

rise to different mechanisms for truncating the scatter at a certain number of


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Fig. 7. Attenuation relationship derived for the 1971 San Fernando earthquake data [Dowrick,1987].

standard deviations above the median, which assumes that for all magnitude and

distance combinations, the physical upper bound on the ground motion is always

at a fixed ratio of the median amplitudes. There is also debate regarding the actuallevel at which the truncation should be applied: proposals range from 2 to 4.5 stan-

dard deviations [Reiter, 1990; Abrahamson, 2000; Romeo and Pristininzi, 2000] and

some widely used software codes employ cut-offs at 6 standard deviations above the

median.

Untruncated lognormal distributions create even more difficulties for DSHA,

since, at least for critical structures, its basis should be to identify the worst-case

scenario. Firstly, it establishes a maximum credible earthquake (MCE) as the basis

for the design. Abrahamson [2000] points out that if the MCE is determined as

the mean value from an empirical relationship between magnitude and rupturedimensions, it is not the worst case; the worst case would be the magnitude at

which the probability distribution is truncated. This truncation requires a physical

rather than statistical basis: upper bounds are required, especially because the

regressions are supported by very few data for large magnitudes [Jackson, 1996].


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66 J. J. Bommer

After fixing the MCE, DSHA calculates design ground motions as the median

or median-plus-one-standard deviation values from strong-motion scaling relation-

ships. Again Abrahamson [2000] points out that this is not the worst case butthen goes on to state the worst case ground motion would be 2 to 3 standard

deviations above the mean. The problem is where between these two limits to

fix the worst case? Probabilistically they are close, corresponding to the 97.7 and

99.9 percentiles respectively, although in terms of spectral amplitudes the effect of

the third standard deviation thrown on can increase the amplitudes by factors of

two, which clearly has very significant implications for design. Here again, physical

upper bounds are needed. Can upper bounds be fixed for ground-motion param-

eters? Reiter [1990] argues that there must be a physical limit on the strength

of ground motion that a given earthquake can generate. It is also interesting tonote that before sufficient strong-motion accelerograms were available for regres-

sion analyses, a number of studies considered possible upper bounds on ground-

motion parameters [e.g. Ambraseys, 1974; Ambraseys and Hendron, 1967; Ida, 1973;

Newmark, 1965; Newmark and Hall, 1969]. Upper bounds need to be established

and procedures for their application developed that take into account current un-

derstanding of epistemic uncertainty. For example, if a deterministic scenario has

included forward directivity effects, does it then make sense to add on two or three

standard deviations when a significant component of the scatter has already been

accounted for?There are many ways that the scatter in attenuation equations can be trun-

cated, including the adaptation of models developed for log-normal distributions

with finite maxima [Bezdak and Solomon, 1983] to ground-motion prediction mod-

els [Restrepo-Velez, 2001]. As PSHA pushes estimates to longer return periods the

issue of truncating the influence of the scatter, in order to avoid physically unrealis-

able ground-motion amplitudes, becomes more important. The Pegasos project, cur-

rently underway to assess seismic hazard at nuclear power plant sites in Switzerland

down to very low rates of exceedance, is taking PSHA to new limits [Smit et al.,

2002]. The ground-motion estimates will be defined by median values, standarddeviations and truncations, with associated confidence intervals for each of these,

for a wide range of magnitude-range distance pairs.

5.5. Time-dependent estimates of seismic hazard

In order to make full use of the output from a PSHA, including estimates of un-

certainty and the expected levels of ground motion for a range of return periods, it

is necessary that the engineering design also follow a probabilistic approach. Such

approaches are now being developed, particularly through the outstanding work ofAllin Cornell and his students at Stanford University [e.g. Bazzurro, 1998]. However,

there are many obstacles to the adoption of these approaches in routine engineering

practice simply because there are few areas of activity where the saying time is

money is as true as it is in the construction industry. One could actually conclude


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that probabilistic assessment of design earthquake actions is far more advanced

than probabilistic approaches to seismic design and for this reason the results of

PSHA are generally not used to their full advantage.The limited time made available for even major engineering projects is reflected

in the very tight deadlines often set for the execution of seismic hazard assessments.

In engineering practice it is not unusual for a hazard assessment for a site to be

carried out in a few weeks, generally making it inevitable that the study will be

based largely on available data published in papers and reports. Under such circum-

stances, and especially where the design considers the seismic performance at only

one limit state, DSHA can represent an attractive option to define a level of ground

motion that is unlikely to be severely exceeded. One advantage of DSHA is that

it immediately releases the hazard analyst from the responsibility of defining thedesign return period, which the client or engineer often passes, quite incorrectly, to

the Earth scientist. More importantly, DSHA is generally more dependent on the

data that is likely to be determined most reliably: the characteristics of the largest

historical earthquakes and the location of the largest geological faults. Since the

actual calculations involved in DSHA are simple, the analyst can carry out sensi-

tivity analyses even when working to a very strict timetable. Furthermore, because

of the transparency of the deterministic approach, peer review can be carried out

swiftly and easily, which may not be the case for a probabilistic assessment where

so many input parameters and assumptions, whose individual influences are oftendifficult to distinguish, need to be defined. One cannot escape from the fact that

expert opinion is of overriding importance, regardless of whether the probabilistic

or deterministic approach is adopted. The value of a logic-tree formulation, with

weights assigned by one analyst, in situations where the design engineer for

whom the provision of earthquake resistance is just one of a series of considerations

that affect siting, dimensions and detailing is seeking a single number to charac-

terise the earthquake action, is questionable. This is not to say that careful use of

multiple expert opinions is not to be encouraged, indeed a Level 4 hazard study as

recommended by SSHAC [1997] provides a very well crafted framework for exactlysuch a process. However, the time scale, and hence cost, required to perform such a

study is beyond the means and the schedule of most engineering projects: to date

the SSHAC Level 4 method has only be applied in the Yucca Mountains project

[Steppet al., 2001] and now the Pegasos project in Switzerland [Smit et al., 2002].

When working to a very short time scale, however, a peer-reviewed DSHA may

be far more useful to the project engineer and ultimately to the provision of an

adequate level of earthquake resistance.

6. Conclusions

There is not a simple dichotomy between probabilistic and deterministic approaches

to seismic hazard assessment many different probabilistic approaches exist and

there is not a standard methodology for deterministic approaches. There is not,


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68 J. J. Bommer

nor does there need to be, a method that can be applied as a panacea in all sit-

uations, since the available time and resources, and the required output, will vary

for different applications. There is no reason why a single approach should be idealfor drafting zonation maps for seismic design codes, for loss estimation studies in

urban areas, for emergency planning, and for site-specific assessments for nuclear

power plants. McGuire [2001] presents an interesting scheme for selecting the rel-

ative degrees of determinism and probabilism according to the application. Woo

[1996] states that the method of (probabilistic) analysis should be decided on the

merits of the regional data rather than the availability of particular software or

the analysts own philosophical inclination. The reality is that both of these views

are partially correct and hence both criteria need to be used simultaneously: the

selection of the appropriate method must fit the requirements of the applicationand also consider the nature of the seismicity in the region and its correlation or

indeed lack thereof with the tectonics. It is not possible to define a set of criteria

that can then be blindly applied to all types of hazard assessment in all regions

of the world and for this reason no such attempt has been made in this paper.

The analyst, after establishing the needs and conditions set by the engineer, should

adapt the assessment both to these criteria and to the region under study. Casting

aside simplistic choices between DSHA and PSHA will help the best approach to be

found and will also allow the best use to be made of the considerable and growing

body of expertise in engineering seismology around the world.The confidence with which seismic probabilities can be calculated does not gen-

erally warrant their rigid use to define design ground motions and wherever possi-

ble the results should at least be checked against deterministic scenarios, wherever

there is sufficient data for these to be defined [McGuire, 2001]. One application in

which the arguments for strict adherence to the total probability theorem cannot

be defended is in the derivation of earthquake actions for code-based seismic design.

The currently very crude definition of earthquake actions in seismic codes could be

greatly improved if it was accepted that it is not necessary to use representations

that attempt to simultaneously envelope all of the possible ground motions thatmay occur at a site.

Finally, one area in which research is required, that will be of benefit to seismic

hazard assessment in general and perhaps in particular to deterministic approaches,

is to identify upper bounds on ground-motion parameters for different combinations

of magnitude, distance and rupture mechanism. The existing database of strong-

motion accelerograms can provide some insight into this issue [e.g. Martnez-Pereira,

1999; Restrepo-Velez, 2001]. Advances in finite fault models for numerical simula-

tion of ground motions could be employed to perform large numbers of runs, with

a wide range of combinations of physically realisable values of the independentparameters, in order to obtain estimates of the likely range of the upper bounds on

some parameters.


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Acknowledgements

The author wishes to thank David M. Boore, Luis Fernando Restrepo-Velez, JohnDouglas and John Berrill for heads up regarding some key references, and partic-

ularly to Ellis Krinitzsky and Tom Hanks for providing pre-prints of papers. The

author has enjoyed and benefited from discussing many of the issues in this pa-

per with others, particularly Norman A. Abrahamson, Amr Elnashai, Rui Pinho,

Nigel Priestley, Sarada K. Sarma and the students of the ROSE School in Pavia.

Robin McGuire, Belen Benito, John Douglas, Nick Ambraseys and Sarada Sarma

all provided very useful feedback on the first draft of this manuscript. The author is

particularly indebted to Dave Boore for an extremely thorough, detailed and chal-

lenging review of the first draft; in the few cases where my determined stubbornness

has led me to ignore his counsel, I have probably done so to the detriment of the

paper. The second draft of the paper has further benefited from thorough reviews

by John Berrill and two anonymous referees, to whom I also extend my gratitude.

References

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