# Understanding the Language of Seismic Risk Analysis

July 2003

Even for those in the industry, the terminology
used in the evolving field of seismic risk analysis can be confusing. Deterministic
analysis, probabilistic loss analysis, level of earthquake, level of confidence,
probability of exceedence, probable maximum loss, scenario upper loss, scenario
expected loss, and probable loss are all terms with particular meaning in the
earthquake field, which could have significant financial and practical consequences
if the meanings are confused.

by Nathan
C. Gould, D.Sc., P.E., S.E.

ABS Consulting

Understanding the terms used in a seismic risk analysis can be a daunting
task for those who do not consider seismic risk analysis their area of expertise.
Even for those well-versed in this area, there is often confusion over the definition
of terms and the introduction of new terms in the evolving field of seismic
risk analysis.

## Deterministic versus Probabilistic Loss Analysis

The projected loss estimates as the result of the earthquake hazard can be
developed using either a deterministic or a probabilistic analysis. Traditionally,
probable maximum loss (PML) assessments were based on deterministic analyses.
Currently, both deterministic and probabilistic analyses are used. To avoid
inconsistencies within the industry regarding the definition of PML, the ASTM
standard E2026-99 suggests that newly defined, more specific terms should be
used to measure projected loss.

The fundamental difference between deterministic and probabilistic analyses
is that deterministic analyses do not consider the probability associated with
the earthquake hazard, whereas probabilistic analyses incorporate the hazard
probability.

In a deterministic analysis, the controlling fault (i.e., the fault which
causes the greatest level of ground shaking) for the building or group of buildings
is determined. An earthquake event of a specified magnitude (associated with
an estimated return period) is then assumed to occur on this fault (at the location
along the fault that causes the greatest damage to the subject building(s))
and this event is used as the basis of the loss analysis. This approach can
intuitively be expected to generate a reasonably conservative "worst-case" scenario
for loss, especially when combined with a 90 percent confidence level on the
loss estimate. However, it does not provide a gauge of the likelihood of this
loss occurring, nor does it consider the combined effects of multiple faults
that may affect the site.

One consequence of this limitation is that deterministic analyses provide
an inconsistent measure of earthquake risk when evaluating areas with different
levels of earthquake activity. For example, locations in San Francisco, Los
Angeles, and Memphis could all develop similar scenario event analyses, whereas
the higher overall seismic activity in Los Angeles and San Francisco present
a higher "risk" in these cities.

A probabilistic analysis accounts for the full range of possible earthquakes,
their location, frequency of occurrence, size, and the propagation of the earthquake
motion from the rupture zone to the site(s) of interest. Uncertainty in each
of these elements and in the damageability of the building(s) is taken into
account. This provides a more complete and "realistic" evaluation of the potential
earthquake losses.

## Level of Earthquake

The concept of "Level of Earthquake" is applicable to deterministic analyses
only, as probabilistic analyses by definition incorporate all possible levels
of earthquake.

The level of earthquake chosen as the basis of a deterministic analysis is
usually measured in terms of estimated return period. The return periods commonly
used are 72-year, 475-year, and 975-year periods. These return periods correspond
to 50, 10, and 5 percent probability of exceedance for a 50-year period (which
is the expected design life for a building). The 475-year return period (or
10 percent probability of exceedance in 50 years) event is the most common standard
used in the industry for assessing seismic risk, and it is also the basis for
most building codes for seismic design.

## Level of Confidence

"Level of Confidence" is generally used in the context of deterministic loss
estimates.

In a deterministic analysis, once it has been assumed that the scenario earthquake
occurs, it is common to associate a level of confidence with the loss to the
building(s). Typically, a 90 percent confidence level is used for the loss estimate.
This means that, given that the scenario occurs, 9 out of 10 identical buildings
would sustain this level of loss or less, and only 1 out of 10 would sustain
more. However, no consideration is given as to the probability of the scenario
earthquake actually occurring.

## Probability of Exceedance

"Probability of Exceedance" (when referring to the loss estimate) is generally
used in the context of probabilistic loss estimates.

A probabilistic analysis, because the probability functions of both the earthquake
hazard and the building damageability are incorporated into the analysis, provides
a fair representation of the actual probability associated with that level of
loss (or greater). The most commonly used probability of exceedance is 10 percent,
and the most commonly used time period is 50 years. Statistically, the loss
which has a 10 percent probability of exceedance in 50 years also has approximately
0.2 percent probability of exceedance in 1 year, and an effective return period
of 475 years.

## Probable Maximum Loss (Based on Deterministic Analysis)

The probable maximum loss (PML) is the traditional measure of earthquake
loss popularized by the insurance and seismic engineering industry in the 1980s.
Historically, the PML is based on a deterministic analysis, using an event on
the controlling fault for a site having a magnitude that is not expected to
occur more than about once in every 475 years (i.e., a 475-year return period).

The PML is historically associated with a 90 percent confidence level on
the structural response of the building (i.e., given that this event occurs,
the PML would not be exceeded by 9 out of 10 buildings having the same structural
features). Because the term "PML" has been in use for a large number of years,
many people in the industry have developed benchmarks by which to judge the
acceptable limits on PMLs for individual buildings. Many lenders have a threshold
PML value in the range of 20 to 30 percent, however, lenders will often accept
higher PML values provided that appropriate earthquake insurance coverage is
in place.

Unfortunately, over the years the industry has become less consistent in
its definition of a PML. Today, there are many variations on how PMLs are defined,
including the level of earthquake used and the confidence level associated with
the PML. For this reason, the recently published ASTM E2026-99 has suggested
that the term PML should be avoided, and instead recommends that newly defined,
more specific terms are used instead.

## Scenario Upper Loss (Based on Deterministic Analysis)

The scenario upper loss (SUL) is a term introduced by ASTM E2026-99. It can
be defined as the earthquake loss to the building with a 90 percent confidence
of non-exceedance (or a 10 percent probability of exceedence), resulting from
a specified event on specific faults affecting the building. If the specified
earthquake hazard is the 475-year return period event, then this term can be
called the SUL475, and this term is the same measurement as the traditional
PML defined above. The SUL can also be based on earthquakes with other return
periods.

## Scenario Expected Loss (Based on Deterministic Analysis)

The scenario expected loss (SEL) is also a term introduced by ASTM E2026-99.
It can be defined as the average expected loss to the building, resulting from
a specified event on specific faults affecting the building. If the specified
earthquake is the 475-year return period event, then this term can be called
the SEL475. The level of confidence associated with the SEL is not necessarily
50 percent; it may be greater than or less than this depending on the damageability
function for the particular building.

## Probable Loss (Based on Probabilistic Analysis)

The probable loss (PL) is another term recently introduced by ASTM E2026-99.
It is defined as the earthquake loss to the building(s) that has a specified
probability of being exceeded in a given time period from earthquake shaking.
The PL can also be based on a specified effective return period associated with
this level of loss. The PL is obtained using a probabilistic analysis, and is
commonly defined as the loss that has a 10 percent probability of exceedance
in 50 years (which corresponds to approximately 0.2 percent annual probability
of exceedance). This measure, which is used by some lenders, can be called the
PL475, because it corresponds to a return period of approximately 475 years.
Another return period used by some lenders is 190 years (this corresponds to
approximately 0.5 percent annual probability of exceedance). This measure can
be called the PL_{190}.

## Summary

To some the discussion of the definition of terms and usage relative to seismic
risk analysis may appear to be mundane and unimportant. However, there can be
significant financial and practical consequences if the meaning of important
terms such as PL, SUL, and PML are confused or misused.

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