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.

Catastrophe Risk Management

July 2003

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.

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.

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" 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" (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.

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.

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.

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.

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}.

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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