Estimating Seismic Risk
Seismic Hazard Analysis

Deterministic Seismic Hazard Analysis (DSHA)

A basic DSHA is a simple process that is useful especially where tectonic features are reasonably active and well defined. The focus is generally on determining the maximum credible earthquake (MCE) motion at the site. The steps in the process are as follows:

1. Identify nearby seismic source zones - these can be specific faults or distributed sources

2. Identify distance to site for each source (nearby distributed sources are a problem)

3. Determine magnitude and other characteristics (ie. fault length, recurrence interval) for each source

4. Establish response parameter of interest for each source as a function of magnitude, distance, soil conditions, etc., using either the envelope or the average of several ground motion attenuation relationships

5. Tabulate values from each source and use the largest value

Where the DSHA is based on tectonic features, it tends to be conservative since the maximum earthquake the fault is "capable" of generating is assumed to occur at the location on the fault closest to the site. DSHA is frequently used in California due to the knowledge of faults and the region's high seismicity.
When a distributed source is considered in the analysis, a distance must be determined. This presents much more of a problem for nearby distributed sources than those which are distant. Often, engineering judgment is used or a back calculation is employed to give the desired answer.

The DSHA method is simple, but it does not treat uncertainties well. Rudimentary statistics can be incorporated into the procedure by taking one standard deviation above median at each step (magnitude, PGA, etc.), which gives a very big, very conservative estimate. However, the DSHA does not account for the probability of an earthquake occuring on a fault.

Probabilistic Seismic Hazard Analysis (PSHA)

Probabilistic Seismic Hazard Analysis rectifies several problems inherent in its deterministic predecessor - the lack of quantification of uncertainty and probability of earthquake occurence. To do this, the PSHA follows a similar process to the DSHA, but the uncertainty is quantified by a probability distribution at each step. Distributions are determined for the magnitude of each earthquake on each source fM(m), the location of the earthquake in or along each source fR(r), and the prediction of the response parameter of interest P[pga>pga'|m,x]. For example:

For a given earthquake "x" of magnitude M and distance R:

P[pga>pga'] = P[pga>pga'|x] P[x]

For all earthquakes:

P[pga>pga'] = ò ò P[pga>pga'|m,r]fm(m)fR(r) dm dr

The details of this procedure are beyond the scope of this course.

PSHA is used for many important projects, and is the basis of the seismic hazard maps found in NEHRP and the UBC, which were the work of USGS committees. PSHA is not without its shortcomings, however. The calculations and theory are very complex and a varying amount of rigor is used by different individuals. Also, many assumptions are involved due to the limited amount of data available.

The basic dilemma is that the actual earthquake can be larger than the hazard analysis predicts, but will likely be smaller than a deterministic estimate. Thus, it is useful to know the difference between a rare and a very rare event. In some places like the San Francisco Bay Area, there is a small difference and a deterministic analysis (which predicts the very rare event) may suffice. However, in other locations such as the New Madrid area, the difference between rare and very rare events is large. The question of what to design for becomes difficult.