Uses for the Seismic Hazard Maps
How do I use these maps?
The maps come in three different probability levels and four different ground motion parameters, peak acceleration and spectral acceleration at 0.2, 0.3, and 1.0 sec. (These values are mapped for a given geologic site condition. Other site conditions may increase or decrease the hazard. Also, other things being equal, older buildings are more vulnerable than new ones.)
The maps can be used to determine (a) the relative probability of a given critical level of earthquake ground motion from one part of the country to another; (b) the relative demand on structures from one part of the country to another, at a given probability level. In addition, (c) building codes use one or more of these maps to determine the resistance required by buildings to resist damaging levels of ground motion.
The different levels of probability are those of interest in the protection of buildings against earthquake ground motion. The ground motion parameters are proportional to the hazard faced by a particular kind of building.
Peak acceleration is a measure of the maximum force experienced by a small mass located at the surface of the ground during an earthquake. It is an index to hazard for short stiff structures.
Spectral acceleration is a measure of the maximum force experienced by a mass on top of a rod having a particular natural vibration period. Short buildings, say, less than 7 stories, have short natural periods, say, 0.2-0.6 sec. Tall buildings have long natural periods, say 0.7 sec or longer. A earthquake strong motion record is made up of varying amounts of energy at different periods. A building natural period indicates what spectral part of an earthquake ground-motion time history has the capacity to put energy into the building. Periods much shorter than the natural period of the building or much longer than the natural period do not have much capability of damaging the building. Thus, a map of a probabilistic spectral value at a particular period thus becomes an index to the relative damage hazard to buildings of that period as a function of geographic location.
Choose a ground motion parameter according to the above principles. For many purposes, peak acceleration is a suitable and understandable parameter.
Choose a probability value according to the chance you want to take. One can now select a map and look at the relative hazard from one part of the country to another.
If one wants to estimate the probability of exceedance for a particular level of ground motion, one can plot the ground motion values for the three given probabilities, using log-log graph paper and interpolate, or, to a limited extent, extrapolate for the desired probability level.
Conversely, one can make the same plot to estimate the level of ground motion corresponding to a given level of probability different from those mapped.
If one wants to estimate the probabilistic value of spectral acceleration for a period between the periods listed, one could use the method reported in the Open File Report 95-596, USGS Spectral Response Maps and Their Use in Seismic Design Forces in Building Codes. (This report can be downloaded from the web-site.) The report explains how to construct a design spectrum in a manner similar to that done in building codes, using a long-period and a short-period probabilistic spectral ordinate of the sort found in the maps. Given the spectrum, a design value at a given spectral period other than the map periods can be obtained.
