There are basically two ways of deriving a probabilistic description of earthquake effects at each site from a probabilistic description of the fault’s activity. The first one is to consider each event (epicenter and magnitude) with its probabilistic description (e.g., the cumulative distribution function over the magnitude), to compute by attenuation function the local effects and losses associated with that precise event and to apply the same probabilistic law to the set of local effects. This means an integration over the local effects of each earthquake. It’s a complex task but it permits detailed study of effects and losses over wide areas. It can be used, for example, to compute the variance of the total future losses in a region. It is the model that has tube used to study such phenomena as the reliability of spatially distributed networks or the full probability distribution of the total economic effects of earthquakes over a region.

It has to be used also if the decision-makers are not assumed to be “risk indifferent. “The second probabilistic model, as developed for the seismic mapping of California, consists of computing for each site the probabilistic contribution to the seismic “loading” from each potential source for a specific period of time.

This model allows one to compute a cumulative distribution function of site seismic effects in one year. Then, for each site, one can derive the cumulative distribution function over the local annual losses. Such an approach decreases considerably the complexity of the computation of the loss since the integration over the various sources and events has been previously done.’

The use of the second model relies on the assumption that the loss in one year can be computed as the loss from the maximal intensity in that year. Its primary limitation, however, is that it is insufficient to determine full distribution information (e.g., the variance) of the total losses at a set of sites in a region. Because the individual site losses are correlated through common causative effects, the marginal site loss distributions are insufficient to calculate the probability distribution of the total regional loss. They do however permit determination of the expected total loss.