Probabilistic Models for Seismic Force Design

Probabilistic procedures for forecasting occurrence and intensities of earthquakes are presented based on the historical record of Modified Mercalli intensities. The occurrence is assumed Poisson for each intensity level. Forecasting is accomplished using Bayesian procedures. Forcasts for the San Francisco region are made for a 10-yr period. The optimization of design decisions is made using a statistical decision theory model. Three alternate designs are compared for a structure on the basis of expected losses for a ten-yr period. The technique of estimating expected losses given an earthquake of each intensity level is illustrated. Time to occurrence problems are also discussed. More complex models using a multinomial model for intensity and Poisson occurrence are introduced including the problem of multiple occurrence, Bayesian forecasting relationships are derived.