Engineers wanted the scattered ground-motion observations reduced to simple empirical relationships that practitioners could apply, and the derivation of these relationships became a central focus of engineering seismology. A measure of shaking intensity was chosen (typically peak ground acceleration or velocity), and the observed variation of this intensity measure was factored into source, path, and site effects by identifying one or more independent control variables—typically, source magnitude, path distance, and site condition (e.g., soil or rock)—and fitting the observations with parameterized curves. The magnitude dependence or scaling and the fall-off of strong-motion amplitude with epicentral distance were together called the attenuation relation.
Lack of data precluded plotting PGA as a function of magnitude and epicentral distance until the 1960s. Figure 2.19 shows an attenuation relationship obtained from the strong-motion data for the 1979 Imperial Valley earthquake. The dispersion in the data resulted in a relative standard deviation of about 50 percent, which was typical. Other relationships described the site response in terms of the correlation between intensity measures and soil and rock conditions, including allowance for nonlinear soil behavior as a function of shaking intensity (Figure 2.20).
As the use of the response spectrum method increased, it became necessary to develop techniques to predict not only the PGA (equivalent to the response spectral value at zero period) but also the response spectra of earthquakes that might occur in the future. This was done initially by developing a library of response spectral shapes that varied with earthquake magnitude and soil conditions; the selected shape was anchored to a peak acceleration obtained from a set of attenuation relationships, each of which predicted the spectral acceleration at a specific period. Eventually, response spectra were computed directly from ground-motion attenuation relationships.
By the 1960s, growing strong-motion databases and scientific understanding enabled site-specific seismic hazard assessments incorporating information about the length and distance of neighboring faults, the history of seismicity, and empirical predictions of ground-motion intensity for events of specified magnitude at specified distances. For major facilities in the western United States, in particular nuclear power plants such as San Onofre and Diablo Canyon (177), seismic hazard assessment focused on the maximum magnitude that each fault could produce, its closest distance to the site, and the PGA for these events. PGA was then the