limited number of fault segments. Other hazard analyses have also incorporated time-dependent probabilities (212). Time-dependent seismic hazard maps have been produced for California by the Southern California Earthquake Center and the California Division of Mines and Geology (CDMG) (213). The CDMG maps show substantial differences from the time-independent maps for certain faults.
Several efforts are also under way to produce urban seismic hazard maps that merge probabilistic seismic hazard assessment with site response and, in some cases, three-dimensional basin effects and rupture directivity. These maps, at scales of 1:24,000 to 1:50,000, could be used for engineering design purposes, loss estimation, and land-use planning.
Seismic waves travel through a medium having a free surface, strong variations (usually increases) of seismic velocity with depth, large-scale lateral variations in seismic velocities related to mountains and sedimentary basins, small-scale lateral variations (scatterers), and dramatically different elastic properties at individual observation sites (local soil conditions). The wave trains generated by even very simple sources, such as explosions, can become highly complex due to propagation through such heterogeneous media. Source effects such as rupture directivity further add to the spatial variation of ground motions (see Section 5.5).
This large degree of variability in ground-motion characteristics presents a formidable challenge to earthquake engineers and engineering seismologists whose role is to characterize ground motions for the seismic design of structures. During the past two decades, careful studies of ground motions from well-recorded earthquakes, the application of rigorous representations of earthquake sources as shear dislocations, and the use of increasingly realistic methods of modeling seismic wave propagation through heterogeneous structures have resulted in a greatly enhanced ability to understand and predict the complex waveforms of strong ground-motion recordings. Common methods to estimate ground motions are summarized below.
Empirical Engineering Models of Strong Ground-Motion Attenuation A convenient collection of recent empirical ground-motion models was published in the 1997 January-February issue of Seismological Research Letters (214). These ground-motion models are for distinct tectonic categories of earthquakes: shallow crustal earthquakes in tectonically active regions, shallow crustal earthquakes in tectonically stable regions, and subduction-zone earthquakes. Subduction-zone earthquakes are further subdivided into those that occur on the shallow plate interface and those