The reduction of the earthquake hazard to the general population is a major problem facing the U.S. and other countries. To this end, it is essential that within earthquake-prone regions new facilities be designed to resist earthquakes and existing structures be retrofitted as necessary. Assessing the free-field ground motion to which a structure will be exposed during its lifetime is a critical first step in the design process. Ground motion is usually specified through seismic design spectra, which essentially prescribe an equivalent lateral force that the structure must withstand without failure. This force is based upon (i) past seismic history in the general geographic location, (ii) position with respect to possible earthquake sources such as active faults, (ii) expected earthquake magnitudes, and (iv) general geologic conditions.
Observations of ground motion during recent strong earthquakes have shown, however, that three-dimensional local site effects, which are normally given only passing attention in design, can be extremely significant, and can adversely affect structural safety. Three common effects often observed in basins or sedimentary valleys are an amplification and significantly longer duration of the surface ground motion with respect to that in rock. In addition, there is a more rapid spatial variation of the ground motion that can cause large differential base motion of extended structures such as bridges or dams.
Examples of these effects are plentiful. Perhaps the most dramatic recent occurrences are those in Mexico City in 1985 and within the San Francisco Bay area during the 1989 Loma Prieta earthquake. For both of these events and their aftershocks, amplifications greater than 4 or 5 and durations of up to 15 to 30 seconds greater than the corresponding motion on rock were quite common, due to local site conditions. Studies of these and other earthquakes indicate that the presence of large sediment-filled basins significantly amplifies the strength of the waves observed within the basins.
It is now generally recognized that while one- and two-dimensional local models can help explain observed behavior in certain situations, a complete quantitative understanding of strong ground motion in large basins requires a simultaneous consideration of three-dimensional effects of earthquake source, propagation path, and local site conditions. See  for a general overview, and [12, 11, 22, 8, 9, 18, 16], for instance, for representative recent work in this field. The large scale associated with modeling strong ground motion in large basins places enormous demands on computational resources, and renders this problem among the ``Grand Challenges'' in high performance computing.