in the overlying softer soil. If nonlinear effects are important, then strong ground motions for large earthquakes can be difficult to predict from the measured accelerations during smaller events. Another complicating factor is that cohesionless soils are also subject to liquefaction and lateral spreading due to pore pressure effects (201). Nevertheless, numerical codes that account for soil nonlinearity are numerous, ranging from equivalent linear models to fully nonlinear models that also incorporate pore-pressure generation (202).

Ground motions at frequencies above 1 hertz are the most damaging motions for small- and moderate-sized structures, and they also contain important information about the seismic source and details of stress on the fault plane. The character of high-frequency ground motions was documented from the analysis of the first strong-motion accelerograms (203). A key parameter is the corner frequency, which scales as the inverse of the rupture duration for events recorded in the far field or to the slip duration at a location on the fault for large events recorded by nearby seismometers. At low frequency, the displacement amplitude spectrum is constant with increasing frequency up to the corner frequency, where it changes slope and rolls off as the square of frequency (204). Correspondingly, the acceleration amplitude spectrum increases with frequency squared below the corner frequency and becomes flat above the corner frequency. Above 5 to 10 hertz, the acceleration spectrum declines rapidly with increasing frequency beyond a transition value denoted by f_max (205). Many theoretical studies have attempted to explain the flat portion of the acceleration spectrum (206). The spatial coherence of ground motions decreases rapidly with increasing frequency (207). Although the cause of this incoherence is not well understood, it may be due in part to focusing effects caused by irregular bedrock topography (208).

• How are the major variations in seismic-wave speeds related to geologic structures? How are these structures best parameterized for the purposes of wavefield modeling?

• What are the contrasts in shear-wave speed across major faults? Are the implied variations in shear modulus significant for dynamic rupture modeling? Do these contrasts extend into the lower crust and upper mantle?

• How are variations in the attenuation parameters related to wave speed heterogeneities? Is there a significant dependence of the attenua-