proximity to the fault to dominate. In the Northridge earthquake, ground-motion amplitude greater than 2 hertz was observed to be highest above the hypocenter on the hanging wall side (6), not around the top edge of the fault, which experienced the longer-period directivity effects. Systematic differences in ground motion have been observed for different faulting types (7), but as yet no clear explanation of this exists. Elucidating how faults radiate seismic energy across the entire frequency band relevant to earthquake engineering (0.1-10 hertz) is a research challenge of major importance.

The amplitude of seismic waves generally decreases as the waves propagate away from the source (as required to conserve energy), but the measurement from large earthquakes always exhibits a high degree of scatter. In seismic hazard analysis, the decay of ground-motion intensity with distance is represented by an attenuation relation, usually derived by fitting smooth functions to the scattered data (see Section 2.7). An objective of current research is to explain the variations in shaking intensity through a more fundamental understanding of the wave propagation process (8). Important physical effects include refraction by variation in the seismic velocity, reflection from surfaces of material discontinuity, and damping by the anelastic response of the rock and soil media. Some of the strongest variations are associated with horizontal layering of the crust and upper mantle. In the 1989 Loma Prieta earthquake, shear waves, critically refracted from the M discontinuity at the base of the crust (SmS waves), were partially responsible for the shaking that damaged parts of San Francisco nearly 90 kilometers from the epicenter (9). Data from aftershocks of the 1994 Northridge earthquake demonstrated that reflections from midcrustal interfaces can increase the shaking from shallow sources at certain shorter distances.

Seismic waves can be amplified or attenuated by three-dimensional structures such as fault-bounded blocks and sedimentary basins. Earthquakes can excite resonance in the deep basins, shaking the soft sediments like jelly. A striking example was the massive destruction and loss of life during the 1985 Michoacan earthquake (moment magnitude [M] 8.0) in the parts of Mexico City underlain by soft, lake-bed clays. The source was in a subduction zone more than 350 kilometers away, which under normal circumstances would have caused little damage; however, sediment resonance was observed to amplify the spectral acceleration at low frequencies (about 0.5 hertz) by factors as large as 8 to 50 times relative to hard-rock sites (10). Other mechanisms for amplification include the focusing of waves by lens-like structures (11) and the generation of surface waves by the fault-bounded edges of sedimentary basins. Basin-edge effects of the latter type were partly responsible for the extreme damage to the Japanese city of Kobe in the 1995 earthquake (Box 2.4).

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