that occur at greater depths within the subducting plate. Significant differences exist in the ground-motion characteristics among these different earthquake categories, as illustrated in Figure 5.14.

The process of developing modern empirical ground-motion attenuation relations has become a routine endeavor. First, a comprehensive set of strong-motion data is compiled in which the following quantities are rigorously quantified or classified: earthquake category (e.g., crustal or subduction), seismic moment and moment magnitude, focal mechanism, geometry of the earthquake’s rupture plane and distance of each recording station from this plane, and recording site conditions. Next, a complex functional form is usually selected and fit to the data. The equations that are developed relate ground-motion parameters (such as peak ground acceleration, response spectral acceleration, strong-motion duration) to the source parameters of magnitude and mechanism, the path parameters (usually source-to-site distance and sometimes focal depth), and local parameters (site geology and sometimes depth to basement rock).

Specification of Uncertainty in Ground-Motion Attenuation Models and SHA The complete description of a ground-motion parameter includes the central estimate of the parameter and its variability. The standard error in the predicted ground-motion level is relatively high; typically the median plus one standard deviation level of ground motion is about a factor of 1.5 to 2 greater than the median value (215).

Seismic hazard calculations for critical facilities include a comprehensive representation of uncertainty commonly separated into epistemic and aleatory components (216). Epistemic uncertainty is due to incomplete knowledge and data and, in principle, can be reduced by the collection of additional information. Aleatory uncertainty is due to the inherently unpredictable nature of future events and cannot be reduced. The total uncertainty is obtained from the combination of the epistemic and aleatory components. The epistemic uncertainty is usually represented by alternative branches on a logic tree, leading to alternative hazard curves. These alternative hazard curves can be used to define hazard curves at different confidence levels. Each hazard curve is produced from an integration over the aleatory component.

Characterization of Site Response Local geological conditions have a primary influence on the amplitude and frequency content of strong ground motions. In particular, the vertical gradient in shear-wave velocity (which generally increases rapidly with depth just below the surface) gives rise to motion amplification due to impedance contrast effects, which may be offset by the effects of viscoelastic damping and nonlinear response of the medium. The simplest way to account for effects of local



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