This report begins with a review of the physical and experimental bases for quantative description of earthquake occurrence rates and geological recurrence rates, to describe the amplitudes and the shape of the magnitude occurrance rate curves for earthquakes in a region. It considers the selection of the maximum earthquake, the limitations of geological observations and the most important sources of uncertainty. Then it presents the concept of uniform risk spectrum with the most recent refinements in this methodology, including more detailed description of the earthquake source zones, and the uncertainties of estimating a summary of the method for generating artificial accelerograms for use in engineering design. The artificial accelerogram can be derived either starting from the uniform risk spectrum computed by NEQRISK program, or by using independently determined Fourier amplitude spectra of the desired strong ground motion.; When the seismic risk at a site is dominated by the presence of an active fault nearby, the analyst may wish to compute the ground motions in terms of some physical model, which produces ground motion in terms of the assumed slip and the faulting characteristics at the earthquake source. A review of several simple sources is presented, as well as of the equations which give such motion explicitly, for simple basic contributions to the strong motion at distances close to the fault. Numerous references are cited which summarize the state of the art in forward modeling procedures of ground motion from kinematic description of the earthquake sources.; For long structures, which are sensitive to relative motions of different multiple supports, when the physical modeling of the local soil and geology requires detailed modeling of local wave scattering and diffraction, simple illustrative example for SH wave scattering is presented. The example presented in this report, in terms of SH waves, is the simplest for such an illustration. Yet it can demonstrate most of the wave propagation phenomena present in other more complex models. For input ground motions, computed either in terms of synthetic accelerograms via empirical scaling and uniform risk spectra or in terms of deterministic physical modeling, the simple two-dimensional example for SH wave scattering shows how, by using transfer function approach and Fourier analysis and synthesis, one can derive motion at multiple support points of long structures.