Several examples are used to verify the domain reduction method (DRM), a two-step finite-element methodology described in a companion article for modeling earthquake ground motion in highly heterogeneous three-dimensional localized regions. The first set involves a simple, flat-layered system. Verification of the DRM for this problem is carried out by comparing the results to those calculated directly by the theoretical Green's function method. Its applicability to more general problems is illustrated by two examples: a basin and a hill with and without a weathered surface layer and with the same stratigraphy. We use a Green's function approach for the first step, which for the examples under consideration needs to be performed only once. For the second step, the domain of computation is reduced in each case to a small neighborhood of the geological feature at hand. The second application considers the ground motion due to a strike-slip double couple buried 14 km below the free surface in an 80-km × 80-km × 30-km region that encloses entirely the Los Angeles basin. This problem is solved first by the finite-element method using the single-step traditional approach, in which the ground motion is calculated simultaneously near the seismic source, along the propagation path, and within the region of interest with a single model that encompasses the entire geological structure, from the source to the region of interest. The DRM is then used to determine anew the ground motion over a much smaller (6-km × 6-km × 0.6-km) region contained within the original domain, and the results of the two methods within this region of interest are compared.
These examples serve to demonstrate that in many applications the DRM can be significantly more efficient than the traditional approach. The DRM can be particularly advantageous (1) if the source is far from the local structure and the local structure is much softer than that of the exterior region, (2) if the localized feature exhibits nonlinear behavior, or (3) if for a prescribed source, one wishes to consider a sequence of simulations in which the properties of the local feature, which might include man-made structures, are varied from one simulation to the next.