We consider a canonical basin, the Moon basin, as our 3-D test model not only because it has an appropriate three-dimensional structure and moderate problem size but also because available results from the boundary integral equation method [41] could be taken for comparisons to verify both numerical methods.
The geological model shown on Figure 1 consists of two different kinds of materials. The shallow half-moon-shaped basin filled with homogeneous soil and surrounded by rock with a contrast of 2 in shear wave velocity. In this model, we only consider a small amount of material damping for soil in the form of Rayleigh damping.
Table 1: Material properties of soil and rock used in the Moon basin model
The finite-element mesh is made up of 27,568 nodes and 148,381 linear tetrahedra. By considering 12 elements per wavelength, the results are moderately accurate up to 1.0 Hz. The effective excitation was used to apply the force equivalent to the case in which a plane Ricker wave with the central frequency of 1/3 Hz is propagating in an arbitrarily inclined direction into the basin. Because we are dealing with a medium-size model, the simulations are performed on a single powerful workstation with 500MB of physical memory. We have run several cases for plane incident wave with different incident angles; one case identical to one used in [42]. In the following I provide some results to illustrate that our 3-D model is correct for simulating this hypothetical earthquake in the idealized basin and that it will be feasible for simulating earthquake ground motion.
Figure 1: Half of 3-D unstructured mesh, moon-shaped basin region (yellow), surrounded rock region (blue and red), element shape: tetrahedra.
Figure 2 shows time histories of displacements along the x-, y- or z-axis
(see inset, Figure 1) at a number of locations along the same three axes,
corresponding to a plane incident SV wave with a Ricker pulse in time
arriving from the negative x-axis and 
with respect to the vertical axis ( 
in Figure 1). The right column corresponds to
results obtained by the FEM while those on the left column are for the BEM [42]. The ordinates are locations along either the x-axis
or y-axis while the abscissas represent time. The overall trends are
essentially identical, i.e., almost the same arrival time, similar wave
patterns, and equal amplitudes, etc.
These initial simulation results are encouraging in several respects:
Therefore, I have started to work on a more complicated and more realistic model to further the objectives of this proposal.
Figure 2: Comparison of results from BEM and FEM simulations for a same case in the Moon basin. Each individual plot represents time history of a certain displacement component along axis x or y on the surface, e.g., u(0,y) is the displacement E-W component along y-axis at x = 0.