A three‐dimensional forward modeling algorithm, allowing arbitrary density and arbitrary wave propagation velocity in lateral and vertical directions, directly solves the acoustic wave equation through spatial and temporal discretization. Spatial partial differentiation is performed in the Fourier domain. Time stepping is performed with a second‐order differencing operator. Modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. Three‐dimensional forward modeling represents a challenge for computer technology. Computation of meaningfully sized models requires extensive calculations and large three‐dimensional data sets which must be retrieved and restored during the computation of each time step. The computational feasibility of the Fourier method is demonstrated by implementation on the multiprocessor CRAY X‐MP computer system using the large secondary memory of the solid‐state storage device (SSD). Calculations use vectorization and parallel processing architecture. The similarity of numerical and analytical results indicates sufficient accuracy for many applications.
Even if most of us can agree on a definition of the “common good” (not a simple matter), there are substantial barriers to establishing public policies in accord with that agreement. The “democratic” element in our political system – the right of voters to choose the men and women who will create our laws – depends on the views of those voters being given considerable weight in determining eventual policy outcomes. Unfortunately, we have developed a political system – both in our elections and in the governing process – that gives disproportionate influence to relatively small numbers of voters (who are also the most partisan) and allows political parties through their closed procedures to limit the choices available to general election voters. Coupled with legislative rules that allow partisans to determine the makeup of legislative committees, the resulting process leaves the common good, however defined, a secondary consideration at best.
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