We present results of an on-going project to assess the applicability in reflection seismology of emerging super
resolution techniques pioneered in digital photography. Our approach involves: (1) construction of a forward model
connecting low resolution seismic images to high resolution ones, and (2) solution of a Tikhonov-regularized ill
conditioned optimization problem to construct a high resolution image from several lower resolution counterparts; the
high and low resolution images derived, respectively, from dense and sparse seismic surveys.
This paper gives an overview of developments at Silicon Graphics in the areas of scalable multiprocessing and visualization. These developments are grounded in a scalable, shared memory architecture that allows a high degree of modularity and enormous flexibility of configuration. The first implementations of this architecture include graphics supercomputers with multiple processors and multiple graphics subsystems, that enable parallelism at all levels, including parallelism applied to single graphics tasks. We first describe this architecture and then discuss the characteristics of its first generation implementations.
We present a domain decomposition procedure for solving the Dirichlet problem for the Laplace equation in the union of two intersecting discs in R2. Each subdomain problem is solved using the boundary integral technique, at each iteration integrating the product of the prior solution multiplied by the normal derivative of the Green's function. The subdomain problems are solved in parallel, in a Jacobi fashion. Numerically, they correspond to multiplying dense matrices by vectors of boundary values. We use DAUB4 wavelets to replace the dense matrices by their sparse approximations, thus reducing the computational complexity. The procedure iterates in `wavelet space', on the wavelet transform of the solution at `internal' boundary points, i.e. at subdomain boundary points not part of the full domain boundary. When the convergence criterion is met, an inverse wavelet transform is applied, and each subdomain problem is solved in full to yield the complete solution. Numerical results are presented.
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