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Vol: 4(4) No: 1 / March 1994 Geophysical Inversion Problem and Tomographic Parallel Algorithms Dusan Tosic Matematicki Fakultet, Univerzitet u Beogradu, Studenntski trg 16, 11000 Beograd, Yugoslavia Keywords: geophysics, topography, parallel algorithms Abstract In this paper a generalization of the parallel algorithm to the solution of Geophysical Inversion Problem is proposed. Some characteristics of the proposed algorithm are described. The generalized algorithm is convenient for MIMD (Multiple Instruction, Multiple Data) parallel computers. Specially, proposed pseudo-codes are adjusted to the Intel iPSC hypercube. References [1] Y. Censor, D. Gordon, Strong Underrelaxation in Kaczmarz’s Method for Inconsistent System, Numer. Math. 41 (1983) 83-92. [2] Y. Censor and G. T. Herman, On Some Optimization Techniques in Image Reconstruction from Projections, Applied Numerical Mathematics 3 (1987) 365-391. [3] Y. Censor, Strong Series-Expansion Reconstruction Methods, Proc of IEEE 71 (3) (1983) 409-419. [4] S. Ivanson, Seismic Borehole Termography – Theory and Computational Methods Proc of IEEE 74 (2) (1986) 328-338. [5] S. Ivanson, Remark on an earlier proposed iterative tomographyc algorithm, Geophys, J. R. astr. Soc. 75 (1983) 855-860. [6] J. E. Peterson, B. N. P. Paulsson, T. V. McEvilly, Applications of algebraic reconstruction techniques to crosshole seismic data, Geophysics 50 (10) (1985) 1566-1580 [7] R. Gordon, R. Bender, G. T. Herman, Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography, J. theor. Biol 29 (1970) 471-781. [8] M. R. Trummer, A Note on ART of Relaxation, Computing 33 (1984) 349-352. [9] M. Gustavsson, S. Ivansson, P. Moren, J. Phil, Seismic Tomography for Rock Quality Determination, in: Proc. Of EAEG-meeting, Budapest, Hungary (1985) 1-6. [10] K. A. Dines and R. J. Lytle, Computerized Geophysical Tomography, Proc of IEEE 67 (7) (1979) 1065-1073. [11] R. D. Radcliff and C. A. Balanis, Reconstruction Algorithms for Geophysical Applications in Noisy Environments, Proc. Of IEEE 67 (7) (1979) 1060-1064. [12] K. Tanabe, Projection Method for Solving a Singular System of Linear Equations and its Applications, Numer. Math 17 (1971) 203-214. [13] S. L. Johnsson, Communication Efficient Basic Linear Algebra Computations on Hypercurbe Arhitectures, J. of Par. And Dist. Comp. 4 (1987) 133-172. [14] D. Tosic, Opis uopstenog paralelnog algoritma za tomografsku ocenu brzina u geofizici, in Proceedings of XVI SIM-OP-IS, Kupari, Yugoslavia (1989) 311-314. [15] D Tosic, Parallel Algorithm for Tomographic Velocity Estimation in Geophysics, in: Proceedings of the International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena, Strasbourg, France (1991) 787-789. [16] Y. Saad and M. H. Schultz, TopologicalProperties of Hypercubes, IEEE Tran. On Comp. 37 (7) (1988) 867-872. [17] C.L. Seitz, The Cosmic Cube, Comm. Of ACM 28 (1) (1985) 22-33. |