Estimating the Parameters of an Inhomogeneous Medium by Probing with Rays.

by J. L. Casti, D. Detchmendy, H. H. Natsuyama, Robert E. Kalaba

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A computationally efficient technique using ray tracing and successive approximation to estimate the index of refraction of an inhomogeneous medium from the times of arrival of a transmitted signal at various receivers. The ray treatment can cope with a medium whose properties vary in two or three dimensions. The inverse problem can be solved iteratively by a search procedure, by a gradient procedure, or by quadratic convergence. Algorithms for computer solution are presented for quadratic convergence. To conserve high-speed storage, one ray at a time is evaluated until all the rays are considered at each iteration. In a numerical example using fourth-order Adams-Moulton integration with a step size of 0.1, computing time on the IBM 7044 was about half a minute. The initial approximation was a homogeneous medium but the estimate was refined in three iterations. First experiments indicate that the method is feasible even with noisy data. 20 pp. Refs. (MW)

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