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

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

Published 1969

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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