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

Purchase Print Copy

 Format Price
Add to Cart Paperback $20.00

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)

This report is part of the RAND research memorandum series. The Research Memorandum was a product of RAND from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.