On an approximate effective speed of propagation

✍ Scribed by Edmond Ghandour

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 479 KB
• Volume: 303
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(77)90076-x

✦ Synopsis

An algorithm is suggested for the determination of an effective speed of propagation for a random medium whose mean speed of propagation is perturbed by a small random term of the white-noise type. We study the propagation of disturbances in the limiting geometrical optics case, and pursue the analysis within the framework of stochastic optimal control. The statement of an appropriate Fermat's principle for the random medium and invoking the principle of dynamic programming lead to a non-linear elliptic equation-the classical Eikonal equation-perturbed by terms associated with the stochastics. This equation and estimates for the departure of the stochastic trajectories from the free-space geodesic path of propagation enable us to calculate the approximate speed.