Abstract

We consider the problem of tracing stochastic rays in an ocean waveguide. The medium’s mean-value speed of propagation is assumed to be perturbed by a white-noise-type term. We formulate a perturbed eikonal equation for this random problem, the formulation being within the framework of stochastic optimal control. This equation is the basis for obtaining an explicit approximate representation for the angle of the stochastic rays which traces their trajectories. It also indicates the deviations induced by the random inhomogeneities from the free-space geodesic path of propagation, as well as the appropriate renormalization of the speed of propagation.

© 1976 Optical Society of America

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  1. J. J. Brandstatter and M. Schoenberg, "Dynamic programming, Fermat's principle and stochastic eikonal equations," J. Franklin Inst. 297–298, Jan. –Dec. (1975).
  2. E. Ghandour, "Propagation of disturbances in a random medium," J. Inst. Math. Appl. (to be published).
  3. R. Bellman, Dynamic Programming (Princeton U. P., Princeton, N.J., 1957).
  4. E. Ghandour, "On an approximate effective speed of propagation," (unpublished).
  5. J. L. Doob, Stochastic Processes (Wiley, New York, 1953).
  6. M. Ewing, C. L. Pekeris, and J. L. Worzel, "Propagation of Sound in the Ocean," Memoir 27, The Geophysical Society of America, 1948.
  7. J. W. Blum and D. S. Cohen, "Acoustic Wave Propagation in an Underwater Sound Channel," J. Inst. Math. Appl. 8, 186–220 (1971).

1971 (1)

J. W. Blum and D. S. Cohen, "Acoustic Wave Propagation in an Underwater Sound Channel," J. Inst. Math. Appl. 8, 186–220 (1971).

Bellman, R.

R. Bellman, Dynamic Programming (Princeton U. P., Princeton, N.J., 1957).

Blum, J. W.

J. W. Blum and D. S. Cohen, "Acoustic Wave Propagation in an Underwater Sound Channel," J. Inst. Math. Appl. 8, 186–220 (1971).

Brandstatter, J. J.

J. J. Brandstatter and M. Schoenberg, "Dynamic programming, Fermat's principle and stochastic eikonal equations," J. Franklin Inst. 297–298, Jan. –Dec. (1975).

Cohen, D. S.

J. W. Blum and D. S. Cohen, "Acoustic Wave Propagation in an Underwater Sound Channel," J. Inst. Math. Appl. 8, 186–220 (1971).

Doob, J. L.

J. L. Doob, Stochastic Processes (Wiley, New York, 1953).

Ewing, M.

M. Ewing, C. L. Pekeris, and J. L. Worzel, "Propagation of Sound in the Ocean," Memoir 27, The Geophysical Society of America, 1948.

Ghandour, E.

E. Ghandour, "On an approximate effective speed of propagation," (unpublished).

E. Ghandour, "Propagation of disturbances in a random medium," J. Inst. Math. Appl. (to be published).

Pekeris, C. L.

M. Ewing, C. L. Pekeris, and J. L. Worzel, "Propagation of Sound in the Ocean," Memoir 27, The Geophysical Society of America, 1948.

Schoenberg, M.

J. J. Brandstatter and M. Schoenberg, "Dynamic programming, Fermat's principle and stochastic eikonal equations," J. Franklin Inst. 297–298, Jan. –Dec. (1975).

Worzel, J. L.

M. Ewing, C. L. Pekeris, and J. L. Worzel, "Propagation of Sound in the Ocean," Memoir 27, The Geophysical Society of America, 1948.

J. Inst. Math. Appl. (1)

J. W. Blum and D. S. Cohen, "Acoustic Wave Propagation in an Underwater Sound Channel," J. Inst. Math. Appl. 8, 186–220 (1971).

Other (6)

J. J. Brandstatter and M. Schoenberg, "Dynamic programming, Fermat's principle and stochastic eikonal equations," J. Franklin Inst. 297–298, Jan. –Dec. (1975).

E. Ghandour, "Propagation of disturbances in a random medium," J. Inst. Math. Appl. (to be published).

R. Bellman, Dynamic Programming (Princeton U. P., Princeton, N.J., 1957).

E. Ghandour, "On an approximate effective speed of propagation," (unpublished).

J. L. Doob, Stochastic Processes (Wiley, New York, 1953).

M. Ewing, C. L. Pekeris, and J. L. Worzel, "Propagation of Sound in the Ocean," Memoir 27, The Geophysical Society of America, 1948.

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