. Acoustic scattering in the ocean. Project TRIDENT; Underwater acoustics; Sound-waves. IV-11 OBSERVER INCIDENT PLANE WAVE. •^- ^1 e = SCATTERING ANGLE FIGURE IV-2 SCATTERING COORDINATES -I'JJt If we drop t±ie time dependence e (see IV-9), die incoming plane wave is represented by: Pq(x) = e ikxi (IV-38) The inhomogeneity is represented by a distribution u (£) < < 1 which is the deviation from unity of the index of refraction. TTie scattering integral to be evaluated is therefore obtained by substituting the incoming plane wave (IV-38) into the scatter- ing integral (IV-37): Pi(x) = - 2k
. Acoustic scattering in the ocean. Project TRIDENT; Underwater acoustics; Sound-waves. IV-11 OBSERVER INCIDENT PLANE WAVE. •^- ^1 e = SCATTERING ANGLE FIGURE IV-2 SCATTERING COORDINATES -I'JJt If we drop t±ie time dependence e (see IV-9), die incoming plane wave is represented by: Pq(x) = e ikxi (IV-38) The inhomogeneity is represented by a distribution u (£) < < 1 which is the deviation from unity of the index of refraction. TTie scattering integral to be evaluated is therefore obtained by substituting the incoming plane wave (IV-38) into the scatter- ing integral (IV-37): Pi(x) = - 2k^ 4TT H ik(r+?i) u(?) (IV-39) V To evaluate this integral in the far field (, at a distance from the inhomogeneity which is large compared to the characteristic size of the inhomogeneity), we must approximate the distance r which is given by: r = |x-?| = (x^ + 5^ - 2x . 5 )^ = x (1+%- 2^ .i-)2 (IV-40) — — — — . X X x arthur S-7001-0307. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Meyer, R. F; Romberg, B. W; Arthur D. Little, Inc. Cambridge, Mass. : Arthur D. Little, Inc.
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