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where p is the pressure in the shadow zone at (x, z), pb the pressure on the shadow boundary at (x^, z), csur the surface sound speed (kms ), gsur the surface sound speed gradient (s—1) and f the frequency (Hz).

A uniform asymptotic expansion at a caustic is used to calculate the pressure in the vicinity of a caustic (Ludwig, 1966). Phase shifts are accumulated as follows: n radians decrease in $ at the (pressure-release) surface; n/2 radians decrease in $ at caustics; and zero phase shift at the (rigid) bottom. The computation of surface-duct propagation by ray theory does not allow for leakage from the surface layer into the underlying medium. Therefore, the AMOS equations are used (Marsh and Schulkin, 1955).

c sur

10.3.2 Reverberation

The basic theory for reverberation modeling was described in Chapter 9. Referring to Figure 10.3, the reverberation pressure at the end of the closed path is determined in NISSM as

Iprev|2 = i |dtrantra(0a,1)p1p2nrec(0a,2)|V dR (10.17)

0 0

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