RODERICK: FORWARD SCATTERED LOW-FREQUENCY SOUND FROM THE SEA SURFACE 



There are certain inherent assumptions with these boundary condi- 

 tions and further approximations were generally made to obtain tractable 

 solutions. One is the Kirchhoff method — that the acoustic field at 

 any point on the surface can be approximated by the field that would 

 be on a plane tangent to that point on the surface. Another is the 

 Fraunhofer phase approximation — in the expansion of the phase of an 

 exponential only the linear terms in the spatial coordinate system 

 are retained. Claude Horton has shown the necessity in certain geo- 

 metrical situations where also quadratic terms should be retained to 

 yield the familiar Fresnel approximation (Melton and Horton, 1970) . 

 Inherent in Eckart's approximation for the normal derivative of the 

 reradiated pressure is the implication of a surface with zero slope. 

 It is also inherently assumed that there is no shadowing such that each 

 facet on the sea surface is completely insonified. Brekhovskikh 

 (1952) has given some restrictions on angle of incidence, surface 

 curvature, and acoustic wavelength for complete insonif ications of 

 the surface irregularities. Research, both theoretical and experi- 

 mental, at the Applied Research Laboratory, University of Texas, into 

 the validity of the above approximations and assumptions has been 

 extremely useful to other investigators in surface scattering. 



We can take the same approach used by Eckart and solve the re- 

 sulting equation for a traveling sinusoidal surface given by 



I, (x,y,t) = h cos [w t - kx cos a - ky sin a] (4) 



With the proviso that the surface slopes are small and other geometric 

 approximations are met, the solution can be compared to experimental 

 results. Roderick (1968, 1969) conducted small-scale tank experiments 

 in which acoustic waves were scattered from a traveling sinusoidal 

 surface created by an electrical-mechanical wave generator. Wave 

 heights and surface wave lengths were accurately measured over the 



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