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



In 1967 B. E. Parkins of BTL published an article (Parkins, 1967) 

 on the Doppler spectrum of scattered sound from a slightly rough and a 

 very rough sea surface. He used what is termed a physical optics 

 approach in his derivation, which is based on the Helmholtz Integral. 

 The approach is based on some fundamental concepts introduced by Carl 

 Eckart in 1953 on scattering from the sea surface (Eckart, 1953) . 

 Eckart's approach is one of the most elegant treatments you will find 

 on surface scattering and before discussing Parkins derivation, we will 

 review some of these concepts. 



The evaluation of the Helmholtz Integral 



4iT P (A) 



//■ 



9v 



exp (ikr 



1 9v 



exp (ikr )' 



'dS (1) 



requires knowledge of two boundary conditions — the value of the re- 

 radiated pressure P on the surface and the value of the derivative of 

 the reradiated pressure 9P /8v on the surface with respect to the 

 surface normal. By assuming that the sea surface is pressure release, 

 the reradiated pressure is set equal to the incident pressure with a 

 180-degree phase shift. 



P + P = on S 

 o 1 



(2) 



To find the value of the derivative of the reradiated pressure with 

 respect to the normal to the surface, Eckart assumes that the slope 

 of the surface irregularities is small and finds the derivative with 

 respect to the normal to the plane surface on which the gentle undu- 

 lations are superimposed. 



9P 

 o 



3v 



3v 



on S 



(3) 



330 



