11. 
LECTURE 11 
NONSPECULAR SCATTERING OF UNDERWATER 
SOUND BY THE SEA SURFACE 
H. Wysor Marsh 
Marine Electronics Office 
AVCO Corporation 
New London, Connecticut 
U.S.A. 
1. INTRODUCTION 
Marsh et al. [1,2] developed a general theory of sound scattering by the 
sea surface, and considered the specular reflection in detail, in connection with 
an analysis of propagation in a surface isothermal layer. 
Nonspecular reflection can also be important in influencing propagation, and 
is especially significant in studying reverberation, or back scattering. 
11.2, NONSPECULAR SCATTERING 
For the theory of nonspecular scattering we havea point of departure follow- 
ing Marsh et al. [2], employing their notation throughout, and using their equation: 
AQ,p) = [1 = 4 yo? ffm) S(l-a,m - B) dl dm) 5(A - 2) 5(u - B) + 4y?0” SA-2,n - B) 
The specular term is that involving the brackets, which they denote by 
Q(A,n) (A — a,p - B) 
We now define the nonspecular term to be I'(A,u) so that 
T(Q,p) = 4y20? S(A - a,p — B) (1) 
To reduce this result, we need the following additional results from the 
work cited: 
S (l,m) Lf pr) Jolrd - v?)?\ dr 
0 
and 
a 2 
h?p(r) =5 { Jo = a 2(@) do 
and : 
AA@)) = Gan? exo 26) 
ousS2 
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