Ill -69 



extremely difficult. The irregularities of the surface are typically of the same 

 order of magnitude as the wavelength of the sound, i.e., between 15 cm and 

 15 m, and we have observed earlier for volume inhomogeneities that this is a 

 bothersome range for analysis. In this range, scattering is highly directional, 

 and dependent on the detailed shape of the scatterer. At the same time, the 

 surface is constantly changing shape, and a realistic description must be sto- 

 chastic in nature. Finally, the motion of the surface causes regions of turbulence 

 just below the surface, and disturbances such as white caps or rain (spray) cause 

 air bubbles in the surface layer. Reflection from this composite surface naturally 

 defies an accurate analysis . 



As a consequence, the work in this field divides sharply into two kinds: 

 on the one hand, experimental work on scattering from the real ocean surface; 

 on the other, theoretical analyses of scattering from an idealized surface (usually 

 sinusoidally corrugated) supported by controlled experiments in pools. The one 

 notable exception is the recent work by Marsh, et al. (Ref. Ill- 27) which attempts 

 to analyze scattering from a stochastic surface and compares in a very limited 

 way its theoretical results with the experimental data obtained in the ocean. 



The ocean experiments have been well summarized in review articles 

 by Urick and Pryce (Ref. III-40), and will therefore not be described here. Very 

 little has been added since their survey in this area. Instead, we shall concentrate 

 on giving some unity to the disjointed theoretical treatments, and hope that this 

 will enhance understanding and stimulate the application of the present theory to 

 explain scattering experiments from the actual ocean surface. 



All authors attack essentially the same theoretical problem. Consider 

 a plane wave* in the water 



/ ^x i k(ax+8y+Yz) - iuJt , , 



' Pinc^^'y'"'^> = Pine ^ <"I-46a) 



(Note: k = — ,a^ + 8^+Y^=l) 



*The upward vertical direction is taken to point along the z-axis, and the sea sur- 

 face is on the average parallel to the (x,y) plane. Because of the special signif- 

 icance of the z-direction, we shall employ (x,y,z) coordinates rather than 

 (x^,Xg,X3 ^' ^^ water lies below the surface, i.e. , z < S (x,y) denotes a point 

 in the water. The z- component of the propagation vector of the incident wave 

 points upward along the z-axis. 



artbur Ii.llxttU.3nc. 



S-7001-0307 



