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INTRODUCTION 



The scattering of rays by a random collection of ice keels has been investigated by the 

 Naval Ocean Systems Center (NOSC). This report presents the results of this investigation. The 

 computer ray program used in this project was reported at the Austin meeting of the Acoustic 

 Society of America in Apnl 1985 and in Ref. 1. 



In a 1976 article in the Journal of the Acoustic Society of America (Ref. 2), 

 O.I. Diachok showed that Twersl y's boss-scattering theory was an effective approach to 

 underice scattering and propagation. A first-term approximation from that theory was shown 

 to give effective results for high frequencies, as did another at low frequencies. The current task 

 derives high-frequency numerical values similar to the former, the main difference being that 

 the individual bosses are of random size. 



This report wiil first discuss the random ice keel model used, and then the ray 

 computation technique. There will then be a discussion of two functions that were derived ct 

 estimated, the angular distribution of rays scattered from the set of keels and the specular 

 scattering coefficient The final section will discuss some of the geome'.ry and mechanics of the 

 computations to explain various observed features of the computed functions. These discus- 

 sions will aid m determining which resulrs arise from given assumptions of the model and 

 provide a basis tor estimating the acoustic properties of real keels. Such ^timations, however, 

 are not attempted here. An alternative view of ice keels, in which their rough or bkek 

 character is emphasized, has been provided by S. Chin-Bing (Ref. 3). 



COMPUTER METHOD 



Figure I indicates the basic computational strategy. A large number of equally spaced 

 rays are launched towards a set of keels represented as parabolas. As the rays emerge from the 

 set of keels, they are accumulated in angular bins. The contents of these bins then represent the 

 scattering characteristics of the keel set. The distance between keels is random, drawn from a 

 rectangular distribution to give 9.5 keels km. The depths of the keels are drawn from a 

 Rayieigh distribution with a mean depth of 4 m. A further parameter, the ratio of depth to 

 width is I to 3 2. Therefore, the keels are all similar geometric figures. Most of these para- 

 meters are taken from Diachok's 1976 article. 



Figure 2 shows details ot an individual keel on an equal length-depth scale. This is the 

 cross section of an elongated object. For simplicity the keel is assumed to be infinite in length 

 The maximum slope of the keel edge is at its upper edge and is 51.3 degrees. The keel model as 

 shown was next modified to simulate an orientation of the keels that is random when viewed 

 from above. This was done by increasing the width o( the keels by a function of a random 

 angle between and 90 degrees — approximately the secant of the angle. However, this 

 function a modified by the fact that, in a given range interval, one is more likely to cross a keel 

 perpendicular to a path than one nearly parallel. 



