practical significance this is always possible), many or even a continuum of, arrival directions will be re- 

 quired to account for most of the ambient noise energy. Thus discrimination between targets and non- 

 targets on the basis of spaticd distribution of the arriving signal is practical cind useful. 



Such discrimination is performed in many passive soneir systems by the use of directional arrays smd 

 beam-formers. 



To make full use of the power of directional discrimination, one must know the directional distri- 

 bution of ambient noise. This knowledge can be acquired by cut-and-try— i.e., by trying out various 

 beam forming methods to see which gives the greatest enhancement of the signal-to-noise ratio— or by 

 controlled experiments to measure particular qualities of ambient noise directionality which we know, a 

 priori, are significant. Neither method is indisputably superior to the other, and both are being used at 

 present. 



A significant amount of effort is being expended to measure ambient noise directionality in the 

 deep ocean with horizontal linear arrays. Characteristically, all of the measurements fall far short of tell- 

 ing all about ambient noise directionality that an analyst might think it reasonable to ask. Some com- 

 promise between simplicity and completeness of rheasurement is needed. This paper is a tutoried analysis 

 of some of the mathematics of directionality measurement with linear arrays, and is intended to help 

 the reader answer the following questions: 



• How can one make requests for ambient noise directionality data which are both useful and easy 

 to fulfill? 



• How can one design better ambient noise directionality measurement techniques, analyses, and 

 model validations? 



• How can one make more effective use of existing ambient noise directioncdity data and results? 



SCOPE 



All of my experience is limited to the use of linear arrays of omnidirectional receivers at low fre- 

 quencies (in the range from 10 to 300 Hz), and so will be this discussion. This band of frequencies is 

 of great practical interest in surveillance. It includes the frequencies where surface shipping guarsmtees 

 that noise from this source will be highly anisotropic. To gain useful information about directionality, 

 we must make coherent measurements with sensors spaced many wavelengths apart. At these frequen- 

 cies, spacings of a few hundred feet are required; spacings of several thousand feet are preferable, if pos- 

 sible. A rigid multidimensional structure of this size is almost unthinkable as a deployable measurement 

 tool for occasional use, but a flexible linear array straightened by static force or dynamic tension is 

 quite practical. 



For the purpose of this discussion, elevation angle will be ignored, and all sound will be treated as 

 though it arrived approximately horizontally. (Some of the consequences of this assumption are dis- 

 cussed in Ref. 1.) The assumption is without general validity; however, it simplifies the specific points I 

 have to make vnthout detracting from their validity. The receiving elements need not be omnidirec- 

 tional (in fact, in the seismic cirray they are not),^ but this generalization will not be considered, nor 

 will the effect of side lobes and of the finite width and non-ideal shape of main beams. Methods for 

 handling these departures from the ideal are well-known, and will not be discussed further here. 



^G. Raisbeck, D. Sullivan, and G. Miller, Ambient Noise Directionality in the EASTLANT II Exercise Arthur D. 



Little, Inc., ADL Report No. 4630274 (Feb. 1974) 



R. Gardner and W. H. Luehrmann, EASTLANT II Project Clear Preliminary Report Seismic Engineering Com- 



pany, Houston, Texas 77027, (3 Jan. 1973) 



S90 



