THE EFFECT OF ROUGH INTERFACES ON SIGNALS 

 THAT PENETRATE THE BOTTOM 



C. W. Horton, Sr. 



Applied Research Laboratories 

 The University of Texas at Austin 



R. J. Urick (1973) stressed the importance of sound trans- 

 mission through the ocean floor in the computation of re- 

 flection loss at the ocean bottom. Strong sub-bottom 

 reflecting layers are not necessary since the wave is 

 refracted upwards when there is a strong velocity gradient, 

 as in sedimentary layers with the properties described by 

 E. Hamilton (1974) for the abyssal plain in the northern 

 Pacific Ocean. The Green's function for a point source in 

 a liquid with a linear velocity gradient was derived by 

 C. L. Pekeris (1946) and D. H. Wood (1969) . This function 

 is used in the Helmholtz integral for the inhomogeneous 

 medium to calculate the properties of the sound beam that 

 enters the bottom, is refracted in a circular arc, and 

 returns to the water column. The effects of roughness at 

 the interface are introduced using the analytical techniques 

 pioneered by Eckart (1953) . The amplitude of the coherent 

 wave and the statistics of phase and amplitude fluctuations 

 will be discussed. Of particular interest are turbidite 

 layers since the acoustic velocity is less than that of 

 water and the normal reflection coefficient may be very 

 small . 



This paper addresses the effects of bottom roughness on sound 

 which refracts in the ocean bottom. The analysis involved a number 

 of simplifying approximations which can be refined in later work. 



Figure 1 displays the environmental parameters of concern to 

 the problem of rays that enter the bottom and are refracted back 

 into the water coliimn. For numerical examples, values obtained by 

 Hamilton (1974) in the Japan Sea abyssal plain will be used. The 

 linearization of the square of the refractive index (Equation 1) 

 permits the solution to be expressed in terms of Airy functions, and 



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