STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



indicate the sum of the proper plus a finite number of improper modes 

 (neglecting the Pekeris branch) . This example shows that sometimes 

 the improper modes offer an excellent approximation to the EJP branch 

 integral. 



REFERENCES 



Bartberger, C, "Normal Mode Solutions and Computer Programs for 

 Underwater Sound Propagation," Part I - Two-Layered and Three- 

 Layered Programs, Report No. NADC-72001-AE; Part II - Program for 

 Arbitrary Velocity Profiles, Report No. NADC-72002-AE, Naval Air 

 Development Center, 4 April 1973. 



Beisner, H. M., "Numerical Calculation of Normal Modes for Underwater 

 Sound Propagation" IBM J. Res. Develop., pp. 53-58, January 1974. 



Brekhovskikh, L. M. , Waves in Layered Media, Academic Press, 

 pp. 454-460, 1960. 



Ewing, W. M. , W. S. Jardetsky, F. Press, Elastic Waves in Layered 

 Media, McGraw-Hill, pp. 126-151, 1957. 



Kutschale, H. W. , "The Integral Solution of the Sound Field in a 

 Multilayered Liquid-Solid Half Space with Numerical Computations 

 for Low-Frequency Propagation in the Arctic Ocean," Lamount- 

 Doherty Geological Observatory, Tech. Report No. 1, 1970. 



Labianca, F. M. , "Normal Modes, Virtual Modes, and Alternative 



Representations in the Theory of Surface Duct Sound Propagation," 

 J. Acoust. Soc. Am. 53, pp. 1137-1157, 1973. 



Newman, A. V., F. Ingenito, et al . , "A Normal Mode Computer Program 

 for Calculating Sound Propagation in Shallow Water with Arbitrary 

 Velocity Profile," Naval Research Laboratory, Washington, NRL 

 Memorandum 2381, January 1972. 



Pedersen, M. A. and D. F. Gordon, "Normal-Mode Theory Applied to 

 Short Range Propagation in an Underwater Acoustic Surface Duct," 

 J. Acoust. Soc. Am. 34, pp. 105-118, 1965. 



150 



