Advances in Acoustics and Vibration

Review Article

Advanced Applications for Underwater Acoustic Modeling

Box 1

Organization of underwater acoustic noise models into two categories.
Ambient noise
 Given: the directional noise intensity per unit solid angle [ 𝑁 𝑠 ( πœƒ , πœ™ ) ] .
   (i) The horizontal noise directionality [ 𝑁 ( πœ™ ) ] is calculated from [ 𝑁 𝑠 ( πœƒ , πœ™ ) ] as:
    ∫ 𝑁 ( πœ™ ) = πœ‹ / 2 βˆ’ πœ‹ / 2 𝑁 𝑠 ( πœƒ , πœ™ ) c o s πœƒ 𝑑 πœƒ .
   (ii) The vertical noise directionality [ 𝑁 ( πœƒ ) ] is calculated from [ 𝑁 𝑠 ( πœƒ , πœ™ ) ] as:
    ∫ 𝑁 ( πœƒ ) = ( 1 / 2 πœ‹ ) 0 2 πœ‹ 𝑁 𝑠 ( πœƒ , πœ™ ) 𝑑 πœ™ .
    (iii) The omnidirectional noise level ( 𝑁 ) is then calculated as:
    ∫ 𝑁 = 0 2 πœ‹ ∫ πœ‹ / 2 βˆ’ πœ‹ / 2 𝑁 𝑠 ( πœƒ , πœ™ ) c o s πœƒ 𝑑 πœƒ 𝑑 πœ™ ,
  or
    ∫ 𝑁 = 0 2 πœ‹ 𝑁 ( πœ™ ) 𝑑 πœ™ .
    (iv) The horizontal angle ( πœ™ ) is measured positive clockwise from true North while the vertical angle ( πœƒ ) is measured
positive upward from the horizontal plane. No receiver beam patterns were convolved with the noise levels 𝑁 ( πœƒ )
and 𝑁 ( πœ™ ) .
Beam-noise statistics
  The averaged noise power at the beamformer output ( π‘Œ ) can be expressed as:
    βˆ‘ π‘Œ = π‘š 𝑖 = 1 βˆ‘ 𝑛 𝑗 = 1 βˆ‘ 𝐴 𝑖 𝑗 π‘˜ = 1 𝑆 𝑖 𝑗 π‘˜ 𝑍 𝑖 𝑗 π‘˜ 𝐡 𝑖 𝑗 π‘˜ ,
where m: number of routes in the basin; n: number of ship types; 𝐴 𝑖 𝑗 : number of ships of type j on route
i (a random variable); 𝑆 𝑖 𝑗 π‘˜ : source intensity of the kth ship of type j on route i (a random variable that is
statistically independent of the source intensity of any other ship); 𝑍 𝑖 𝑗 π‘˜ : intensity transmission ratio from
ship 𝑖 𝑗 π‘˜ to the receiving point; 𝐡 𝑖 𝑗 π‘˜ : gain for a plane wave arriving at the array from ship 𝑖 𝑗 π‘˜