Advanced Applications for Underwater Acoustic Modeling

Box 2

Organization of underwater acoustic reverberation models into two categories.

Cell scattering:

Cell-scattering models assume:

(1) a homogeneous distribution of scatterers throughout the area or volume producing reverberation at any given time;

(2) a sufficiently high density of scatterers to ensure that a large number of scatterers occurs in an elemental volume (𝑑𝑉)

or area (𝑑𝐴) at range 𝑟.

The projector beam pattern is denoted by 𝑏(𝜃,𝜙) and the axial intensity at unit distance is 𝐼₀.

The receiver beam pattern is denoted by 𝑏^(𝜃,𝜙) and 𝑠_𝑣 is the ratio of the intensity of the scattering produced by

a unit volume at a distance of 1 m from the volume to the intensity of the incident sound wave.

The equivalent plane-wave volume reverberation level (RL_𝑣) is

   RL_𝑣=10log₁₀[(𝐼₀/𝑟⁴)𝑠_𝑣∫_𝑣𝑏(𝜃,𝜙)𝑏^′(𝜃,𝜙)𝑑𝑉].

The plane-wave level of boundary reverberation is

   RL_𝑏=10log₁₀[(𝐼₀/𝑟⁴)𝑠_𝑏∫𝑏(𝜃,𝜙)𝑏^′(𝜃,𝜙)𝑑𝐴].

Point scattering:

Point-scattering models are based on a statistical approach that assumes the scatterers are randomly distributed

throughout the ocean. The echoes from each individual scatterer are then summed to compute the reverberation level.