Spherical modal series (SPHMS) solution

Spherical modal series (SPHMS) backscatter model. Supports rigid, pressure-release, fluid-filled, shelled (pressure-release/liquid/gas). Frequencies in Hz; sound speed in m/s; density in kg/m^3. Material properties may be contrasts or absolute (contrasts derived relative to seawater). Full equations and boundary-condition details are documented in the SPHMS vignette.

Value

No value; this help topic documents the SPHMS model.

Usage

This model is accessed via:


target_strength(
  ...,
  model="sphms",
  boundary,
  sound_speed_sw,
  density_sw,
  m_limit
)

Arguments

boundary: Boundary condition at a spherical surface. One of "fixed_rigid", "pressure_release", "liquid_filled", "gas_filled", "shelled_pressure_release", "shelled_liquid", or "shelled_gas". See the boundary conditions documentation for more details on these different boundary conditions.
sound_speed_sw: Seawater sound speed (\(m~s^{-1}\)).
density_sw: Seawater density (\(kg~m^{-3}\)).
m_limit: Optional model truncation limit used to cap the number of modes in the numerical calculation.

Theory

The modal series solution for a sphere expands backscatter from a spherical scatterer in spherical Bessel/Hankel modes. The form function is:

\( f_{bs} = -\frac{i}{k_w} \sum_{n=0}^{\infty} (-1)^n (2n+1) A_n, \)

References

Anderson, V.C. (1950). Sound scattering from a fluid sphere. The Journal of The Acoustical Society of America, 22: 426-431.

Examples

subset(available_models(), model == "sphms")
#>       model  slot  source persistent aliases
#> sphms sphms SPHMS builtin      FALSE