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SPHMS

Source: vignettes/sphms/index.Rmd
index.Rmd

Overview

Benchmarked Validated
Theory Implementation

The spherical modal-series solution (SPHMS) calculates scattering from an unshelled, homogeneous sphere in an exterior fluid. It is the package’s primary spherical reference model.

Core idea

Expand the incident, scattered, and interior fields in spherical partial waves, apply the selected interface condition independently at each angular order, and sum the far-field coefficients. This separation is exact for a spherical interface (Anderson 1950; Hickling 1962).

Best for

  • Fixed-rigid, pressure-release, liquid-filled, or gas-filled spheres
  • Canonical checks of boundary and material-property effects
  • Spherical reference cases for approximate or more general solvers

Supports

  • Sphere geometry carried by FLS or GAS scatterers
  • Homogeneous interiors with seawater as exterior medium 1
  • Monostatic complex amplitude, backscattering cross-section, and target strength

Main assumptions

  • A perfectly spherical, unshelled interface
  • Homogeneous properties within each region
  • Linear time-harmonic acoustics
  • No elastic shear waves, viscous layer, or nonspherical orientation effects

Validation status

  • Benchmarked against the canonical spherical spectra stored in benchmark_ts.
  • Validated against KRMr and echoSMs on shared penetrable-sphere cases.

Family pages

  • Implementation: object construction, boundaries, output, and comparisons
  • Theory: field expansions, boundary systems, and modal coefficients

References

Anderson, Victor C. 1950. “Sound Scattering from a Fluid Sphere.” The Journal of the Acoustical Society of America 22 (4): 426–31. https://doi.org/10.1121/1.1906621.
Hickling, Robert. 1962. “Analysis of Echoes from a Solid Elastic Sphere in Water.” The Journal of the Acoustical Society of America 34 (10): 1582–92. https://doi.org/10.1121/1.1909055.