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SPHMS

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

Overview

Benchmarked Validated
Theory Implementation

These pages follow the classical exact sphere literature for fluid, elastic, and approximate shell limits (Anderson 1950; Faran 1951; Hickling 1962).

The spherical modal series solution (SPHMS) is the package’s exact canonical solution for unshelled homogeneous spheres in an exterior fluid. Because the Helmholtz equation separates exactly in spherical coordinates, each angular order remains algebraically local after the boundary conditions are imposed.

Core idea

Represent the incident, scattered, and interior fields in spherical partial waves, enforce the chosen boundary condition at the spherical interface, and sum the retained orders into the far-field backscatter. SPHMS is the natural spherical benchmark for the rest of the package.

Best for

  • Rigid, pressure-release, liquid-filled, and gas-filled spheres
  • Canonical benchmark comparisons and sanity checks
  • Problems where exact spherical geometry is a reasonable physical idealization

Supports

  • Sphere shapes on FLS or GAS objects
  • Medium-indexed spherical theory with medium 1 as seawater and medium 2 as the sphere interior
  • Direct target-strength calculations from exact spherical coefficients

Main assumptions

  • Perfectly spherical interface
  • Homogeneous material properties in each region
  • Linear, time-harmonic acoustics
  • No elastic shell or viscous intermediate layer

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, spectra, and software comparisons
  • Theory: full spherical separation, boundary conditions, and coefficient derivations

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.
Faran, James J. 1951. “Sound Scattering by Solid Cylinders and Spheres.” The Journal of the Acoustical Society of America 23 (4): 405–18. https://doi.org/10.1121/1.1906780.
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.