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HPA

Source: vignettes/hpa/index.Rmd
index.Rmd

Overview

Benchmarked Validated
Theory Implementation

These pages follow Johnson’s asymptotic fluid-sphere formulation and Stanton’s generalized approximate backscatter formulas (Johnson 1977; Stanton 1989).

The high-pass approximation (HPA) is a compact asymptotic backscatter family that interpolates between a Rayleigh-style low-frequency limit and a reflection-controlled high-frequency limit.

Core idea

Build a rational approximation whose numerator reproduces the low-ka scattering strength and whose denominator suppresses unphysical growth as frequency increases, then adapt the geometric prefactors to spheres, spheroids, and cylinders.

Best for

  • Fast approximate spectra for simple canonical bodies
  • Broad trend studies when an exact modal solve is unnecessary
  • Weakly contrasting or moderately reflecting targets represented by simple shapes

Supports

  • Sphere, prolate spheroid, straight cylinder, and bent-cylinder branches
  • Contrast bookkeeping relative to seawater as medium 1
  • Very fast monostatic backscatter estimates

Main assumptions

  • Asymptotic interpolation rather than an exact boundary-value solution
  • Shape-specific prefactors carried from the source literature
  • Best interpreted as a broadband approximation, not a resonance-resolving solver

Validation status

  • Benchmarked against canonical asymptotic target families rather than as an exact modal solver.
  • Validated against the spherical echoSMs::HPModel branch and the published Johnson/Stanton algebra.

Family pages

  • Implementation: quick workflows and validation tables
  • Theory: Rayleigh term, reflection limit, and shape-specific completions

References

Johnson, Richard K. 1977. “Sound Scattering from a Fluid Sphere Revisited.” The Journal of the Acoustical Society of America 61 (2): 375–77. https://doi.org/10.1121/1.381326.
Stanton, Timothy K. 1989. “Simple Approximate Formulas for Backscattering of Sound by Spherical and Elongated Objects.” The Journal of the Acoustical Society of America 86 (4): 1499–1510. https://doi.org/10.1121/1.398711.