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Phase-compensated distorted wave Born approximation

Source: vignettes/pcdwba/pcdwba-implementation.Rmd
pcdwba-implementation.Rmd

acousticTS implementation

Validated Experimental
Overview Theory

PCDWBA follows the phase-compensated weak-scattering formulation for broadside elongated targets (Chu and Ye 1999; Chu et al. 1993).

The phase-compensated distorted wave Born approximation is available through target_strength(..., model = "pcdwba"). The implementation is intended for weakly scattering fluid-like bodies and uses the same curved-cylinder bookkeeping whether the target starts as a canonical bent cylinder or an arbitrary fluid-like profile.

This page checks the implementation against two source-level references:

PCDWBA is validated here against source-level reference implementations rather than against a separate published benchmark table. The ZooScatR source agrees exactly on the shared case, while the remaining Echopop drift is attributable to that implementation’s interpolated Bessel evaluation.

Reference case

The comparison uses a single reproducible bent-cylinder case:

  • length 15 mm
  • radius 1 mm
  • taper order 10
  • curvature ratio rho_c / L = 3
  • density contrast g = 1.02
  • sound-speed contrast h = 1.02
  • broadside incidence
  • 12-200 kHz in 2 kHz steps
  • 51 integration nodes in all three implementations

In acousticTS, that target is built as:

library(acousticTS)

pcdwba_object <- fls_generate(
  shape = cylinder(
    length_body = 0.015,
    radius_body = 0.001,
    taper = 10,
    radius_curvature_ratio = 3,
    n_segments = 50
  ),
  g_body = 1.02,
  h_body = 1.02,
  theta_body = pi / 2
)

pcdwba_object <- target_strength(
  object = pcdwba_object,
  frequency = seq(12e3, 200e3, by = 2e3),
  model = "pcdwba",
  sound_speed_sw = 1500,
  density_sw = 1026
)

head(extract(pcdwba_object, "model")$PCDWBA)
##   frequency         ka                        f_bs     sigma_bs        TS
## 1     12000 0.05026548 -6.147156e-07+7.354948e-11i 3.778753e-13 -124.2265
## 2     14000 0.05864306 -8.131273e-07+1.148885e-10i 6.611760e-13 -121.7968
## 3     16000 0.06702064 -1.027176e-06+1.682542e-10i 1.055090e-12 -119.7671
## 4     18000 0.07539822 -1.251059e-06+2.344088e-10i 1.565149e-12 -118.0544
## 5     20000 0.08377580 -1.478570e-06+3.137691e-10i 2.186169e-12 -116.6032
## 6     22000 0.09215338 -1.703221e-06+4.063858e-10i 2.900962e-12 -115.3746

Validation outputs

Comparison summary

Comparison Max abs. \Delta TS (dB) Mean abs. \Delta TS (dB)
acousticTS vs echopop 0.073947 0.001123
acousticTS vs ZooScatR-source 0.000000 0.000000
echopop vs ZooScatR-source 0.073947 0.001123

The ZooScatR and acousticTS outputs are indistinguishable on this grid. Echopop remains close but evaluates the cylindrical Bessel term through interpolation rather than a direct nodewise call. The largest mismatch is near 112 kHz. Replacing the interpolated J_1(x)/x value with a direct call collapses the residual onto the acousticTS and ZooScatR curve, identifying the drift as numerical rather than geometrical.

Spectrum overlay

Pre-rendered PCDWBA comparison showing ZooScatR, acousticTS, and echopop spectra together with the acousticTS residuals against the two references.

Closing note

The two source-level comparisons exercise the same governing model through independent code paths. acousticTS reproduces the direct ZooScatR calculation on this case and remains close to Echopop across the comparison band.

References

Chu, Dezhang, Kenneth G. Foote, and Timothy K. Stanton. 1993. “Further Analysis of Target Strength Measurements of Antarctic Krill at 38 and 120 kHz: Comparison with Deformed Cylinder Model and Inference of Orientation Distribution.” The Journal of the Acoustical Society of America 93 (5): 2985–88. https://doi.org/10.1121/1.405818.
Chu, Dezhang, and Zhen Ye. 1999. “A Phase-Compensated Distorted Wave Born Approximation Representation of the Bistatic Scattering by Weakly Scattering Objects: Application to Zooplankton.” The Journal of the Acoustical Society of America 106 (4): 1732–43. https://doi.org/10.1121/1.428036.
Gastauer, Sven, Dezhang Chu, and Martin J. Cox. 2019. “ZooScatR—An <Span Style="font-Variant:small-Caps;">r</Span> Package for Modelling the Scattering Properties of Weak Scattering Targets Using the Distorted Wave Born Approximation.” The Journal of the Acoustical Society of America 145 (1): EL102–8. https://doi.org/10.1121/1.5085655.
Lucca, Brandyn, and Wu-Jung Lee. 2026. OSOceanAcoustics/Echopop: V0.6.0. Zenodo. https://doi.org/10.5281/ZENODO.18975959.