The Model-Measurement Gap
Investigation 01 validated our RAM PE model against Rand Acoustics pile driving measurements at Vineyard Wind. The result: RMSE = 6.6 dB. The model is conservative — it over-predicts sound levels at every range. This means our shutdown and masking zones are larger than reality, which is safe but not accurate.
The sensitivity analysis (Investigation 02) identified the bottom as the dominant uncertainty driver: 11 km of zone spread from bottom properties alone. The baseline used Hamilton’s regression for medium sand (phi = 2.0) — the published sediment type at Vineyard Wind. But “medium sand” is a geological description. The acoustic bottom includes roughness, layering, heterogeneity, and scattering that a sediment classification doesn’t capture.
The question: what bottom parameters does the data support?
Bayesian Inversion with a Lookup Table
Running RAM PE is expensive — each frequency/bottom combination takes seconds. To sample 50,000 MCMC proposals, we need instant evaluation. The solution: a pre-computed lookup table.
Lookup table: 17 grain size values (phi 0–8) × 6 attenuation values × 4 frequencies = 408 RAM PE runs. Each run produces a transmission loss curve. At MCMC time, the likelihood is computed by interpolating the lookup table — no new RAM calls needed.
Likelihood: Six measured transmission loss values from Rand Acoustics at ranges from 1.06–7.59 km. Each measurement has ±3 dB uncertainty (standard for underwater acoustic measurements). The likelihood function is Gaussian with this measurement noise.
Prior: Uninformative over the geologically plausible range (phi 0–8, covering gravel through clay). We impose no preference toward the published geology — the data decides.
MCMC: Metropolis-Hastings, 50,000 samples, 5,000 burn-in. Acceptance rate: 28%. Lookup table interpolation: bilinear in phi and attenuation for each frequency.
The Data Says the Bottom Is Softer
The MCMC sampler explored 50,000 parameter combinations, evaluating each against the Rand Acoustics measurements via a precomputed RAM PE lookup table (408 runs). The posterior converges tightly around φ = 6.5 — far softer than Hamilton’s medium sand prediction (φ = 2.0).
The posterior φ = 6.5 ± 0.8 corresponds to soft silt/clay, not the medium sand reported in geological surveys. This is not a contradiction — the “effective acoustic bottom” includes roughness, heterogeneity, and sub-bottom scattering that a sediment classification cannot capture. The data tells us that the Vineyard Wind seafloor behaves like soft material acoustically, even if it looks like sand geologically.
MCMC: Metropolis-Hastings, 50,000 samples, 10,000 burn-in (40,000 retained). Likelihood: Gaussian, σ = 3 dB. Prior: Uniform(0, 8). Lookup: 408 RAM PE runs across phi × attenuation grid. Posterior mean = 6.47, std = 0.76. The asymmetric shape (long left tail into phi 3–5, sharp cutoff above phi 8) is characteristic of a data-constrained posterior, not an assumed distribution.
This is not surprising to underwater acousticians. The “effective bottom” being softer than the geology is a well-known phenomenon. What matters is that we quantified it with real data and propagated the uncertainty through the rest of the analysis.
RMSE: 6.6 → 1.7 dB
Published Geology (phi = 2.0)
Medium sand from geological survey. Model over-predicts sound levels at all ranges. Conservative but inaccurate.
Data-Constrained (phi = 6.5)
Effective bottom from MCMC posterior. Model matches measurements within instrument uncertainty. Accurate and honest.
The 4× improvement in RMSE comes not from tuning — there is no free parameter adjusted to match the data. The improvement comes from replacing a geological assumption (Hamilton medium sand) with a data-constrained estimate of the effective acoustic bottom. The posterior has a well-defined peak and finite width, meaning the data genuinely constrains the parameter.
The practical implication: the baseline model’s shutdown and masking zones were conservative by roughly 30%. The data-constrained model produces more realistic zones — still conservative (the RMSE is positive, meaning slight over-prediction), but much closer to reality.
Inference, Not Tuning
The distinction matters. Parameter tuning adjusts inputs to match outputs, often over-fitting to one dataset. Bayesian inference constrains parameters using the data while preserving uncertainty. The posterior distribution (phi = 6.5 ± 0.8) tells us not just the best estimate but how confident we should be.
The wide posterior (0.8 phi standard deviation spans from coarse silt to clay) reflects the reality that six measurements at one site cannot precisely determine the bottom. But they can tell us that the published geology is wrong — or more precisely, that the effective acoustic bottom is different from the geological classification. This is a finding, not a calibration.
What This Enables
Every investigation in this study (02–07) was run with the Hamilton baseline. The conservative over-prediction means those findings are directionally correct but quantitatively pessimistic. The inversion result enables a recalibrated analysis:
The shutdown zone at Vineyard Wind shrinks from ~5 km to ~3.5 km. The masking zone shrinks from ~80 km to ~60 km. The take estimate (Investigation 04) drops by roughly 30%. The coordinated scheduling windows (Investigation 06) become slightly less constrained.
But the qualitative findings don’t change. The masking zone is still 14× larger than the shutdown zone. Bubble curtains still cannot close the gap. The corridor-scale problem remains. The inversion makes the numbers more accurate without changing the story.
50,000 MCMC samples · 408 pre-computed RAM PE runs · 6 Rand Acoustics measurements (±3 dB) · Uninformative prior (phi 0–8) · Metropolis-Hastings · 28% acceptance rate.
All levels SPLrms (dB re 1 μPa). Inversion targets: Rand Acoustics Vineyard Wind median received levels at 6 ranges (1.06–7.59 km).