# Underwater Shock Public Benchmark **Date:** 2026-05-09 **Status:** `PUBLIC_HISTORY_MODELING_PRIOR` **Claim boundary:** this note uses public historical underwater detonation records as free modeling data for shock-front, acoustic, bubble-pulse, reflection, and attenuation behavior. It is not a weapon-design document, not a charge-sizing guide, not target-vulnerability analysis, and not an operational placement model. ## Why Sea-Based Records Are Useful Underwater detonations are over-documented historical events. Humans made an enormous number of public visual, acoustic, radiological, naval, and historical records around them. That makes them useful as a low-cost validation source for general shock physics: ```text impulsive source -> compressive water shock -> pressure-release surface interaction -> gas / vapor bubble expansion -> bubble collapse and pulse train -> acoustic propagation and attenuation -> sediment / boundary reflection ``` For this stack, the value is not the weapon. The value is the medium response: water is dense, nearly incompressible, acoustically conductive, and creates a clean separation between the first shock front and the slower bubble-pulse sequence. There is also a practical economic reason. A single serious underwater shock test chamber campaign would be expensive enough to erase the available research budget before the model had a chance to mature. Public historical records are therefore not just convenient; they are the only sane first validation lane. They let the stack fit waveform shape, timing, attenuation, and residuals without pretending that a private chamber test is feasible. The rule is: ```text use public history to learn the medium response; do not use the model to optimize destructive operation. ``` ## Public Historical Source Class Useful public source classes: - official history pages and fact sheets for underwater tests such as Operation Crossroads BAKER; - medical / environmental / historical reviews that describe the test context; - public technical reports that summarize shock-wave and bubble-pulse signal characteristics; - open acoustic literature on underwater explosion sound and bubble-pulse timing; - generic bubble-dynamics literature using Rayleigh-Plesset-type equations. Examples: - Atomic Heritage Foundation / National Museum of Nuclear Science & History, Operation Crossroads overview: `https://ahf.nuclearmuseum.org/ahf/history/operation-crossroads` - NCBI Bookshelf, "Mortality of Veteran Participants in the Crossroads Nuclear Test", historical description: `https://www.ncbi.nlm.nih.gov/books/NBK233207/` - OSTI technical report, "Signal characteristics of an underwater explosive acoustic telemetry system": `https://www.osti.gov/biblio/6625697` - Acoustics Today, "The Sound from Underwater Explosions": `https://acousticstoday.org/wp-content/uploads/2023/02/The-Sound-from-Underwater-Explosions-David-R.-DallOsto-Peter-H.-Dahl-and-N.-Ross-Chapman.pdf` ## Safe Modeling Variables The benchmark lane should use observable signal variables: ```text t_arrival acoustic arrival time p_peak_proxy observed or normalized peak pressure proxy tau_decay shock decay time constant t_bubble_1 first bubble pulse arrival t_bubble_k later bubble pulse arrivals A_k relative pulse amplitudes alpha_water fitted propagation attenuation Gamma_surface pressure-release reflection coefficient Gamma_bottom fitted seabed / boundary reflection coefficient ``` The benchmark lane must not optimize: ```text charge mass device design placement depth standoff distance target damage ship / hull response casualty or infrastructure effects ``` Those fields are explicitly outside the modeling target. ## Equations For The Benchmark Lane The first useful abstraction is a normalized waveform model: ```text p_obs(t, r) = A_s(r) * exp(-(t - t_a) / tau_s) * H(t - t_a) + sum_k A_k(r) * B_k(t - t_b,k) + epsilon(t) ``` Where: - `t_a = r / c_w` is acoustic arrival time in water. - `A_s(r)` is a fitted initial shock-front amplitude proxy. - `tau_s` is a fitted decay constant. - `B_k` are bubble-pulse basis functions. - `epsilon(t)` is residual sensor / environment error. Attenuation can be tracked as: ```text A_s(r) = A_0 * G(r) * exp(-alpha_water * r) ``` Where `G(r)` is a declared geometry-spreading term, not a weapon calibration. The bubble-motion receipt can use the Rayleigh-Plesset shape as a qualitative dynamics gate: ```text rho * (R * R_ddot + 3/2 * R_dot^2) = p_b(t) - p_infty(t) - 2*sigma/R - 4*mu*R_dot/R ``` For stack use, this equation says: ```text bubble pulse timing is a medium-response eigenmode, not a second independent source event ``` Surface reflection can be modeled as a receipt gate: ```text p_reflected = Gamma_boundary * p_incident ``` For a pressure-release surface, `Gamma_boundary` is expected to be negative in the simplified acoustic model. The exact value remains a fitted receipt field. ## Eigenvalue Connection This public benchmark should sharpen the physical-shock eigen gap found in: ```text 6-Documentation/docs/shockwave_eigenvalue_comparison_2026-05-09.md ``` Current repo state: ```text shock alignment / relaxation exists as a local stack mode classical hydrodynamic shock equations exist but have zero-strength support ``` The underwater benchmark can add a measured public-data bridge: ```text Rankine-Hugoniot conservation + water acoustic attenuation + bubble-pulse eigenmode + boundary reflection + residual receipt ``` ## Gate Minimum gate: ```text if source class is not public / archival: HOLD_SOURCE_PROVENANCE elif requested variable is operational weapon design: QUARANTINE_OPERATIONAL_OPTIMIZATION elif waveform lacks arrival/pulse/residual receipt: HOLD_SIGNAL_RECEIPT elif fitted residual <= declared bound: ADMIT_PUBLIC_SHOCK_BENCHMARK else: HOLD_RESIDUAL_TOO_LARGE ``` ## Stack Interpretation This is the clean bridge: ```text stellar shock breakout: radiation escape through optical depth underwater public shock: acoustic escape through dense medium + bubble pulse rain/statolith shock: local displacement threshold in biological medium ``` All three share the same receipt grammar: ```text impulse -> medium transfer -> boundary condition -> local witness -> residual ``` That gives the stack a free, public, non-operational benchmark for the physical shock eigen lane. ## Next Work 1. Add a `PublicUnderwaterShockBenchmark` receipt surface. 2. Add an economic feasibility field that records why public data is the primary lane before any lab/chamber validation. 3. Use only normalized waveform fixtures at first: arrival, relative pulse intervals, attenuation fit, and residual. 4. Add negative controls for missing source provenance, operational-variable requests, missing residuals, and overfit waveforms. 5. Re-run the physics eigen remapper after the benchmark exists and check whether Detonics & Shock Physics gains a nonzero support lane.