Methodology: 10-Phase Forensic Acoustic Pipeline

Case FA-2026-001 | Systematic framework for muzzle blast source localization

Each phase feeds the next. No phase can be skipped or reordered. The pipeline is designed so that errors in any phase propagate forward as quantifiable uncertainties rather than undetected biases.

EVIDENCE INTAKE

▸SHA-256 hash verification of all original files

▸Chain of custody documentation

▸Working copy extraction — originals are never modified

▸File format and metadata inspection

RECORDING CHARACTERIZATION

▸Sample rate identification (48kHz for R1, 44.1kHz for R2–R4)

▸AGC (Automatic Gain Control) detection — R1 has no AGC (amplitude-reliable); R2–R4 have active AGC (only arrival times usable)

▸Peak and RMS level measurement, spectral profile analysis

▸Reflection cataloging — 1st, 2nd, 3rd reflections identified and timed

▸Rise time measurement for propagation quality assessment

ENVIRONMENTAL PARAMETERS

Local weather data determines the speed of sound, the single most important physical constant in the analysis.

85°F

Temperature

37%

Humidity

1404m

Elevation

855.6 hPa

Pressure

Speed of sound: 349.7 m/s via Cramer 1993 humidity correction.

Sensitivity: ±2°F → ±0.7 m/s → ±0.58ms at 100m propagation distance.

ACOUSTIC EVENT CLASSIFICATION CRITICAL PHASE

A supersonic gunshot produces two distinct acoustic events that must be separated:

SUPERSONIC CRACK

High-frequency (4–8kHz), conical wavefront (line source). Arrives FIRST. Cannot be used for TDOA — produces location smear along bullet trajectory.

MUZZLE BLAST

Low-frequency (<500Hz), spherical wavefront (point source). Arrives SECOND. The only valid TDOA source — produces a single intersection point.

The crack precedes the blast at all 4 receivers, confirming a supersonic projectile. Broadband onset picks are contaminated by the crack, which arrives 10–24ms before the blast.

RECEIVER GEOLOCATION

▸KML placement against satellite imagery, ±0.5m accuracy

▸Local coordinate system: Origin = stage center (40.27758°N, 111.71395°W), X = East, Y = North

▸Key geometry: R2 and R3 are only 1.6m apart; R1 is the only receiver north of stage

▸Array spread: 18.6m E-W × 24.1m N-S

TOA MEASUREMENT

▸LP 500Hz zero-phase Butterworth filter applied to isolate blast core

▸Zero-phase critical: standard IIR filters introduce group delay that shifts apparent onset time

▸Threshold-based onset picking with confidence assessment per receiver

▸R2 & R3: High confidence | R1 & R4: Moderate confidence

SYNCHRONIZATION

▸Manual alignment in Ableton Live on PA vocal content ("GREAT" spoken just before gunshot)

▸GCC-PHAT cross-correlation verification across 9 overlapping windows (200–4000Hz speech band)

▸Sub-sample parabolic interpolation: R1, R2, R3 locked at <0.01 samples; R4 at ±1 sample

▸Accuracy: ±1 sample at 48kHz = ±0.021ms

▸Closure test: PASSED — max error 0.03 samples (0.6μs) across all triplets

▸Drift check: None detected (early vs late speech ±0.005ms)

TDOA MULTILATERATION

▸Grid search for initial position estimate

▸Levenberg-Marquardt least squares refinement

▸PA propagation correction applied as systematic uncertainty bound

▸Reference receiver: R2 | RMSE: 0.005ms for best-fit model

UNCERTAINTY ANALYSIS

▸Monte Carlo simulation: 10,000 iterations with perturbed positions (±0.5m), TOAs (±1.0ms), and speed of sound (±0.7 m/s)

▸Jackknife leave-one-out: test solution stability when each receiver is removed

▸PA model sensitivity: 5 independent PA correction models compared

▸Result: 95% confidence ellipse of 2.4 × 1.0m

REPORTING

▸This website — all data, methods, and parameters published for peer review

▸Reproducible: all inputs fully specified; any forensic acoustician can verify

▸KMZ files available for independent analysis (FA-2026-001_complete.kmz)