Practical Identifiability of the Weak-Shock Transition Criterion from OSIRIS-REx Reentry Infrasound

Ground-based infrasound provides a passive means of detecting and characterizing elevated hypersonic sources, but parameter recovery is limited by covariance between source and propagation effects. Controlled spacecraft reentries are rare, well-constrained hypersonic sources for testing weak-shock models because vehicle geometry and trajectory are known independently. The 24 September, 2023, OSIRIS-REx Sample Return Capsule reentry was recorded by 39 ground-based infrasound stations, with direct arrivals associated by eigenray tracing with emission points at 44–62 km altitude and Mach 8–37. Using the ReVelle weak-shock treatment, this study examines whether the weak-shock transition (WST) coefficient C can be constrained independently of the blast-radius normalization k. Joint analysis shows strong k–C covariance: the apparent optimum in C shifts across the reference range as k varies, while the profiled residual remains weakly dependent on C. For the 23 stations within the weak-shock-continuation limit at the reference normalization k = 0.399, the nominal 95% range of the coefficient covers the full 1–100 domain once the period uncertainties are inflated to the model-data misfit. These ranges are indicative under the adopted error model rather than calibrated confidence intervals. This behavior reflects the low logarithmic period sensitivity, SC ≈ 0.034, such that doubling C produces the same local-period response as a 3.2% change in k. WST sensitivity varies with transition geometry, and geometries favorable for signal reception differ from those most sensitive to C. Period therefore constrains source scale more effectively than the WST coefficient. As an example, an Orion-sized body on the same trajectory would yield periods 3.9 times the capsule values (near the three-quarter power of the diameter ratio) with equally weak dependence on C.