Independent identifiability of the weak-shock transition coefficient

Determine whether the weak-shock transition coefficient can be constrained independently of the cylindrical blast-wave source normalization in period-based infrasound analyses of hypersonic atmospheric entries.

Background

The paper compares period-based infrasound predictions under different weak-shock transition criteria and finds that the observed periods are only weakly sensitive to this coefficient over the sampled propagation ranges. However, the authors distinguish this weak sensitivity from demonstrating that the coefficient itself can be estimated independently of the source normalization. The resulting parameter-identifiability issue is explicitly left unresolved.

References

It does not establish whether can be constrained independently of the source normalization, which remains a separate parameter-identifiability question.

— Period-Inverted Blast-Radius Normalization for a Non-Ablating Hypersonic Reentry Source Using OSIRIS-REx Capsule Infrasound  (2609.19141 - Silber, 16 Sep 2026) in Section 1, Introduction

The 39 observation points establish a strong monotonic trend (Spearman = −0.84, < 0.001), but the physical cause of this structure cannot be uniquely identified from this dataset alone. Along the single OSIRIS-REx entry trajectory, altitude, velocity, Mach number, ambient density, pressure, and deceleration co-vary systematically. As a result, the observations cannot determine whether the trend is primarily controlled by Mach number, atmospheric density, source altitude, changing aerodynamic coupling, emission-point assignment, or some combination of these factors.

— Period-Inverted Blast-Radius Normalization for a Non-Ablating Hypersonic Reentry Source Using OSIRIS-REx Capsule Infrasound  (2609.19141 - Silber, 16 Sep 2026) in Section 4.2, Interpretation of Altitude and Mach Structure in and

Future work should extend these calibrations to additional controlled reentries, space-debris events, and well-observed bolides to determine which aspects of,, and are source-class specific and which reflect more general cylindrical blast-wave behavior.

— Period-Inverted Blast-Radius Normalization for a Non-Ablating Hypersonic Reentry Source Using OSIRIS-REx Capsule Infrasound  (2609.19141 - Silber, 16 Sep 2026) in Section 5, Conclusions