Exact Amplitude--Delay Information Crossover for an Idealized Helical DAS Array

Abstract

Helical distributed acoustic sensing (DAS) geometries couple directional strain amplitude and propagation phase, yet their respective contributions to bearing information and their compatibility with practical extraction chains are usually left implicit. For an idealized point-channel helix with unknown complex source amplitude, we prove an exact finite-array frequency at which amplitude and delay information are equal and derive a continuous full-turn corollary exposing radius, pitch, winding-angle, and elevation dependence. The finite expression matches a separately constructed information ratio on 723 prespecified geometries to a maximum relative error of 4.24 x 10^(-15). Because an array-domain bound is comparable to a processing-chain estimate only under compatible observation constructions, we also audit a prespecified Hann--DFT--MUSIC chain. Its long, bin-aligned records match the array-domain pseudo-true bearing, whereas short zero-padded controls do not. A 118,500-estimate study then validates local sandwich variance and its combination with squared pseudo-true bias over prespecified mismatch conditions. These are model-level information and compatibility results, not field-performance bounds for gauge-averaged cables.