Bearing Information and Geometric Bias in Finite-Gauge Helical DAS Arrays With Calibration Uncertainty

Abstract

Finite gauge averaging can preserve signal energy while removing directional information. We analyze this loss and geometric bias in helical distributed acoustic sensing arrays under a longitudinal-plane-wave model. A phase-preserving angular filter distinguishes complete response cancellation from nonzero single-mode responses for which an unknown complex source amplitude absorbs the dependence on bearing. Near an integer-turn information null, an endpoint formula gives the coefficient of quadratic information recovery for a finite array. Analytic remainder bounds and a radius-uncertainty exclusion band provide local criteria for gauge selection. Finite sampling can suppress the recovery entirely. Decomposing the radius derivative separates rotation accumulated through registration from other shape changes. In a 60-channel synthetic example, a 2\% radius increase produces $13.287^\circ$ pseudo-true bias at fixed arc coordinates but $0.00559^\circ$ at fixed material winding coordinates. A continuous-domain comparison confirms that the nominal frequency--gauge choice maximizes worst-case conditional information over the tested bearing range and $\pm2\%$ radius interval. In an off-grid, full-circle estimation study, the task selected by signal energy has 3.05 times the mean squared error of the nominal choice. Nominal and interval-aware rules select the same action and have identical errors. Finite calibration changes the predicted risk but leaves this choice unchanged over the tested budgets.