2-D Phase Unwrapping in DAS Based on Transport-of-Intensity-Equation: Principle, Algorithm and Field Test

Seismic exploration demands high temporal-spatial resolution and cost-effective deployment. Distributed acoustic sensing (DAS), an emerging seismic exploring technology utilizing optic-fiber cables, supports intensified and real-time observation of geological activities. Phase unwrapping, a critical step in deriving disturbance from DAS raw data, traditionally relies on phase continuity, assuming the original phase difference between adjacent measurements is less than \pi. This dependency leads to suboptimal performance in cases of insufficient sampling rates, abrupt strain changes, or excessive noise, resulting in stripe-like errors in the output. This paper proposes a novel approach to address phase unwrapping issues in DAS with a two-dimensional (2-D) perspective by treating accumulated results from multiple DAS traces collectively. The principle of the 2-D algorithm based on the Transport of Intensity Equation (TIE) is introduced comprehensively. An iterative strategy is used to enhance the performance of the TIE-based method. In field tests, the application of 2-D method successfully eliminates stripe-like errors in the output. Besides, taking the measurements from geophone as reference, the ground motion from DAS processed by two unwrapping methods are compared thoroughly, showing advantages of the 2-D method over the conventional one. Additionally, source localization based on the Time Difference of Arrival method is carried for positioning human stepping signals, demonstrating an error of 11.7 cm. 2-D phase unwrapping algorithms apply to all phase-demodulation-based sensing techniques and are suitable for recovering spatially correlated objects such as seismic waves, thus having great potential in the field of seismic monitoring.