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.