Strain field reconstruction from helical-winding fiber distributed acoustic sensing and its application in anisotropic elastic reverse time migration

Optical fiber-based distributed acoustic sensing (DAS) technology has been a popular seismic acquisition tool due to its easy deployment, wide bandwidth, and dense sampling. However, the sensitivity of straight optical fiber to only single-axis strain presents challenges in fully characterizing multi-components seismic wavefields, making it difficult to use these data in elastic reverse time migration (ERTM). The helical-winding fiber receives projecting signals projected onto the fiber from all seismic strain field components and has the potential to reconstruct those strain components for ERTM imaging. Here we give detailed mathematical principles of helical fiber-based DAS with crucial parameters such as pitch angle, gauge length and rotating angle. At least six points of DAS responses are required in one or several winding periods to rebuild the strain fields within the seismic wavelength. The projecting matrix of conventional regular helical-winding fiber is singular and ill-conditioned, which results in computation challenges for the inverse of the Hessian matrix for strain component reconstruction. To tackle this problem, we develop a non-regular variant-pitch angle winding configuration for helical fiber. Our winding design is validated using the rank and condition number of the projecting matrix, which is proven as an important tool in the reconstruction of the original seismic strains. The recovered strain components from the DAS response are then used to backward propagate receiver wavefields in ERTM with an efficient P/S decoupled approach. To sum up, we develop a novel winding design of helical fiber to recover the strain fields, and then propose an efficient 3D anisotropic P/S wave-mode decomposition method for generating vector P- and S-wavefields during their propagation. Both methods are applied to build an anisotropic DAS-ERTM workflow for producing PP- and PS- images. Two synthetic examples demonstrate the effectiveness of our approach.