Introduction to phase transmission fibre-optic sensing of seismic waves

TL;DR

This paper develops a theoretical framework linking phase changes in fibre-optic signals to seismic-induced deformations, enabling distributed seismic sensing through optical fibres with considerations of fibre curvature and refractive index variations.

Contribution

It derives an exact non-linear relation between phase changes and deformation tensor, and simplifies it for seismic applications, connecting phase shifts to in-line strain and refractive index variations.

Findings

Phase changes relate to deformation tensor and refractive index.

Straight fibres produce zero phase change unless deformations are widespread.

Curved fibre segments contribute more to phase change measurements.

Abstract

This manuscript is concerned with phase changes of signals transmitted through deforming optical fibres. As a first result, it establishes an exact relation between observable phase changes and the deformation tensor along the fibre. This relation is non-linear, and it includes effects related to both local changes in fibre length and deformation-induced changes of the local speed of light or refractive index. In seismic applications, where the norm of the earthquake-induced deformation tensor is orders of magnitude smaller than 1, a useful first-order relation can be derived. It simply connects phase changes to an integral over in-line strain along the fibre times the local refractive index. Under the assumption that spatial variations of the refractive index are fast compared to the seismic wavelength, this permits a direct synthesis of phase change measurements from distributed strain measurements, for instance, from Distributed Acoustic Sensing (DAS). A more detailed analysis of the first-order relation reveals that a perfectly straight fibre would produce zero phase change measurements, unless deformation was sufficiently widespread to affect the starting and end points of the fibre. If this condition is not met, non-zero measurements can only result from curvature of the fibre or from a heterogeneous distribution of the refractive index. Segments of the fibre that are strongly curved generally make larger contributions to the observed phase change.