Sensitivity kernels for transmission fibre optics

Fibre-optic sensing based on transmission offer an alternative to scattering-based distributed acoustic sensing (DAS). The ability to interrogate fibres that are thousands of kilometres long opens opportunities for studies of remote regions, including ocean basins. However, by averaging deformation along the fibre, transmission systems produce integrated instead of distributed measurements. They defy traditional interpretations in terms of simple seismic phases, thereby inherently requiring a full-waveform approach. For this, we develop a formalism to calculate sensitivity kernels of transmitted optical phase changes with respect to (Earth) structure using optical phase delay measurements. We demonstrate that transmission-based sensing can effectively provide distributed measurements when optical phase delays are analysed in different time windows. The extent to which a potentially useful sensitivity coverage can be achieved depends on the fibre geometry, and specifically on its local curvature. This work establishes a theoretical foundation for tomographic inversions and experimental design using transmission-based optical sensing.