Geometric Filtering in Curved Fibre-Optic Sensing—I. Planar-Arc Response and a Deployment Decision Map

Distributed Acoustic Sensing (DAS) and integrated fibre-optic sensing (IFOS) measure an optical phase change that integrates axial strain along a fibre, whose path often bends and loops. We show how planar bending controls the angular and spectral sensitivity of this measurement, an effect we call geometric filtering. Separating the integrated strain into endpoint and curvature terms, we derive the exact plane-wave response of a circular-arc fibre as a Bessel series valid at any wavelength and opening angle. At long wavelengths the response of any fibre path follows from a geometrical tensor, the gauge average of the tangent dyad. It depends on the shape of the path but not on its size. Bending fills the broadside blind spot of a straight fibre to P waves and weakens its sensitivity to SH waves. For smooth, symmetric single-apex bends, the height-to-chord ratio sets the P-wave pattern: dipole-like below about 0.13 and nearly omnidirectional above about 0.46. A closed loop acts as an areal dilatometer: it senses P waves equally from every azimuth and is blind to SH waves at all wavelengths. At finite wavelengths the opening angle filters the Bessel orders. This limits the number of terms required and turns the gauge-length notches of a straight fibre into the Bessel rings of a closed loop. For a point source, the plane-wave response requires the source to be many wavelengths away, far compared with the fibre footprint, and beyond the footprint squared over the wavelength. The last condition defines a Fibre Fresnel Number. We condense these criteria into a Decision Map that selects the response model from fibre geometry, signal frequency, and source distance, and apply it to eight DAS and IFOS deployments. Fibre geometry is thus a design variable for geometric filtering: it can make a fibre segment selectively sensitive to certain azimuths and wavelengths. Preliminary version (v1). Part I of two companion papers; Part II treats helically wound cables. To be submitted to Geophysical Journal International.