On the mechanical coupling of a fiber optic cable used for distributed acoustic/vibration sensing applications—a theoretical consideration

In recent years, fiber optic cables are increasingly used for the acquisition of dynamic strain changes for seismic surveys. When considering seismic amplitudes, one of the first questions arising is the mechanical coupling between optical fiber and the surrounding medium. Here we analyse the interaction of ground movement with a typical telecom-grade fiber optic cable from an existing telecommunication network deployed in a sand filled trench at the surface. Within the cable, the optical fiber is embedded in a gel-filled plastic tube. We apply Hooke's law to calculate the stress needed to strain the optical fiber throughout the cable structure. In case the stress magnitude at the cable–sand interface as well as the gel–optical fiber interface is below the yield strength of the respective material, sand and gel, it can be regarded as an elastic medium. Hence, a multilayer radial symmetric model can be used to calculate the coupling of the optical fiber with the surrounding medium. We show that the transfer function has a $-3$ dB lower cut-off wavelength of about 22 m. The magnitude response of this telecom-grade fiber optic cable is therefore almost perfect at typical low frequency seismic waves. The approach presented here can be applied to various cable designs to estimate the strain transfer between ground movement and an optical fiber. (technical note)