Use of Symmetry in Calibration of Looped Duplex DTS Measurements

A looped duplex Distributed Temperature Sensing (DTS) deployment uses a bifilar arrangement of two optical fibres in the same cable or conduit. On one end of the cable the ends of the fibres are spliced together. The other ends are connected to a (double ended) DTS system or one end is connected to a (single ended) DTS system. A light pulse shot from one end will eventually emerge from the other end and vice versa. Back scattered Raman-shifted photons will thus be detected twice for each posistion along the cable or conduit but delayed in time by twice the distance from the symmetry point (turn around sub) divided by the speed of light in the fibre.

Calibration of a DTS system requires, first and foremost that differential loss; i.e. the difference in optical attenuation between Stokes and anti-Stokes backscattered signals, is compensated for. It will be shown that residual errors due to uncompensated differential loss can only be due to the uneven part of the (non-uniform) differential loss distribution. A 
bifilar deployment is therefore highly insensitive to uncompensated differential loss because ageing, chemical or mechanical damage to the cable as well as thermal or mechanical strain may vary over the length of the cable but remain symmetrical and therefore even with respect to the turn around sub.

By writing the (non-)uniform differential loss as the sum of an even and an uneven part it is possible to derive an equation for the residual error of a DTS temperature measurement expressed as an integral over the uneven part of the differential loss distribution only. Thus it is possible to estimate any residual temperature error under field conditions. Such a capability is especially useful where no access to one end of the cable is possible, such as is the case in borehole applications.