Читать книгу Distributed Acoustic Sensing in Geophysics - Группа авторов - Страница 22

A DAS interrogator measures, in accordance with Equation 1.13, the speed difference between two sections of fiber that are separated by interferometer length L₀ (referred to also as the gauge length), as presented in Figure 1.10. In pulse‐to‐pulse consideration, the DAS response is linearly proportional to the fiber elongation averaged over the gauge length in the nanometer scale, or strain rate in the nanostrain per second scale. The consideration can also be extended to multiple pulses by time integration of the DAS signal. So, if fiber rests initially and ground displacement equals to zero u(z, t₁) = 0, then:

(1.22)

meaning a time integrated DAS signal can be considered as an output of a huge caliper that is measuring fiber elongation between two points with sub‐nanometer precision. This measuring principle is different from that of a geophone but is similar to an electromagnetic linear strain seismograph that can measure changes in distance between two points on the ground (Benioff, 1935).

Figure 1.10 Illustration of two time‐consecutive measurements when DAS output is proportional to fiber elongation between two probe pulses.