Here is the workflow how we can derive the strain / pressure ratio from LF-DAS and gauge data.

Poisson’s ratio estimation

Summary

LFDAS data -> strain
Pressure gauge data -> pressure

Then we can calculate the Poisson’s ratio use these datasets.

Theory

LF-DAS data -> Strain

From Lindsey, 2020 we have:

\[\varepsilon_{xx}=\frac{\lambda}{4\pi nL_G\zeta}\Delta\Phi\]

OR time deriviative:

\[\dot\varepsilon_{xx}=\frac{\lambda}{4\pi n L_G\zeta}\frac{\Delta\Phi}{\Delta t}\]

Where the incident wavelength $\lambda$= 1550 nm, refractive index n = 1.4682, and gauge length $L_G$= 4.08 m, the scalar coefficient $\zeta$ = 0.79 accounts for stress-induced birefringence, which governs the optical phase shift in response to axial strain as measured by the LF-DAS.

This equation can convert degree change (raw data) ($\Delta \Phi$) to strain rate. Then I calculate the value:

1. Our raw data $\Delta \Phi$, frequency $f=1$ Hz, raw unit rad/10430.4
2. The coefficient

\[c=\frac{\lambda}{4\pi nL_G\zeta}=\frac{1550 nm}{4\times 3.14\times4.08m\times0.79}=\frac{1.55\times10^{-6}\ m}{40.483 m}=3.82\times10^{-8}\]

Pressure -> Strain

Use Hooke’s Law we can convert pressure to strain

\[\varepsilon=\frac PE\]

Where $P$ is the pressure measured, $E$ is the Young’s Modulus for the material.

Then we are able to measure the Poisson’s ratio(apparent).

Use Cases

In code 2025-04-14-Poisson-Ratio-Code.

References

Lindsey, Nathaniel J., Horst Rademacher, and Jonathan B. Ajo‐Franklin. 2020. “On the Broadband Instrument Response of Fiber‐Optic DAS Arrays.” Journal of Geophysical Research. Solid Earth 125 (2): e2019JB018145.