radians_to_strain

radians_to_strain(
    patch: Patch ,
    gauge_length = None,
    wave_length: float = 1.5500000000000002e-06,
    stress_constant: float = 0.79,
    refractive_index: float = 1.445,
)

Convert data in radians to strain (rate).

This applies the simple formula found in Lindsey, Rademacher, and Ajo-Franklin (2020) to convert data whose units have a radians component to strain.

Parameters

Parameter	Description
gauge_length (\(L_g\))	The gauge length in meters.
wave_length (\(\lambda\))	The laser wavelength in m.
stress_constant (\(\zeta\))	The stress constant.
refractive_index (\(n\))	The refractive index of the cable.

Examples

import dascore as dc
patch = (
    dc.get_example_patch()
    .update_attrs(data_units="rad", gauge_length=10)
    .radians_to_strain()
)
assert patch.attrs.data_type == "strain"

Note

Equation 3 of Lindsey, Rademacher, and Ajo-Franklin (2020): \[ \epsilon_{xx}(t, x_j) = \frac{\lambda}{4 \pi n L_{g} \zeta} \Delta \Phi \]

The output data_type is set from the converted data units; it is “strain_rate” when they are strain per unit time (eg rad/s becomes strain/s) and “strain” otherwise.

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.