| a(z) | arbitrary function |
| A 0 | fiber elongation corresponding to 1 rad of phase shift |
| A(z, t) | output of DAS |
| A1(z) | output of DAS with first order algorithm |
| A2(z) | output of DAS with second order algorithm |
| b(z) | arbitrary function |
| c | optical speed of light in fiber |
| C | speed of sound |
| D | DAS dynamic range |
| e(t′) | optical field of coherent input pulse |
| E(t′) | optical field on photodetector |
| ℑ(K, F) | Fourier transforms of seismic signal |
| ℑ | Fourier transform symbol |
| F | frequency of sound |
| F MAX | maximum frequency of sound |
| F S | pulse repetition rate or sampling frequency |
| G(z) | geophone antenna response |
| hυ | energy quant |
| Im Z | imaginary part of interference output |
| Ij (z, t) | intensity trace for different interferometric output |
| I(z, t) | photodetector intensity trace |
| j | integer number |
| K | acoustic angular wavenumber |
| K z | acoustic angular wavenumber along fiber |
| K e | ratio of optical to physical length of fiber |
| L | fiber length |
| L P | integration length |
| L 0 | interferometer length also known as gauge length |
| L S | scattering zones spacing |
| M | number of scattering zones |
| n eff | fiber effective refractive index |
| N F | noise figure of amplifier |
| N | number of photons per second |
| p(z) | averaging function |
| P 0 | input peak power |
| P | number of different interferometric ports or pulses |
| R BS | backscattering coefficient of fiber |
| r0(z) | distribution of reflection/scattering coefficient along fiber axis |
| r(z) | distribution of reflection/scattering coefficient along fiber axis with optical phase shift included |
| Re Z | real part of interference output |
| t′ | “fast” optical time scale |
| t | “slow” acoustic time scale |
| u(z, t) | ground displacement |
| u | parameter of function |
| v(z) | fiber local speed along its axis and also ground speed |
| V(z) | interference visibility along fiber |
| x | parameter of integration: coordinate along fiber axis |
| z | coordinate along fiber axis |
| z 1 | parameter of function |
| z 2 | parameter of function |
| β | optical wave propagation constant of fiber |
| β 0 | unperturbed optical wave propagation constant of fiber |
| ΔΩ(z) | distance variation of Doppler shift along fiber |
| Δv | distance variation of ground speed |
| ΔF | geophone bandwidth |
| δ | the Dirac delta function |
| ε 1 | maximum recoverable strain for first order algorithm |
| ε 2 | maximum recoverable strain for second order algorithm |
| ε min | minimum strain level |
| Φmin | phase noise |
| Γ | incident angle of seismic wave |
| λ | laser wavelength |
| Λ | spacing of geophones |
| μ | flicker noise coefficient |
| ω | circular frequency of light |
| Ω(z) | Doppler frequency shift of light |
| ψ 0 | phase shift between delayed optical fields in interferometer |
| Φ | shift of backscattered light |
| ρ | backscattering intensity coefficient |
| θ(z) | Heaviside step function |
| τ(z) | input pulse |
| τ | optical pulsewidth |
