Deformation basics — phase · LOS · fringes
InSAR measures cm-to-mm-level ground range changes from the phase difference between two SAR images of the same place, its core formula being Δφ=(4π/λ)·ΔR. For Sentinel-1 (λ=5.6cm C-band) a single fringe equals about 2.8cm (=λ/2) of line-of-sight (LOS) displacement. Because SAR can only measure displacement along the satellite line-of-sight, separating east-west and vertical motion requires combining ascending and descending orbits. In the production pipeline the interferogram produces a phase difference wrapped to −π~π, SNAPHU unwraps it, and it is then converted into ΔR to yield the LOS displacement.
Capturing range change through phase
- SAR's real weapon is not brightness but the wave phase; shooting the same place twice, it compares the round-trip range difference at the nano-to-centimeter level.
- The core formula is Δφ=(4π/λ)·ΔR, where λ is the wavelength (Sentinel-1 C-band=5.6cm), ΔR is the satellite-to-ground range change, and Δφ is the phase change wrapped into the −π~π range.
- Because the wavelength is around 5.6cm, even a few-cm shift changes the phase greatly — when the satellite-to-mountain range changes by 2.8cm, SAR detects it through phase.
- Since it observes with active waves even in night, cloud, or typhoon conditions that block optical cameras, it is the standard tool for immediate disaster response.
- phase change (wrapped to −π~π)
- wavelength — Sentinel-1 C-band = 5.6cm
- satellite-to-ground range change
Reading fringes
- InSAR results show repeating red-blue-green-yellow stripes, i.e. fringes, where each single stripe denotes a fixed amount of LOS displacement.
- On Sentinel-1 (λ=5.6cm) 1 fringe equals about 2.8cm (=λ/2), 10 fringes about 28cm, and tens to hundreds indicate earthquake-scale fault motion.
- More fringes mean larger displacement, and narrower stripe spacing means deformation with a steeper gradient.
| Fringe count | LOS displacement | |
|---|---|---|
| One fringe | 1 fringe | ~2.8cm (= λ/2) |
| Ten fringes | 10 fringes | ~28cm |
| Earthquake-scale | Tens to hundreds | Fault-motion scale |
The LOS constraint — combining ASC + DESC
- SAR measures only motion along the satellite line-of-sight (LOS), so purely horizontal motion is barely visible.
- So one obtains the LOS from two orbits: Ascending, which looks obliquely from the northeast, and Descending, which looks obliquely from the northwest.
- Geometrically decomposing the two LOS lets one split the motion into east-west and vertical components, so in practice both ASC and DESC are processed.
The pipeline — from phase difference to displacement
- Coregistration aligns the pixels of the two SLCs, then the interferogram produces a phase difference wrapped to −π~π.
- Coherence is a QA metric indicating result reliability, and SNAPHU unwraps the wrapped phase into a continuous unwrapped phase.
- Finally the Phase → Displacement step converts Δφ into ΔR to produce the LOS displacement result.
The LOS constraint is an absolute practical trap — a strike-slip earthquake with only horizontal motion is nearly invisible from ASC alone, so combining ASC+DESC is essential. Also, more fringes are not always real displacement — atmospheric effects (APS) or unwrap errors can masquerade as fringes, so results must always be read paired with QA metrics, especially coherence.