Your InSAR velocity is not subsidence — and here is when that actually matters

22 October 2026 · about 9 min read

By the senior geotechnical engineer · insarwatch

A deformation map lands on your desk. Every point carries a velocity, the colour ramp runs from blue to red, and the caption says subsidence rate (mm/yr). It is the single most common labelling mistake in the whole InSAR-to-engineering pipeline, and it survives because the numbers look plausible: a point showing −12 mm/yr near a pump station probably is going down, and −12 feels like the right kind of number to write next to it. But the satellite never measured −12 mm/yr of subsidence. It measured −12 mm/yr along one particular viewing direction, and the gap between those two statements ranges from a twenty-percent bookkeeping footnote to a factor-of-two interpretation error, depending on where the point is and what is moving it. This article walks through the three layers of that gap — geometry, sign convention, and track geometry — and then draws the line that matters in practice: when you can safely ignore the correction, and when you cannot.

Layer one: the satellite measures along a tilted line

SAR antennas look sideways, not straight down. For Sentinel-1 the incidence angle — the tilt of the viewing direction away from vertical — runs roughly 30° near the centre of the image swath to about 46° at its edge. The satellite reports the projection of the true displacement vector onto that tilted line of sight, and a projection is always shorter than the vector it comes from. A purely vertical displacement of 10 mm shows up in the LOS as 10·cos θ: about 8.7 mm at 30°, about 6.9 mm at 46°. Inverting the relationship — dividing the LOS velocity by cos θ — recovers the vertical component, and that is the entire mathematics of the LOS to vertical converter. The catch is that dividing by cos θ is only correct if the motion really was vertical. Where it was not, the division produces a number that is not the vertical component of anything; it is an artifact with units of mm/yr.

The systematic understatement is easy to state and easy to underestimate in day-to-day work. At a 35° incidence angle — a typical mid-swath value — the LOS velocity is only 82% of the vertical rate. A settlement bowl whose true maximum is −15 mm/yr presents as −12.3. If your screening threshold sits at −10, the uncorrected map says "above threshold" either way; if it sits at −15, the uncorrected map quietly keeps the point below the line. The error is proportional and one-sided, which means averaging over many points does not remove it — every point is biased the same direction. That is the fundamental difference between this error and the random noise terms in an error budget: noise can be averaged, bias cannot.

Layer two: the sign convention trap

Before any geometry can be corrected, the sign has to be understood, and there is no industry-wide standard. Some processors export LOS displacement as negative-toward-the-satellite (a descending surface is negative); others follow the radar convention of positive range change, which makes subsidence positive. Some exporters reverse the sign at export; a few analysts reverse it again in a spreadsheet "to make it intuitive". The result in real project folders is a mix where adjacent columns from the same processing batch disagree.

The failure mode is worse than a wrong number — it is a plausible wrong number. Flip the sign of a settlement bowl and you get an uplift dome of the same magnitude; both look like legitimate geodesy, and nothing in the plot flags the error. The defence is procedural, not technical: check the exporter's documentation once, verify the convention against one point whose behaviour you know from an independent source — a benchmark, a GNSS monument, a structure you have seen — and record the convention in the CSV header or the delivery note. The sample data shipped with this workbench uses negative-is-subsidence, and every tool states its assumption so that a column imported with the opposite convention fails loudly instead of silently.

Layer three: ascending and descending tracks disagree — and that is information

The cos θ correction assumes the motion is vertical. On slopes, embankments and creep-prone hillsides, it often is not: mass moves along its own dip direction, and that movement has a horizontal component the LOS mixes in. A single viewing geometry cannot separate the two — this is not a processing deficiency but a geometric fact, the same fact that makes one photograph insufficient to reconstruct a 3-D scene. Where an ascending and a descending track both cover the area, their lines of sight differ, and the pair can be solved for vertical and east-west components together. Where they disagree sharply over a slope, the disagreement itself is the diagnostic: it means the motion has a horizontal component, and treating the LOS as "subsidence with a correction factor" will under-report the hazard while feeling rigorous.

Engineering consequence: near-scoped classification tools that consume vertical velocity, such as the gradient and hazard classifier, assume the input really is vertical. Feeding them uncorrected or slope-contaminated LOS values does not just scale the answer — it can move points across class boundaries in the wrong direction, because the horizontal contribution can carry either sign. On a project where the deliverable is a hazard zoning map rather than a rate map, the geometry question stops being a bookkeeping preference and becomes part of the safety argument.

When you can safely skip the correction

Not every use demands it, and pretending otherwise breeds carelessness at the moments that matter. The correction is genuinely optional in three situations. First, relative screening: if the question is "which parts of this area move most?", a uniform geometry over a small area applies nearly the same projection everywhere, and the ranking survives uncorrected. Second, order-of-magnitude triage: deciding whether a 40 km² basin is subsiding at 2 or 20 mm/yr does not need the last 18%. Third, internal comparison of same-track data: two points from the same swath can be compared without any geometry correction at all, because their incidence angles differ by at most a few degrees.

The correction stops being optional the moment a number leaves the screening context: any figure destined for a report, any comparison against a threshold or a code limit, any cross-validation against GNSS or levelling, and any pooling of ascending with descending results. A levelling benchmark measures vertical motion; comparing it to an uncorrected LOS velocity creates a residual of twenty-plus percent that no amount of data quality can explain, and the validation exercise fails for a reason that has nothing to do with the data.

A five-minute routine that keeps the issue closed

The full correction, done deliberately, takes minutes per file. The routine this workbench is built around: confirm the sign convention from the exporter's documentation and state it in the file; confirm that each row carries its own incidence angle rather than a scene-average (the difference matters at swath edges, where cos θ varies by several percent across a single scene); convert LOS to vertical with each point's own angle; and carry the conversion into the deliverable's uncertainty statement rather than treating it as exact. The LOS converter performs the per-point conversion and flags rows missing an angle or a convention, and its output drops straight into the error budget, where the incidence-angle term sits alongside atmosphere and decorrelation instead of being forgotten here.

None of this makes InSAR fragile. It makes InSAR legible — a measurement with a stated geometry, a stated sign, and a stated uncertainty is one that survives the review meeting. The velocity map that simply says "subsidence" is the one that gets reopened six months later, by someone holding a levelling run that disagrees by exactly the factor the geometry predicted all along.