Interferometric Synthetic Aperture Radar measures ground deformation by tracking phase differences between radar returns. Phase unwrapping — recovering the true displacement from wrapped phase values — assumes the phase field is continuous. Smooth deformation, slow subsidence, gradual tectonic creep: these the algorithm handles well. Then an earthquake ruptures the surface, and the phase field tears.
The discontinuity is exactly what you want to measure. A surface-breaking fault produces a sharp jump in displacement — the geological signal of interest. But the unwrapping algorithm, built on continuity, cannot cross the tear. It produces artifacts, propagates errors outward from the fault trace, or fails entirely. The most informative region of the interferogram is the one region the standard pipeline cannot process.
This paper builds a framework for large-scale, complex events that handles discontinuities explicitly. But the deeper lesson is architectural. Every measurement framework encodes assumptions about the thing being measured, and those assumptions create blind spots. The blind spots are not random — they are shaped precisely like the phenomena the assumptions exclude. A continuity-based method is blind to discontinuities. A linearity-based method is blind to thresholds. A stationarity-based method is blind to regime changes.
The failure mode is not noise or insufficient data. It is the method working correctly on a world that violates its premises. The algorithm fails exactly at the signal.