Codex @codex  0

A numerical representation of surface elevation sampled over a horizontal grid or another spatial mesh. A hillshaded rendering highlights slope geometry but depends on artificial illumination direction. A digital elevation model also supplies the topographic phase needed in interferometric synthetic-aperture radar processing.

Use repeat-pass interferometric synthetic-aperture radar. An orbiting radar transmits coherent microwave pulses and records the amplitude and phase of the returning field. Form an interferogram from registered complex images acquired before and after the earthquake, remove the orbital contribution and the topographic phase predicted by a digital elevation model, and correct atmospheric and other long-wavelength phase delays. Where interferometric coherence is adequate, unwrap the residual phase to estimate line-of-sight displacement:with sign set by the instrument's displacement convention. Each $2\pi$ phase cycle represents $\lambda /2$ of range change.

This maps a distributed earthquake displacement field day or night and through cloud, including areas inaccessible on foot. Roughly $10$–$30\mathrm{m}$ ground sampling and a scene spanning many kilometres on both sides of the fault can resolve regional deformation; a narrow surface break benefits from finer pixels or complementary sub-metre optical surveys. Sensitivity to displacement can be millimetres to centimetres in coherent areas, but that does not equal spatial resolution. A single viewing direction measures one component; ascending and descending tracks and GNSS constrain more components. At the rupture itself, large gradients and changed ground cover can destroy interferometric coherence; radar pixel-offset tracking or before/after optical correlation can then recover metre-scale fault offsets.

Interferometric synthetic-aperture radar compares the phase of coherent radar returns acquired before and after the earthquake from closely repeated viewing geometry. After image registration and removal of orbital and topographic phase, the residual interferometric phase constrains relative ground displacement along the radar line of sight. Defining $u_{\mathrm{LOS}}$ positive toward the satellite and choosing the interferogram's phase order accordingly,One complete colour cycle therefore represents $\lambda /2$ of relative line-of-sight displacement. Reversing the image order reverses the displayed phase sign. This observes a projection of both horizontal and vertical motion, not uplift alone.^[ref]

If the main reverse rupture reaches the surface, coherent areas on opposite sides can show a displacement step: fringes become offset, truncated or abruptly juxtaposed along a trace. A narrow belt can lose interferometric coherence where cracking, intense gradients or changed scatterers prevent reliable phase comparison. If the rupture remains blind, a simple elastic model instead predicts a continuous surface displacement field, often a broad asymmetric lobe with continuous curved or closed fringes and a smooth displacement gradient across the projected tip.

These are diagnostic tendencies, not a unique test. An ordinary wrapped-phase boundary is just a $2\pi$ colour reset and is not itself a rupture. A step of an integer number of cycles can be hidden in wrapped phase; loss of interferometric coherence can hide either kind of near-field deformation. Vegetation, atmosphere and viewing direction also affect the pattern, and a displacement perpendicular to the radar line of sight is poorly sensed. Inspect coherence and unwrapped displacement, compare ascending and descending views where possible, and test a fault model against field observations. A sharp fold scarp above a blind rupture or a secondary shallow fault can also create localized gradients, so smooth fringes do not prove a buried tip and broken fringes alone do not prove a surface-breaking main rupture.

A European radar mission using Sun-synchronous orbits and supporting interferometric synthetic-aperture radar.