{
  "id": "r09_coherence",
  "order": 19,
  "tag": "mechanism",
  "eyebrow": "09 \u00b7 The obstruction",
  "title": "In a dwell, time diversity and coherence are the same axis, and you cannot have both",
  "question": "Could any sub-aperture design measure slow ground motion from one dwell?",
  "finding": "No. Slow time and look angle are the same axis in a dwell product, so looks separated by seconds are separated by degrees, and natural ground decorrelates over a fraction of a degree. Measured on the real acquisition, coherence with the band-centre look falls to half by 0.98 s of separation and to a tenth by 1.76 s, identically on the pyramid and on open desert. Ground motion in the microseism band needs lags of about a second, by which point there is little coherence left to register. The published protocols avoid this by using lags of tens of milliseconds, which keeps them coherent and makes them blind to the motion they invoke.",
  "limitations": "Coherence is measured over one patch of one acquisition at 8 per cent sub-aperture width; a wider sub-aperture averages more and decorrelates differently. Strong stable point scatterers, such as corner reflectors or some built structures, hold coherence far longer than the natural desert measured here, so this curve is the distributed-target case, not a universal limit.",
  "method": "61 sub-apertures of 8 per cent bandwidth swept across the processed Doppler support of a real Khafre and a real desert crop; complex coherence computed against the band-centre look over the interior of each crop; separation converted to slow time through the product Doppler rate and to aspect angle through the carrier wavelength and platform speed.",
  "figures": [
    {
      "file": "/Users/eugene/prj/sar/results/r09_coherence/figs/r09_coherence.png",
      "caption": "<b>The constraint behind everything else.</b> Left: complex coherence between sub-aperture looks of the real Giza acquisition and the band-centre look, against their separation in slow time. Coherence is gone within a few seconds on the pyramid and on open desert alike. The shaded strip is the lag the published reference and offset bands actually use, which is why they stay coherent. Right: the same curve read the other way, as the coherence still available when the lag is long enough to sample a given period of ground motion. The microseism band sits where almost nothing is left."
    }
  ],
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        "label": "Khafre pyramid",
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        "tenth_coherence_s": 1.7623256528598659,
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        "label": "Open plateau",
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