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Earth and Space Sciences · 术语表

什么是 Checkerboard test？

Definition 1.17 University Earth and Space Sciences — Year 3 · 第 1 章 — Seismology and Earth Imaging

A checkerboard test is a resolution test in which the synthetic model is a regular pattern of alternately fast and slow cells: synthetic residuals computed through the real ray geometry, with noise of the size of the real errors, are inverted with the same parametrisation and damping. Where the pattern is recovered, structures of that size can be resolved; where it is smeared or lost, they cannot.

A checkerboard test (invented geometry). (a) The synthetic model: blocks 100\, km across, 3\,\% fast (blue) or slow (red). (b) The 20 sources (stars), the 32 stations (triangles) and some of the rays, all within 45 of the vertical. (c) With light damping the blocks are found, but noisy, with anomalies up to about 8\,\% where few rays cross (colours saturate at 4\,\%). (d) With heavy damping the pattern is clean, but its amplitude is reduced, most of all along the side edges, where few rays cross and all at similar angles.
A checkerboard test (invented geometry). (a) The synthetic model: blocks 100 km100\,\mathrm{km} across, 3 %3\,\% fast (blue) or slow (red). (b) The 20 sources (stars), the 32 stations (triangles) and some of the rays, all within 45∘45{}^{\circ} of the vertical. (c) With light damping the blocks are found, but noisy, with anomalies up to about 8 %8\,\% where few rays cross (colours saturate at 4 %4\,\%). (d) With heavy damping the pattern is clean, but its amplitude is reduced, most of all along the side edges, where few rays cross and all at similar angles.
The trade-off curve of the checkerboard test, for damping values from 0.1 to 1000\, km (the kernel is in kilometres, with equal errors). Along the flat part, more damping costs almost no fit: the model shrinks by losing noise. The knee lies where the misfit rises through the level expected from the noise alone, √480 = 1.095\, s; the two damped models of the previous figure lie on either side of it, and the norm of the true checkerboard, 33.9\,\%, between them. Beyond the knee the damping removes structure the data require.
The trade-off curve of the checkerboard test, for damping values ε\varepsilon from 0.1 to 1000 km1000\,\mathrm{km} (the kernel is in kilometres, with equal errors). Along the flat part, more damping costs almost no fit: the model shrinks by losing noise. The knee lies where the misfit rises through the level expected from the noise alone, σ480=1.095 s\sigma\sqrt{480} = 1.095\,\mathrm{s}; the two damped models of the previous figure lie on either side of it, and the norm of the true checkerboard, 33.9 %33.9\,\%, between them. Beyond the knee the damping removes structure the data require.
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