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Earth and Space Sciences · 术语表

什么是 Ray parameter, turning point？

又称： ray parameter · turning point (of a seismic ray)

Definition 1.2 University Earth and Space Sciences — Year 3 · 第 1 章 — Seismology and Earth Imaging

The constant $p = r\sin i/v(r)$ of a ray in a spherically symmetric Earth is its ray parameter, in seconds per radian. At the surface it is $p = R\sin i_0/v_0$ , where $i_0$ is the take-off angle and $v_0$ the speed at the surface. The point where the ray is horizontal ( $i = 90{}^{\circ}$ ) is its turning point (of a seismic ray), at the radius $r_t$ where

\frac{r_t}{v(r_t)} = p .

Below it the ray rises again, symmetric about the radius through the turning point.

A ray in a spherical Earth cut into shells of uniform speed (schematic, not to scale). In each shell the ray is straight; at each boundary it refracts by Snell’s law, away from the radius when the speed increases downwards. The quantity r i/v keeps the same value p along the ray; the ray is horizontal at its turning point, where r/v = p, and rises again symmetrically. — A ray in a spherical Earth cut into shells of uniform speed (schematic, not to scale). In each shell the ray is straight; at each boundary it refracts by Snell’s law, away from the radius when the speed increases downwards. The quantity $r\sin i/v$ keeps the same value $p$ along the ray; the ray is horizontal at its turning point, where $r/v = p$ , and rises again symmetrically.

P rays from a surface source through the reference model PREM, traced through 2-km shells, for take-off angles from 2 to 34 from the vertical. Blue: rays turning in the mantle, which reach at most 98.5; they bend up because the speed increases with depth, and the kinks near the top mark the discontinuities of the model, at 220, 400 and 670\, km. Red: rays entering the core, bent sharply down at the core–mantle boundary, where the speed drops; the rays that turn in the outer core first reach the surface again at 143.8. Between lies the shadow zone of direct P (grey arc), reached only by weak waves passing through or reflected off the inner core. — P rays from a surface source through the reference model PREM, traced through 2-km shells, for take-off angles from $2{}^{\circ}$ to $34{}^{\circ}$ from the vertical. Blue: rays turning in the mantle, which reach at most $98.5{}^{\circ}$ ; they bend up because the speed increases with depth, and the kinks near the top mark the discontinuities of the model, at 220, 400 and $670\,\mathrm{km}$ . Red: rays entering the core, bent sharply down at the core–mantle boundary, where the speed drops; the rays that turn in the outer core first reach the surface again at $143.8{}^{\circ}$ . Between lies the shadow zone of direct P (grey arc), reached only by weak waves passing through or reflected off the inner core.

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