Indexing the archive…
Your Universe of Digital Possibilities
No one has seen the Earth’s core. Quakes send waves through it, and seismometers round the world time what comes back: a shadow where no strong P arrives, S waves that stop and never return. In 1913 Gutenberg read the core’s radius off that shadow; in 1936 Inge Lehmann noticed faint arrivals inside it and inferred a solid core within the liquid one. Rebuild the Earth from its travel times alone, then turn around.
In flat layers sin i / v is kept across every interface; in a sphere the kept quantity is r sin i / v — the ray parameter. Where the velocity drops (the liquid core under the mantle) rays bend away and leave a shadow on the surface.
In a spherically layered Earth a ray keeps r sin i / v all the way down and back — Snell’s law with the radius folded in. It turns where r / v(r) = p; and where the velocity drops, as under the mantle, no ray can turn at all: those depths leave a shadow at the surface.
The slope of the travel-time curve at a distance Δ is the ray parameter of the ray that lands there — the record section measures p directly. A shadow is a stretch of Δ where no ray lands; a kink is a layer where the velocity jumps.
The exact inverse of the travel-time curve: for the ray landing at Δ₁ with parameter p₁, the integral gives the radius r₁ where it turned, and v(r₁) = r₁ / p₁. It needs p to fall steadily with distance — a slow layer, which no ray turns in, breaks it, and that layer is in the null space.
The Orfeo Edition’s seventh shadow is a literal one: the core’s. The rebuild sees only times on a curve; the misfit is all it can count before turning around; and where no ray turns — a slow layer, the last stretch above the core, the core’s velocities themselves — it says so, or names the prior it leans on. The ray’s bending at an interface is The Ray’s; a body heard from its outside is The Drum; and rebuilding an interior from its line integrals is The Scan.