Illustrated Physics
physics, drawn
Concept

Travel time — where it appears

The time a wave takes to go from source to receiver, read as a function of distance. For earthquakes, travel-time curves of P and S waves fix the distance to the source from the gap between their arrivals, and inverted depth by depth they give the speeds inside the Earth.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Three arrivals, and the one that overtakes. Arrival time against distance from the shot for a 35 km crust at 6 km/s over a mantle at 8 km/s: the direct wave, a line through the origin with slope 1/v₁; the reflection from the base of the crust, a hyperbola; and the head wave, a straight line of slope 1/v₂ that begins at the critical distance, 79 km, where it touches the reflection. Close to the shot the direct wave arrives first. The head wave starts later but travels most of its path at the faster speed, and beyond the crossover distance, 185 km, it arrives first and stays first. At 300 km it beats the direct wave by 4.8 s, though it has travelled 26 km further.

The wave that arrives first by going the long way

A shot fired at the ground sends a wave straight along the surface layer to a distant listener, and another down to a faster rock beneath, along the boundary and back up. The second path is longer, and beyond a certain distance it arrives first, because most of it is run at the faster speed. Huygens's construction shows what the second wave is: a front drawn by wavelets that the disturbance racing along the faster floor sends up into the slower layer, the Mach cone of a source moving faster than the layer can carry sound. Reading where it overtakes the direct wave gave Andrija Mohorovičić the thickness of the Earth's crust in 1909, and gives every refraction survey since the depth to whatever lies beneath.

waves · Huygens Earthquake waves through the Earth, and the ring they do not reach. Paths of compressional (P) waves from an earthquake at the top of the Earth, traced through the mantle, the liquid outer core (orange) and the solid inner core (darker), drawn in one half of a cross-section: rays that stay in the mantle (blue) and rays that pass through the core (red), with Snell's law applied shell by shell to a reference model of the Earth's speeds. The mantle rays curve back up because the speed rises with depth, and reach the surface no further than 97° from the source. Rays that strike the core are bent sharply inward, because the speed drops from 13.7 to 8.1 km/s at its surface, and those that turn in the liquid outer core come out no closer than 144°. Between the two, marked on both sides, is a ring of the surface that these direct P waves do not reach: the P-wave shadow, which is how the core was found. A few rays that just enter the solid inner core (purple, dashed), where the speed jumps up again, are bent back out early and land inside the shadow, as close as 115° — the faint arrivals from which the inner core was found.

The shadow that shows the core is liquid

Nobody has been more than a few kilometres into the Earth, and its interior was mapped from the timing of earthquake waves alone. The decisive observations were of waves that do not arrive. Seismometers between about 100° and 140° from a large earthquake record no direct compressional wave, because something deep inside bends the rays away; and over two-fifths of the planet beyond 100° no direct shear wave arrives at all, because that something cannot be sheared. A slow, liquid core casts both shadows, and a few faint waves inside the first one revealed a solid core within it.

waves · Wave motion

Named alongside it

The objects these essays reach for when they reach for this one.

CausticCritical angleCrossover distanceEarths coreHead waveHuygens principleThe Mach coneMohorovicic discontinuityRefractionRefraction seismologySeismic wavesShadow zone

All concepts