Illustrated Physics
physics, drawn
Concept

Shear modulus — where it appears

The stiffness of a solid against a change of shape at constant volume: the shear stress needed per unit of shear strain. It sets the speed of shear waves, the square root of the modulus over the density, and is zero for a liquid, which therefore carries no shear wave at all.

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

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 The sideways shaking that arrives longest waves first. The transverse ground motion 3000 km from a sudden shear source, synthesised from the computed dispersion of the fundamental Love wave in a 35 km crust, with periods from about 8 to 120 seconds. Nothing arrives before 11.0 minutes, the travel time at the mantle's shear speed. Then the longest periods come in first — 80 s waves at their group velocity of 4.23 km/s, after 11.8 min — and the period shortens steadily through the train, 30 s waves arriving at 14.3 min. The strongest shaking comes last, near 14.8 min, where the group velocity passes through its minimum and waves over a band of periods arrive together. Read off a real seismogram, the arrival time of each period is the crust's dispersion curve, and the crust's thickness with it.

The shaking a uniform Earth could not carry

Early seismographs recorded a large sideways shaking that arrived after the body waves and before the Rayleigh wave, and no theory of a uniform Earth allowed it: a horizontal shear wave at a free surface reflects as itself and nothing holds it there. Augustus Love showed in 1911 that a layer does. A crust slower than the rock beneath traps the shaking between a perfect mirror at the top and total reflection at the bottom, and because the long waves reach deeper and run faster, the order in which the periods arrive is a measurement of how thick the crust is.

waves · Wave motion

Named alongside it

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

Seismic wavesCausticCutoffDispersionEarths coreElastic wavesGroup velocityGuided wavesRefractionShadow zoneSnell's lawTotal internal reflection

All concepts