Drag the earthquake around the surface and watch P and S waves travel through the planet.
t = 0.0 minHover over the planet for layer data
Travel-time curves

1. Seismic waves

An earthquake is sudden slip on a fault. The released strain energy radiates as elastic waves. Body waves travel through the interior:

  • P (primary) waves are compressional: particles move back and forth along the direction of travel. They are fastest and arrive first.
  • S (secondary) waves are shear waves: particles move at right angles to the direction of travel. They are slower and cannot pass through liquids.
$$v_P=\sqrt{\frac{K+\tfrac43\mu}{\rho}},\qquad v_S=\sqrt{\frac{\mu}{\rho}}$$

$K$ is the bulk modulus, $\mu$ the shear modulus and $\rho$ the density. A liquid has $\mu=0$, so $v_S=0$: shear waves cannot travel through it. For typical crustal rock $v_P\approx6$ km/s and $v_S\approx3.5$ km/s. Surface waves (Love and Rayleigh waves) travel along the surface more slowly, but often have the largest amplitudes and cause much of the damage.

2. Rays bend: Snell's law in a sphere

Seismic waves bend for the same reason light bends when it enters water: their speed changes. Seismic velocity generally increases with depth, so rays curve back up towards the surface. At a sharp boundary rays refract according to Snell's law; in a spherical Earth the conserved quantity along a ray is the ray parameter:

$$\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2},\qquad p=\frac{r\,\sin i}{v(r)}=\text{constant along the ray}$$

3. Shadow zones reveal the core

At the core–mantle boundary (2891 km depth) the P-wave speed drops from about 13.7 to 8.1 km/s because the outer core is liquid iron alloy. P waves entering the core bend sharply towards the normal and emerge far beyond 140°, leaving a P-wave shadow zone between about 104° and 140° from the epicentre. S waves cannot cross the liquid outer core at all, so there is no direct S beyond about 104°: the S-wave shadow zone. Beno Gutenberg used the shadow to locate the core in 1914; in 1936 Inge Lehmann explained faint P arrivals inside the shadow zone by a distinct inner core with a higher P-wave speed that reflects and refracts waves into the shadow. That the inner core is solid was established later, from the Earth's free oscillations in the early 1970s.

The lab uses a smoothed, PREM-like velocity model without the crust and upper-mantle discontinuities. Its direct P and S rays reach about 96° and 100°; in the real Earth, waves diffracted along the core boundary extend the observed edge to about 104°.

4. Locating an earthquake

Both waves leave the hypocentre together, so the delay between their arrivals grows with distance $d$:

$$\Delta t=t_S-t_P=d\left(\frac1{v_S}-\frac1{v_P}\right)\quad\Rightarrow\quad d=\frac{v_Pv_S}{v_P-v_S}\,\Delta t\approx8.2\ \text{km s}^{-1}\times\Delta t$$

for $v_P=6.0$ km/s and $v_S=3.46$ km/s (a common rule of thumb is $d\approx8\Delta t$ for local earthquakes; it is only approximate because real velocities vary). One station gives a circle of possible epicentres; three stations fix the point where the circles meet: trilateration, often called triangulation. Strictly, $d$ is the distance to the hypocentre, so for a focus at depth $h$ the epicentral distance is $\sqrt{d^2-h^2}$; for shallow rift earthquakes the difference is small.

5. Magnitude

Charles Richter (1935) defined the local magnitude from the largest amplitude $A$ (mm) recorded on a Wood–Anderson seismograph, corrected for distance. A widely used nomogram form is

$$M_L=\log_{10}A+3\log_{10}(8\,\Delta t)-2.92$$

Magnitude is logarithmic: one unit means 10 times the amplitude. Modern catalogues use the moment magnitude $M_w=\tfrac23(\log_{10}M_0-9.1)$, where $M_0=\mu A_f\bar s$ (rigidity × fault area × average slip, in N m), because $M_L$ saturates for large earthquakes.

6. Energy

$$\log_{10}E\,[\text{J}]\approx1.5\,M+4.8\quad\Rightarrow\quad \frac{E_2}{E_1}=10^{1.5\,(M_2-M_1)}$$

Each step of one magnitude releases about $10^{1.5}\approx32$ times more energy; two steps, 1000 times. Magnitude measures the size of the earthquake; intensity (e.g. Modified Mercalli, I–XII) describes the shaking and damage at a particular place.

7. Why some buildings suffer more

A building behaves like a damped oscillator with a natural period that grows with height; a common rule of thumb is

$$T_n\approx0.1\,N\ \text{s}\quad(N=\text{number of storeys}),\qquad f_n=\frac1{T_n}$$

Under harmonic ground shaking at frequency $f$, the steady-state drift is amplified by

$$D(r)=\frac1{\sqrt{(1-r^2)^2+(2\zeta r)^2}},\qquad r=\frac{f}{f_n},\qquad D_{\max}\approx\frac1{2\zeta}\ \text{at resonance}$$

so with 5% damping a building in resonance moves about 10 times more than the static deflection. Soft sediments amplify long-period shaking, which is why in the 1985 Michoacán earthquake buildings of roughly 6–15 storeys on the old lake bed of Mexico City, whose natural periods matched the ≈2 s period of the amplified ground motion, collapsed in large numbers while lower and much taller buildings nearby fared better. Engineers respond with base isolation (flexible bearings that lengthen the period of the whole building to 2–3 s, away from typical ground-motion periods) and tuned mass dampers (a heavy pendulum or block tuned to the building's frequency, as in Taipei 101).

8. Plate tectonics

Most earthquakes occur at plate boundaries: divergent (plates move apart, e.g. mid-ocean ridges and continental rifts), convergent (one plate subducts beneath another, producing the largest earthquakes and volcanic arcs) and transform (plates slide past each other, e.g. the San Andreas Fault).

Example 1: Distance from S − P

  1. A station in Nairobi records P at 10:14:06.2 and S at 10:14:18.6. $\Delta t=12.4$ s.
  2. $\frac1{v_S}-\frac1{v_P}=\frac1{3.46}-\frac1{6.0}=0.2890-0.1667=0.1223$ s/km.
  3. $d=12.4/0.1223=101$ km (rule of thumb: $8\times12.4\approx99$ km).
  4. Origin time: $t_0=t_P-d/v_P=06.2-101/6.0=06.2-16.9=-10.7$ s, so borrow a minute: 10:14:06.2 − 16.9 s = 10:13:49.3. The earthquake happened about 17 s before the P wave arrived.

Example 2: Local magnitude

  1. Peak amplitude $A=8$ mm on the Wood–Anderson record; $\Delta t=12.4$ s.
  2. $M_L=\log_{10}8+3\log_{10}(8\times12.4)-2.92=0.903+3\times1.997-2.92=3.97$.
  3. A station twice as far away ($\Delta t=24.8$ s) would record an amplitude about $2^3=8$ times smaller (1 mm) for the same earthquake, because $3\log_{10}2=0.90$.

Example 3: How much bigger?

  1. Compare M 5.0 and M 7.0: amplitude ratio $10^{2}=100$; energy ratio $10^{1.5\times2}=10^3=1000$.
  2. Energy of M 7.0: $\log_{10}E=1.5\times7+4.8=15.3$, $E=2.0\times10^{15}$ J.
  3. In tonnes of TNT ($4.184\times10^9$ J each): about 480,000 t, roughly 32 Hiroshima-sized bombs (≈15 kt each).

Example 4: Resonance in a 10-storey building

  1. $T_n\approx0.1\times10=1.0$ s, so $f_n=1.0$ Hz, $\omega_n=2\pi$ rad/s.
  2. Ground: PGA 0.2 g $=1.96$ m/s² at 1.0 Hz (resonance). Static drift $a/\omega_n^2=1.96/39.5=0.050$ m.
  3. The dynamic amplification is $D=1/\sqrt{(1-r^2)^2+(2\zeta r)^2}$ with $r=f/f_n$. At resonance $r=1$, so with $\zeta=0.05$: $D=1/(2\times0.05)=10$, so the roof moves about 0.50 m relative to the ground.
  4. Height ≈ 30 m: drift ratio $0.50/30=1.7\%$, enough for serious structural damage. At 3 Hz instead, $r=3$ and $D=1/\sqrt{64+0.09}=0.125$, so the roof moves only $0.050\times0.125\approx6$ mm: barely any motion.
  1. Find the shadow. Place a seismometer in the P-wave shadow zone (between 104° and 140° from the epicentre): click the planet's surface to place it and read Distance Δ. What arrives there, and why? (auto-checked)
  2. Pinpoint it. Locate a mystery earthquake to within 15 km using your own P and S picks on all three stations. (auto-checked when you press Check, before revealing the answer)
  3. Measure the magnitude. Enter peak amplitudes for all three stations so that your mean ML is within 0.3 of the true value. Read each amplitude from the largest S-wave swing on the trace (hover to read values). (auto-checked when you press Check, before revealing the answer)
  4. A thousand times. In the energy panel, set two earthquakes whose energy ratio is about 1000. How many magnitude units apart are they? (auto-checked)
  5. Resonance. Make the 20-storey building reach a drift ratio above 2% with steady shaking of 0.15 g or less. Hint: shake it at its own natural frequency $f_n = 1/T_n$ (Theory 7) and wait a few seconds for the sway to build up. (auto-checked)
  6. Engineer a fix. With the same shaking, bring every building below 0.5% drift using a protection system. (auto-checked)
  7. Soft soil. Play an earthquake record on rock and then on soft lake sediments. Which buildings suffer in each case, and why? Keep the record and its strength the same and change only the Site; record the peak drift ratio of each building. Expect: on rock the short-period shaking (around 2–3 Hz) hits the low, stiff buildings; soft sediments shift the energy to about 0.5 Hz, near the natural frequency of the tallest building, so it sways most.

A continent splitting apart

The East African Rift System is the largest active continental rift on Earth, running from the Afar region of Ethiopia southwards for thousands of kilometres. Here the African continent is slowly splitting into the Nubian plate to the west and the Somali plate to the east, at rates of a few millimetres per year (faster in the north near Afar, slower further south).

In Kenya, the eastern branch (the Gregory Rift or Kenya Rift) forms a spectacular valley bounded by steep normal-fault escarpments such as the Mau and the Aberdares/Kikuyu escarpment. As the crust stretches, blocks drop down between faults to form a graben. Hot mantle rising beneath the rift feeds volcanoes such as Longonot, Suswa and Menengai, as well as the geothermal fields at Olkaria near Lake Naivasha that supply a large share of Kenya's electricity.

Most rift earthquakes are small and shallow, but larger events do occur. The 1928 Subukia earthquake (about magnitude 6.9) is among the largest recorded in Kenya. Ground cracks that open suddenly in the rift floor, such as the fissure near Mai Mahiu in 2018, are mostly linked to erosion of loose volcanic sediments along older lines of weakness after heavy rain, rather than to the rift "opening" overnight.

The map in the Locate an epicentre lab is a simplified sketch of the central Kenya Rift: lakes Baringo, Bogoria, Nakuru, Elementaita, Naivasha and Magadi, the volcanoes Menengai, Longonot and Suswa, and seismometers at Nairobi, Nakuru and Narok. Positions are approximate.