Earthquake Mechanics: Focus, Epicenter, and Seismic Waves

An earthquake is a sudden shaking of the ground caused by the release of stored elastic energy when rock breaks and slips along a fault; the focus (hypocenter) is the point underground where the rupture starts, the epicenter is the point on the surface directly above it, and seismic waves carry the energy outward. In brief: the main types of seismic waves are P-waves (fast compressional body waves), S-waves (slower shear body waves that cannot pass through liquids) and surface waves (slowest and most destructive). Magnitude measures the energy released (each whole step is about 32 times more energy), while intensity measures the effects of shaking at a place. Large undersea earthquakes can cause tsunamis.

Earthquakes kill more people than most other natural hazards, and understanding their mechanics is the basis of safer buildings and warnings. This guide explains how earthquakes occur, the focus, epicenter and the seismic waves, magnitude and intensity, and tsunamis, compares the wave types in a table, works through calculations of distance, energy and tsunami speed, outlines the history of seismology and corrects common mistakes.

What causes earthquakes?

Most earthquakes occur at plate boundaries, where the plates move slowly past, toward or away from each other. Friction locks the rocks along a fault, so they bend and store elastic strain energy (the elastic rebound theory, proposed by Harry Fielding Reid after the 1906 San Francisco earthquake). When the stress exceeds the strength of the rock or the friction, the fault slips suddenly and the stored energy is released as seismic waves. Earthquakes also occur in the interior of plates on old faults, and they can be induced by volcanic activity, mining, reservoirs and wastewater injection. The focus is the point where the rupture begins, which may be shallow (0–70 km), intermediate (70–300 km) or deep (300–700 km, only in subduction zones). The epicenter is the point on the surface directly above the focus. Shallow earthquakes are generally the most damaging. Small earthquakes called foreshocks may come before, and aftershocks follow the main shock for days to months.

What are seismic waves?

• P-waves (primary): compressional waves in which the particles move back and forth in the direction of travel, like sound. They are the fastest (about 5–8 km/s in the crust), arrive first, and can travel through solids, liquids and gases.
• S-waves (secondary): shear waves in which the particles move at right angles to the direction of travel. They are slower (about 3–4.5 km/s in the crust), arrive second, and can only travel through solids, so they do not pass through the liquid outer core.
• Surface waves: Love waves (horizontal shaking) and Rayleigh waves (a rolling motion) travel along the surface. They are the slowest, arrive last, but have the largest amplitude and cause most of the damage.

A seismometer records the waves as a seismogram. Because P-waves and S-waves travel at different speeds, the time interval between their arrivals increases with distance from the epicenter. With the distances from three or more stations, the epicenter is located by triangulation (circles drawn around each station intersect at the epicenter).

How are earthquakes measured?

Magnitude is a number related to the energy released at the source. Charles Richter introduced the Richter scale in 1935 for California; today the moment magnitude scale (M_w) is used, which is based on the size of the fault rupture and the slip. The scale is logarithmic: each increase of 1 unit means 10 times larger ground-motion amplitude and about 31.6 times (10^1.5) more energy. The energy in joules is approximately log₁₀E = 1.5M + 4.8. Intensity describes the effects of the shaking on people, buildings and the ground at a particular place, using the Modified Mercalli scale (I to XII), and it varies with distance from the epicenter, the depth, the type of ground (soft sediment shakes more) and the quality of the buildings. One earthquake has a single magnitude but many intensities.

What are tsunamis?

A tsunami is a series of long ocean waves generated by a sudden displacement of the sea floor, most often by a large subduction-zone earthquake (magnitude 7.5 and over), but also by underwater landslides and volcanic eruptions. In deep water, the wave has a very long wavelength (hundreds of kilometers) and a small height (less than a meter), and it travels at a speed v = √(g × h), where h is the water depth, so at 4,000 m depth it is about 198 m/s, or 713 km/h. Near the coast, the water becomes shallower, the wave slows and the height increases, and it can reach many meters in height. The sea may withdraw first. Warnings are given by networks of seabed pressure sensors and buoys, and by seismic data, such as the Pacific Tsunami Warning System.

Seismic waves compared

Worked example: distance, energy and tsunami speed

1. Distance from the S–P interval: take P-waves at 6.0 km/s and S-waves at 3.5 km/s. The time delay between the S and P arrivals is Δt = d/3.5 − d/6.0 = d × (0.2857 − 0.1667) = 0.119 d (in seconds, with d in km). If the interval measured on the seismogram is 12 s, then d = 12 ÷ 0.119 = about 100 km (equal to Δt × 8.4 km/s).
2. Arrival times for 100 km: P arrives after 100 ÷ 6.0 = 16.7 s and S after 100 ÷ 3.5 = 28.6 s, and the difference is 28.6 − 16.7 = 11.9 s, which confirms the result.
3. Energy ratio: an M7 earthquake releases energy E = 10^{(1.5 × 7 + 4.8)} = 10^15.3 = 2.0 × 10¹⁵ J. An M5 earthquake releases 10^12.3 = 2.0 × 10¹² J. The ratio is 10^{1.5 × 2} = 10³ = 1,000, so M7 releases 1,000 times as much energy as M5, and the ground motion amplitude is 10² = 100 times larger.
4. Tsunami speed in deep water: v = √(9.81 × 4,000) = √39,240 = 198 m/s = 713 km/h.
5. Travel time across the ocean: a distance of 5,000 km (5,000,000 m) takes 5,000,000 ÷ 198 = 25,250 s = 7.0 hours. This gives time for warnings at distant coasts, but not near the source.
6. Slowing near the coast: at a depth of 50 m, the speed is √(9.81 × 50) = 22 m/s = 80 km/h, so the wave slows to about one-ninth of its deep-water speed (22 ÷ 198), and the wave piles up and rises.

How did seismology develop?

Zhang Heng in China made an early seismoscope in 132 CE. Modern seismology began in the late 19th century with seismographs, and the 1906 San Francisco earthquake led to the elastic rebound theory. Charles Richter and Beno Gutenberg developed magnitude scales in the 1930s, and the moment magnitude scale was introduced by Hiroo Kanamori and Thomas Hanks in 1979. The 2004 Indian Ocean earthquake and tsunami (magnitude about 9.1) killed over 200,000 people and led to a global tsunami warning network; the 2011 Tōhoku earthquake in Japan (magnitude about 9.0–9.1) caused a tsunami that killed about 18,000 people. Today, thousands of seismometers and GPS stations monitor the movement of the ground.

Which mistakes are common?

Mistake 1: Treating the epicenter as the place where the earthquake starts

The rupture starts at the focus underground. The epicenter is the point on the surface above it.

Mistake 2: Using magnitude and intensity as the same measure

Magnitude is the size of the earthquake at its source, and intensity is the strength of shaking at a place.

Mistake 3: Thinking that a magnitude 7 earthquake is only slightly larger than a magnitude 6

It has 10 times the ground motion amplitude and about 32 times the energy.

Mistake 4: Believing that earthquakes can be predicted exactly

Scientists can estimate probabilities over decades and give seconds of early warning, but cannot predict the day and place of an earthquake.