How Earthquakes Actually Happen
Elastic rebound theory, fault asperity friction, seismic wave propagation (P, S, surface waves), and the Richter moment magnitude scale
“Why does solid rock, which seems completely rigid, bend like a rubber band before snapping in a catastrophic earthquake?”
For centuries, earthquakes were feared as sudden, unpredictable spasms of the ground, believed to be caused by underground winds, divine fury, or subterranean volcanic explosions. Today, we know that earthquakes are the mechanical release of colossal elastic strain energy stored in the crust. As tectonic plates grind past each other, microscopic friction along jagged rock faces—called asperities—locks the fault line in place. While the deep plates keep moving centimeters per year, the locked surface rocks bend, warp, and stretch like an immense geological rubber band. When accumulated stress finally exceeds the rock's frictional strength, centuries of pent-up energy detonate in seconds. In this deep dive, we explore the physics of seismic rupture: elastic rebound theory, the difference between P-waves, S-waves, and surface waves, the logarithmic mathematics of the Moment Magnitude scale, and why soil liquefaction can topple buildings without cracking their walls.
To understand the failure modes and edge cases detailed in this piece, we recommend familiarizing yourself with these foundational mechanisms first:
The Bent Fence
On the morning of April 18, 1906, an enormous earthquake shattered the city of San Francisco, California.
The ground shook violently for nearly a minute. Gas mains ruptured, triggering fires that incinerated 28,000 buildings and killed over 3,000 people.
In the weeks following the disaster, a professor of geology at Johns Hopkins University named Harry Fielding Reid walked hundreds of kilometers along the San Andreas Fault, surveying rural farmland in Marin and Sonoma counties.
He noticed a bizarre sight on a ranch:
A straight wooden fence crossed the fault line. After the earthquake, the fence was severed cleanly in two.
The western side of the fence had jumped 6 meters (20 feet) to the northwest relative to the eastern side.
THE SEVERED FENCE: SAN ANDREAS FAULT (1906)
BEFORE 1906 (Continuous Line) AFTER 1906 (Sheared Offset)
Western Plot Eastern Plot Western Plot Eastern Plot
┌──────────────┐ ┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ │ │ │ │ │ │ │
│ =====[FENCE]══════│══════ │ │ =====[FENCE] │ │ │
│ │ │ │ │ │ │ │
└──────────────┘ └──────────────┘ └──────────────┘ │ │
│ │ │ =====[FENCE] │
▼ ▼ │ │
San Andreas Fault Line └──────────────┘
▲
6-meter offset!
More importantly, Reid surveyed older geodetic boundary markers that had been installed across California decades earlier by the Coast and Geodetic Survey.
He discovered that in the thirty years before the earthquake, the land had not been stationary:
- Farmland 10 kilometers west of the fault had been creeping slowly northwest at roughly 3 centimeters per year.
- Farmland 10 kilometers east of the fault had remained anchored.
- But right at the fault line itself, the rocks had refused to move.
Instead of sliding smoothly, the rocks straddling the fault had bent, twisted, and warped like a massive wooden bow being pulled back by an archer.
In 1910, Reid published the conceptual breakthrough that forms the foundation of modern seismology: Elastic Rebound Theory.
1. Elastic Rebound Theory and Stick-Slip Friction
Why didn't the fault slide smoothly?
As we explored in How Plate Tectonics Actually Works, the Pacific Plate is relentlessly grinding northwest past the North American Plate at roughly 3 to 5 centimeters per year.
At depths greater than 15 kilometers, temperatures exceed $350^\circ\text{C}$. The rock is warm and ductile: it deforms plastically and slides smoothly without earthquakes.
Near the surface, however, the upper 10 to 15 kilometers of the crust is cold, brittle, and subjected to thousands of tons of lithostatic pressure:
THE STICK-SLIP FRICTION CYCLE
1. INTER-SEISMIC (Stick Phase) 2. CO-SEISMIC (Slip Phase)
┌──────────────────────────────┐ ┌──────────────────────────────┐
│ Tectonic plates push at 3 cm/yr│ │ Stress exceeds static friction;│
│ Fault is locked by friction │ ──────────► │ fault unzips at 3 km/second! │
│ Rock bends & stores elastic E│ │ Centuries of strain released │
│ (Duration: 50 to 500 years) │ │ (Duration: 5 to 60 seconds) │
└──────────────────────────────┘ └──────────────────────────────┘
The Microscopic Toothwork: Asperities
Under an electron microscope, even the smoothest polished slab of granite looks like the jagged Himalayas: a jagged landscape of microscopic peaks and valleys called asperities.
When two tectonic plates press together under millions of atmospheres of normal stress ($\sigma_n$), these microscopic teeth bite into each other:
- The fault locks solid. This is the Stick Phase.
- The deeper plates continue moving inexorably.
- Because rock has elasticity, the brittle crust bends like a stiff steel spring.
For centuries—100 years, 200 years, sometimes 500 years—the fault stays locked. Elastic strain energy accumulates in the deformed rock at billions of joules per cubic kilometer.
The Coulomb Rupture
According to the Coulomb Failure Criterion, rock will hold until the accumulated shear stress ($\tau$) exceeds the static frictional resistance ($\tau_f$):
$$\tau > \tau_f = c + \mu (\sigma_n - P_f)$$
Where $c$ is cohesion, $\mu$ is the friction coefficient, $\sigma_n$ is normal stress, and $P_f$ is pore fluid pressure.
Eventually, stress exceeds the breaking point of the strongest asperity.
The microscopic tooth snaps. That sudden failure instantly transfers all its load to the neighboring asperity, which snaps instantly, triggering a catastrophic cascading zipper effect: the Slip Phase.
The bent crust violently snaps back to its relaxed shape in a matter of seconds.
That sudden snap is an earthquake.
Constant plate motion (2–10 cm/yr) applies continuous shear stress across the fault boundary.
Static friction on asperities locks the fault; surrounding bedrock flexes, storing elastic strain energy.
Shear stress exceeds static friction; fault asperity fails at initial hypocenter ignition point.
Fracture propagates along fault plane at shear-wave velocity (~3 km/s), releasing centuries of strain.
Stored elastic energy converts into acoustic body waves (P, S) and destructive surface waves.
2. Anatomy of a Rupture: Hypocenter vs. Epicenter
When an earthquake strikes, news broadcasts immediately report its epicenter.
Most people picture the epicenter as the spot where the earthquake happened underground. This is inaccurate:
HYPOCENTER (FOCUS) vs. EPICENTER
EPICENTER
(Point on Earth's Surface)
│
▼
Earth's Surface ────────────────■──────────────────────────────────
│
│ Depth (e.g., 10 km)
│
▼
(★) HYPOCENTER (Focus)
Initial point of physical rupture
where fault begins to unzip!
- Hypocenter (or Focus): The actual three-dimensional point inside the crust where the rock first shears and fractures. This can range from shallow (0–20 km, the most destructive) to intermediate (70–300 km) or deep subduction zones (up to 700 km).
- Epicenter: The geographic point on Earth's surface directly vertically above the hypocenter.
An earthquake is not a single point; it is a rupture plane.
In a massive magnitude 9.0 subduction megathrust earthquake (like Japan in 2011 or Sumatra in 2004), the rupture begins at the hypocenter and unzips an underwater fault plane 500 to 1,000 kilometers long and 150 kilometers wide, moving at roughly 3 kilometers per second for four agonizing minutes!
3. The Four Seismic Waves: How the Ground Shakes
When the fault snaps, the released elastic energy radiates outward in all directions in the form of Seismic Waves.
These waves are divided into two fundamental families: Body Waves (which travel through the interior of the planet) and Surface Waves (which travel exclusively along the crust like ripples on a pond).
THE FOUR SEISMIC WAVES
BODY WAVES (Deep Interior) SURFACE WAVES (Crustal Surface)
┌──────────────────────────────┐ ┌──────────────────────────────┐
│ 1. P-Wave: Compressional/Fast│ │ 3. Love Wave: Side-to-Side │
│ (Vibrates along motion) │ │ (Shears foundations) │
│ │ │ │
│ 2. S-Wave: Transverse Shear │ │ 4. Rayleigh Wave: Ocean Roll │
│ (Cannot travel in liquid!)│ │ (Elliptical ground roll) │
└──────────────────────────────┘ └──────────────────────────────┘
1. The P-Wave (Primary / Compressional Wave)
- Speed: The fastest seismic wave ($5\text{--}8 \text{ km/s}$ in crust; up to $13 \text{ km/s}$ in mantle). It arrives first at any seismograph station.
- Motion: Longitudinal compressional wave—identical to an acoustic sound wave in air. As it passes, it alternately compresses and dilates the rock parallel to the direction the wave is traveling: $$\dots \text{P-U-S-H} ;\longleftrightarrow; \text{P-U-L-L} \dots$$
- Medium: Because liquids and gases can be compressed, P-waves travel through solids, liquids, and gases alike.
When a P-wave hits the surface beneath your feet, it feels like a sudden vertical jolt or a sharp thud. Animals often hear the deep rumble of P-waves converting into sound waves in the air seconds before the violent shaking begins.
2. The S-Wave (Secondary / Shear Wave)
- Speed: Roughly 60% the speed of a P-wave ($3\text{--}5 \text{ km/s}$). It arrives second.
- Motion: Transverse shear wave. It displaces rock particles perpendicular to the direction of wave travel (side-to-side or up-and-down), like flicking a jump rope: $$\dots \text{S-H-E-A-R} ;\updownarrow; \text{S-H-E-A-R} \dots$$
- The Liquid Rule: Liquids and gases have zero shear modulus ($\mu = 0$). You cannot "shear" water; water molecules simply slip past each other.
Therefore, S-waves physically cannot travel through liquids.
THE PROOF OF THE LIQUID CORE
Earthquake at North Pole (0°)
(★)
╱ ╲
╱ ╲
╱ [S] ╲ S-waves travel through solid mantle
╱ ╲
├───────────┤
│ LIQUID │ S-waves CANNOT enter liquid outer core!
│OUTER CORE │
├───────────┤
╲ ╱
╲ ╱ S-WAVE SHADOW ZONE:
╲ ╱ No S-waves ever detected past 104°!
───── Proves outer core is 100% molten liquid!
This simple physical fact allowed British geologist Richard Dixon Oldham in 1906 to make one of the greatest discoveries in science:
When a major earthquake occurs, seismographs around the world record S-waves up to an angular distance of 104°. Beyond 104°, all S-waves vanish completely!
This massive "S-wave shadow zone" on the other side of the planet proved that deep within the Earth sits a colossal sphere of liquid metal: the molten outer core.
3. Surface Waves: The Bringers of Destruction
When P and S waves hit the free boundary of Earth's surface, their interference generates Surface Waves.
They travel slower than body waves ($2\text{--}4 \text{ km/s}$), but because their energy is trapped in two dimensions along the surface (attenuating by $\frac{1}{r}$ rather than $\frac{1}{r^2}$ like body waves), surface waves carry the vast majority of destructive energy:
- Love Waves ($L$): Discovered by A. E. H. Love in 1911. They whip the ground violently from side to side in a horizontal plane. Buildings are engineered to support vertical gravitational loads, but Love waves apply intense horizontal shearing that snaps structural columns and collapses bridges.
- Rayleigh Waves ($R$): Discovered by Lord Rayleigh in 1885. They roll through the earth like ocean swells, moving soil particles in backward rotating vertical ellipses. Standing on the ground during large Rayleigh waves, you can literally see the ground rolling toward you in visible waves.
4. The Mathematics of Violence: The Moment Magnitude Scale
When an earthquake strikes, the public still refers to the "Richter Scale."
Developed by Charles Richter and Beno Gutenberg at Caltech in 1935, the original local magnitude scale ($M_L$) measured the physical needle swing on a specific type of torsion seismograph (the Wood-Anderson seismometer) in Southern California.
The Richter scale had a fatal flaw: for massive earthquakes ($M > 7.5$), the needle swing maxed out. It suffered from magnitude saturation. A magnitude 8.0 and a magnitude 9.5 produced the exact same maximum needle deflection, making it impossible to measure the true energy of colossal megathrust earthquakes.
In 1979, Caltech seismologist Hiroo Kanamori and Thomas Hanks developed the modern, universal gold standard: the Moment Magnitude Scale ($M_w$).
Calculating Seismic Moment ($M_0$)
Moment magnitude is not based on needle deflections. It is calculated directly from the fundamental physical work done by the fault:
$$M_0 = \mu \cdot A \cdot D$$
Where:
- $\mu$ is the shear modulus (rigidity) of the faulted rock (typically $30 \text{ Gigapascals}$).
- $A$ is the surface area of the fault that ruptured (Length $\times$ Width, in $\text{m}^2$).
- $D$ is the average distance the rock slipped (in meters).
The Seismic Moment ($M_0$) has units of Newton-meters ($\text{N}\cdot\text{m}$)—the exact physical unit of energy and work!
The Moment Magnitude ($M_w$) is then calculated using the logarithmic formula:
$$M_w = \frac{2}{3} \log_{10}(M_0) - 6.07$$
The Explosive Power of Base 10
Because $M_w$ is scaled by $\frac{2}{3} \log_{10}$, each step on the scale represents a staggering jump in physical power:
THE MOMENT MAGNITUDE ENERGY EXPLOSION
MAGNITUDE JUMP AMPLITUDE INCREASE ENERGY RELEASE JUMP
─────────────────────────────────────────────────────────────────────────────
+ 1.0 Magnitude 10× Ground Shaking 31.6× Energy Released
+ 2.0 Magnitude 100× Ground Shaking 1,000× Energy Released
+ 3.0 Magnitude 1,000× Ground Shaking 31,622× Energy Released
Every single whole number increase on the moment magnitude scale releases $10^{1.5} \approx 31.62$ times more energy!
- A Magnitude 7.0 earthquake does not release "a little bit more" energy than a Magnitude 6.0; it releases 32 times more energy.
- A Magnitude 8.0 releases 1,000 times more energy than a 6.0!
- The 1960 Great Chilean Earthquake ($M_w = 9.5$), the largest earthquake ever recorded in human history, ruptured a fault 1,000 kilometers long with 20 meters of slip, releasing energy equivalent to thousands of nuclear warheads detonating simultaneously.
5. Soil Liquefaction: When Solid Ground Becomes Liquid
One of the most terrifying phenomena in an earthquake has nothing to do with falling bricks: Soil Liquefaction.
In cities built on reclaimed land, loose river silt, or saturated sand (such as Tokyo Bay, Christchurch, New Zealand, or San Francisco's Marina District), the soil is packed with water:
THE MECHANICS OF SOIL LIQUEFACTION
STABLE SEDIMENT (Resting) LIQUEFIED SEDIMENT (Shaking)
┌──────────────────────────────┐ ┌──────────────────────────────┐
│ Grain-to-grain contact; │ │ Cyclic shear breaks contacts;│
│ friction supports heavy │ ───► │ water pressure skyrockets; │
│ buildings on surface. │ │ sand grains float in water! │
└──────────────────────────────┘ └──────────────────────────────┘
Friction supports weight Zero shear strength!
Pore water relaxed Buildings sink into liquid mud!
- In dry or resting soil, sand grains rest firmly against each other. Static friction between grains supports the weight of heavy skyscrapers.
- The microscopic voids between grains are filled with water (pore water).
- When seismic S-waves and surface waves hit the ground, cyclic shearing shakes the sand grains back and forth.
- The grains attempt to settle into a tighter packing arrangement. But the water cannot drain away fast enough.
- The weight of the soil transfers from the solid sand grains onto the incompressible water. Pore water pressure skyrockets.
- The effective friction between sand grains drops to zero.
The soil suddenly loses all shear strength. It transforms into a pressurized liquid quicksand.
During the 1964 earthquake in Niigata, Japan, four-story apartment buildings did not collapse or shatter: they remained completely intact, tipped over sideways like toy blocks, and sank several feet into the liquefied ground.
The Breathing Planet
Earthquakes are the audible pulse of an active, living planet.
They are the inevitable physical consequence of:
- Deep mantle convection driving rigid lithospheric plates across the globe.
- Coulomb static friction locking jagged rock asperities in place for centuries.
- The sudden, catastrophic release of elastic strain energy along fault planes.
- Acoustic body waves and surface waves radiating across the planet at supersonic speeds.
A planet with earthquakes is a planet whose interior is still hot, churning, and alive—sustaining the magnetic core that shields our atmosphere and driving the plate tectonic cycle that recycles the chemistry of life.
In our next explainer, How Volcanoes Actually Erupt, we follow molten rock as it escapes the crushing pressures of the interior: the buoyancy of magma chambers, dissolved gas exsolution, and the explosive physics of volcanic eruptions.
Where to Go From Here
Explore companion architectures or dive deeper into downstream mechanisms.
How the Atmosphere Regulates Earth's Temperature
Why isn't the Earth a frozen ball of ice at -18°C, and how do trace gases like carbon dioxide trap heat without blocking incoming sunlight?
How the Water Cycle Shapes the Planet
How does the sun lift 500,000 cubic kilometers of water into the sky every year to sculpt mountains and grind continents into the sea?
Verified Specifications & Architectural References
This explainer is grounded in primary-source engineering specifications, regulatory circulars, and standard documentation.
The California Earthquake of April 18, 1906: Report of the State Earthquake Investigation Commission
The seminal historical monograph that established the Elastic Rebound Theory of earthquakes.
Quantitative Seismology (2nd Edition)
The authoritative mathematical textbook on elastodynamics, wave propagation, and seismic source representation theorems.
Earthquakes (5th Edition)
Comprehensive introduction to seismic recording, fault mechanisms, ground shaking hazard, and tsunami generation.