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EARTH EXPLAINED · LESSON GUIDE

Earthquakes 201

Inside an earthquake

Video 12:16Level Grades 9–12 · Introductory university seismologyStandards HS-ESS2-1, HS-ESS2-3, HS-ESS3-1, HS-ESS3-2, HS-PS4-1
Language English

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How does a fault load and break, how do scientists read an earthquake's waves, how does one earthquake lead to the next, and what do those waves reveal deep inside the planet?

In June 1929, a strong earthquake shook the South Island of New Zealand, and faint waves reached stations in Russia, in a zone where, by every theory of the time, the Earth's core should have kept them out. In 1936, the Danish seismologist Inge Lehmann explained them: inside the liquid core there must be a second, inner core, where waves travel faster. This advanced lesson follows an earthquake from start to finish, in five steps. How a fault loads: the plates keep moving while the fault stays locked, so the rock beside it bends and stores strain (elastic rebound, Harry Fielding Reid, 1910); GPS, slow slip events and trenches dug across faults show this earthquake cycle at work. How it breaks: the rupture starts at the hypocenter and spreads at typically 2 to 3 km a second, and the area that slipped, the slip and the rock's stiffness give the seismic moment, on which moment magnitude is built. How scientists read the waves: the delay between P and S waves gives the distance, the first push or pull at each station draws the 'beach ball' that shows how the fault moved, and radar satellites map the ground's motion. How one earthquake leads to the next: the Gutenberg–Richter, Omori and Båth laws describe how many earthquakes and aftershocks to expect; stress transfer marched great earthquakes westward along the North Anatolian Fault from 1939 to 1999; wastewater injection set off earthquakes in Oklahoma; and Parkfield, California, showed why forecasts give odds, never a date. And what the waves reveal: the base of the crust (the Moho), a liquid outer core, and Lehmann's solid inner core.

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Learning objectives After this lesson, students can:

  1. Describe the earthquake cycle and elastic rebound, and explain how GPS measurements, coupling and slow slip events show a fault loading between earthquakes.
  2. Explain how trenches dug across faults record past earthquakes, and how dating their layers shows how often a fault breaks.
  3. Describe how a rupture starts at the hypocenter and spreads, relate its length and duration to the earthquake's size, and calculate seismic moment (rigidity × area × slip) and moment magnitude.
  4. Use the time between the P and S waves to estimate the distance to an earthquake, and explain how many stations together locate it.
  5. Identify normal, reverse and strike-slip faults, explain how first motions at stations (the 'beach ball') reveal how a fault moved, and explain why the first magnitude reported for a great earthquake can be too low.
  6. Apply the Gutenberg–Richter, Omori and Båth laws to earthquake and aftershock counts, and explain stress transfer, induced earthquakes and why forecasts give probabilities rather than dates.
  7. Explain how seismic waves revealed Earth's layers: the Moho, the S-wave shadow and the liquid outer core, and Inge Lehmann's inner core.

Before watching

Key vocabulary ★ extension terms for older students

Earthquake cycle
The repeating life of a fault: it stays locked and loads for decades or centuries while the plates keep moving, breaks in seconds to minutes in an earthquake, then locks and begins to load again.
Elastic rebound
The explanation Harry Fielding Reid gave in 1910, from land surveys made before and after the 1906 San Francisco earthquake: rock beside a locked fault bends slowly, storing strain, then snaps back when the fault slips.
Coupling
How tightly a fault is stuck. A fully coupled fault stores almost all of the plates' motion as strain, year after year. The 2011 earthquake off northeastern Japan showed the plates there had been locked right out to the trench.
Slow slip event
Slip on a fault too slow to cause shaking anyone feels, lasting days to weeks. Beneath northern Washington State and southwestern British Columbia, part of the deep plate boundary slips about an inch (a few centimeters) about every 14 months; GPS revealed these events around 2000.
Paleoseismology★
The study of earthquakes from before written records, read in trenches dug across faults: layers of soil torn and offset by past earthquakes, dated to show how often a fault has broken over thousands of years (as at Pallett Creek on the San Andreas fault).
Hypocenter and rupture
The hypocenter is the point on a fault where an earthquake starts, where the stress first beats the friction. The rupture is the break spreading out from there across the fault, typically at 2 to 3 km a second; a few ruptures run faster than the S waves they send out.
Seismic moment
The size of an earthquake: the rock's rigidity (stiffness) times the area of fault that slipped times the average slip, M₀ = μAD, in newton-meters. The modern magnitude scale is built on it.
Moment magnitude (Mw)
The standard magnitude scale, calculated from the seismic moment (Hanks and Kanamori, 1979). Each whole step means about 32 times more energy released, and it keeps growing for the largest earthquakes.
Magnitude saturation★
When a fast magnitude method stops growing for very large earthquakes and so comes out too low. Japan's first tsunami warning in 2011 used a magnitude of 7.9; the final magnitude was 9.0.
Normal, reverse and strike-slip faults
The three main ways a fault breaks. Normal: the crust is pulled apart and one block drops. Reverse: the crust is squeezed and one block rides up over the other. Strike-slip: the two sides slide past each other sideways.
Focal mechanism (beach ball)
A symbol showing how a fault moved, drawn from whether the first motion of the ground at each station was a push or a pull. It gives two possible fault planes; aftershocks or the break at the surface show which one slipped.
InSAR★
Interferometric synthetic aperture radar: comparing radar images of the ground taken from a satellite before and after an earthquake. Each band of color (fringe) is a few centimeters of motion toward or away from the satellite, about 2.8 cm for the common C-band radar.
Gutenberg–Richter law
For each step down in magnitude, there are about ten times as many earthquakes. Worldwide, about 1,500 of magnitude 5 to 5.9 strike in an average year, but only about one of magnitude 8 or more.
Omori's law
Aftershocks fade in a regular way, described by Omori in Japan in 1894: their rate falls roughly as one over the time since the main shock, so ten days after it they come about a tenth as often as on the first day.
Båth's law
The largest aftershock is, on average, about 1.2 magnitudes smaller than the main shock (Båth, 1965).
Stress transfer
An earthquake moves stress as well as releasing it: the rock just beyond the ends of the broken fault is loaded further, pushing the next segment closer to breaking.
Induced earthquake
An earthquake set off by people, for example by pumping large volumes of wastewater deep underground, which raises the pressure inside old faults until they slip.
Moho
The boundary between the crust and the mantle, found by Andrija Mohorovičić in 1909: about 35 km down under the continents and about 5 to 10 km under the oceans.
Shadow zone
Where an earthquake's direct waves do not arrive. S waves never appear more than about 104° around the globe from an earthquake, because they cannot pass through the liquid outer core; direct P waves are missing from about 104° to 140°, then reappear.
Inner core
The Earth's solid iron-nickel center, about 1,220 km in radius and about 6,000 °C, about as hot as the surface of the Sun. Inge Lehmann inferred it in 1936 from faint P waves where none should have been; that it is solid was shown later.

Chapter outline Select a time to play from there

0:00Introduction

In June 1929, a strong earthquake shook the South Island of New Zealand. In Copenhagen, the seismologist Inge Lehmann studied the records it left at stations around the world: faint waves had reached stations in Russia, in a zone where, by every theory of the time, the Earth's core should have kept them out. In 1936 she published her answer: deep inside the liquid core there must be a second, inner core, where waves travel faster, and it had bent those waves into the forbidden zone. The lecture follows an earthquake from start to finish: how a fault loads and breaks, how scientists read its waves, how one earthquake leads to the next, and what the waves reveal deep inside the planet.

1:00The Loading

The plates drift a few centimeters a year, but along most faults the two sides stay stuck. The rock nearby bends like a springboard under a growing weight; Harry Fielding Reid showed this in 1910 from land surveys made before and after the great San Francisco earthquake, and called it elastic rebound. That is the earthquake cycle: load for decades or centuries, break in seconds or minutes, lock again. In California, GPS receivers anchored to the ground track their positions to within a fraction of an inch (a few millimeters), and near a locked fault the stations closest to it lag behind: the ground is bending. Coupling is how tightly a fault is stuck; off northeastern Japan, the 2011 earthquake showed the plates had been locked right out to the trench, and in places the seafloor shifted about 50 m (more than 150 feet). Beneath Washington State and British Columbia, slow slip events move part of the deep plate boundary about an inch (a few centimeters) over a couple of weeks, about every 14 months, with no shaking felt, and each one adds load to the locked part above. Trenches dug across faults show layers torn and offset by past earthquakes; dating them shows how often a fault has broken over thousands of years.

3:20The Break

An earthquake starts at one point, the hypocenter, where the stress first beats the friction, and the rupture races outward across the fault, typically at 2 to 3 km a second; a few run even faster than the S waves they send out. A moderate earthquake is over in a few seconds; in the 2004 Sumatra earthquake, the rupture tore northward for about 8 minutes along more than 1,300 km of fault. An earthquake's size, its seismic moment, is the area of fault that broke times how far it slipped times the stiffness of the rock, and the modern magnitude scale is built on it; each whole step means about 32 times more energy released. Most earthquakes start within about 70 km of the surface, but where one plate dives beneath another they follow the sinking slab down to about 700 km. In 1994, a magnitude 8.2 earthquake, one of the largest deep earthquakes ever recorded, started about 630 km beneath Bolivia and was felt as far away as Canada.

4:44Reading the Waves

P waves squeeze and stretch the rock and travel fastest; S waves shake it from side to side and arrive later; surface waves are the slowest and cause much of the damage. For a nearby earthquake, each second between the P and S arrivals means about 8 km of distance, and hundreds of stations together pin down the spot within seconds. Faults break in three main ways: normal (pulled apart), reverse (pushed together) and strike-slip (sideways). Whether the first motion at each station is a push or a pull draws a 'beach ball' that shows how the fault moved: for the magnitude 7.8 earthquake in Türkiye in February 2023, a strike-slip break, with aftershocks tracing it along the East Anatolian Fault. Pinning down the size takes longer: in 2011, Japan's first tsunami warning, about three minutes in, used a magnitude of 7.9, because the fast method maxes out for the largest earthquakes; the estimate was raised in steps to 9.0. The final number, the moment magnitude, comes from the fault's area and slip and does not stop growing for the largest earthquakes. Radar satellites compare images taken before and after an earthquake and draw bands of color, each a few centimeters of ground motion, that trace the fault that broke.

7:07Earthquakes Talk to Each Other

For each step down in magnitude there are about ten times as many earthquakes: worldwide, more than a thousand of magnitude 5 or more in a typical year, but only about one of magnitude 8 or more (Gutenberg–Richter). Aftershocks fade in a regular way, found in Japan in the 1890s (Omori's law): ten days after the main shock they come about a tenth as often as on the first day, and a hundred days after, about a hundredth. The largest aftershock is on average about 1.2 magnitudes smaller than the main shock (Båth's law), so damaged buildings should stay empty until they are checked. An earthquake also moves stress onto the rock beyond the ends of the break. Along the North Anatolian Fault in Türkiye, large earthquakes marched from east to west starting in 1939; a study of the ten largest found that nine had been pushed closer to failure by the ones before them, and in August 1999 the march reached Izmit, close to Istanbul. People can unlock faults too: in Oklahoma, wastewater pumped deep underground raised earthquakes of magnitude 3 or more from about two a year to more than 900 in 2015, and the largest, magnitude 5.8 near Pawnee in 2016, was felt across several states. Forecasts give odds, never a date: Parkfield, California, had six moderate earthquakes between 1857 and 1966, roughly one every 22 years, but the one forecast for before 1993 came in 2004. Modern forecasts combine the cycle, the trench record and stress transfer into odds for each fault over decades; the U.S. Geological Survey also issues one-year forecasts for earthquakes caused by people.

10:04Seeing Inside the Earth

Waves generally speed up as they go deeper, so their paths curve gently back toward the surface, like the shimmer of a mirage over a hot road. In 1909, Andrija Mohorovičić noticed that waves from a nearby earthquake arrived in two sets, some by a faster, deeper path, and found the base of the crust, the Moho: about 35 km down under the continents. More than a quarter of the way around the globe from an earthquake, S waves vanish and never return, while P waves reappear on the far side: S waves cannot pass through liquid, so the outer core is molten. Lehmann's faint waves had crossed the liquid core and been bent by something faster inside it: an inner core about 1,220 km in radius, later shown to be solid iron and nickel, about as hot as the surface of the Sun. No one has drilled deeper than about 12 km; most of what we know about everything below comes from timing earthquake waves, and modern networks map the deep Earth in three dimensions from millions of records.

11:32Three Things

A fault loads for decades, breaks in minutes and locks again: the earthquake cycle. The waves reveal where a fault broke, how it moved and how big the break was, and each earthquake passes stress on to the next. And the same waves have mapped the inside of the planet, down to its solid core. Every earthquake is a message from inside the planet.

Common misconceptions For the teacher

MisconceptionAn earthquake happens all at once, at the epicenter.

What the evidence showsAn earthquake starts at one point on the fault, the hypocenter, and the rupture spreads from there, typically at 2 to 3 km a second. Small earthquakes are over in seconds, but the 2004 Sumatra rupture kept going for about 8 minutes along more than 1,300 km of fault. The epicenter only marks the spot on the surface above the starting point; the shaking comes from the whole break.

MisconceptionLots of small earthquakes let off pressure and prevent a big one.

What the evidence showsEach step up in magnitude means about 32 times more energy but only about a tenth as many earthquakes. Worldwide, the roughly 1,500 earthquakes of magnitude 5 to 5.9 in an average year together release only about a quarter of the energy of a single magnitude 8. Small earthquakes cannot keep up with the strain, and each earthquake moves stress onto the rock beyond it, which can push neighboring parts of a fault closer to breaking.

MisconceptionOnce the main earthquake is over, the danger is over within a few days.

What the evidence showsAftershocks fade slowly (Omori's law): ten days after the main shock they still come about a tenth as often as on the first day, and a hundred days after, about a hundredth. The largest aftershock is on average only about 1.2 magnitudes smaller than the main shock (Båth's law), so after a magnitude 7, an aftershock near magnitude 6 is no surprise. Damaged buildings should stay empty until they are checked.

MisconceptionThe first magnitude announced is the true one; if it changes, the scientists got it wrong.

What the evidence showsFast methods give a first number within minutes so that warnings can go out, but they max out (saturate) for the largest earthquakes. In 2011, Japan's first tsunami warning used a magnitude of 7.9; the estimate was raised in steps to 9.0 (the USGS gives 9.1). The final moment magnitude comes from the whole record, so several numbers in the first hour are expected revisions, not mistakes.

MisconceptionA fault that breaks regularly can be predicted to the year, and one that hasn't broken in a while is 'overdue'.

What the evidence showsParkfield, California, had moderate earthquakes in 1857, 1881, 1901, 1922, 1934 and 1966, roughly every 22 years. In 1985 scientists forecast the next one before 1993; it came in 2004, eleven years after the window closed. Faults are regular enough to forecast, but not regular enough to keep a timetable, so forecasts give odds over years and decades, never a date.

MisconceptionScientists know what is inside the Earth because they have drilled down to see it.

What the evidence showsThe deepest hole ever drilled goes down only about 12 km, about a third of the way through the continental crust, which is about 35 km thick. Most of what we know about the deep interior comes from timing earthquake waves: Mohorovičić found the base of the crust in 1909, the S-wave shadow shows the outer core is liquid, and Inge Lehmann inferred the inner core in 1936, later shown to be solid.

Discussion questions

  1. GPS shows the ground beside a locked fault bending by a few millimeters a year. What can those measurements tell scientists about the next earthquake on that fault, and what can't they tell them?
  2. A beach ball gives two possible fault planes. For the 2023 earthquake in Türkiye, the aftershocks showed which one broke. What other evidence could you use, and why does it matter which plane slipped?
  3. Along the North Anatolian Fault, nine of the ten largest earthquakes since 1939 were pushed closer to failure by the ones before them. If you were preparing Istanbul for the next one, how would you use that finding, and what would you tell the public?
  4. In Oklahoma, wastewater disposal from oil and gas operations set off hundreds of earthquakes a year. Who should decide how much earthquake risk an industry may cause, and what data would you want before deciding?
  5. The Parkfield earthquake came eleven years after its forecast window closed. Was the experiment a failure? What did scientists gain by filling the area with instruments before it struck?
  6. Inge Lehmann inferred a whole inner core from a few faint waves that arrived where none should have. What makes an explanation of a place no one can ever visit convincing? What later evidence made hers stronger?

Quiz Choose an answer; it checks itself

1.GPS stations sit on both sides of a locked fault. What do the stations closest to the fault show between earthquakes?

2.The 2004 Sumatra rupture ran more than 1,300 km in about 8 minutes. About how fast did it spread?

3.Seismic moment, the basis of the modern magnitude scale, is calculated from which three things?

4.A station records the S wave from a nearby earthquake 10 seconds after the P wave. About how far away is the earthquake?

5.A 'beach ball' (focal mechanism) is drawn from what?

6.Japan's first tsunami warning in 2011 was based on a magnitude of 7.9; the final magnitude was 9.0. Why was the first number low?

7.By Omori's law, about how often do aftershocks come ten days after a large earthquake, compared with the first day?

8.A magnitude 7.0 earthquake strikes. By Båth's law, what is the largest aftershock likely to be, on average?

9.What shows that the Earth's outer core is liquid?

10.What did Inge Lehmann conclude in 1936 from faint waves recorded in Russia after the 1929 New Zealand earthquake?

Written response

1. Describe the earthquake cycle on a locked fault. Then explain how three kinds of evidence (GPS, slow slip events and trenches dug across faults) let scientists watch it, and why slow slip events beneath Washington State and British Columbia matter for the locked part of the fault above.

What a strong answer includes

On a locked fault the plates keep moving but the two sides stay stuck, so the rock beside the fault bends and stores strain for decades or centuries. When the stress beats the friction, the fault breaks in seconds to minutes and the bent rock snaps back (elastic rebound, Reid, 1910); then the fault locks and begins to load again. GPS receivers anchored to the ground track their positions to within a few millimeters: near a locked fault, the stations closest to it lag behind the plates' motion, which shows the ground bending. Slow slip events, revealed by GPS around 2000, are slips of about an inch (a few centimeters) over a couple of weeks, too slow to feel; beneath Washington State and British Columbia they happen on the deep plate boundary about every 14 months. Trenches dug across faults show layers of soil torn and offset by past earthquakes, and dating the layers shows how often the fault has broken over thousands of years. Slow slip matters because each event adds load to the locked part of the fault above, moving it a little closer to its next earthquake.

2. A large earthquake is recorded at stations around the world. Explain how seismologists find (a) where it is, (b) how the fault moved, and (c) how big it was. Use the 2023 earthquake in Türkiye and the 2011 earthquake off Japan, and explain why the first magnitude for a great earthquake can be too low.

What a strong answer includes

(a) P waves travel fastest and arrive first; S waves arrive later. For a nearby earthquake, each second between them means about 8 km, and the distances from many stations cross at one spot, found within seconds. (b) At some stations the first motion of the ground is a push, at others a pull; mapped around the source, they draw a beach ball that shows the type of faulting and two possible fault planes. For the magnitude 7.8 earthquake in Türkiye in February 2023 it showed a strike-slip break, and the aftershocks along the East Anatolian Fault showed which plane had slipped. (c) The final size is the moment magnitude, calculated from the seismic moment: the area that slipped times the slip times the rock's rigidity. Fast methods give a first number within minutes, but they saturate for the very largest earthquakes: Japan's first tsunami warning in 2011, about three minutes in, used a magnitude of 7.9, raised in steps to 9.0. Great ruptures also keep breaking for minutes (about 8 for Sumatra in 2004), so the whole record is needed before the final number is known.

3. Explain stress transfer, using the North Anatolian Fault in Türkiye. Then use the Parkfield experiment in California to explain why earthquake forecasts give probabilities rather than dates.

What a strong answer includes

When a fault segment breaks, its stress is not only released but moved: the rock just beyond the ends of the rupture is loaded further, pushing the next segment closer to failure. Along the North Anatolian Fault, starting in 1939, a series of large earthquakes marched from east to west over sixty years; a study of the ten largest (magnitude 6.7 or more) found that nine had been brought closer to failure by the ones before them. In August 1999 the march reached Izmit (magnitude 7.6), close to Istanbul, and calculations of the transferred stress raised the odds of a strong earthquake near the city. At Parkfield, on the San Andreas fault, moderate earthquakes struck in 1857, 1881, 1901, 1922, 1934 and 1966, roughly every 22 years. In 1985 scientists forecast the next one before 1993 and filled the area with instruments, but it came in 2004, eleven years after the window closed. Faults are regular enough to forecast but not to keep a timetable, so modern forecasts, such as California's fault-by-fault UCERF3, combine the earthquake cycle, the trench record and stress transfer into probabilities over decades, never a date.

Going deeper University and advanced high school

Locating an earthquake from the S-minus-P time

In the crust, P waves travel at roughly VP = 6 km/s and S waves at roughly VS = 3.5 km/s. Both leave the hypocenter at the same moment, so the delay between their arrivals at a station grows with the distance d: tS − tP = d/VS − d/VP. Solving for the distance gives d = (tS − tP) × VP·VS ÷ (VP − VS).

ProblemShow that, with these speeds, each second of S-minus-P time means about 8 km. Three stations record S-minus-P times of 5.0 s, 8.0 s and 12.0 s for the same nearby earthquake: how far is it from each? Why do you need at least three stations to fix the epicenter on a map, and why does this simple rule work only for nearby earthquakes?

Worked answer

VP·VS ÷ (VP − VS) = (6 × 3.5) ÷ 2.5 = 8.4 km per second of delay, about 8 km. The distances are 5.0 × 8.4 ≈ 42 km, 8.0 × 8.4 ≈ 67 km and 12.0 × 8.4 ≈ 100 km (about 40, 64 and 96 km with the 8 km rule). One distance only says the earthquake lies somewhere on a circle around that station; two circles usually cross at two points; the third circle picks one of them. (Strictly the circles are spheres, and with more stations the depth is found too.) For distant earthquakes, the waves dive deep into the mantle, where both travel faster, and their paths curve, so seismologists use travel-time tables calculated for the whole Earth instead of a single pair of crustal speeds.

Seismic moment, slip and moment magnitude

The seismic moment is M₀ = μ·A·D: the rigidity of the rock μ (about 3 × 1010 Pa for crustal rock), times the area that slipped A, times the average slip D. Moment magnitude is Mw = (2/3)(log₁₀M₀ − 9.1), with M₀ in newton-meters; rearranged, M₀ = 101.5 Mw + 9.1. Hanks and Kanamori's original form, Mw = (2/3)log₁₀M₀ − 10.7 with M₀ in dyne-centimeters, gives values within about 0.03 of this one.

Problem(a) A model fault 50 km long and 20 km wide slips an average of 1.3 m. Calculate M₀ and Mw. (b) A model subduction rupture 500 km long and 200 km wide slips an average of 10 m (use the same μ). Calculate Mw, and how many times larger its moment is than in (a). (c) If each rupture spreads from one end at 2.5 km/s, about how long does each take to break? Compare with the 2004 Sumatra rupture, more than 1,300 km in about 8 minutes.

Worked answer

(a) A = 5 × 104 m × 2 × 104 m = 1 × 109 m², so M₀ = 3 × 1010 × 1 × 109 × 1.3 ≈ 3.9 × 1019 N·m; log₁₀M₀ ≈ 19.59, and Mw = (2/3)(19.59 − 9.1) ≈ 7.0. A magnitude 7 breaks a fault about 50 km long, as in the lecture. (b) A = 5 × 105 m × 2 × 105 m = 1 × 1011 m², so M₀ = 3 × 1010 × 1 × 1011 × 10 = 3 × 1022 N·m; log₁₀M₀ ≈ 22.48, and Mw = (2/3)(22.48 − 9.1) ≈ 8.9. Its moment is 3 × 1022 ÷ 3.9 × 1019 ≈ 770 times larger, which matches the difference of about 1.93 in magnitude: 101.5 × 1.93 ≈ 780. (c) 50 km ÷ 2.5 km/s = 20 s; 500 km ÷ 2.5 km/s = 200 s, more than 3 minutes. Sumatra: 1,300 km ÷ 480 s ≈ 2.7 km/s, so the same rule fits, and the largest earthquakes shake for minutes because their ruptures take minutes to finish.

How many earthquakes of each size: Gutenberg–Richter and Båth

The Gutenberg–Richter law is log₁₀N = a − b·M, where N is the number of earthquakes of magnitude M or more in a region and a span of time, and b is usually close to 1: about ten times as many for each step down. Each step up releases about 101.5 ≈ 32 times more energy. Båth's law says the largest aftershock is on average about 1.2 magnitudes smaller than the main shock; the aftershocks themselves follow the Gutenberg–Richter law too.

Problem(a) Worldwide, about 1,500 earthquakes of magnitude 5 to 5.9 strike in an average year, and about one of magnitude 8 or more. With b = 1, how many of magnitude 6 to 6.9, and of 7 to 7.9, would you expect each year? (b) Treat each of the 1,500 as a magnitude 5.0. How does their total energy compare with one magnitude 8? Can small earthquakes let off the strain that makes great ones? (c) After a magnitude 7.0 main shock, what is the expected largest aftershock, and, with b = 1, about how many aftershocks of magnitude 4.8 or more and 3.8 or more should follow?

Worked answer

(a) Each step up has about a tenth as many: about 150 of magnitude 6 to 6.9 and about 15 of 7 to 7.9 each year, and then about 1.5 of magnitude 8 or more, consistent with 'about one'. (The USGS catalog for 2000 to 2019 averages about 140 and 14 a year.) (b) Three steps is 101.5 × 3 = 104.5 ≈ 32,000 times the energy, so 1,500 magnitude 5.0s release only about 1,500 ÷ 32,000 ≈ 1/20 of one magnitude 8. Counting their real spread from 5.0 to 5.9 raises that to about a quarter, still far less than one great earthquake: the energy is dominated by the largest earthquakes, so small ones cannot relieve the strain. (c) 7.0 − 1.2 = 5.8. If about one aftershock reaches 5.8, then with b = 1 about 10 reach 4.8 or more and about 100 reach 3.8 or more. These are averages; real sequences vary widely.

How aftershocks fade: Omori's law

Omori (1894) found that the rate of aftershocks falls off roughly as one over the time since the main shock. The modified form seismologists use is n(t) = K ÷ (c + t)ᵖ, where n is the number of aftershocks a day, t the time since the main shock in days, c a short time (usually well under a day), and p is close to 1. With p = 1 and c much smaller than t, n(t) ≈ K ÷ t, and the total number of aftershocks between days t₁ and t₂ is K·ln(t₂ ÷ t₁).

ProblemOne day after a large earthquake, aftershocks above a chosen magnitude are coming at a rate of 200 a day (so K = 200). (a) Estimate the rate on day 10 and on day 100. (b) How many aftershocks come between day 1 and day 10, between day 10 and day 100, and between day 100 and day 1,000? (c) What does the answer to (b) mean for a city deciding when people can go back into damaged buildings?

Worked answer

(a) n(10) ≈ 200 ÷ 10 = 20 a day, a tenth of the first day's rate; n(100) ≈ 200 ÷ 100 = 2 a day, a hundredth, as in the lecture. (b) K·ln 10 = 200 × 2.30 ≈ 460 in each interval: about 460 from day 1 to day 10, about 460 from day 10 to day 100, and about 460 from day 100 to day 1,000 (nearly three years). Each tenfold stretch of time brings about as many aftershocks as the one before, only spread more thinly. (c) The sequence fades quickly but lasts a long time, and by Båth's law one of the later aftershocks could still be strong. Damaged buildings should stay empty until they are inspected, and aftershock forecasts are updated for weeks to months, not days. (In real sequences p is often a little above 1, so later stretches are somewhat quieter, and eventually the rate falls back to the region's normal background.)

Shadow zones and the size of the core

Distances around the globe are measured as the angle at Earth's center between the earthquake and the station. S waves never arrive more than about 104° from an earthquake, because they cannot cross the liquid outer core. Direct P waves are missing from about 104° to about 140°: they slow down when they enter the liquid outer core and are bent, then reappear farther on. Earth's radius is about 6,371 km.

Problem(a) Convert 104° into a distance along the surface. (b) Assume, too simply, that waves travel in straight lines. The last S wave to escape the core just grazes it; its straight path from the earthquake to a station 104° away is a chord whose closest point to the center is R·cos(52°). Estimate the radius of the core. (c) The measured radius of the core is about 3,480 km. Real paths curve back toward the surface because waves speed up with depth. Does that make the straight-line estimate too large or too small? (d) Lehmann's faint P waves reached stations in Russia at about 111° and 135°, inside the P-wave shadow. Why did they point to something inside the core?

Worked answer

(a) The circumference is 2π × 6,371 ≈ 40,030 km, so 104° is 104/360 × 40,030 ≈ 11,560 km, more than a quarter of the way around (90°, about 10,000 km), as in the lecture. (b) 6,371 × cos 52° ≈ 6,371 × 0.616 ≈ 3,920 km. (c) Too large. Because waves speed up with depth, a real path between two points sags deeper than the straight chord between them, so the wave that grazes the core and comes up 104° away has reached deeper than the chord's 3,920 km: the core is smaller, about 3,480 km in radius, with its top about 2,890 km down. (d) In a core that was liquid all the way through, P waves would be bent so that none came up between about 104° and 140°. Waves that did arrive there must have been bent back by a region inside the core where they travel faster: Lehmann's inner core, about 1,220 km in radius.

Standards alignment

Next Generation Science Standards

HS-ESS2-1

Develop a model to illustrate how Earth's internal and surface processes operate at different spatial and temporal scales to form continental and ocean-floor features.

In this episode: The earthquake cycle: plate motion of a few centimeters a year stored for decades to centuries and released in seconds to minutes; slow slip; normal, reverse and strike-slip faults; earthquakes along a sinking slab to about 700 km.

HS-ESS2-3

Develop a model based on evidence of Earth's interior to describe the cycling of matter by thermal convection.

In this episode: Seismic evidence for Earth's layers: the Moho, the S-wave shadow and the liquid outer core, Lehmann's solid inner core, and three-dimensional maps of the mantle from millions of wave records.

HS-ESS3-1

Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity.

In this episode: Aftershock laws and the advice to keep damaged buildings empty; stress transfer and Istanbul's raised odds; forecasts as probabilities (Parkfield, California's fault-by-fault forecast).

HS-ESS3-2

Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.

In this episode: Supporting: earthquakes induced by wastewater disposal from oil and gas operations in Oklahoma, and the one-year forecasts the USGS began issuing for them.

HS-PS4-1

Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

In this episode: P, S and surface waves and their speeds; distance from the S-minus-P time; waves speeding up with depth and bending, which revealed the Moho, the shadow zones and the inner core.

Advanced Placement

AP Environmental Science, Unit 4

Earth Systems and Resources: plate tectonics, faults and earthquakes, and Earth's structure.

In this episode: Plate boundaries and fault types, the earthquake cycle, and the layers of the Earth found by seismic waves.

AP Environmental Science, Unit 6

Energy Resources and Consumption: fossil fuels and the environmental effects of extracting them.

In this episode: Supporting: earthquakes induced by oil and gas wastewater disposal in Oklahoma.

University courses

Introductory seismology

The earthquake cycle and elastic rebound; rupture, seismic moment and moment magnitude; locating earthquakes; fault types and focal mechanisms; earthquake statistics (Gutenberg–Richter, Omori, Båth); stress transfer; Earth structure from seismic waves.

In this episode: The lesson covers the main topics of a first seismology course, with worked problems on location, moment magnitude, earthquake counts, aftershock decay and the shadow zones.

Natural hazards

Paleoseismology and recurrence; aftershock hazard; induced seismicity; long-term and one-year earthquake forecasts.

In this episode: Trenches, Omori's and Båth's laws, Oklahoma, Parkfield and California's fault-by-fault forecast.

Transcript The narration, word for word

0:00Introduction

In June 1929, a strong earthquake shook the South Island of New Zealand. In Copenhagen, a seismologist named Inge Lehmann studied the records it left at stations around the world. Faint waves had reached stations in Russia, in a zone where, by every theory of the time, the Earth's core should have kept them out.

She spent years on that puzzle. In 1936, she published her answer. Deep inside the liquid core, there must be a second, inner core, where waves travel faster. That inner core had bent those waves into the forbidden zone. No one has ever been there. An earthquake showed it to her, and by the end of this lecture, you'll see how.

In this lecture, we'll follow an earthquake from start to finish. We'll see how a fault loads and breaks, and how scientists read its waves. Then we'll see how one earthquake leads to the next, and what the waves reveal deep inside the planet.

1:00The Loading

Earth's outer shell is broken into plates that drift a few centimeters a year. Where two meet, the boundary between them is a fault, and most of the time the two sides are stuck together, even as the plates keep moving.

1:13The rock near a stuck fault slowly bends, like a springboard under a growing weight. In 1910, a geologist named Harry Fielding Reid showed this from land surveys made before and after the great San Francisco earthquake of 1906. He called it elastic rebound: decades of slow bending, then a sudden snap back.

1:34That's the earthquake cycle. The fault loads for decades or centuries, breaks in seconds or minutes, then locks and begins to load again. Every large earthquake is one turn of that cycle.

1:48Scientists can watch the loading happen. GPS receivers anchored to the ground track their own position to within a fraction of an inch, a few millimeters. Far from a locked fault, stations ride along with their plates, but the ones close to it lag behind. The ground is bending.

2:06How tightly a fault is stuck is called its coupling. A fully coupled fault stores almost all of the plates' motion, year after year. Off northeastern Japan, the great earthquake of March 2011 showed the plates there had been locked right out to the trench, where the Pacific plate dives under Japan. When that boundary let go, the seafloor shifted, in places by about 50 meters, more than 150 feet.

2:33Not every fault stays perfectly still while it loads. Beneath Washington State and British Columbia, the deep part of the plate boundary slips an inch or so, a few centimeters, over a couple of weeks, about every 14 months. Nobody feels it. GPS revealed these slow slip events around the year 2000. Scientists watch them closely, because each one adds load to the locked part of the fault above.

3:00The cycle leaves a record in the ground. Geologists dig trenches across faults and read the layers of soil like pages in a book. Where a layer is torn and offset, an earthquake broke it. Dating those layers shows how often a fault has broken over thousands of years.

3:20The Break

An earthquake doesn't break the whole fault at once. It starts at one point, the hypocenter, where the stress first beats the friction. From there, the break, or rupture, races outward across the fault, typically at 2 to 3 kilometers every second. A few ruptures even outrun some of the waves they send out.

3:39The larger the earthquake, the longer the break keeps going. A moderate one is over in a few seconds. In the great Sumatra earthquake of 2004, the rupture kept tearing northward for about eight minutes, along more than 1,300 kilometers of fault.

3:56How much fault breaks, and how far it slips, sets an earthquake's size. Scientists multiply three things: the area of fault that broke, how far its two sides slipped, and how stiff the rock is. The result, the seismic moment, is what the modern magnitude scale is built on. Each whole step on the scale means about 32 times more energy released.

4:18Most earthquakes start within about 70 kilometers of the surface. But where one plate dives beneath another, earthquakes follow the sinking plate down, as deep as about 700 kilometers. In 1994, one of the largest deep earthquakes ever recorded struck about 630 kilometers beneath Bolivia. It was felt as far away as Canada.

4:44Reading the Waves

The break sends out waves. P waves squeeze and stretch the rock, like a push along a spring, and they travel fastest. S waves shake it from side to side, and arrive later. Where they reach the surface, surface waves roll outward along the ground. They're the slowest, and they cause much of the damage.

5:03The gap between the P and S waves tells a station how far away the earthquake is. For a nearby one, each second of that gap means about 8 kilometers. Three stations are enough to pin down the spot, and networks of hundreds do it within seconds.

5:19Faults break in three main ways. In a normal fault, the crust stretches and one block drops. In a reverse fault, it's squeezed and one block rides up over the other. In a strike-slip fault, the two sides slide past each other sideways.

5:34The waves themselves reveal which way a fault broke. At some stations, the first motion of the ground is a push; at others, a pull. Mapped around the globe, those pushes and pulls draw a pattern seismologists call a beach ball. In February 2023, a magnitude 7.8 earthquake struck Türkiye. Its beach ball showed a strike-slip break, and its aftershocks traced that break along the East Anatolian Fault.

6:02The size takes longer to pin down. In 2011, Japan's first tsunami warning, about three minutes after the shaking began, was based on a magnitude of 7.9. The fast method maxes out for the very largest earthquakes, and the estimate was raised, in steps, to 9. The quick numbers serve the warnings; the final one comes from the whole record.

6:27That final number is the moment magnitude, worked out from the fault's area and slip. Unlike older scales, it doesn't stop growing for the largest earthquakes. So a great earthquake can show several magnitudes in its first hour, as quick estimates give way to the moment magnitude.

6:45Radar satellites can map a whole earthquake at once. By comparing images taken before and after, they draw bands of color where the ground moved, each band about 3 centimeters, about an inch, of motion toward the satellite. The pattern traces the fault that broke, even where no one can reach it.

7:07Earthquakes Talk to Each Other

Earthquakes follow rules of their own. For each step down in magnitude, there are about ten times as many. Worldwide, there are more than 1,000 earthquakes of magnitude 5 or more in a typical year, but only about one of magnitude 8 or more.

7:22After a large earthquake come aftershocks, and they fade in a regular way, a pattern the seismologist Fusakichi Omori found in Japan in the 1890s. Ten days after the main shock, they come about a tenth as often as on the first day. A hundred days after, about a hundredth.

7:40The largest aftershock is, on average, about 1.2 smaller in magnitude than the main earthquake. So after a magnitude 7, a strong aftershock near magnitude 6 is no surprise, and damaged buildings should stay empty until they're checked.

7:59An earthquake doesn't only release stress. It moves it. Where the broken fault ends, the stress on the rock just beyond it rises, and the next segment is pushed closer to breaking.

8:11The North Anatolian Fault in Türkiye shows it clearly. Starting in 1939, a series of large earthquakes marched along it from east to west over 60 years. A study of the ten largest found that nine had been pushed closer to failure by the ones before them. In August 1999, the march reached Izmit, close to Istanbul, and raised the odds of a strong earthquake beneath Istanbul.

8:38People can unlock faults too. In Oklahoma, oil and gas operations pumped huge volumes of salty wastewater deep underground, raising the pressure inside old faults until they slipped. Earthquakes of magnitude 3 or more jumped from about two a year to more than 900 in 2015. Oklahoma's largest, a magnitude 5.8 near Pawnee in 2016, was felt across several states.

9:07All of this goes into forecasting, which gives odds, never a date. The small town of Parkfield, California, sits on the San Andreas fault. Between 1857 and 1966, six moderate earthquakes struck there, roughly one every 22 years.

9:24In 1985, scientists forecast the next one before 1993, and filled the area with instruments to catch it. It came in 2004, 11 years after the forecast window closed. Faults are regular enough to forecast, but not regular enough to keep a timetable.

9:43So modern forecasts combine the cycle, the record in the trenches, and GPS measurements of the loading, into odds for each fault over the coming decades. After Oklahoma's surge, the U.S. Geological Survey began issuing one-year forecasts for earthquakes caused by people, too.

10:04Seeing Inside the Earth

The same waves that shake the ground travel through the whole planet. Deeper rock is under enormous pressure, and waves generally speed up as they go down. So their paths curve gently back toward the surface, like the shimmer of a mirage over a hot road.

10:19In 1909, a Croatian scientist named Andrija Mohorovičić noticed that waves from a nearby earthquake arrived in two sets. Some had taken a faster path through deeper rock. He had found the bottom of the crust, a boundary still named after him: the Moho.

10:38Far deeper, the waves reveal the core. More than a quarter of the way around the globe from an earthquake, S waves vanish, and they never return. P waves fade out too, then reappear on the far side. S waves can't pass through liquid. The outer core is molten.

10:55And that brings us back to Inge Lehmann. The faint waves in Russia had crossed the liquid core, and been bent by something faster inside it. It was an inner core, with a radius of about 1,200 kilometers. Later work showed it's solid iron and nickel, about as hot as the surface of the Sun. Modern networks map the deep Earth in three dimensions, from millions of these records.

11:19No one has drilled deeper than about 12 kilometers. Most of what we know about everything below comes from timing earthquake waves at stations around the world.

11:32Three Things

So, three things to remember. First, a fault loads for decades, breaks in minutes, and locks again: the earthquake cycle. Second, the waves reveal where a fault broke, how it moved and how big the break was, and each earthquake passes stress on to the next. And third, those same waves have mapped the inside of the planet, down to its solid core.

11:54Every earthquake is a message from inside the planet. Inge Lehmann read one from 1929, and found a world no one will ever visit.

Sources

  1. Lehmann, I. (1936). P′. Publications du Bureau Central Séismologique International, Série A, Travaux Scientifiques, 14, 87–115. As described in: American Physical Society (2023). September 1936: Seismologist Inge Lehmann Concludes That Earth Has an Inner Core. APS News. www.aps.org/apsnews/2023/08/seismologist-lehmann-earth-inner-coreUsed for: The 1929 New Zealand earthquake, the stations in Russia, and Lehmann's 1936 inner core
  2. European Geosciences Union, Seismology Division blog. In Lehmann's Terms: the Story of the Singular Seismic-Wave Spotter. blogs.egu.eu/divisions/sm/?p=10703Used for: Lehmann's records and her interpretation of the waves as bent by a faster inner core
  3. Dziewonski, A. M., & Gilbert, F. (1971). Solidity of the inner core of the Earth inferred from normal mode observations. Nature, 234, 465–466. doi.org/10.1038/234465a0Used for: That the inner core is solid
  4. Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P., & Morard, G. (2013). Melting of iron at Earth's inner core boundary based on fast X-ray diffraction. Science, 340, 464–466. doi.org/10.1126/science.1233514Used for: The inner core's temperature, about 6,000 °C
  5. Lawson, A. C., et al. (1908–1910). The California Earthquake of April 18, 1906: Report of the State Earthquake Investigation Commission. Carnegie Institution of Washington. Vol. 2: H. F. Reid, The Mechanics of the Earthquake (1910). archive.org/details/californiaearthq872caliUsed for: Elastic rebound, from surveys before and after the earthquake
  6. Fujiwara, T., Kodaira, S., No, T., Kaiho, Y., Takahashi, N., & Kaneda, Y. (2011). The 2011 Tohoku-Oki earthquake: Displacement reaching the trench axis. Science, 334, 1240. doi.org/10.1126/science.1211554Used for: The seafloor's shift of about 50 m; the fault locked out to the trench
  7. Dragert, H., Wang, K., & James, T. S. (2001). A silent slip event on the deeper Cascadia subduction interface. Science, 292, 1525–1528. doi.org/10.1126/science.1060152Used for: Slow slip found with GPS
  8. Rogers, G., & Dragert, H. (2003). Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip. Science, 300, 1942–1943. doi.org/10.1126/science.1084783Used for: Slow slip about every 14 months beneath northern Washington and southwestern British Columbia
  9. Brudzinski, M. R., & Allen, R. M. (2007). Segmentation in episodic tremor and slip all along Cascadia. Geology, 35, 907–910. doi.org/10.1130/G23740A.1Used for: How often slow slip recurs along different parts of Cascadia
  10. Sieh, K. E. (1978). Prehistoric large earthquakes produced by slip on the San Andreas Fault at Pallett Creek, California. Journal of Geophysical Research, 83(B8), 3907–3939. doi.org/10.1029/JB083iB08p03907Used for: Trenches dug across faults (paleoseismology)
  11. Bao, H., Ampuero, J.-P., Meng, L., Fielding, E. J., et al. (2019). Early and persistent supershear rupture of the 2018 magnitude 7.5 Palu earthquake. Nature Geoscience, 12, 200–205. doi.org/10.1038/s41561-018-0297-zUsed for: Ruptures faster than the S waves (about 4.1 km/s at Palu)
  12. Lay, T., Kanamori, H., Ammon, C. J., Nettles, M., et al. (2005). The great Sumatra-Andaman earthquake of 26 December 2004. Science, 308, 1127–1133. doi.org/10.1126/science.1112250Used for: The 2004 rupture: more than 1,300 km in about 8 to 10 minutes
  13. Ammon, C. J., Ji, C., Thio, H.-K., Robinson, D., et al. (2005). Rupture process of the 2004 Sumatra-Andaman earthquake. Science, 308, 1133–1139. doi.org/10.1126/science.1112260Used for: The 2004 rupture's length and duration
  14. Hanks, T. C., & Kanamori, H. (1979). A moment magnitude scale. Journal of Geophysical Research, 84(B5), 2348–2350. doi.org/10.1029/JB084iB05p02348Used for: Seismic moment and moment magnitude
  15. Wells, D. L., & Coppersmith, K. J. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the Seismological Society of America, 84(4), 974–1002. doi.org/10.1785/BSSA0840040974Used for: Rupture lengths for magnitudes 5, 7 and 9
  16. U.S. Geological Survey. Earthquake Magnitude, Energy Release, and Shaking Intensity. www.usgs.gov/programs/earthquake-hazards/earthquake-magnitude-energy-release-and-shaking-intensityUsed for: About 32 times the energy for each whole step of magnitude
  17. U.S. Geological Survey. M 8.2 – Bolivia, June 9, 1994. Event page. earthquake.usgs.gov/earthquakes/eventpage/usp0006dzcUsed for: The deep Bolivia earthquake: magnitude, depth of about 631 km, felt as far as Toronto
  18. U.S. Geological Survey. Focal mechanisms, or 'beachballs'. www.usgs.gov/programs/earthquake-hazards/focal-mechanisms-or-beachballsUsed for: Fault types and focal mechanisms; the two possible fault planes
  19. U.S. Geological Survey. M 7.8 – Pazarcık earthquake, Kahramanmaraş earthquake sequence, Türkiye, February 6, 2023. Event page. earthquake.usgs.gov/earthquakes/eventpage/us6000jllzUsed for: The 2023 earthquake's magnitude and strike-slip mechanism
  20. Reitman, N. G., Tan, M. M., Bürgi, P., Hatem, A. E., DuRoss, C. B., & Briggs, R. W. (2026). High-resolution surface deformation and slip distribution observations for the 2023 Kahramanmaraş, Türkiye, earthquake sequence help constrain the rupture process. Bulletin of the Seismological Society of America. pubs.usgs.gov/publication/70277053Used for: The rupture on the East Anatolian Fault
  21. Japan Meteorological Agency (2013). Lessons learned from the tsunami disaster caused by the 2011 Great East Japan Earthquake and improvements in JMA's tsunami warning system. www.data.jma.go.jp/eqev/data/en/tsunami/LessonsLearned_Improvements_brochure.pdfUsed for: The first tsunami warning at 14:49, about three minutes in, based on magnitude 7.9; saturation
  22. Hoshiba, M., Iwakiri, K., Hayashimoto, N., Shimoyama, T., et al. (2011). Outline of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0): Earthquake Early Warning and observed seismic intensity. Earth, Planets and Space, 63, 547–551. doi.org/10.5047/eps.2011.05.031Used for: How the first magnitude estimates grew
  23. IRIS / EarthScope Consortium. Educational animations and classroom resources, including 'Seismic shadow zones and P waves'. www.iris.edu/hq/inclassUsed for: P, S and surface waves; distance from the S-minus-P time; curving wave paths; the shadow zones
  24. U.S. Geological Survey. ANSS Comprehensive Earthquake Catalog (ComCat): earthquake search. earthquake.usgs.gov/earthquakes/searchUsed for: Yearly numbers of earthquakes of each magnitude (Gutenberg–Richter)
  25. Utsu, T., Ogata, Y., & Matsu'ura, R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 43, 1–33. doi.org/10.4294/jpe1952.43.1Used for: Omori's law (1894) and its modified form
  26. Båth, M. (1965). Lateral inhomogeneities of the upper mantle. Tectonophysics, 2, 483–514. doi.org/10.1016/0040-1951(65)90003-XUsed for: Båth's law: the largest aftershock about 1.2 magnitudes smaller
  27. Stein, R. S., Barka, A. A., & Dieterich, J. H. (1997). Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering. Geophysical Journal International, 128, 594–604. pubs.usgs.gov/publication/70019873Used for: Stress transfer: nine of ten large ruptures brought closer to failure by those before
  28. Parsons, T., Toda, S., Stein, R. S., Barka, A., & Dieterich, J. H. (2000). Heightened odds of large earthquakes near Istanbul: An interaction-based probability calculation. Science, 288, 661–665. pubs.usgs.gov/publication/70022614Used for: Istanbul's raised odds after Izmit, 1999
  29. U.S. Geological Survey. Myths and Misconceptions About Induced Earthquakes. www.usgs.gov/programs/earthquake-hazards/myths-and-misconceptions-about-induced-earthquakesUsed for: Oklahoma's earthquakes linked to wastewater disposal; magnitude 3 or more, from about two a year to more than 900 in 2015
  30. U.S. Geological Survey. M 5.8 – 14 km NW of Pawnee, Oklahoma, September 3, 2016. Event page. earthquake.usgs.gov/earthquakes/eventpage/us10006jxsUsed for: The Pawnee earthquake
  31. Petersen, M. D., et al. (2016). 2016 one-year seismic hazard forecast for the Central and Eastern United States from induced and natural earthquakes. U.S. Geological Survey Open-File Report 2016–1035. pubs.usgs.gov/publication/ofr20161035Used for: One-year forecasts for earthquakes caused by people
  32. Bakun, W. H., Aagaard, B., Dost, B., Ellsworth, W. L., et al. (2005). Implications for prediction and hazard assessment from the 2004 Parkfield earthquake. Nature, 437, 969–974. doi.org/10.1038/nature04067Used for: Parkfield: the earthquakes of 1857–1966, the 1985 forecast, and the 2004 earthquake
  33. Field, E. H., & 2014 Working Group on California Earthquake Probabilities (2015). UCERF3: A New Earthquake Forecast for California's Complex Fault System. U.S. Geological Survey Fact Sheet 2015–3009. pubs.usgs.gov/fs/2015/3009Used for: Fault-by-fault forecasts for California over decades
  34. Dziewonski, A. M. (1984). Mapping the lower mantle: Determination of lateral heterogeneity in P velocity up to degree and order 6. Journal of Geophysical Research, 89(B7), 5929–5952. doi.org/10.1029/JB089iB07p05929Used for: Three-dimensional maps of the mantle from wave travel times (seismic tomography)

Images in the episode: USGS, NOAA and NASA (public domain), with maps from NASA/USGS Landsat via NASA GIBS; animations by EarthWatch 24-7. Full credits: earthwatch247.com/credits.html.

Cite this lesson

EarthWatch 24-7. (2026). Earthquakes 201: Inside an earthquake [Video lesson]. Earth Explained: Earthquakes 201. https://earthwatch247.com/learn/earthquakes-201/

Answer key

  1. C. The stations far from the fault drift with their plates, but those closest to a locked fault lag behind: the rock is bending and storing strain, the loading half of the earthquake cycle.
  2. A. 1,300 km ÷ (8 × 60 s) = 1,300 km ÷ 480 s ≈ 2.7 km a second, within the typical rupture speed of 2 to 3 km a second. The longer the fault that breaks, the longer the shaking lasts.
  3. D. M₀ = rigidity × area × slip (Hanks and Kanamori, 1979). The swing on a single seismogram was the basis of older scales, which stop growing for the largest earthquakes.
  4. B. For a nearby earthquake, each second between the P and S arrivals means about 8 km: 10 × 8 ≈ 80 km. The distances from three or more stations cross at the epicenter.
  5. A. Pushes and pulls mapped around the source show how the fault moved. For the magnitude 7.8 earthquake in Türkiye in 2023, the beach ball showed a strike-slip break.
  6. C. Fast methods serve the warnings but max out for the largest earthquakes. The moment magnitude, from the fault's area and slip, does not, so the estimate was raised in steps to 9.0 (the USGS gives 9.1).
  7. B. The rate falls roughly as one over the time since the main shock: ten days on, about a tenth; a hundred days on, about a hundredth.
  8. D. The largest aftershock is on average about 1.2 magnitudes smaller than the main shock: 7.0 − 1.2 = 5.8. That is why damaged buildings should stay empty until they are checked.
  9. C. S waves cannot pass through liquid, so the outer core casts an S-wave shadow; P waves can, and reappear on the far side. No hole has gone deeper than about 12 km.
  10. A. A faster inner core had bent the waves into the zone where the core should have kept them out. That the inner core, about 1,220 km in radius, is solid was shown later.

Written response

  1. On a locked fault the plates keep moving but the two sides stay stuck, so the rock beside the fault bends and stores strain for decades or centuries. When the stress beats the friction, the fault breaks in seconds to minutes and the bent rock snaps back (elastic rebound, Reid, 1910); then the fault locks and begins to load again. GPS receivers anchored to the ground track their positions to within a few millimeters: near a locked fault, the stations closest to it lag behind the plates' motion, which shows the ground bending. Slow slip events, revealed by GPS around 2000, are slips of about an inch (a few centimeters) over a couple of weeks, too slow to feel; beneath Washington State and British Columbia they happen on the deep plate boundary about every 14 months. Trenches dug across faults show layers of soil torn and offset by past earthquakes, and dating the layers shows how often the fault has broken over thousands of years. Slow slip matters because each event adds load to the locked part of the fault above, moving it a little closer to its next earthquake.
  2. (a) P waves travel fastest and arrive first; S waves arrive later. For a nearby earthquake, each second between them means about 8 km, and the distances from many stations cross at one spot, found within seconds. (b) At some stations the first motion of the ground is a push, at others a pull; mapped around the source, they draw a beach ball that shows the type of faulting and two possible fault planes. For the magnitude 7.8 earthquake in Türkiye in February 2023 it showed a strike-slip break, and the aftershocks along the East Anatolian Fault showed which plane had slipped. (c) The final size is the moment magnitude, calculated from the seismic moment: the area that slipped times the slip times the rock's rigidity. Fast methods give a first number within minutes, but they saturate for the very largest earthquakes: Japan's first tsunami warning in 2011, about three minutes in, used a magnitude of 7.9, raised in steps to 9.0. Great ruptures also keep breaking for minutes (about 8 for Sumatra in 2004), so the whole record is needed before the final number is known.
  3. When a fault segment breaks, its stress is not only released but moved: the rock just beyond the ends of the rupture is loaded further, pushing the next segment closer to failure. Along the North Anatolian Fault, starting in 1939, a series of large earthquakes marched from east to west over sixty years; a study of the ten largest (magnitude 6.7 or more) found that nine had been brought closer to failure by the ones before them. In August 1999 the march reached Izmit (magnitude 7.6), close to Istanbul, and calculations of the transferred stress raised the odds of a strong earthquake near the city. At Parkfield, on the San Andreas fault, moderate earthquakes struck in 1857, 1881, 1901, 1922, 1934 and 1966, roughly every 22 years. In 1985 scientists forecast the next one before 1993 and filled the area with instruments, but it came in 2004, eleven years after the window closed. Faults are regular enough to forecast but not to keep a timetable, so modern forecasts, such as California's fault-by-fault UCERF3, combine the earthquake cycle, the trench record and stress transfer into probabilities over decades, never a date.

Going deeper

  1. Locating an earthquake from the S-minus-P time: VP·VS ÷ (VP − VS) = (6 × 3.5) ÷ 2.5 = 8.4 km per second of delay, about 8 km. The distances are 5.0 × 8.4 ≈ 42 km, 8.0 × 8.4 ≈ 67 km and 12.0 × 8.4 ≈ 100 km (about 40, 64 and 96 km with the 8 km rule). One distance only says the earthquake lies somewhere on a circle around that station; two circles usually cross at two points; the third circle picks one of them. (Strictly the circles are spheres, and with more stations the depth is found too.) For distant earthquakes, the waves dive deep into the mantle, where both travel faster, and their paths curve, so seismologists use travel-time tables calculated for the whole Earth instead of a single pair of crustal speeds.
  2. Seismic moment, slip and moment magnitude: (a) A = 5 × 104 m × 2 × 104 m = 1 × 109 m², so M₀ = 3 × 1010 × 1 × 109 × 1.3 ≈ 3.9 × 1019 N·m; log₁₀M₀ ≈ 19.59, and Mw = (2/3)(19.59 − 9.1) ≈ 7.0. A magnitude 7 breaks a fault about 50 km long, as in the lecture. (b) A = 5 × 105 m × 2 × 105 m = 1 × 1011 m², so M₀ = 3 × 1010 × 1 × 1011 × 10 = 3 × 1022 N·m; log₁₀M₀ ≈ 22.48, and Mw = (2/3)(22.48 − 9.1) ≈ 8.9. Its moment is 3 × 1022 ÷ 3.9 × 1019 ≈ 770 times larger, which matches the difference of about 1.93 in magnitude: 101.5 × 1.93 ≈ 780. (c) 50 km ÷ 2.5 km/s = 20 s; 500 km ÷ 2.5 km/s = 200 s, more than 3 minutes. Sumatra: 1,300 km ÷ 480 s ≈ 2.7 km/s, so the same rule fits, and the largest earthquakes shake for minutes because their ruptures take minutes to finish.
  3. How many earthquakes of each size: Gutenberg–Richter and Båth: (a) Each step up has about a tenth as many: about 150 of magnitude 6 to 6.9 and about 15 of 7 to 7.9 each year, and then about 1.5 of magnitude 8 or more, consistent with 'about one'. (The USGS catalog for 2000 to 2019 averages about 140 and 14 a year.) (b) Three steps is 101.5 × 3 = 104.5 ≈ 32,000 times the energy, so 1,500 magnitude 5.0s release only about 1,500 ÷ 32,000 ≈ 1/20 of one magnitude 8. Counting their real spread from 5.0 to 5.9 raises that to about a quarter, still far less than one great earthquake: the energy is dominated by the largest earthquakes, so small ones cannot relieve the strain. (c) 7.0 − 1.2 = 5.8. If about one aftershock reaches 5.8, then with b = 1 about 10 reach 4.8 or more and about 100 reach 3.8 or more. These are averages; real sequences vary widely.
  4. How aftershocks fade: Omori's law: (a) n(10) ≈ 200 ÷ 10 = 20 a day, a tenth of the first day's rate; n(100) ≈ 200 ÷ 100 = 2 a day, a hundredth, as in the lecture. (b) K·ln 10 = 200 × 2.30 ≈ 460 in each interval: about 460 from day 1 to day 10, about 460 from day 10 to day 100, and about 460 from day 100 to day 1,000 (nearly three years). Each tenfold stretch of time brings about as many aftershocks as the one before, only spread more thinly. (c) The sequence fades quickly but lasts a long time, and by Båth's law one of the later aftershocks could still be strong. Damaged buildings should stay empty until they are inspected, and aftershock forecasts are updated for weeks to months, not days. (In real sequences p is often a little above 1, so later stretches are somewhat quieter, and eventually the rate falls back to the region's normal background.)
  5. Shadow zones and the size of the core: (a) The circumference is 2π × 6,371 ≈ 40,030 km, so 104° is 104/360 × 40,030 ≈ 11,560 km, more than a quarter of the way around (90°, about 10,000 km), as in the lecture. (b) 6,371 × cos 52° ≈ 6,371 × 0.616 ≈ 3,920 km. (c) Too large. Because waves speed up with depth, a real path between two points sags deeper than the straight chord between them, so the wave that grazes the core and comes up 104° away has reached deeper than the chord's 3,920 km: the core is smaller, about 3,480 km in radius, with its top about 2,890 km down. (d) In a core that was liquid all the way through, P waves would be bent so that none came up between about 104° and 140°. Waves that did arrive there must have been bent back by a region inside the core where they travel faster: Lehmann's inner core, about 1,220 km in radius.