Why does the next town shake harder in the same earthquake?
― Soft ground swells the shaking
After an earthquake, the news shows a list of seismic intensities. Often the next town, at almost the same distance from the epicenter, registers one grade higher. The difference isn't down to buildings or luck — it's the ground beneath your feet. A soft layer of soil can swell shaking arriving from below into something much bigger.
At night, your phone buzzes with an earthquake alert. The shaking stops quickly. You turn on the TV, and a map shows intensity numbers.
Your town registers a "weak 5". But the town on the hill across the river shows only a "4". The distance from the epicenter is almost identical.
Same earthquake, almost the same distance — so why does the shaking differ? The answer lies in what's "inside" the ground.
Only two reasons make shaking bigger
Earthquake shaking travels up from deep, hard bedrock. When it enters soft soil, it slows down. That slowed momentum gets squeezed into a narrower space, so the width of the shaking grows.
Soft soil layers, like a swing, tend to shake at a fixed rhythm. If that rhythm is present in the earthquake's shaking, the shaking keeps building. This is called resonance.
Neither of these has anything to do with the size of the earthquake itself. The same shaking, received by different ground, can end up many times bigger at the surface.
Shaking "swells" in soft ground
Look at Figure 1. On the left is a town where hard bedrock runs all the way to the surface. On the right is a town where a soft layer of sand or mud sits on top of the same hard bedrock. Both receive the same size of shaking from below.
The speed shaking travels at depends heavily on how hard the ground is: roughly 700 m/s in hard bedrock, versus roughly 100 m/s in soft mud. Where the shaking slows down, later shaking catches up with earlier shaking. The momentum being carried piles up and compresses.
It's the same mechanism as waves growing taller as they reach shallow water offshore. Waves also slow down in shallow water, and grow taller as a result. In the calculation behind Figure 1, depending on how soft the layer is, the width of the shaking can grow to roughly 3 times as much.
When the width of the shaking triples, the seismic intensity rises by roughly one grade. That's because intensity is defined on a scale that climbs by a fixed step each time the shaking doubles, then quadruples, and so on. The "one grade higher in the next town" from the opening scene is almost exactly this amount of difference.
A soil layer grows shaking at its own favourite rhythm
Soft soil layers have another troublesome property: the whole layer tends to shake at a fixed rhythm. For a layer 20 m thick with a shaking speed of 100 m/s, the estimated rhythm is about 0.8 seconds per round trip.
Earthquake shaking is a mix of many rhythms, from fast to slow. If the soil layer's favourite rhythm happens to be among them, the shaking builds up — just like pushing a swing at exactly the right moment. Look at the left side of Figure 2. The ground surface at the top of the layer shakes the most, while the boundary with the bedrock barely moves at all.
Buildings have their own favourite rhythms too. A rough rule of thumb is "storeys × 0.1 seconds," so an 8-storey building has a period of about 0.8 seconds. When the ground's rhythm matches a building's, resonance stacks on resonance. In the 1985 Mexico earthquake, mid-rise buildings on ground built over a former lakebed are reported to have collapsed in clusters in the capital, more than 300 km from the epicenter.
In soft soil layers, shaking doesn't just get bigger — it also tends to last longer. The shaking bounces back and forth within the layer and struggles to escape. So if you feel "ours shook longer" after an earthquake, that may not just be your imagination.
It's said to be common on land reclaimed from the sea or a lake, low flat ground along rivers, former marshes or paddy fields, and valleys filled in during development. All of these are relatively young ground, made of sand and mud carried and deposited by water.
So what should we do?
Residents can't change how hard the ground is. But you can check in advance whether your own ground shakes easily. Knowing that lets you set priorities for preparation.
- Protect your head first when it shakesGet under a desk, or shield your head with a bag or cushion, and stay low. Move only after the shaking stops.
- Sleep where furniture can't fall on youHouses on ground that shakes more easily get their furniture shaken harder. Keep tall furniture away from where you sleep.
- Check how "shake-prone" your area is, as a familyYou can check your ground's softness using your municipality's hazard map or the national National Research Institute for Earth Science and Disaster Resilience map.
Secure furniture to the walls, and decide in advance on a "safe spot" in your home, away from windows and hanging lights. Once the shaking stops, check for fires, and call 119 if anyone is injured. If the building feels tilted or you notice cracks, don't force yourself to stay — evacuate. Also follow your municipality's evacuation instructions.
Summary
Even in the same earthquake, what determines the shaking at the surface is the ground underfoot. A soft layer squeezes the slowed shaking, swelling its width to roughly 3 times, and also grows the shaking at a rhythm set by the layer's thickness. That's why, even at the same distance from the epicenter, the intensity can differ by a full grade.
How big the shaking is isn't decided by the earthquake alone.
Half of it is decided by the ground under your own feet.
How shaking arrives from below is explained in Why does the "rattle" of an earthquake always come before the "sway"?, and how soft ground can further collapse is covered in Why does liquefaction turn the ground into "water"? The mechanism of waves rising in shallow water is shared with our tsunami article, and the mechanism of shaking building up when rhythms match is shared with our swing article.
- Put a jelly (or pudding) turned out of its cup onto a plate. Lining up a firm jelly and a soft one side by side makes the difference easy to see.
- Shake the plate gently from side to side, slowly. Check that the top of the jelly moves more than the plate does.
- Gradually speed up the rhythm of shaking. Find the rhythm at which the top of the jelly shakes the most. The softer the jelly, the slower the rhythm should be for the biggest shake.
The plate is the "bedrock," and the jelly is the "soft layer." You can also try how a taller jelly has a slower favourite rhythm.
Want to know more? ― Terms, formulas, and textbook linksWe mark clearly which level each part belongs to, from middle-school science to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school Physics or Earth Science
- HS+Advanced high-school content, or textbook sidebar material
- Univ.Not taught in high school — university specialist content (seismology, earthquake engineering)
- ResearchNot yet settled even as university "accepted theory" — an active research topic
MSTerms: this phenomenon has a name
- Site amplification: shaking being made bigger by soft soil layers near the surface. The amplification factor is called the "surface soil amplification factor," and published as maps.
- Natural period: the time for one round trip of the rhythm a soil layer or building shakes at most easily.
- Resonance: when incoming shaking's rhythm matches the natural period, and the shaking grows large.
MSHSChecking with formulas: how much does the width of the shaking grow?
We assume the momentum carried by the shaking (the flow of energy) isn't lost across the boundary. Then, the slower and softer the layer, the more the width of the shaking must grow to carry the same momentum. From this idea we estimate the amplification factor for the shaking's width, and the layer's favourite period.
| In symbols | As ÷ Ab ＝ √( ρb × Vb ÷ ( ρs × Vs ) ) ／ T ＝ 4 × H ÷ Vs |
| In words | Amplification factor of shaking width = the square root of (bedrock density × bedrock speed) ÷ (layer density × layer speed). Favourite period = 4 × layer thickness ÷ layer speed |
| Where it comes from | The first comes from conservation of the energy flow carried by the shaking (proportional to density × speed × width squared) across the boundary. The second comes from resonance occurring when the layer's thickness equals exactly one quarter of the shaking's wavelength. |
| Symbol | Meaning and unit |
|---|---|
| As, Ab | Width of shaking in the soil layer, and in the bedrock |
| ρb, ρs | Density of bedrock, soil layer (unit: g/cm³) |
| Vb, Vs | Speed of shear-wave shaking through bedrock, soil layer (unit: m/s) |
| H | Thickness of the soft soil layer (unit: m) |
| T | Favourite period of the layer (unit: seconds) |
| Bedrock density and speed (typical) | 2.0 g/cm³, 700 m/s |
| Soft mud layer density and speed (typical) | 1.6 g/cm³, 100 m/s |
| Layer thickness (example) | 20 m |
| Rule of thumb for building period | 0.1 s per storey |
| Bedrock "density × speed" | 2.0 × 700 ＝ 1400 |
| Layer "density × speed" | 1.6 × 100 ＝ 160 |
| Ratio | 1400 ÷ 160 ＝ 8.75 |
| Amplification factor for shaking width | Square root of 8.75 is about 2.96. Roughly ×3 |
| Rise in intensity (log₁₀ of 3 is about 0.48) | 2 × 0.48 ＝ 0.96 |
| Numerator of the period | 4 × 20 ＝ 80 |
| Layer's favourite period | 80 ÷ 100 ＝ 0.8 s |
| Storeys of a matching building | 0.8 ÷ 0.1 ＝ 8 storeys |
In a soft mud layer, the width of the shaking grows to roughly 3 times that in bedrock — about one grade of intensity. A 20 m-thick layer tends to shake at a rhythm of 0.8 seconds, which can resonate with an 8-storey-ish building. Real amplification factors vary with the layering and the strength of the shaking.
HSHS+Seen as a wave property
HSEarthquake shaking is also a wave. Wave speed is "wavelength ÷ period," and the period doesn't change across a boundary. So shaking entering a slower layer compresses into a shorter wavelength. When a standing wave forms with a node at the bottom of a layer of thickness H and an antinode at the surface, the layer's thickness is one quarter of the wavelength. That's the origin of the period formula 4H÷Vs — the same form as resonance in an air column with one closed end.
HS+Seismic intensity is set by the "instrumental intensity," calculated from acceleration recorded by seismometers. Instrumental intensity is defined to increase by roughly twice the common logarithm of the acceleration, so it rises by about 0.6 when shaking doubles, and by about 1 when it triples.
Univ.Impedance ratio and the ground's transfer function
The product of density × speed is called "seismic impedance" in seismology — the same quantity as acoustic impedance in sound. The square-root formula in the main text is an approximation for when properties change gradually. For a single layer with a sharp boundary, the surface shaking is described by a "transfer function" whose amplification factor varies with period. The factor peaks at the resonant period, and its height is set by the impedance ratio and the layer's damping. In practice, the natural period is estimated from records at surface and underground seismometers, or from the horizontal-to-vertical spectral ratio (H/V spectral ratio) of ambient microtremors. The 1985 Mexico earthquake is a textbook example of long-period site amplification caused by lakebed sediments.
📖 For the derivation of the formulas and further detail: Wikipedia (Japanese): "Acoustic impedance" ／ Wikipedia (Japanese): "1985 Mexico earthquake"
ResearchWhat's still not fully understood
- Strong shaking softens the soil. As shaking gets stronger, soil grains shift against each other, making the layer even softer and its period longer. How accurately this "nonlinear" behaviour can be predicted is still an active research question.
- Shaking piles up at basin edges. In deep sedimentary basins that form plains, shaking bent at the edges can overlap, and damage is said to sometimes concentrate in bands. Predicting where this overlap occurs requires detailed surveys of the underground shape.
- Resolution limits of hazard maps. Published shake-proneness maps are averaged over blocks of a few hundred metres. Even within the same block, a filled-in valley and the original ridge can shake differently, making house-by-house assessment a difficult challenge.
So the content of this article, too, is "the explanation as currently understood." In particular, treat the amplification numbers as simplified estimates of the soil's properties.
Links to the curriculum (by level)
| Level | Subject/unit | Where in this article |
|---|---|---|
| MS | Science, "Changes in the land (earthquakes)" | Seismic intensity, shaking travelling up from below |
| HS | Physics "Waves" / Earth Science "Earthquakes" | Wavelength and period, quarter-wavelength resonance |
| HS+ | Definition of instrumental intensity (common logarithm) | Roughly one grade for a ×3 increase in shaking |
| Univ. | Seismology / earthquake engineering | Seismic impedance, transfer function, H/V spectral ratio |
| Research | Strong-motion seismology | Soil nonlinearity, concentration of shaking at basin edges |
| ― | Everyday life | Checking your ground, securing furniture, choosing where to sleep |
- National Research Institute for Earth Science and Disaster Resilience (防災科学技術研究所), "J-SHIS Seismic Hazard Station" (map of surface soil amplification factors)
- Japan Meteorological Agency website (防災科学技術研究所) (explanation of seismic intensity and instrumental intensity)
- Wikipedia (Japanese): "1985 Mexico earthquake"
- Hiroaki Yamanaka (ed.), "The Science of Ground Shaking in Earthquakes — The Emerging Picture of Strong Ground Motion" (地震の揺れを科学する ― みえてきた強震動の姿), University of Tokyo Press
- Cabinet Office (内閣府), "National Map of Ground Shake-Proneness" (地盤のゆれやすさ全国マップ)
※This article is a general-audience science explainer. The figures given are approximations intended to aid understanding of the underlying mechanism. For actual evacuation decisions or judgments about building safety, please follow the instructions of your municipality, fire department, local authorities, and information released by the Japan Meteorological Agency.