• White Seisma physics T-shirt, front view (flat-lay mockup), view 1

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Seisma

The Gutenberg–Richter Law Physics

\[\log_{10} N = a - b\,M\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Seisma strikes the fault line and sends out a staircase of cracks: many small ones, few large ones, each step rarer than the last.

The Physics

Beno Gutenberg and Charles Richter found in 1944, for California earthquakes, that the number of quakes at or above a magnitude falls off exponentially with magnitude. The constant a sets a region's overall activity; the slope b is typically close to 1, so each step up in magnitude is about ten times rarer.

log₁₀ N = a − bM

  • N: number of quakes of magnitude M or more
  • M: magnitude
  • a: regional activity constant
  • b: slope, usually near 1

Gutenberg & Richter, “Frequency of earthquakes in California”, Bull. Seismol. Soc. Am. 34, 185 (1944).

Honest caveat: b is not universal: about 0.8–1.2 is a common range for tectonic quakes, and volcanic or induced swarms can differ more. The power law is often linked to self-organised criticality, but that is debated.

On the shirt

Front: Seisma, the pixel-art character, with “TEN TIMES RARER”. Back: the Gutenberg–Richter law, the ten-times-rarer rule, the regional range of b and the 1944 paper. Printed on a unisex tee.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Dla skali: rozmiar M ma 20 in (50.80 cm) szerokości, czyli około 3.143 × 1034 długości Plancka (lP = 1.616255 × 10−35 m). Miarka krawiecka jest szybsza.

Measurements in inches, ±1.5 in tolerance.

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Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

I keep the tally of the shaking Earth. Small quakes are everywhere; big ones are rare, and the ratio follows a rule.

In 1944 Beno Gutenberg and Charles Richter counted California's earthquakes and found that the logarithm of the number at or above a magnitude M falls in a straight line: log₁₀ N = a − bM. With b = 1, each step up in magnitude is ten times rarer. There are about ten times as many magnitude-4 quakes as magnitude-5 ones.

The b-value is not universal. It varies from region to region, usually between about 0.8 and 1.2. Why nature follows a power law here, self-organised criticality or something else, is still debated.

Equations

\[\log_{10} N = a - b\,M\]
SymbolMeaningUnit
\(N\) number of earthquakes of magnitude M or more (in a region and time window) \(\mathrm{1}\)
\(M\) earthquake magnitude \(\mathrm{1}\)
\(a\) productivity constant of the region and window \(\mathrm{1}\)
\(b\) b-value, usually near 1 (about 0.8 to 1.2) \(\mathrm{1}\)

Sources

  1. Gutenberg & Richter (1944) Frequency of earthquakes in California, Bull. Seismol. Soc. Am. 34, 185
  2. USGS, Earthquake Magnitude, Energy Release, and Shaking Intensity

Field notes

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