Seisma: Gutenberg–Richter Law
Mechanics, Chaos & Fluids arc, page 109 of 193. Back to The Pixelated Physics Universe
Who they are
Seisma strikes the fault line and sends out a staircase of cracks: many small ones, few large ones, each step rarer than the last.
Seisma is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
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.
$$ \begin{gathered} \log_{10} N = a - b\,M \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $N$ | number of earthquakes of magnitude M or more (in a region and time window) | 1 |
| $M$ | earthquake magnitude | 1 |
| $a$ | productivity constant of the region and window | 1 |
| $b$ | b-value, usually near 1 (about 0.8 to 1.2) | 1 |
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.
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Gutenberg & Richter (1944) Frequency of earthquakes in California, Bull. Seismol. Soc. Am. 34, 185
- USGS, Earthquake Magnitude, Energy Release, and Shaking Intensity
Crossovers
Seisma meets Ekmara (Ekman Spiral). Ekmara's spiral moves the ocean's surface waters. Seisma's quakes move the crust. Both are Earth sciences that use physics to read a planet in motion.
Seisma meets Flickermoth (1/f Pink Noise). Seisma's earthquakes follow a power law in size, and Flickermoth's noise follows a power law in frequency. Both have been linked to self-organised criticality, though that link is debated for each.
Wear the lore
Concept keywords: Gutenberg–Richter Law, Seisma, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics