The logarithmic ruler of earthquakes. One step up the scale is ten times the ground motion on the seismograph — and about thirty-two times the energy released. The number is small; the range it hides is enormous. Down the center, data flows: two magnitudes go in, the engine computes the ratios, the proven jump comes out. The blue team builds and defends it; the red team tries to break it.
source Richter, C. F., An instrumental earthquake magnitude scale, Bull. Seismol. Soc. Am. 25 (1), 1–32 (1935) — doi:10.1785/BSSA0250010001. Rendered, not quoted.
A magnitude is not the shaking itself — it is the logarithm of the shaking:
M = log₁₀(A) − log₁₀(A₀) = log₁₀(A / A₀), where A is the maximum trace amplitude and A₀ is a fixed reference (Richter's standard Wood–Anderson seismograph, epicentre-corrected to 100 km).
Because the ruler is logarithmic, a whole unit is a factor of 10 in amplitude and 10^1.5 ≈ 31.6 in energy. Live table for the current pair:
| M | amplitude × | energy × |
|---|
Ten times per step — Richter 1935. The magnitude M = log₁₀(A/A₀), ten times the amplitude and ~31.6× the energy per whole unit, is the logarithmic ruler laid against the-seismic-waves an earthquake radiates.
The waves are the thing measured; this scale is the ruler. P and S arrivals fix where and when; the peak amplitude of that same record, fed through the log, fixes how big. Each sphere is the next one's premise.
The blue team's live check: recompute the amplitude and energy ratios from the definition and confirm the fixed points — 10× per unit of amplitude, 31.6× per unit of energy, a billion-fold from M3 to M9. If red makes the scale linear, this badge is where it shows.
Feed the engine two magnitudes: a reference quake and a larger event. The whole scale is one definition applied twice:
| quantity | law | per +1 unit |
|---|---|---|
| amplitude | A ∝ 10^M | × 10 |
| energy | E ∝ 10^(1.5·M) | × 31.6 |
| energy (+2) | 10^(1.5·2) | × 1000 |
The seismograph gives amplitude A; the log gives M; the Gutenberg–Richter relation log₁₀E ≈ 1.5M + 4.8 gives the energy. That is the whole game — and it is what you feed the panel below.
Two seismograms drawn to the same scale — the reference trace is smaller by exactly the amplitude ratio. A one-unit gap already flattens the smaller quake to a tenth.
Move either slider — every ratio is computed from the log definition on the spot, never looked up.
What the machine produces, proven from M = log₁₀(A/A₀): one unit is 10× the amplitude and ≈31.6× the energy; two units is 1000× the energy; and from M3 to M9 the energy grows a billion-fold (10^9). Small numbers, gigantic ranges.
The blue team's witness (left) confirms these ratios live; the red team (right) tries to flatten the scale to a line.
For great earthquakes seismologists use moment magnitude Mw (Kanamori, 1977), built from the physical seismic moment, which does not saturate. Mw is tuned to agree with Richter in the mid-range — so the log-of-amplitude idea survives, but "the Richter scale" is no longer the working instrument for the largest events. Saturation cap is a modelling AMBER — band-dependent, not a single sharp value.
"The Richter scale runs from 1 to 10." Cut. It is open-ended — the log has no ceiling. The largest recorded is the 1960 Chile quake at Mw ≈ 9.5; nothing forbids a 10.
"Each step is ten times stronger." Corrected. Ten times the amplitude, but ~31.6× the energy. "Stronger" hides which one — the engine reports both.
"Richter measures the energy released." Cut. It measures the log of a trace amplitude; energy is a derived quantity, 10^(1.5M), not the raw reading.
"Modern quakes are rated on the Richter scale." Kept, corrected. Headlines say Richter; agencies report Mw — pinned to agree in the middle by design.
The red team's move: make the scale linear — let amplitude and energy scale as M itself, so a magnitude 6 is only 1.2× a magnitude 5 instead of 10×. The blue team's witness (window 7) is watching.
Flatten the log to a straight line and the 10×-amplitude / 31.6×-energy fixed points collapse — the witness recomputes, disagrees with the known ratios, and turns red. Nothing is faked; the attack is real and it is caught.