A single law — Gutenberg & Richter, 1944 — says small earthquakes outnumber big ones, ten to one for every step down the scale. So why did last month's global catalog list more magnitude-4.4 quakes than magnitude-3.0 ones? Not because the ground obliged. Because the catalog is two instruments wearing one coat, and you can see the seam. Live from USGS.
How many quakes at each magnitude · — · count on a log scale
the seam at M≈4
regional networks — heard only where wired
global network switches on — heard everywhere
Gutenberg–Richter · count of quakes at or above each magnitude · log scale
b = —
N ≥ M (counted)
b = 1.0 above the seam — the real slope
one line across everything — the FAULT
How this was made. Every earthquake M≥1.0 in the
USGS / ComCat global catalog
over the last 30 days, binned by magnitude in steps of 0.1.
Gutenberg–Richter
(B. Gutenberg & C. Richter, 1944): the number of quakes at or above magnitude M falls
as log₁₀N = a − bM, a straight line, with b≈1 — each unit of magnitude, ten times fewer
quakes. The slope b is fit by maximum likelihood (Aki 1965; standard error after Shi & Bolt 1982).
The
magnitude of completeness M
c is the magnitude above which the catalog
catches everything; below it, the counts roll over because detection fails, not because the
earth stops. The catch here: the merged catalog has
two M
c's — a low one
over instrumented land, a high one (≈4.5) where the global network sees the whole planet —
so the histogram is bimodal and a single b is undefined. The
FAULT fits one line across
the seam (b≈0.35) and extrapolates it to great earthquakes. Truth-checks:
GREEN reproduces both b-values and the seam hump
from the raw events;
FAULT trusts the single b
and overpredicts M≥6 ninefold. Snapshot baked on wake; the catalog is live.