One Catalog, Three b-Values: The Estimator Spread in the Gutenberg–Richter b-Value, Priced on the USGS Global Catalog, 2014–2023

The Gutenberg–Richter b-value is quoted like a measurement of the Earth. It comes with a small formal error, and the error reads like the number is settled. But b does not come out of the ground. It comes out of an estimator, and the field uses several. I fixed one public catalog before touching it — the USGS global catalog, 2014–2023, 152,861 events at magnitude 4.0 and above — wrote down three standard estimators and a verdict bar in advance, and ran them. At the headline completeness magnitude of 4.5 (74,967 events), maximum likelihood gives b = 1.231, least squares on the cumulative curve gives b = 1.077, and least squares on binned counts gives b = 1.060. The spread between the estimators is 0.171. The largest formal error any of them quotes is 0.022. The spread beats the quoted errors by a factor of 7.8, so the claim registered in advance stands: on this catalog, the choice of estimator moves b by far more than any estimator's own error admits. A sensitivity run at completeness magnitude 5.0 gives the same verdict at a smaller size. The claim is sized to this one catalog and this one window. It says nothing about any other catalog. It says that here, a b-value quoted without its estimator is a number with an unpriced term in it.