One Region, One Magnitude Type: The b-Value Spread on a Single Ruler

Papers #146 and #153 priced two unpriced choices hiding inside the Gutenberg–Richter b-value: the estimator (three standard estimators of b disagree by more than their own error bars) and the declustering (removing aftershocks moves that disagreement by more than the error bars too, in either direction). Both papers carried a limit on their faces: the catalogs mixed magnitude types — mb, mww, mwr and others printed side by side as if they were one ruler. This paper removes the mixture. It takes #153's Japan catalog — 3,556 events, 2014–2023, magnitude 4.5 and above — and keeps only the events whose magnitude type is exactly mb: 2,871 events, 80.7 percent of the catalog. Same region, same years, same three estimators, same Gardner–Knopoff declustering, same bars, all registered before the filter was applied. The clean pattern does not survive the cleaning. On the raw single-type catalog the estimator spread is 0.191, inside the largest formal error, 0.243 — not priced, where #153's mixed catalog was priced at the same cut. On the declustered single-type catalog the spread grows to 0.329 and is priced. And the declustering change itself, 0.138, falls under its bound of 0.243: on the single-type catalog, declustering is inert by the registered bar, where #153 found it a priced axis. The verdict is MIXED, printed at full size. The paper also prints why "one magnitude type" is not the pure control it sounds like: the types are not assigned at random. Every event at magnitude 6.5 or above in this catalog carries a moment type; the mb ruler stops at 6.3. Filtering to one type does not just clean the ruler — it cuts the top off the catalog, and the b-value knows it.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23869804
Primary Topic
earthquake and tectonic studies
Type
preprint
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preprint

One Region, One Magnitude Type: The b-Value Spread on a Single Ruler

William Alexander Aldred
4 links
Zenodo (CERN European Organization for Nuclear Research)
earthquake and tectonic studies
preprint

One Region, One Magnitude Type: The b-Value Spread on a Single Ruler

William Alexander Aldred
preprint en

Abstract

Papers #146 and #153 priced two unpriced choices hiding inside the Gutenberg–Richter b-value: the estimator (three standard estimators of b disagree by more than their own error bars) and the declustering (removing aftershocks moves that disagreement by more than the error bars too, in either direction). Both papers carried a limit on their faces: the catalogs mixed magnitude types — mb, mww, mwr and others printed side by side as if they were one ruler. This paper removes the mixture. It takes #153's Japan catalog — 3,556 events, 2014–2023, magnitude 4.5 and above — and keeps only the events whose magnitude type is exactly mb: 2,871 events, 80.7 percent of the catalog. Same region, same years, same three estimators, same Gardner–Knopoff declustering, same bars, all registered before the filter was applied. The clean pattern does not survive the cleaning. On the raw single-type catalog the estimator spread is 0.191, inside the largest formal error, 0.243 — not priced, where #153's mixed catalog was priced at the same cut. On the declustered single-type catalog the spread grows to 0.329 and is priced. And the declustering change itself, 0.138, falls under its bound of 0.243: on the single-type catalog, declustering is inert by the registered bar, where #153 found it a priced axis. The verdict is MIXED, printed at full size. The paper also prints why "one magnitude type" is not the pure control it sounds like: the types are not assigned at random. Every event at magnitude 6.5 or above in this catalog carries a moment type; the mb ruler stops at 6.3. Filtering to one type does not just clean the ruler — it cuts the top off the catalog, and the b-value knows it.

Zenodo (CERN European Organization for Nuclear Research)
earthquake and tectonic studies
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