One Region, Two Catalogs: The b-Value Spread, Declustered

Paper #146 priced a quiet problem in seismology: on one fixed global catalog, the three standard estimators of the Gutenberg–Richter b-value disagree with each other by 0.171 — nearly eight times the largest formal error any of them quotes. That catalog was used the way the service ships it, aftershocks and all, and #146 said so on its face. This paper asks the obvious next question. Is some of that spread the aftershocks' fault? Take one dense regional catalog — the USGS Japan box, 2014–2023, 3,556 events at magnitude 4.5 and above — decluster it by a standard method whose windows were fixed in advance, and run the same three estimators on both versions. The answer is yes, and the size is not small. Declustering moves the estimator spread by 0.126, more than twice the largest formal error in the run: it is a priced axis, the same order of size as the estimator axis itself. At the headline cut the spread shrinks (0.241 down to 0.115) once the aftershocks come out. At the higher completeness cut it grows (0.114 up to 0.238). Same catalog, same method, opposite directions — which is exactly the finding. A b-value now carries *two* unpriced choices, the estimator and the declustering, and the second one does not even push in a fixed direction. The declustering itself took out 74.4 percent of the catalog, and that appetite is printed here too, because a method that removes three quarters of the data is part of the result, not a footnote to it.