Oklahoma M3+ earthquakes fell faster after 2016 than pressure models fit to 2010-2016 disposal data predicted; pressure loss in 1-4 years was necessary and a memory term gave inconsistent gains

Question: after the 2015-2016 cuts in wastewater disposal, does the Oklahoma earthquake rate follow the pressure level, the pressure increase, a pressure history with memory (Kaiser type), or a pressure that dissipates? Approach: we used monthly volumes of 4,545 Class II disposal wells (OCC Form 1012A, 2006-2025) and declustered USGS ComCat M>=3 events inside Oklahoma (Zaliapin and Ben-Zion nearest-neighbour method). A 2-D diffusion model on 0.05 degree cells gave a pressure proxy with diffusivity D and optional loss time L. Each model had a shrunk productivity for each cell. We fit the models on 2010-2016 (1,317 events) and forecast 2017-01 to 2026-10 (423 events). We repeated this with fits to 2018 and to 2026, and with sensitivity variants. Results: all models fit to 2010-2016 predicted too many events. The closed pressure-level model predicted 16 times the observed count, rate-state with closed pressure 5.6 times, pressure-increase (seismogenic index) and Kaiser models 2.7 times, and the leaky pressure-level model 2.4 times. Pressure loss with an e-folding time of 1-4 years was necessary in all fit windows. The leaky level model was better than the pressure-increase and Kaiser models by 0.58 nats per event in 2017-2026 (95% cell bootstrap 0.40-0.77) and by 2.57 (2.07-3.05) when fit to 2018. A hysteresis factor (p/p_max)^n gave inconsistent gains across four designs (+0.33, -0.23, +0.28, +0.14 nats per event). With Arbuckle-labelled volumes it gave near-correct counts (493 for 423 events; 178 for 141), but with all disposal volumes the full-period fit selected n = 0.16. A seismic-depletion factor had no support. Even the full-period leaky fit expected 1.7 times the 96 events of 2020-2026. Declustered M>=3 events fell from 501 in 2015 to 5 in 2025. Limitations: single-layer linear diffusion, no poroelastic stress, no injection depth or plug-back information, no Kansas or Texas wells, uncertain formation labels, and many compared models without correction for selection.

induced seismicity · Oklahoma · wastewater disposal · pore pressure diffusion · Kaiser effect · seismogenic index · rate-and-state · earthquake forecasting · seismicity recovery · Arbuckle