ANADEF: A Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting
Abstract
Spatially resolved stress proxies and rate-based seismicity models are increasingly combined for regional earthquake forecasting, yet formally testing their non-redundancy remains largely unaddressed. We present the Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting (ANADEF) pipeline, integrating a stress-sensitive Gutenberg--Richter b-value field, estimated via a penalized 2D B-spline inversion, with a stationary background rate (μ) from space--time ETAS stochastic declustering. Applied to the Zagros Fold--Thrust Belt using an 18-year catalog (n=40,731, MN≥1.5, 2006--2024) under a two-stage protocol with non-overlapping training (2006--2014) and target (2015--2024) windows, the model achieves, for Mw≥5.0 (N=55), a retrospective Area Skill Score S=0.69 (95\% CI: 0.64--0.73), reducing alarmed area from τ≈0.38 (μ-only) to τ≈0.28 while retaining hit rate ν=92.7%; since thresholds are calibrated on the evaluation catalog, these are in-sample, not out-of-sample, estimates. A nested permutation procedure re-optimizing thresholds within each null realization tests whether b-value adds information beyond μ, absorbing the optimization bias. Significance is null-model dependent: cell-wise randomization yields p=0.012, while a conservative spatial-structure-preserving null gives weaker, non-significant evidence (p=0.057)---incremental stress information is suggestive but not unambiguously established. Calibrated thresholds were frozen and applied to updated 2015--2024 fields, generating an unvalidated, forward-looking spatial alarm template for 2025--2029. These results establish a reproducible, statistically transparent methodology for testing, rather than assuming, complementarity between stress-sensitive and rate-based predictors, offering a candidate operational template pending prospective validation.
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BibTeX
@misc{mohammadigheymasi2026anadef,
title = {{ANADEF: A Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting}},
author = {Hamzeh Mohammadigheymasi and Muhammed Hossein Mousavi and Nuno Pombo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06920},
eprint = {2609.06920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06920},
}
RIS
TY - UNPB
TI - ANADEF: A Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting
AU - Hamzeh Mohammadigheymasi
AU - Muhammed Hossein Mousavi
AU - Nuno Pombo
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06920
UR - https://arxiv.org/abs/2609.06920
AB - Spatially resolved stress proxies and rate-based seismicity models are increasingly combined for regional earthquake forecasting, yet formally testing their non-redundancy remains largely unaddressed. We present the Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting (ANADEF) pipeline, integrating a stress-sensitive Gutenberg--Richter b-value field, estimated via a penalized 2D B-spline inversion, with a stationary background rate (μ) from space--time ETAS stochastic declustering. Applied to the Zagros Fold--Thrust Belt using an 18-year catalog (n=40,731, M_N≥1.5, 2006--2024) under a two-stage protocol with non-overlapping training (2006--2014) and target (2015--2024) windows, the model achieves, for M_w≥5.0 (N=55), a retrospective Area Skill Score S=0.69 (95\% CI: 0.64--0.73), reducing alarmed area from τ≈0.38 (μ-only) to τ≈0.28 while retaining hit rate ν=92.7%; since thresholds are calibrated on the evaluation catalog, these are in-sample, not out-of-sample, estimates. A nested permutation procedure re-optimizing thresholds within each null realization tests whether b-value adds information beyond μ, absorbing the optimization bias. Significance is null-model dependent: cell-wise randomization yields p=0.012, while a conservative spatial-structure-preserving null gives weaker, non-significant evidence (p=0.057)---incremental stress information is suggestive but not unambiguously established. Calibrated thresholds were frozen and applied to updated 2015--2024 fields, generating an unvalidated, forward-looking spatial alarm template for 2025--2029. These results establish a reproducible, statistically transparent methodology for testing, rather than assuming, complementarity between stress-sensitive and rate-based predictors, offering a candidate operational template pending prospective validation.
ER -