Reliability-constrained spatial b-value mapping via kernel-weighted kNN with the magnitude-difference estimator and effective sample size

We present a framework for spatial Gutenberg–Richter (GR) b -value mapping in which three criteria are explicitly and jointly quantified and enforced: spatial locality (each local estimate uses only events within a bounded distance of the evaluation point), statistical support (each estimate is required to rest on a sufficient number of complete-magnitude events), and estimator uncertainty (a confidence measure is computed and reported for every estimate). The method couples (i) a kernel-smoothed map of event density with (ii) a local b -value estimator that, at each grid point, uses the k nearest earthquakes and computes b from the positive differences between their magnitudes following the method of Lippiello and Petrillo (in J Geophys Res Solid Earth 129(2):e2023JB027849, 2024. https://doi.org/10.1029/2023JB027849 ), which is robust to catalog incompleteness, and (iii) an effective sample size Neff N eff that measures how many events effectively contribute to each local estimate once the distance weighting is taken into account. Locality is imposed by requiring the radius rₖ r k enclosing the k nearest events to stay below a chosen bound rₘₐₓ r max ; statistical support is imposed by minimum values of Neff N eff and of the local complete-magnitude event count nₜₐᵢₗ n tail ; uncertainty is obtained by a weighted bootstrap that yields a map of the standard error (SE) of b , together with percentile-based $$95%$$ 95 % confidence intervals. The pair (k,rₘₐₓ) ( k , r max ) is chosen by a single numerical score that combines spatial coverage, locality, support, and uncertainty. We test the estimator on a synthetic catalog whose true b ( x , y ) field is known by construction, and then apply the framework to a catalog of N=42,007 N = 42 , 007 events recorded across Turkiye between 18 January 2023 and 30 September 2025 by the Kandilli Observatory and Earthquake Research Institute (KOERI). The resulting maps reveal interpretable spatial variations in b while suppressing estimates in regions where the data do not provide adequate information.