Time-dependent magnitude homogenization and its impact on seismic completeness, b-values, and aftershock productivity: insights from the New Zealand earthquake catalogue

Earthquake catalogues commonly integrate heterogeneous magnitude scales whose relationships evolve in time and space, introducing systematic biases in statistical seismology. Here I quantify the impact of magnitude-scale heterogeneity using the GeoNet earthquake catalogue (New Zealand, 2003–2025). I develop a time-dependent magnitude homogenization framework based on moment tensor solutions, deriving a proxy moment magnitude Mw* M w ∗ through sliding-window regressions. The relationship between catalogue magnitude and moment magnitude is strongly non-stationary, with significant temporal variations in both slope and intercept, as well as spatial differences across tectonic domains. These variations propagate directly into seismicity metrics. When evaluated on a common magnitude scale, the magnitude of completeness Mc M c is systematically higher than that inferred from the original catalogue, with local discrepancies exceeding one magnitude unit. Similarly, when both estimates are expressed on a common homogenized magnitude scale, residual b-value differences are generally modest but temporally and spatially structured, indicating that a substantial fraction of the apparent discrepancy is explained by the non-stationary magnitude transformation itself. The strongest effects are observed in clustering properties: although aftershock productivity follows an exponential scaling with magnitude in both representations, homogenized magnitudes yield a steeper productivity exponent (α ≈ 1.08 vs. 1.01) and a reduced branching proxy. These results demonstrate that magnitude heterogeneity introduces coherent, scale-dependent distortions in completeness, b -value, and clustering metrics, potentially leading to misinterpretation of seismicity patterns if not explicitly accounted for.