Fractal Tomography and the Fisher Information Barrier of Seismicity: Addressing the Origin of Dual Paradoxes via Precision-Calibrated Bayesian Inference

Facundo Firmenich , Pau Firmenich, León Firmenich

The spatial organization of seismicity presents dual multi-decade paradoxes: (1) earthquake catalogs exhibit quasi-planar correlation dimensions (D2 ≈ 2.0–2.6) despite volumetric lithospheric deformation (geometric projection paradox), and (2) Bayesian inference systematically yields D3 ≈ 3.0 contradicting structural geology (Bayesian saturation paradox). We address both through the Fractal Tomography Framework, establishing a precision-aware explanation of both paradoxes by integrating: (1) precision-calibrated Bayesian analysis of
50,190 Pan-American earthquakes, (2) high-precision validation with 166,920 Japanese events across three JUICE-relocated sequences (Hi-Net, σ < 0.7 km; ≈ 11× precision improvement), (3) systematic depth-stratified analysis, and (4) global ISC-GEM validation (σh ≈ 10–30 km).

We identify precision-dependent Bayesian saturation as a fundamental methodological artifact: when location uncertainty exceeds a semi-empirically calibrated threshold σc = 2.3 ± 0.4 km (Fisher Information Barrier), inference spuriously converges to D3 = 3.00. Hi-Net validation breaks this saturation, revealing genuine multi-planar structure with D3 = 2.39–2.95 (three JUICE sequences; all Pboundary = 0.0%). Within the Japan subduction zone, we discover systematic dimensional reduction with depth: shallow megathrust (D2 = 2.41) → intermediate slab (D2 = 2.18) → deep slab (D2 = 1.89), supporting progressive Benioff zone planarization.

This work demonstrates that rigorous confrontation of methodological limitations transforms apparent weaknesses into fundamental discoveries, establishing precision-calibrated dimensional inference as a new standard for seismic fractal analysis.