Earthquake size distributions are slightly different in compression vs extension

This study investigates how tectonic kinematics influences the Gutenberg–Richter b-value that governs the ratio of small to large earthquakes. Prior work indicates that b varies with differential stress, depth, and tectonic regime, with higher values typically in extension and lower in compression. However, commonly used grouping strategies—by focal mechanism or by predefined seismotectonic zones—can mix disparate geodynamic settings or rely on subjective boundaries, potentially biasing b-value estimates. The authors aim to develop and test an alternative, reproducible grouping method based on interseismic geodetic strain rates and stress orientations to delineate compressional and extensional crustal volumes. Using Italy as a case study with dense geodetic coverage and high-quality instrumental seismicity, they test whether b-values differ between these kinematic regimes and assess whether previously reported large differences could reflect undersampling from overly fragmented zonations. The work is relevant to seismic hazard analyses, where accurate b-values are critical.

The Gutenberg–Richter relation describes earthquake size distributions and the b-value is known to depend on stress and tectonic environment. Regional and global studies have reported depth dependence (typically larger b at shallow depths) and systematic differences among regimes: around 1.0 for strike-slip, >1 in extension, and <1 in compression. Prior approaches to relate b to tectonics include classifying events by focal mechanisms or assigning earthquakes to seismotectonic zones. Both can mix different geodynamics (e.g., back-arc extension vs mid-ocean ridge spreading within "normal-faulting" classes; subduction-related vs continental thrusting within "thrust" classes) or depend on subjective, sharp boundaries that may not reflect true interseismic deformation. Recent work highlights pitfalls in completeness estimation and short-term aftershock incompleteness and emphasizes robust statistical handling when estimating b.

• Study area and rationale: Italy is used due to dense GNSS and reliable instrumental catalogs. The southern boundary is limited to ~N39.6° to exclude Calabria, where forearc extension and subduction compression conflict; long-term kinematics there would require explicit fault models.
• Geodetic strain-rate modeling: The 2D horizontal strain-rate tensor is obtained by jointly inverting GNSS horizontal velocities and interpolated SHmax directions using NeoKinema on a ~15 km spaced finite-element grid. The objective function combines fit to velocities and stress orientations with a stiff-continuum constraint, adopting Ag=10^-4 m^2; model prediction errors are ~0.34 mm/yr (velocities) and ~10° (stress). The regional RMS interseismic strain-rate parameter is μ≈6.56×10^-9 yr^-1, tuned iteratively.
• Kinematic classification from strain tensor: Principal horizontal strain rates ε1h (compressional, more negative) and ε2h (extensional, more positive) define kinematics in a Cartesian plane. First quadrant indicates normal-faulting (extension), third quadrant thrust-faulting (compression), second quadrant transitions between transtension, strike-slip, and transpression. Transtension vs transpression partition in the second quadrant is set with k1=0.25 via ε2h > −(1−k1)ε1h (transtension) or ε2h < −(1−k1)ε1h (transpression); consistency is verified with the modeled principal components and observed earthquake kinematics.
• Definition of zones: Extensional and compressional domains are delimited where ε11h+ε22h >0 and <0, respectively, using horizontal strain-rate isolines near +12×10^-10 yr^-1 for extension and −6×10^-10 yr^-1 for compression. Sensitivity tests use alternative isolines (|ε1|≈16×10^-9 yr^-1 for extension; |ε1|≈9×10^-9 yr^-1 for compression). Areas with insufficient data coverage (e.g., Adriatic offshore) are excluded. The extensional region excludes volcanic areas.
• Seismic catalogs and depth limits: The instrumental HORUS catalog (2005-04-16 to 2022-12-31) with homogenized moment magnitudes is used. Events are restricted to depth ≤15 km to focus on shallow crustal regimes and avoid mixed/deep seismicity on the Adriatic slab. A sensitivity test to 25 km yields similar results.
• Completeness assessment and STAI handling: Completeness (Mc) is estimated using the Lilliefors-based approach; Mc≈1.8 is found for Italy to 30 km depth. To mitigate short-term aftershock incompleteness (STAI), for 3 days after events Mw≥5.5, Mc is increased by +1.0. Visual checks of incremental number vs magnitude and vs (Magnitude−Mc) plots reveal residual incompleteness at Mc=1.8; thus, Mc=2.5 (with +1.0 during STAI) is adopted operationally to ensure completeness.
• b-value estimation and uncertainty: The Taroni (2021) estimator, suitable for variable completeness, is used to estimate b and its standard error, including unbiased and binning corrections. 95% confidence intervals are computed via normal approximation.
• Statistical testing: Differences between b-values for the two zones are evaluated via the Utsu test. Sensitivity to higher completeness thresholds (up to Mw 2.7; with STAI completeness 3.7) is explored.
• Validation of kinematic assignment: Consistency between modeled kinematics and observed focal mechanisms is assessed using IPSI, RCMT (1997–2022), and Italian CMT (1976–2015) catalogs by computing the ratio of seismic moment with rake-consistent mechanisms to total moment in each zone under multiple zone boundary choices.
• Comparative experiment with alternative zonations: A two-step learning/testing experiment compares local b-values computed in 13 Stucchi et al. zones overlapping the two geodetic zones versus global b-values from the two geodetic zones. Catalog is split temporally uniformly into learning (20–33%) and testing (80–67%) subsets. Bayes Factors aggregate evidence across zones; log Bayes Factors indicate strength of evidence favoring the geodetic-zone model.

• Kinematic zones: Geodetic inversion yields coherent compressional (Southern Alps) and extensional (Apennines) domains consistent with independent geological and seismological evidence. Seismic moment ratios with kinematics matching the model are high: ~0.96–0.99 depending on catalog and zone boundary choice (e.g., RCMT: compression 0.966/0.960; extension 0.985/0.984; Italian CMT: compression ~0.949–0.954; extension ~0.987–0.988; with second nodal plane choices raising ratios to ~0.962–0.994).
• b-values: For Mw≥2.5 and depth ≤15 km, extension b=1.13±0.01 (N≈5077), compression b=0.98±0.03 (N≈978). Across completeness thresholds Mc 2.5–2.7 (with STAI handling), extension b is consistently and significantly larger than compression (Utsu p<0.05). The 95% CI ranges across both regimes are narrow (≈0.92–1.16 overall), indicating modest differences.
• Comparison to prior studies: Differences between extension and compression are smaller than previously reported for Italy (e.g., prior compressional b≈0.75–0.78 vs 0.98 here). Applying the present method and Mw catalog to prior zonations reduces discrepancies, suggesting part of earlier differences arose from magnitude scale and zoning choices.
• Model comparison: In learning/testing experiments aggregating 13 local zones, log Bayes Factors strongly to decisively favor using the two geodetically defined b-values over per-zone b-values (e.g., log BF ≈ 3–15 depending on split), indicating that small-zone b-value variability largely reflects undersampling.
• Sensitivity: Results are stable to alternate zone boundaries and to increasing depth cutoff to 25 km or completeness thresholds up to Mw 2.7.

The study demonstrates that grouping earthquakes by interseismic geodetic kinematics provides a reproducible way to delineate compressional and extensional regimes that align with independent observations. Within these objectively defined zones, b-values differ in the expected sense (higher in extension than compression), supporting the hypothesis that differential stress influences size distributions. However, the observed difference in Italy is modest, challenging previous reports of larger contrasts that likely resulted from mixed kinematics and undersampled, fragmented zonations. The strong Bayes Factor support for a two-zone model implies that b-value overdispersion across many small adjacent regions is largely stochastic, not necessarily reflecting real physical contrasts. This has direct implications for probabilistic seismic hazard analysis: adopting simpler, kinematically coherent zones can yield more stable b-values and reduce arbitrariness. While Italian results show modest contrasts, larger differences may occur in global settings where extension and compression include oceanic ridges and subduction zones.

By inverting GNSS velocities and stress orientations to derive 2D strain-rate tensors, the authors define extensional and compressional domains in Italy and show that b-values are significantly higher in extension than compression, but the differences are smaller than often reported. They validate the kinematic assignments with focal mechanisms and demonstrate, via Bayes Factor tests, that using two geodetically derived b-values better explains independent data than many small-zone b-values. The work argues that geodetic strain rates and stress directions provide independent, reproducible criteria for seismotectonic zoning, mitigating undersampling and arbitrariness and improving inputs to seismic hazard modeling. Future research could extend this framework to other regions with adequate geodetic coverage, incorporate explicit treatment of strike-slip regimes where data permit, and assess how inclusion of oceanic and subduction environments affects b-value contrasts.

• Data coverage limitations preclude robust analysis of offshore/deep strike-slip events in the Adriatic Sea; these may involve different physics and complex stress regimes.
• Calabria is excluded due to conflicting processes (forearc extension vs subduction compression) requiring explicit fault modeling to recover long-term kinematics.
• Analysis is restricted to shallow events (≤15 km) to avoid mixed regimes; while tested up to 25 km, deeper contributions are not fully explored.
• Completeness estimation, though carefully handled (STAI adjustment and visual diagnostics), remains subject to potential underestimation; results rely on adopting Mc=2.5 (and +1.0 during STAI).
• The approach assumes interseismic geodetic strain rates approximate earthquake kinematics; transient or local effects not captured by the model could introduce biases.
• Extensional domain excludes volcanic areas; results may not generalize to volcanic settings where b-values can be higher.