What this research found
The Gutenberg-Richter frequency-magnitude relation, which supplies the recurrence rates behind probabilistic seismic hazard models, was fitted to a decade of Southern California seismicity: 211,606 earthquakes recorded between 2010 and 2019 in the US Geological Survey national catalogue. Maximum-curvature estimation placed the magnitude of completeness at 1.0, and maximum-likelihood fitting of the 117,536 events at or above that threshold returned a b-value of 0.633 with a bootstrap 95% confidence interval of 0.630 to 0.636. The write-up then argues against taking that figure at face value, since it sits below the 0.8 to 1.1 range typical for the region.
- The fitted relation gives the base-10 logarithm of the count of events at or above a magnitude as 5.703 minus 0.633 times that magnitude, estimated from the 117,536 events at or above the completeness threshold of 1.0 — roughly 55.5% of the catalogue — whose mean magnitude is 1.636.
- The power law holds across about three decades of magnitude, from 1.0 up to roughly magnitude 4, with a Wiemer and Wyss goodness-of-fit statistic of 88.3%. Departure from the fitted line appears only in the sparsely populated upper tail rather than as systematic curvature through the bulk of the distribution.
- The bootstrap confidence interval on the b-value spans just 0.630 to 0.636, and its standard deviation of 0.0016 closely matches the analytic standard error of 0.0018. The analysis is explicit that this tightness reflects sample size alone: shifting the completeness threshold from 1.0 to 1.5 would move the b-value by far more than the interval's entire width.
- The b-value of 0.633 falls below the 0.8 to 1.1 range usually reported for Southern California, for two reasons. Maximum curvature underestimates completeness when detection falls off gradually, and the decade pools two enormous aftershock sequences — El Mayor-Cucapah in 2010 and Ridgecrest in 2019 — whose early aftershocks fall below the temporarily elevated detection threshold.
- Extraction had to work around the catalogue service's ceiling of 20,000 events per query, which returns an error rather than silently truncating. 120 monthly seed windows were queried with recursive bisection of any that overflowed, expanding to 121 intervals because April 2010, the El Mayor-Cucapah month, needed splitting. Of 211,631 raw records, 25 were dropped for missing magnitudes.
How it was done
Every event typed as an earthquake within 32 to 36 degrees north and 120 to 114 degrees west was extracted from the USGS and ANSS Comprehensive Catalogue through the FDSN event web service, covering the ten calendar years 2010 through 2019 in UTC. Magnitudes were binned at a width of 0.1, matching their reported precision, and the completeness threshold was taken as the mode of the resulting non-cumulative frequency-magnitude distribution. The b-value came from the Aki maximum-likelihood estimator with the Utsu correction for discrete magnitude bins, and the a-value from the count of events above the threshold. Sampling uncertainty was quantified with 1,000 non-parametric bootstrap resamples under a fixed seed, and fit quality with the Wiemer and Wyss statistic, which compares observed and model-predicted cumulative counts bin by bin.
Data sources
- USGS and ANSS Comprehensive Catalogue, accessed through the FDSN event web service on 11 July 2026 — 211,606 cleaned earthquakes for 2010 to 2019, magnitudes −0.91 to 7.2, 97.1% reported as local magnitude
- Aki (1965), Bulletin of the Earthquake Research Institute 43:237, and Utsu (1965) — maximum-likelihood b-value estimator and its binning correction
- Wiemer and Wyss, Bulletin of the Seismological Society of America 90:859 (2000) — maximum-curvature completeness estimation and the goodness-of-fit statistic
- Field et al., Uniform California Earthquake Rupture Forecast version 3, USGS Open-File Report 2013-1165 — regional context for expected b-values
Limitations
A single decade-averaged completeness threshold hides the temporary rise in detection threshold that follows a large mainshock, so aftershocks logged just above the static value of 1.0 are in reality below the instantaneous one; a goodness-of-fit or entire-magnitude-range estimator would likely put completeness nearer 1.3 to 1.7. The catalogue also blends seven magnitude types without conversion to a common scale, and the result is one pooled fit across the whole region and decade rather than resolved in space or time.
How this research was produced
K-Dense Web planned and ran this seismology investigation end to end — gathering the sources, carrying out the analysis, producing the figures, and drafting the report. The full session transcript, including every intermediate step, is available to view.
