Statistics

Seismic hazard

Nuclear physics

Completeness (order theory)

Scaling

Magnitude (astronomy)

Seismology

Statistical physics

Geology

Physics

Organic chemistry

Mathematics

Astronomy

Exponential distribution

Exponential decay

Exponential function

Earthquake magnitude

Hazard

Mathematical analysis

Geometry

Chemistry

Richter magnitude scale

Seismological Research Letters

Earthquake catalogs describe the distribution of earthquakes in space, time, and magnitude, which is essential information for earthquake forecasting and the assessment of seismic hazard and risk. Available high-resolution (HR) catalogs raise the expectation that their abundance of small earthquakes will help better characterize the fundamental scaling laws of statistical seismology. Here, we investigate whether the ubiquitous exponential-like scaling relation for magnitudes (Gutenberg–Richter [GR], or its tapered version) can be straightforwardly extrapolated to the magnitude–frequency distribution (MFD) of HR catalogs. For several HR catalogs such as of the 2019 Ridgecrest sequence, the 2009 L’Aquila sequence, the 1992 Landers sequence, and entire southern California, we determine if the MFD agrees with an exponential-like distribution using a statistical goodness-of-fit test. We find that HR catalogs usually do not preserve the exponential-like MFD toward low magnitudes and depart from it. Surprisingly, HR catalogs that are based on advanced detection methods depart from an exponential-like MFD at a similar magnitude level as network-based HR catalogs. These departures are mostly due to an improper mixing of different magnitude types, spatiotemporal inhomogeneous completeness, or biased data recording or processing. Remarkably, common-practice methods to find the completeness magnitude do not recognize these departures and lead to severe bias in the b-value estimation. We conclude that extrapolating the exponential-like GR relation to lower magnitudes cannot be taken for granted, and that HR catalogs pose subtle new challenges and lurking pitfalls that may hamper their proper use. The simplest solution to preserve the exponential-like distribution toward low magnitudes may be to estimate a moment magnitude for each earthquake.

Inconsistencies and Lurking Pitfalls in the Magnitude–Frequency Distribution of High-Resolution Earthquake Catalogs