On the consistency of earthquake moment rates, geological fault data, and space geodetic strain: the United States

New and dense space geodetic data can now map strain rates over continental-wide areas with a useful degree of precision. Stable strain indicators open the door for space geodesy to join with geology and seismology in formulating improved estimates of global earthquake recurrence. In this paper, 174 GPS/VLBI velocities map United States’ strain rates of 30.0 × 10−8 yr−1 with regional uncertainties of 5 to 50 per cent. Kostrov’s formula translates these strain values into regional geodetic moment rates. Two other moment rates M̄˙seismic and M̄˙geologic, extracted from historical earthquake and geological fault catalogues, contrast the geodetic rate. Because M̄˙geologic, M̄˙seismic and M̄˙geodetic derive from different views of the earthquake engine, each illuminates different features. In California, the ratio of M̄˙geodetic to M̄˙geologic is 1.20. The near-unit ratio points to the completeness of the region’s geological fault data and to the reliability of geodetic measurements there. In the Basin and Range, northwest and central United States, both M̄˙geodetic and M̄˙seismic greatly exceed M̄˙geologic. Of possible causes, high incidences of understated and unrecognized faults probably drive the inconsistency. The ratio of M̄˙seismic to M̄˙geodetic is everywhere less than one. The ratio runs systematically from 70–80 per cent in the fastest straining regions to 2 per cent in the slowest. Although aseismic deformation may contribute to this shortfall, I argue that the existing seismic catalogues fail to reflect the long-term situation. Impelled by the systematic variation of seismic to geodetic moment rates and by the uniform strain drop observed in all earthquakes regardless of magnitude, I propose that the completeness of any seismic catalogue hinges on the product of observation duration and regional strain rate. Slowly straining regions require a proportionally longer period of observation. Characterized by this product, gamma distributions model statistical properties of catalogue completeness as proxied by the ratio of observed seismic moment to geodetic moment. I find that adequate levels of completeness should exist in median catalogues of 200 to 300 year duration in regions straining 10−7 yr−1 (comparable to southern California). Similar levels of completeness will take more than 20 000 years of earthquake data in regions straining 10−9 yr−1 (comparable to the southeastern United States). Predictions from this completeness statistic closely mimic the observed M̄˙seismic to M̄˙godetic ratios and allow quantitative responses to previously unanswerable questions such as: ‘What is the likelihood that the seismic moment extracted from an earthquake catalogue of X years falls within Y per cent of the true long-term rate?’ The combination of historical seismicity, fault geology and space geodesy offers a powerful tripartite attack on earthquake hazard. Few obstacles block similar analyses in any region of the world.