ALBERT

Description: We have obtained new results in the statistical analysis of global earthquake catalogues with special attention to the largest earthquakes, and we examined the statistical behaviour of earthquake rate variations. These results can serve as an input for updating our recent earthquake forecast, known as the ‘Global Earthquake Activity Rate 1’ model (GEAR1), which is based on past earthquakes and geodetic strain rates. The GEAR1 forecast is expressed as the rate density of all earthquakes above magnitude 5.8 within 70 km of sea level everywhere on earth at 0.1 x 0.1 degree resolution, and it is currently being tested by the Collaboratory for Study of Earthquake Predictability. The seismic component of the present model is based on a smoothed version of the Global Centroid Moment Tensor (GCMT) catalogue from 1977 through 2013. The tectonic component is based on the Global Strain Rate Map, a ‘General Earthquake Model’ (GEM) product. The forecast was optimized to fit the GCMT data from 2005 through 2012, but it also fit well the earthquake locations from 1918 to 1976 reported in the International Seismological Centre-Global Earthquake Model (ISC-GEM) global catalogue of instrumental and pre-instrumental magnitude determinations. We have improved the recent forecast by optimizing the treatment of larger magnitudes and including a longer duration (1918–2011) ISC-GEM catalogue of large earthquakes to estimate smoothed seismicity. We revised our estimates of upper magnitude limits, described as corner magnitudes, based on the massive earthquakes since 2004 and the seismic moment conservation principle. The new corner magnitude estimates are somewhat larger than but consistent with our previous estimates. For major subduction zones we find the best estimates of corner magnitude to be in the range 8.9 to 9.6 and consistent with a uniform average of 9.35. Statistical estimates tend to grow with time as larger earthquakes occur. However, by using the moment conservation principle that equates the seismic moment rate with the tectonic moment rate inferred from geodesy and geology, we obtain a consistent estimate of the corner moment largely independent of seismic history. These evaluations confirm the above-mentioned corner magnitude value. The new estimates of corner magnitudes are important both for the forecast part based on seismicity as well as the part based on geodetic strain rates. We examine rate variations as expressed by annual earthquake numbers. Earthquakes larger than magnitude 6.5 obey the Poisson distribution. For smaller events the negative-binomial distribution fits much better because it allows for earthquake clustering.

Description: The project Seismic Hazard Harmonization in Europe (SHARE), completed in 2013, presents significant improvements over previous regional seismic hazard modeling efforts. The Global Strain Rate Map v2.1, sponsored by the Global Earthquake Model Foundation and built on a large set of self-consistent geodetic GPS velocities, was released in 2014. To check the SHARE seismic source models that were based mainly on historical earthquakes and active fault data, we first evaluate the SHARE historical earthquake catalogues and demonstrate that the earthquake magnitudes are acceptable. Then, we construct an earthquake potential model using the Global Strain Rate Map data. SHARE models provided parameters from which magnitude–frequency distributions can be specified for each of 437 seismic source zones covering most of Europe. Because we are interested in proposed magnitude limits, and the original zones had insufficient data for accurate estimates, we combine zones into five groups according to SHARE's estimates of maximum magnitude. Using the strain rates, we calculate tectonic moment rates for each group. Next, we infer seismicity rates from the tectonic moment rates and compare them with historical and SHARE seismicity rates. For two of the groups, the tectonic moment rates are higher than the seismic moment rates of the SHARE models. Consequently, the rates of large earthquakes forecast by the SHARE models are lower than those inferred from tectonic moment rate. In fact, the SHARE models forecast higher seismicity rates than the historical rates, which indicate that the authors of SHARE were aware of the potentially higher seismic activities in the zones. For one group, the tectonic moment rate is lower than the seismic moment rates forecast by the SHARE models. As a result, the rates of large earthquakes in that group forecast by the SHARE model are higher than those inferred from tectonic moment rate, but lower than what the historical data show. For the other two groups, the seismicity rates from tectonic moment rate, historical data and SHARE models are consistent. For four groups, the maximum magnitudes used by SHARE are fairly consistent with the probable maximum magnitudes inferred from tectonic strain rates. This study demonstrates that: (1) the strain-rate data are useful for constraining seismicity rates and magnitude limits; and (2) SHARE seismic source models and historical earthquake catalogues are satisfactory.

Description: In our paper published earlier we discussed forecasts of earthquake focal mechanism and ways to test the forecast efficiency. Several verification methods were proposed, but they were based on ad hoc, empirical assumptions, thus their performance is questionable. We apply a conventional likelihood method to measure the skill of earthquake focal mechanism orientation forecasts. The advantage of such an approach is that earthquake rate prediction can be adequately combined with focal mechanism forecast, if both are based on the likelihood scores, resulting in a general forecast optimization. We measure the difference between two double-couple sources as the minimum rotation angle that transforms one into the other. We measure the uncertainty of a focal mechanism forecast (the variability), and the difference between observed and forecasted orientations (the prediction error), in terms of these minimum rotation angles. To calculate the likelihood score we need to compare actual forecasts or occurrences of predicted events with the null hypothesis that the mechanism's 3-D orientation is random (or equally probable). For 3-D rotation the random rotation angle distribution is not uniform. To better understand the resulting complexities, we calculate the information (likelihood) score for two theoretical rotational distributions (Cauchy and von Mises-Fisher), which are used to approximate earthquake source orientation pattern. We then calculate the likelihood score for earthquake source forecasts and for their validation by future seismicity data. Several issues need to be explored when analyzing observational results: their dependence on forecast and data resolution, internal dependence of scores on forecasted angle and random variability of likelihood scores. Here, we propose a simple tentative solution but extensive theoretical and statistical analysis is needed.