Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA , GLOBAL EARTHQUAKE FORECAST

Global forecast advantages: 1. High magnitude threshold (M=5.8). Fewer volcanic and man-induced events, less aftershocks (less than 25%). 2. High event rate – thus fast rigorous testing (1 year or less). 3. High quality initial data – global catalogs are more uniform and homogeneous. 4. Number degrees of freedom in forecast model is small and well-controlled.

See also more extensive presentation:

Modern earthquake catalogs include origin time, hypocenter location, and second-rank seismic moment tensor for each earthquake. The DC tensor is symmetric, traceless, with zero determinant: hence it has only four degrees of freedom -- one for the norm of the tensor and three for the 3-D orientation of the earthquake focal mechanism. An earthquake occurrence is considered to be a stochastic, tensor-valued, multidimensional, point process. Earthquake Phenomenology

World seismicity: 1976 – 2012 (Global Centroid Moment Tensor Catalog)

Statistical studies of earthquake catalogs -- time, size, space, focal mechanism Catalogs are a major source of information on earthquake occurrence. Since late 19-th century certain statistical features were established: Omori (1894) studied temporal distribution; Gutenberg & Richter (1941; 1944) -- size distribution. Quantitative investigations of spatial patterns started late (Kagan & Knopoff, 1980). Focal mechanism investigations (Kagan, 1982; 1991; 2009; 2012), Kagan & Jackson,

Advantages of this distribution: Simple (only one more parameter than G-R); Has a finite integrated moment (unlike G-R) for  < 1; Fits global subcatalogs slightly better than the gamma distribution.

Review of results on spectral slope,  Although there are variations, none is significant with 95%-confidence. Kagan’s [1999] hypothesis of uniform  still stands.

Earthquake rate forecasting The fractal dimension of earthquake process is lower than the embedding dimension: Space – 2.2 in 3D,Time – 0.5 in 1D. This allows us to forecast rate of earthquake occurrence – specify regions of high probability and use temporal clustering for short-term forecast -- evaluating possibility of new event. Long-term forecast: Spatial smoothing kernel is optimized by using first temporal part of a catalog to forecast its second part.

Kernel optimi zation: I_0 vs I_1 and I_2

Forecast: Long-term earthquake rate based on GCMT catalog present. 0.1 x 0.1 degree, Magnitude M>=5.8

Forecast: Short-term earthquake rate based on GCMT catalog present. 0.1 x 0.1 degree, Magnitude M>=5.8

Error diagram tau, nu for global long- term seismicity (M > 5.0) forecast. Solid black line -- the strategy of random guess. Solid thick red diagonal line is a curve for the global forecast. Blue line is earthquake distribution from the PDE catalog in (forecast); magenta line corresponds to earthquake distribution from the PDE catalog in (Kagan, PAGEOPH, 2007).

Bird, P., D. D. Jackson, Y. Y. Kagan, C. Kreemer, and R. S. Stein, GEAR1: a Global Earthquake Activity Rate model constructed from geodetic strain rates and smoothed seismicity, BSSA, accepted 2015/06/18 Fig. 1: Two parent forecasts at threshold magnitude m5.767+: (A) Seismicity parent forecast for years Mercator projection. Logarithmic color ‐ (or gray ‐ ) scale shows the rate density of epicentroids corresponding to shallow (≤70 km) hypocentroids, in units of (km)^ ‐ 2 year^ ‐ 1. (B) Tectonics parent forecast for years Conventions as in part (A), and identical color scale. Equal to model SHIFT-GSRM2f of Bird and Kreemer (2015).

Preferred hybrid forecasts for threshold magnitude m5.767+, both with and without overlay of test earthquakes: (A) Preferred hybrid forecast H* (log ‐ linear, with exponent d = 0.6 on Seismicity) for years compared to 1694 shallow test earthquakes from GCMT catalog years 2005 ‐ For test earthquakes of m > 6, focal mechanism is shown on lower focal hemisphere. (B) GEAR1 forecast (preferred hybrid H*, updated to end ‐ 2013) for years 2014 and after. Mercator projection. Logarithmic color scale shows the rate density of epicentroids corresponding to shallow (≤70 km) hypocentroids, in units of (km)^ ‐ 2 year^ ‐ 1.

Kagan & Jackson, GJI, Focal mechanism forecast is calculated by summing seismic moment tensors in 1000 km distance area and evaluating eigenvectors of the sum tensor. We compare this source forecast with other mechanisms to measure degree of uncertainty (\Phi_1).

Focal mechanism forecast , based on

Earthquake forecast conclusions We present an earthquake forecast program which quantitatively predicts both long- and short-term earthquake probabilities. The program is numerically and rigorously testable both retrospectively and prospectively as done by CSEP worldwide, as well as in California, Italy, Japan, New Zealand, etc. It is ready to be implemented as a technological solution for earthquake hazard forecasting and early warning.

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