Global models for short-term earthquake forecasting and predictive skill assessment

Abstract

We present rigorous tests of global short-term earthquake forecasts using Epidemic Type Aftershock Sequence models with two different time kernels (one with exponentially tapered Omori kernel (ETOK) and another with linear magnitude dependent Omori kernel (MDOK)). The tests are conducted with three different magnitude cutoffs for the auxiliary catalog (M3, M4 or M5) and two different magnitude cutoffs for the primary catalog (M5 or M6), in 30 day long pseudo prospective experiments designed to forecast worldwide M ≥ 5 and M ≥ 6 earthquakes during the period from January 1981 to October 2019. MDOK ETAS models perform significantly better relative to ETOK ETAS models. The superiority of MDOK ETAS models adds further support to the multifractal stress activation model proposed by Ouillon and Sornette (2005). We find a significant improvement of forecasting skills by lowering the auxiliary catalog magnitude cutoff from 5 to 4. We unearth evidence for a self-similarity of the triggering process as models trained on lower magnitude events have the same forecasting skills as models trained on higher magnitude earthquakes. Expressing our forecasts in terms of the full distribution of earthquake rates at different spatial resolutions, we present tests for the consistency of our model, which is often found satisfactory but also points to a number of potential improvements, such as incorporating anisotropic spatial kernels, and accounting for spatial and depth dependant variations of the ETAS parameters. The model has been implemented as a reference model on the global earthquake prediction platform RichterX, facilitating predictive skill assessment and allowing anyone to review its prospective performance.

Are Large Earthquakes Preferentially Triggered by Other Large Events?

“…It increases more slowly than the rupture length, suggesting that this characteristic time does not scale with rupture duration. For the final training period, the exponent of the Omori law increases as 0.46 + 0.15 m for both models, that is, in a manner very similar to previous results (Nandan, Kamer et al., 2021; Ouillon & Sornette, 2005; Ouillon et al., 2009; Sornette & Ouillon, 2005; Tsai et al., 2012) reported for many regional and global catalogs.…”

“…It is predicted by physically based models, such as the multifractal stress activation model (Ouillon & Sornette, 2005; Ouillon et al., 2009; Sornette & Ouillon, 2005; Tsai et al., 2012) and the state‐and‐rate friction model (Dieterich, 1994). Model 2 is the same as Model 1, but with a modified time kernel$${T}_{\mathrm{norm}}{\left\{t-{t}_{i}+c\left({m}_{i}\right)\right\}}^{-p\left({m}_{i}\right)}{e}^{-\frac{t-{t}_{i}}{\tau }}$$, where $$c\left({m}_{i}\right)={c}_{0}1{0}^{{c}_{1}{m}_{i}}$$ (Davidsen et al., 2015; Dieterich, 1994; Hainzl, 2016a; Narteau et al., 2005; Scholz, 1968; Shcherbakov et al., 2004) and p = p 0 + p 1 m i (Nandan, Kamer et al., 2021; Ouillon & Sornette, 2005; Ouillon et al., 2009; Sornette & Ouillon, 2005; Tsai et al., 2012). Thus, the regularizer and the exponent of the time kernel feature exponential and linear dependence on the magnitude of the mainshock, respectively. Model 3 is defined by the following equation for the conditional seismicity rate of events of magnitude m : …”

“…Based on recent empirical evidences (Nandan, Kamer et al., 2021; Nandan, Ouillon, & Sornette, 2019; Nandan, Ram et al., 2021; Nichols & Schoenberg, 2014; Ouillon & Sornette, 2005; Ouillon et al., 2009; Sornette & Ouillon, 2005; Spassiani & Sebastiani, 2016; Tsai et al., 2012), we propose a suite of four models that generalize ETAS and are tested against it. Model 1 uses the conditional seismicity rate given by Equation 1 but extends the standard ETAS model with a space‐varying background intensity function (Nandan, Ram et al., 2021; Zhuang et al., 2002) given by Equation 6, with the guiding idea that the future background earthquakes occur mostly in regions where the intensity of past background earthquakes has been high. $$$\begin{array}{r}\hfill \mu \left(x,y\right)={T}^{-1}\sum\limits _{i=1}^{N}I{P}_{i}{\pi }^{-1}Q{D}^{2Q}{\left({\left(x-{x}_{i}\right)}^{2}+{\left(y-{y}_{i}\right)}^{2}+{D}^{2}\right)}^{-1-Q}\end{array}$$$ where IP i is the independence probability of the earthquake. It is not known a priori but estimated iteratively using the EM algorithm used to invert the parameters (see Section 3.2).…”

“…$${T}_{\mathrm{norm}}{\left\{t-{t}_{i}+c\left({m}_{i}\right)\right\}}^{-p\left({m}_{i}\right)}{e}^{-\frac{t-{t}_{i}}{\tau }}$$, where $$c\left({m}_{i}\right)={c}_{0}1{0}^{{c}_{1}{m}_{i}}$$ (Davidsen et al., 2015; Dieterich, 1994; Hainzl, 2016a; Narteau et al., 2005; Scholz, 1968; Shcherbakov et al., 2004) and p = p 0 + p 1 m i (Nandan, Kamer et al., 2021; Ouillon & Sornette, 2005; Ouillon et al., 2009; Sornette & Ouillon, 2005; Tsai et al., 2012). Thus, the regularizer and the exponent of the time kernel feature exponential and linear dependence on the magnitude of the mainshock, respectively.…”

Embracing Data Incompleteness for Better Earthquake Forecasting

“…In the case of the 2010 events, the main earthquake occurred outside of California and thus network coverage can play a role, as well as the absence of a large fraction of aftershocks due to the boundaries of the considered region. Furthermore, triggering parameters can differ between regions, sequences and can also depend on the magnitude of the mainshocks (Nandan et al., 2019; Nandan, Kamer, et al., 2021; Nandan, Ouillon, et al., 2021; Ouillon & Sornette, 2005; Sornette & Ouillon, 2005). These dependencies can increase the representation of the active region and particular sequences in the catalog and lead to sudden changes in the overall parameters.…”