Adaptive smoothing of seismicity in time, space and magnitude for long-term and short-term earthquake forecasts
Abstract
We present new methods for long-term and short-term earthquake forecasting that employ space, time, and magnitude kernels to smooth seismicity.
These forecasts are applied to Californian and Japan seismicity and compared with other models. Our models are purely statistical and rely on very few assumptions about seismicity.
In particular, we do not use Omori-Utsu law. The magnitude distribution is either assumed to follow the Gutenberg-Richter law or is estimated non-parametrically with kernels.
We employ adaptive kernels of variable bandwidths to estimate seismicity in space, time, and magnitude bins.
For long-term forecasts, the long-term rate in each spatial cell is defined as the median value of the temporal history of the smoothed seismicity rate in this cell,
circumventing the relatively subjective choice of a declustering algorithm. For short-term forecasts, we simply assume persistence, that is, a constant rate over short time windows.
Our long-term forecast performs slightly better than our previous forecast based on spatially smoothing a declustered catalog.
Our short-term forecasts are compared with those of the epidemic-type aftershock sequence (ETAS) model.
Although our new methods are simpler and require fewer parameters than ETAS, the obtained probability gains are surprisingly close.
Nonetheless, ETAS performs significantly better in most comparisons,
and the kernel model with a Gutenberg-Richter law attains larger gains than the kernel model that non-parametrically estimates the magnitude distribution.
Finally, we show that combining ETAS and kernel model forecasts, by simply averaging the expected rate in each bin,
can provide greater predictive skill than ETAS or the kernel models can achieve individually.
