Quantifying Earthquake Predictability and Advancing Forecasting Models

In earthquake forecasting, a significant gap exists between complete randomness and full predictability. Shannon's information entropy provides a conceptual framework for quantifying randomness in stochastic systems. Predictability, in this context, is defined as the reduction in entropy relative to a completely random system. When a forecasting model is applied to observational data, its performance is constrained by two factors: its inherent predictability (referred to as its predictability capacity) and the predictability inherent in the observational data.

For the widely used ETAS model, the corresponding system of complete randomness is a stationary Poisson process with the same mean occurrence rate. Numerical computations demonstrate that an ETAS model with a higher branching ratio and denser clusters exhibits a greater predictability capacity.

It is well established that known predictabilities in seismicity include spatiotemporal clustering and spatial inhomogeneity. However, significant predictability in earthquake magnitude has not been identified, despite ongoing debates about characteristic earthquakes and magnitude dependencies within earthquake clusters.

The following conclusions can be drawn:

(1) Determining the upper limit of each model's forecasting performance is as important as testing its forecasting consistency.

(2) The key to improving forecasting lies in developing more informative models with lower system entropy rates. While model calibration (e.g., enhanced fitting procedures) can provide some improvement, these gains are inherently limited.

(3) To achieve better practical performance in forecasting earthquake magnitudes, we must move beyond the Gutenberg-Richter law and the assumption of magnitude independence. But how?