Combining earthquake forecasts using differential probability gains

Abstract

We describe an iterative method to combine seismicity forecasts. With this method, we produce the next generation of a starting forecast by incorporating predictive skill from one or more input forecasts. For a single iteration, we use the differential probability gain of an input forecast relative to the starting forecast. At each point in space and time, the rate in the next-generation forecast is the product of the starting rate and the local differential probability gain. The main advantage of this method is that it can produce high forecast rates using all types of numerical forecast models, even those that are not rate-based. Naturally, a limitation of this method is that the input forecast must have some information not already contained in the starting forecast. We illustrate this method using the Every Earthquake a Precursor According to Scale (EEPAS) and Early Aftershocks Statistics (EAST) models, which are currently being evaluated at the US testing center of the Collaboratory for the Study of Earthquake Predictability. During a testing period from July 2009 to December 2011 (with 19 target earthquakes), the combined model we produce has better predictive performance -in terms of Molchan diagrams and likelihood -than the starting model (EEPAS) and the input model (EAST). Many of the target earthquakes occur in regions where the combined model has high forecast rates. Most importantly, the rates in these regions are substantially higher than if we had simply averaged the models.

Regional Earthquake Likelihood Models II: Information Gains of Multiplicative Hybrids

“…Later, Imoto (2006Imoto ( , 2007 generalized the notion of multiple earthquake precursors to earthquake probabilities or rates estimated from multidisciplinary observations and showed that multiplicative probability gains could theoretically still be obtained without the independence assumption. See also Faenza and Marzocchi (2010) and Shebalin et al (2014) for applications of a statistical model with multiplicative structure to earthquake forecasting. In the statistical literature, it is recognized that multiplicative models are often appropriate for modeling of count data (e.g., McCullagh and Nelder, 1989).…”

On the monitoring of seismic activity using the algorithms of discrete mathematical analysis

“…Their proportion is shown in the error diagram along the ordinate axis (Figure 2). The abscissa shows the probability of an accidental earthquake ≥ 5 in a cell with a prediction in accordance with a given model of seismicity [Shebalin et al, 2014]. As a rule, the simplest model of seismicity is used, in which the probability of an earthquake is proportional to the number of earthquakes registered in a given cell, with a magnitude, for example, ≥ 4.…”

“…We evaluated the effectiveness of the developed method using error diagram [Shebalin et al, 2014] (Figure 4). For this purpose, the considered time and space were divided into cells.…”

“…In the error diagram (Figure 4), the abscissa shows the probability of an accidental earthquake with L ≥ 6.5 in the cell with a prediction, the ordinate shows the fraction of errors such as "missed targets", the diagonal corresponds to random guessing [Dzeboev, 2017;Shebalin et al, 2011]. To estimate an accidental entry of a strong earthquake in a cell with a prediction, the simplest model of seismicity was used in which the probability of an earthquake is proportional to the number of earthquakes with L ≥ 5.5 recorded in a given spatial cell [Kossobokov and Shebalin, 2003;Shebalin et al, 2014]. The greater the deviation of the error diagram from the diagonal, the more effective the algorithm is [Shebalin et al, 2011].…”

Earthquake interevent time distribution in Kachchh, Northwestern India

“…However, the primary issue with these approaches is that many disastrous earthquakes do not reappear on previously identified faults (Lee et al 2011). To address this limitation, statistical seismology of earthquake occurrence and forecasting has become essential for seismic hazard assessment of large geographical areas (Jordan 2006;Shebalin et al 2014).…”