# How Useful Are Strain Rates for Estimating the Long-Term Spatial Distribution of Earthquakes?
## 3 Results
### Error Diagrams  
A hybrid model can perform poorly in an independent testing period either because the covariates that contribute to it are not well correlated with earthquake locations or because the model is overfitted to a training period in which the covariates are better correlated with earthquake locations than in the testing period. Molchan error diagrams give an indication of the correlation between covariates and earthquake locations in different time periods independent of any model fitting. For the error diagram analysis, we have split the 36-year reverse testing period into three separate 12-year periods.  
In the forward testing period 2012-2015, the non-strain-rate covariates PPI and PMF and strain covariates BSS and HWS are well-correlated with the locations of target earthquakes, as shown by the error diagrams deviating far below the diagonal (Figure 6). The ASS for each of these covariates is rather high, between 0.85 and 0.88. HWS has the highest ASS of 0.88. Again, this may be due to the partial overlap between the forward testing  
Figure 6: Molchan error diagrams for covariates (**a**) HWS, (**b**) BSS, (**c**) GSS, (**d**) PPI, (**e**) PMF, and (**f**) FLT, and target earthquakes in the forward test period 2012-2015.  
The range of variations in ASS values for a single covariate is an indicator of how widely the correlation varies between time periods. For the PMF covariate (Figure 7a), the correlation is equally high during fitting and forward testing periods (\(ASS_{1987-2006}=ASS_{2012-2015}=~{}0.85\)) and lowest during 1951-1962 (\(ASS_{1951-1962}=~{}0.72\)). For the PPI covariate (Figure 7b), the correlation with earthquake locations is highest during 2012-2015 (\(ASS_{2012-2015}=~{}0.84\)) and lowest during 1963-1974 (\(ASS_{1963-1974}=~{}0.70\)). For the FLT covariate (Figure 7c), the correlation is highest during the forward testing period (\(ASS_{2012-2015}=~{}0.72\)) and lowest during 1975-2006 (\(ASS_{1975-1986}=~{}0.56\), \(ASS_{1987-2006}=~{}0.57\)). For the HWS covariate (Figure 7d), the correlation is highest during 2012-2015 (\(ASS_{2012-2015}=~{}0.88\)) and lowest during 1963-1974 (\(ASS_{1963-1974}=~{}0.68\)). For the BSS covariate (Figure 7e), the correlation is highest during 2012-2015 (\(ASS_{1987-2006}=0.87\)) and lowest during 1963-1974 (\(ASS_{1963-1974}=0.65\)). For the GSS covariate (Figure 7f), the correlation is highest during 1987-2006 (\(ASS_{1987-2006}=0.81\)) and lowest during 1951-1962 (\(ASS_{1951-1962}=0.60\)). The low ASS can be explained by the fact that many of the target events in 1951-1962 were located where GSS had a value of zero (Figure 8).  
The variation of ASS values with time period is plotted for each covariate in Figure 9. No covariate has a consistently higher ASS than the other covariates across all time periods. As can be seen, the highest ASS among the covariates in 1951-1962 is that of PPI, in 1963-1974 that of PMF, in 1975-1986 that of GSS, in 1987-2006 that of BSS, and in 2012-2015 that of HWS. At the other end of the scale, the FLT covariate has the lowest ASS value in all time periods except 1963-1974, in which it shares the lowest value with BSS. Among the strain rate covariates, the highest ASS value is that of the HWS from 1951 to 1962 and 2012 to 2015, GSS from 1963 to 1974 and 1975 to 1986, and BSS from 1987 to 2006. Figure 9 also shows that the HWS covariate has a higher ASS value than BSS in all time periods except 1987-2006--the fitting period for the multiplicative models.