# How Useful Are Strain Rates for Estimating the Long-Term Spatial Distribution of Earthquakes?
## 4 Discussion  
The low information gain of hybrid models including strain rate covariates in reverse testing is consistent with the relatively low ASS values of the strain rate covariates and low strain rate values associated with target earthquakes from 1951 to 1986. The ASS values of the strain rate covariates in the reverse testing period are not only lower than in the fitting period but are also lower than the ASS values of the PPI and PMF covariates during the reverse testing period (Figures 7 and 8). The contrast of ASS values between the fitting and reverse testing periods is particularly strong for BSS. This explains the negative IGPEs for hybrids with BSS in the reverse testing period (Figure 3c). Similarly, the large IGPE for hybrids with HWS in forward testing is consistent with the high ASS for HWS in 2012-2015 and with the slow tailing off between 2010 and 2020 of the trend in HWS associated with target earthquakes. Evidently, if the forward testing  
Figure 11: Fault covariate values for targeted earthquakes against magnitude, 1951–2020. The solid black line shows the smoothed scatter plot. The blue triangles depict the values of the FLT covariate for each target earthquake. period were extended through to 2020, hybrids including HWS would have continued to perform well. Differences between the three present strain rate models can be attributed to the differences in the geodetic datasets on which they were based and the evolving techniques for estimating strain rates from the geodetic data. The most recently developed of the three models is the HWS model, which was published in 2020. HWS was derived from the most complete data and up-to-date techniques and showed the best correlation with the locations of the most recent earthquakes (Figure 7). However, all three strain rate models exhibit a disappointingly low correlation with the locations of earthquakes from 1951 to 1986. The implicit assumption behind the fitting of hybrid models to estimate long-term earthquake rates is that the correlation between the covariates and the locations of target earthquakes is stable over time. Alternatively, if not stable over time, the correlation during the fitting period should be indicative of the long-term correlation. The correlations for PPI and PMF appear to be more stable over time than those for the strain rate covariates, based on the ASS variations. PPI and PMF represent features that are expected to affect earthquake occurrence over a long time frame. The greater instability of the correlation for strain rate covariates may be attributed to the short-term non-stationarity of earthquake occurrence. The strain rate covariates are most highly correlated with earthquake occurrence within the time period of the data on which they are based or within a few years after (Figure 7). Without a dense GNSS network and extensive historical and paleo-seismicity records, it is not possible to pinpoint temporal and spatial variations of strain rates. Recently, [PERSON] et al. obtained high temporal histories of slip rates for three parallel normal faults in central Greece with progressive clusters using in situ 36 Cl cosmogenic dating [28]. They also had access to associated GNSS recordings of a dense network. They compared regional decadal geodetic strain rates with strain rates derived from slip-rate pulses over a few thousand years on each fault. They found that strain builds up across a fault system over thousands of years, but not all individual faults actively slip at the same time. They discussed how the available geodetic data alone was not capable of pinpointing the switchover of slip from one fault to another over time. In comparison, New Zealand has neither a dense GNSS network nor a comparable record of fault slip histories. The density of GNSS stations has been progressively improving but is still sparse in some parts and limited to onshore regions [14]. Obviously, this affects the accuracy of the strain rate models in NZ offshore regions, where many of the earthquakes occur.