# How Useful Are Strain Rates for Estimating the Long-Term Spatial Distribution of Earthquakes?
## 1 Introduction  
Estimation of the long-term spatial distribution of earthquakes is an essential component of Probabilistic Seismic Hazard Analysis (PSHA). In the traditional approach to PSHA, the estimation is based mainly on the combined information from studies of the long-term slip rates and rupture histories of mapped faults and spatial smoothing of the locations of past earthquakes. However, other emerging data streams, including geodetic observations from the global navigation satellite system (GNSS) and derived strain-rate models, seem to offer promise for improving the estimation [1; 2; 3; 4; 5]. In a revision of the New Zealand (NZ) National Seismic Hazard Model (NZNSHM) currently being undertaken, we are interested in assessing the relative value of different available data inputs, including information from fault studies, tectonics, the earthquake catalogue, and strain rate models, for estimating the long-term spatial distribution of earthquakes. In particular, we are interested in assessing how strongly strain rate estimates based on a few decades of geodetic data should be weighted when estimating the long-term spatial distribution of earthquakes.  
A multiplicative hybrid modelling framework [6] was developed to optimally combine a set of spatially gridded forecasts submitted to the five-year regional earthquake likelihoodmodels (RELM) experiment in California [7; 8]. It was found that, although one best model strongly outperformed all others individually [9], it was possible to find several hybrid models that could outperform the best individual model over the 5-year period of the experiment. Such hybrid models were formed from pairs of models, including the best model as the baseline.  
Multiplicative hybrid modelling has since been used to combine gridded information from fault, earthquake, and strain rate covariates in NZ [10; 11] with a simple Stationary Uniform Poisson (SUP) baseline earthquake likelihood model. When hybrids only of fault- and earthquake-based variables were considered, any hybrid model that included one particular covariate called \"Proximity to Mapped Faults\" (PMF) outperformed all hybrids without PMF in both a 20-year fitting period and an independent testing period [10]. The PMF covariate was derived from the locations of NZ mapped faults and their estimated slip rates. Subsequently, [PERSON] et al. [11] used models for maximum shear, rotational and dilatational strain rates by [PERSON] [12], based on GNSS data from 1996-2011, as additional covariates. They found that any hybrid including shear strain rate (BSS) outperformed all hybrids not including BSS in both the 20-year fitting period and an independent testing period.  
In the present study, we restrict our attention to (maximum) shear strain rate models. In addition to BSS, we consider the global shear strain rate model of [PERSON] et al. [13] based on GNSS data over the period 1996-2013 (GSS) and an updated NZ strain rate model by [PERSON] [14] based on GNSS data from 1995-2013 (HWS). We analyse the performance of multiplicative hybrids during the fitting and testing periods used by [PERSON] et al. [11] with GSS and HWS as alternative strain rate covariates. We then examine the stability of the multiplicative modelling results by testing them against earthquakes from 1951 to 1986. Furthermore, we evaluate the strain rate and other covariates as earthquake predictors using Molchan error diagrams. We also produce smoothed scatter plots of covariate values corresponding to targeted earthquakes against time from 1951 to 2020. These results are relevant to the question of how useful strain rate estimates are for the assessment of long-term seismic hazards.