title: Geodetic deformation model for the 2022 update of the New Zealand National Seismic Hazard Model
Creators: name: Johnson, Katelyn M
name: Wallace, Laura M.
name: Maurer, J.
name: Hamling, Ian J.
name: Williams, Charles A.
name: Rollins, Chris
name: Gerstenberger, Matt C.
name: Van Dissen, Russ J.
Publisher: name: GNS Science
Year: 2022

description: In order to incorporate geodetic measurements of contemporary deformation into the 2022 revision of the New Zealand National Seismic Hazard Model (NSHM), we develop strain rate and fault slip deficit rate models derived from New Zealand’s interseismic Global Navigation Satellite Systems (GNSS)-derived velocity field. Four strain-rate maps, derived from different methodologies, underpin elastic deformation models that are based on inversions of strain rate for slip deficit rates on the suite of faults being used in the New Zealand NSHM 2022 fault model. The methodology adopted for the geodetic-based deformation model here is different from the more commonly adopted methods for estimating long-term fault slip rates using elastic block models or fault-based deep-slipping dislocation models. The need to estimate a geodetic slip rate for the large number of often closely spaced faults in the fault model preclude the use of standard block models, and rapid tectonic rotation of the eastern North Island, observed in the velocity field, makes fault-based models (that do not explicitly include block rotations) difficult to implement. The key advantages of the strain-rate inversion approach adopted here are that it obviates the need to model block rotations and is not hindered by the large number of closely spaced faults. Furthermore, the strain-rate inversion method directly estimates the slip deficit rate, which is the difference between the long-term slip rate on the fault and the present-day creep rate. Slip deficit is assumed to drive the rate of interseismic elastic strain accumulation, much of which we assume will be relieved in future earthquakes. We compute strain-rate maps from the GNSS-derived velocity field using two purely statistical methods and two elasticity-based methods. The statistical methods include VELMAP, which solves for a spatially smooth velocity field by balancing the misfit between fitting observed velocities and minimising the Laplacian of the velocity field. The other uses geostatistical methods of variogram analysis and kriging to build realisations of the velocity and strain-rate fields with covariance structure inherent to the observed velocities. The physics-based methods derive a continuous velocity field using elasticity solutions. These methods solve for a distribution of body forces in an elastic thin plate that explain the observed velocity field and then compute the strain-rate field from the estimated distribution of forces. The Vertical Derivatives of Horizontal Stress (VDoHS) method uses the finite element method to compute elastic responses, while the body-force method adopts analytical expressions for the body-force responses. The principal result from the strain-rate maps is that the mean maximum shear strain rate is similar across all methods, while the spatial distribution of dilatation and strain-rate style differs more significantly. The maximum shear strain rate averaged across the country varies between about 0.1 and 0.12 micro-strain/yr (~20% variation) and the dilatation rate between about 0.015 and 0.023 micro-strain/yr (~40% variation). The dilatation rates appear to show the impact of different types of spatial interpolation methods, with VDoHS and body-force results being relatively smooth, while VELMAP and geostatistics are comparatively rougher but with different characteristics. The uncertainties of the four methods are also quite variable and reflect the assumptions of the method, while differences between methods highlight these assumptions. In particular, there are large differences in the strain rates estimated offshore by the various methods. The uncertainties of the VDoHS, body force and VELMAP methods are small relative to the differences between methods, while the geostatistical method has uncertainty larger than the differences. The inversion of strain-rate maps for slip deficit rate is based on the commonly held assumption in nearly every geodetic-based inversion for slip rates that the majority of present-day strain-rate field is elastic strain due to interseismic coupling across actively slipping faults. Under this assumption, the strain-rate field is linearly related to the slip deficit rates on faults. We discretise the New Zealand NSHM 2022 community fault model into rectangular slip patches in an elastic half space and solve for the spatial distribution of slip deficit rates on faults by inverting the four strain-rate maps. We conduct suites of inversions with and without the geologic slip rate model as a prior on slip deficit rates. The differences in slip deficit rate across all four strain-rate map inversions is typically less than 3–4 mm/yr for the high-rate faults. There are some notable differences between the geologic slip-rate model and the slip deficit inversion results. The geodesy-based inversions infer higher slip rates on belts of faults along the major strike-slip systems, including the Alpine Fault, the Marlborough Fault System and the northern part of the North Island Dextral Fault Belt. The geodesy-based inversions also infer systematically higher slip deficit rates on a complex system of reverse and strike-slip faulting in northern Canterbury and on some faults in the Otago region. The geodetic rates are systematically lower along the near-shore part of the Hikurangi margin. The slip deficit rate models explain 70–80% of the total strain-rate field; the remaining 20–30% of the strain-rate field cannot be mapped to slip deficit rates on faults. Residual strain rates that are not explained by slip deficit rates on faults are relatively low, with maximum shear strain rates typically less than about 0.1 micro-strain/yr. However, the residual strain rates are not randomly distributed; there are systematic spatial patterns to the style of the residual strain-rate field. indicating a potential tectonic origin to the residual strain rates. Finally, the depth distribution of slip deficit rate is not well resolved by the inversions on most of the faults. (The authors)