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Synthetic Seismicity of Multiple Interacting Faults and its use for Modelling Strong Ground Motion Russell Robinson & Rafael Benites Institute of Geological & Nuclear Sciences Limited, P.O. Box 30368, Lower Hutt, New Zealand Ph: +64-4-5701444 New Zealand AUSTRALIAN PLATE 45 mm/a North Island tectonic and bathymetric setting Chatham Islands /a m 5m 3 Image from NIWA National Institute of Water and Atmospheric Research Ltd South Island PACIFIC PLATE Wellington region topography Major faults of the Wellington region Wellington Fault 0 20 Depth (km) 40 60 PACIFIC PLATE 80 80 60 40 20 0 -20 Distance from Wellington (km) -40 -60 -80 Earthquake Commission (EQC) A small fraction of fire insurance premiums is used for earthquake insurance They asked GNS: • What is the probability of two (or more ) large earthquakes in the Wellington region within a few years of one another? • What sort of shaking should we expect from a large earthquake on the Wellington Fault? Synthetic Seismicity: • Computer model of a network of interacting faults and a driving mechanism. • Generates long catalogues of seismicity so that questions can be answered by statistical analysis. • Computationally efficient but reasonably realistic. • Fault properties are tuned to reproduce known slip rates/directions and other fault properties. Features: • Coulomb Failure Criterion. • Static/dynamic friction law, modified to include healing. • Okada’s (1992) dislocation routines for calculating induced stresses. • Stress propagation is at the shear wave velocity. Features: • Induced changes in pore pressure are included. • Mimics dynamic rupture effects to some degree. • All interaction terms are kept in RAM. • The program has been “parallelized” to run on a Beowulf PC cluster. Fault Interactions Stress history of a single cell Model faults Wellington Fault Fault Length: 75 km Fault Width: 20 km Fault Dip: 90o Cell Size: 1 x 1 km Coefficient of Friction: Asperity regions: Random between 0.65 and 0.95 Non-Asperity: Random between 0.40 and 0.70 Stress Drop: 25% Static/Dynamic Strength: 0.85 Healing Time: 3.0 s Dynamic Enhancement Factor: 1.2 Pore Pressure: Initially ~ hydrostatic; varies with time Stress Propagation Velocity: 3.0 km/s Typical ‘Characteristic’ Event Moment: 1.41 x 1020 N-m; Rupture Area Average Slip Area of Asperities Area of Largest Asperity Radius of Largest Asperity Num. of Asperities Area Covered by Asperities Average Asperity Slip Contrast Corner Spatial Wavenumber, Along Strike Along Dip Slip Duration Rupture Duration Mw 7.40 Model Sommerville (1999) 1500 km2 2810 km2 2.35 m 1.96 m 345 km2 630 km2 272 km2 458 km2 ~9 km2 13 km 2 + 1 very small 2.6 23% 22% 1.67 2.01 0.01 km-1 0.01 km-1 3.0 s ~30 s 0.01 km-1 0.02 km-1 2.55 s - Final slip distribution Rupturing ‘snapshots’ for a characteristic Wellington Fault event North Station East The whole rupture occurs in N time steps. In each time step n there are NR subfaults breaking METHOD •Discrete wave number •Generalised reflection/transmission coefficients (Bouchon 1979, Kennet 1973, Chin and Aki 1991) In the plane k-z ky k kx k x , k y ΨSV k x , k y ΨSH k x , k y Nr sin X Pm Φ k x , K y nm k x , k y exp( iωtn ) n 1 m 1 X Pm Ψ N k x , k y N n 1 n Nr sin XSm ψ nmk x , k y exp( iωtn ) m 1 XSm in which tn is the time shift corresponding to the time step n, XP and XS are the directivity correction factors for P and S waves, respectively, applied to each subfault m, and defined by: XP ωL υ p / υr cos θ 2 p XS ωL υs / υr cos θ 2 s with r = average rupture velocity, L = length of the subfault m, and the angle between the point source corresponding to the subfault m and the station. The components of the wavefield contribution of each subfault in the k-z plane are rotated to the geographical coordinates. The complete wavefield in the source layer L is computed from: ik ux i vL uz 2μL v L k τ zx τ zz μl l L for P-SV waves; and for SH waves, where: ik iγL ik i vL μl l L 2μL v L k 2μL γ L k μl l L u y - ik μ γ k τ zy L L 1 1 2k ω / β L ω / SV SV ΨSH Ψ SH 2 v L ω2 / 2L k 2 2 ik μl l L 2μL γ L k μL γ L k ik k k 2x k 2y lL i γL β 2L k 2 2 1 2 L 2 2 1 2 The propagation through the layers is performed by applying the generalized reflection/transmission coefficients. Ground displacement at x=5 km, y=70 km Velocity and acceleration www.gns.cri.nz Russell Robinson & Rafael Benites Institute of Geological & Nuclear Sciences Limited, P.O. Box 30368, Lower Hutt, New Zealand Ph: +64-4-5701444