Earthquake modelling with complex geometries by curved grid finite-difference method

Transcription

1 FSEF2017, Shenzhen, China Nov 27 Dec. 1, 2017 Earthquake modelling with complex geometries by curved grid finite-difference method Zhenguo Zhang Department of Earth and Space Sciences, Southern University of Science and Technology Nov 30, 2017 Acknowledgements: Xiaofei Chen, Wei Zhang from SUSTech Wenqiang Zhang, Hanqing Huang from USTC Ping en Li, CAS Haohuan Fu, Tsinghua Univ. 1

2 Content Introduction Basic theory of curved grid FDM Examples 2

3 Simple case: planar fault + regular free surface 3

4 Geo-morphological Setting of the Wenchuan Earthquake Source region is located at the boundary of tectonic blocks, where there are large and sharp changes in the crustal structure, 4 topography and hazards.

5 Topography effect on ground motion Ground motion simulation of Wenchuan earthquake Zhang et al.,

6 Simulated ground motion-peak ground motion of 2015 Nepal earthquake China seismic intensity distribution 6

7 Compare for cases with and without topography 7

8 Compare for cases with and without topography 8

9 Compare for cases with and without topography 9

10 Topography effect on ground motion Ground motion simulation for Yangminshan region of Taiwan Lee et al.,

11 Real fault surface Magnola fault outcrop Candela et al. (2009) 11

12 Roughness fault Self-affinity in 2-D Candela et al. (2009) 12

13 Shi and Day,

14 Which method? So a powerful numerical method is needed to be solve elastodynamic equations with these geometrical complexities FDM, FEM, SEM, FVM, Dis-Galerkin, 14

15 Which method? So a powerful numerical method is needed to be solve elastodynamic equations with these geometrical complexities FDM, FEM, SEM, FVM, Dis-Galerkin, Curved-grid finite-difference method (CG-FDM) 15

16 Content Introduction Basic theory of curved grid FDM Examples 16

17 Curved Grids FDM (1) Basic Equations: Boundary-conforming transform Free surface Free surface Physical space Computational space Boundary-conforming transform Zhang et al. (2012) GJI 17

18 Curved Grids FDM (2) Traction Image Method Free surface Free Surface Condition: T n σ 0 Physical Space T T x y 1, x xx, y xy N 1 N, x yx, y yy Mirroring anti-symmetric mapping at free surface 18

19 Curved Grids FDM (3) Split Nodes Zhang et al. (2014) GJI 19

20 Basic mathematics 20

21 Basic mathematics 21

22 New defined variables Momentum equation: 22

23 Lower order FD scheme We usually densify the grid near fault plane in the normal direction of it. 23

24 Free surface Simple 2-D cartoon Zhang et al., BSSA,

25 Content Introduction Basic theory of curved grid FDM Examples 26

26 Benchmark problem TPV28 Compared with FEM SOM 27

27 Normal Parallel Vertical 28

28 Seismogram comparison Normal Parallel Vertical 29

29 Full-space, roughness fault dh =20 m λ min =80 m 30

30 Half-space, TPV29 31

31 32

32 Elastic model TPV29 Viscoplastic model TPV30 More results can be found at SCEC website 33

33 Topographical effect Zhang et al. (2016) GRL 34

34 Peak slip velocity on fault planes Huang et al., 2018 GJI 35

35 PGV-Fault normal component Huang et al., 2018 GJI 36

36 Tangshan earthquake simulation on Sunway TaihuLight 37

37 Tangshan earthquake simulation on Sunway TaihuLight 38

38 39

39 Tectonic Stress NE Principal compressive stress field North Side: NE South Side: NEE σ v = ( ρ 0 -ρ f ) gh σ H = 0.75 σ v σ h = 0.35 σ v 40

40 Dynamic rupture process 41

41 Ground Motion Simulation site effect Comparison with different spatial resolutions (red: 20m, blue: 100m) Quaternary sediments (digitized from W. Chen, 1987) Low filtering to 0.5Hz and normalized 42

42 Dynamic rupture simulation of Wenchuan earthquake (Shen et al., 2009) 43

43 Simulations with planar fault Final Slip Distributions 44

44 Simulation of Rupture dynamics (Non-planar fault model) Final Slip Distributions 45

45 Non-planar fault model (Shen et at., 2009) Planar fault model 46

46 Scenario earthquake modelling with CG-FDM 47

47 Shanxi rift Li et al., 2015, GJI 48

48 Shanxi rift Li et al., 2015, GJI 49

49 Shanxi rift Three events by geological survey: (3.74 ± 0.060) (3.06±0.26) ka (8.35 ± 0.090) (3.74 ± 0.060) ka (10.66 ± 0.85) (8.35 ± 0.09) ka M>7 Li et al., 2015, GJI 50

50 Fault model Surface trace 3D model 51

51 Media model 52

52 Regional stress R=(σ 1 -σ 2 )/(σ 1 -σ 3 ) σ 1 > σ 2 > σ 3 Li et al., 2015, GJI 53

53 Parameters Grid spacing:100m Fault length:110*20km Dipping angle: 60, normal fault Friction parameters: Dc=0.4 μ s =0.42 μ d =0.26 (σ H -σ h )/(σ v -σ h )=0.8 54

54 Parameters: tectonic stress 0-14km σ v =(ρ- ρ w )gh(vertical), σ H =0.9ρgh(240 azimuth) σ h =0.5ρgh(330 azimuth) 14-19km changing to σ v =σ H =σ h 55

55 Friction law: 56

56 Results Mw=7.5 Duration time: 30s Dipping slipping with little right-lateral component 57

57 Different nucleation location Note: The moment magnitudes of four earthquakes are close. Moment releasing rate 58

58 59

59 Rupture 60

60 σ h Azimuth:

61 Chinese seismic intensity 62

62 Take-home messages We design a method CG-FDM which has the ability of modeling the dynamic rupture and strong ground motion of earthquake with complex geometries Topographic effect are needed to accurately evaluate the strong ground motion of earthquakes Rupture pattern can be modified by the irregular free surface 63

63 Thank you! 64