THESIS, Munich, 13.06.2006

Using Numerical Green’s Function Method to Investigate Ground Motion Variation

In collaboration with Heiner Igel, LMU,

Alain Cochard, LMU, Michael Ewald, LMU.

Haijiang Wang

LMU

Outline

• Motivation (source related ground motion uncertainty)

• Numerical Green‘s Function approach• Uncertainty – due to hypocentre location• Uncertainty – due to varying slip distribution• Conclusions

Motivation

Ewald et al., 2006

Amplitude amplification Duration time elongationBasin effect

But few attention was paid on source complexity (3D) ...

Motivation

For large earthquake, point source is not sufficient and at least kinematic finite source is necessary to describe the source process

• Special attention should be paid to the directivity

• Source complexity• Static displacement (asperity)• Rupture velocity• Slip velocity

Numerical Green‘s Function

• Theory

• Optimal largest subfault size

• Study area and fault

• Database created

Numerical Green‘s Function

N

iiiiiiiijj Astgtv

1

0 )(),(),( xx

Theory

Numerical Green‘s Function

Optimal subfault size – homogeneous case

Accuracy increases with the increase of

• cut-off frequency• rupture velocity• magnitude

Spatial discretization (km)

1000

Temporal discretization (s)

0.0822

S-wave velocity (km/s) 3.9

Simulation time (s) 50

Study area (km) 150×130x60

PML Nodes 10

Constant slip rate (m/s) 1

Numerical Green‘s Function

Study area

N

SCEC cvm version3

Numerical Green‘s Function

Newport Inglewood Fault

SCEC cfm

• M6.4 Long Beach earthquake in 1933 (Hauksson and Gross, 1991)

• Probable source for a damaging earthquake

• Near-vertical plane and predominant right-lateral slip (SCEC cfm)

Grant and Shearer, 2004

Numerical Green‘s Function

Verification – heterogeneous case

subfault size 1.5 km can be applied as the principal subfault size to the generation of the NGF data base

Spatial discretization 300 m

Temporal discretization 0.018 s

Lowest S-wave velocity 1.4 km/s

Simulation time 65

Number of cells 550×500x150

PML Nodes 10

Magnitude 7.0

Fault dimension 16 x36 km

Numerical Green‘s Function

Database

Spatial discretization (km) 0.300

Temporal discretization (s) 0.01811

Lowest S-wave velocity (km/s) 1.400

Simulation time (s) 65

Number of cells 550×500x150

Fault length dimension (km) 60×19

Surface grid distance (m) 600

Ground motion components 6

Total database size (Tb) 1.5

Summary 1

• Equation for synthesization of NGFs is developed.

• Optimal subfault size is investigated both for homogeneous media and heterogeneous media.

• Database is created for the Newport Inglewood fault embedded in the Los Angeles basin with appropriate setup.

Uncertainty - Hypocentre

Outline

• Motivation• Hypocentre locations• Velocity snapshots• Basin amplification

• PGV characteristics variation with hypocentre location

Uncertainty - Hypocentre

Static displacement and hypocentres

Guatteri et al., 2005

Uncertainty - Hypocentre

Velocity snapshots

Uncertainty - Hypocentre

Velocity Profiles

Uncertantity - Hypocentre

PGV characteristics

Uncertantity - Hypocentre

Varying source depth

Summary 2

• Horizontal hypocentre variation influences the ground motion

• Vertical hypocentre variation has only slight influence on the ground motion

• In the area far from the fault, the medium plays main role on ground motion variation while in the area very close to the fault plane the hypocentre does

Uncertainty - Slip

Outline

• Quasi-dynamic rutpure process generation

• Directivity effect

• Slip variation effect

• PGV characteristics

Uncertantity - Slip

Guatteri et al., 2005

Quasi-dynamic rutpure process

Uncertantity - Slip

Wang et al., 2006, submitted to ESG

Uncertantity - Slip

Directivity

Somerville et al., 1997 Aki & Richards, 2002

Uncertantity - Slip

Different directivity on

different components

the fault perpendicular component is dominated by the directivity effect and the fault parallel and vertical components have significant contribution from the 3-D structure (basin effects) and slip distribution.

Wang et al., 2006, submitted to ESG

Uncertantity - Slip

Three individual slips

Wang et al., 2006, submitted to ESG

Uncertantity - Slip

PGV characteristics: maximum value and standard deviation

Wang et al., 2006, submitted to ESG

Summary 3

• Directivity effect dominates the fault perpendicular component

• Fault parallel and vertical components have significant contribution from the 3-D structure (basin effects) and slip distribution.

• Slip asperity elevates the ground motion in its nearby area.• The maximum seismic motion variation on the surface is do

minated by directivity.

Conclusions

We investigate the ground motion variations due to sets of parameters using our new-developed method Numerical Green’s Function…

1. Horizontal hypocentre location variations influence the ground motion.

2. Dominant directivity effect on the fault perpendicular component is confirmed by our simulations while fault parallel components are controled by both the source properties and the basin structure, for this specific case.

3. Slip asperity elevates the ground motion in its nearby area.

4. The maximum seismic motion variation on the surface is dominated by directivity.

Future Works

• Investigation of rotational motions– Peak rotational motions– Attenuation relations for rotations– Source vs. 3D effects for rotations

End

Thanks