1.
THESIS, Munich,
Using Numerical Green’s Function Method to Investigate Ground Motion Variation
Haijiang Wang
LMU
What affects the ground motion can be splitted into two discplines: source properties and media. In the recent time, lots of simulations have been carried out to investigate the basin strucure effect. But how the source physics influcence the seismic motion is still not well enough investigated. For one seismic active fault or fault system, considering the source physics complexity, lots of different earthquake need to be simulated to complement the earthquake engineer‘s demand for the aim of earthquake hazard analysis.
In this talk, by taking the advantage of our new develped method – Numerical green‘s function method, we do a set of simulations to investigate the source physics effect on the ground motion during earthquakes which, in the future, may probably happen on the Newport Inglewood fault embedded in the Los Angeles basin.
In collaboration with Heiner Igel, LMU, Alain Cochard, LMU, Michael Ewald, LMU.

2. Outline Motivation (source related ground motion uncertainty)
Motivation (source related ground motion uncertainty)
Numerical Green‘s Function approach
Uncertainty – due to hypocentre location
Uncertainty – due to varying slip distribution
Conclusions
First I briefly introduce the present situation of the earthquake simulation and give the motivation of this work.
Then the NGF method is briefly descripted and verificated both in the homogeneous medium and heterogeneous medium.
Withe the NGF database available, 24 inter-events with same static displacement but different hypocentre are caried out to show how ground motion is affected by the hypocentre variation.
The we fixed the hypocentre but adopt different rutpure process to show the source physics effect on the ground motion.

3. Motivation Basin effect Amplitude amplification
Basin effect
Ewald et al., 2006
Amplitude amplification
Duration time elongation
Normally inside the basin, especially at the deep edge of the basin, larger ground motion amplitude is observed comparing outside the basin. And the ground motion durate for longer time, too. This two phenomena can be well reproduced by the mordern earthquake simulation like what Michael has done for the 1992 local magnitude 5.9 Roemond earthquake happened in the Lower Rhine Embayment.
But few attention was paid on source complexity (3D) ...

4. 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
And for large earthqukae, at least kinematic finite source is necessary to descript how the fault moves during an earthquake.
Kinematic finite source simulation have been carried out for homogeneous medium and the results show that directivity affects differently to the fault perpendicular and parrallel ground motion component.
These three groups of parameters are used to describe the kinematic finite source. Static displacement can be achieved by the inversion of the recorded ground motion. The area with higher final slip is defined as asperity and normally will lead to larger ground motion in its nearby area.
Considering the source complexity for a possible earthquake, lots of simulation need to be carried out. In order to fullfill this aim, we suggest one new method, namely the Numerical Green‘s Function method.

5. Numerical Green‘s Function
Theory
Optimal largest subfault size
Study area and fault
Database created
We describe the basic idea behind the numerical green‘s function method.
Then decide the optimal largest subfault size for one hypothesis homogeneous medium.
The Los Angeles basin and the Newport Inglewood fault are chosen to apply this method.
With the optimal largest subfault size decided, we create the database.

6. Numerical Green‘s Function
Theory
Ground motion is recorded at one station on the surface during an large earthquake. Here is the fault plane for this large earthquake and we can enlarge it to the right. When this earthquake occurs, each part, roughly described with those rectangular, of the fault plane is excited one by one, moves with a specific pattern, and radiate an impulse energy which propagates through the media to that station. The forward mentioned ground motion is actually the synthesization of all these individual energies. We call these individual energy as the Numerical Green’s Function which include the radiation pattern and the wave propagation path information.
So the general idea behind the NGFs method is to provide all these individual energies and present an appropriate way to synthesize these NGFs according to different source processes.
When calculating the Green’s functions, all grid points occupied by one sub-fault are sliding at the same time with the same pattern. The resulting discontinuous behavior - compared to the continuous solution - will introduce errors into the ground motion synthesization. These errors were investigated first for one hypothesis homogeneous medium.

7. Numerical Green‘s Function
Optimal subfault size – homogeneous case
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
It is straightforward that the larger the subfault size used, the larger could be this discontinuity. Considering the generation of a NGF data base is computationally expensive, one should attempt to find a minimum number of subfaults necessary to achieve scenario ground motions with sufficient accuracy.
The solution with subfault size of 0.5 km is first created and taken as the “continuous” solution. Peak correlation coefficient (PCC) between the seismograms of the differently discretized solution (Fig. a, top right corner), like 1.5 km and 1.8 km, respectively, and the “continuous” solution are used to show the accuracy of the discretized solution, where high PCC means high accuracy and PCC equals 1 means the seismograms are identical.
The rupture starts at the left side of the fault plane and propagated unilaterally to the right. In the triangle area right behind the rupture propagation, the PCC values are small with minimum value of top right corner, the time between the tow obvious differences is around 17 s which is right the total duration time of the breaking for that M7 earthquake.
When the seismograms are filtered with cut-off period of 4.0 s, the minimum PCC value of the study area are higher than those filtered with cut-off period of 3.0 s.
the accuracy is observed to increase with the rupture velocity in Fig c.
the magnitude (fault dimension) increase will lead to bigger accuracy in Fig d.
Accuracy increases with the increase of
cut-off frequency
rupture velocity
magnitude

8. Numerical Green‘s Function
Study area
study area, rotated in order to have one horizontal grid axis parallel to the NI fault.
The velocity model is based on the elastic part of the SCEC 3-D velocity model for the Los Angeles (LA) Basin (Version 3, N
SCEC cvm version3

9. Numerical Green‘s Function
Grant and Shearer, 2004
Newport Inglewood Fault
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)
SCEC cfm

10. 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
The accuracy of the synthesized ground motions as a function of sub-fault size is investigated for a M7 earthquake with a computational setup and source parameters given in left Table.
As an indicator of the accuracy we compare the peak ground velocity (PGV) over the whole surface area covering frequencies up to 0.5 Hz.
PGV difference (x-component) between the discretized solution (subfault size of 1.8 km) and the “continuous” solution is shown in fig a (note the sign of the PGV difference). The largest difference is m/s in the exact position of the largest PGV, 1.1 m/s.
To be on the safe side we chose subfault size of 1.5 km as the principal subfault size to the generation of the NGF data base.

11. Numerical Green‘s Function
Database
Spatial discretization (km)
0.300
Temporal discretization (s)
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

12. 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.

13. Uncertainty - Hypocentre
Outline
Motivation
Hypocentre locations
Velocity snapshots
Basin amplification
PGV characteristics variation with hypocentre location
A question of considerable practical relevance to estimates of seismic hazard is how variations of the hypocenter location for a given final slip distribution influence the shaking for a characteristic earthquake of a given magnitude. Amongst many other possibilities, this is the question we will focus on in this sample study:

14. Uncertainty - Hypocentre
Static displacement and hypocentres
we assume the existence of a characteristic M7 earthquake on the entire NI fault and synthesize ground motions for a 4x6 regular grid of hypocenter locations in the seismogenic zone (5-15 km depth)
The final slip distribution is generated randomly with a given isotropic correlation length (5 km). The slip histories are calculated quasi-dynamically following Guatteri et al. (2005) accounting for the accelerating tendency of the crack front due to dynamic loading and the high stress-drop promotion of fast rupture propagation. The shear-modulus on the fault is kept constant and corresponds to a shear velocity of 3.2 km/s.
Guatteri et al., 2005

15. Uncertainty - Hypocentre
Velocity snapshots
In this slide, snapshot of the y-component velocity at the surface is shown. Source and basin related effects on ground motion are obvious in this figure. Due to the unilaterally rupture propagation from right to left, most energy are recorded on the surface at the left of the fault plane, or little energy is observed behind the rupture propagation. Unsymmetrical wave front at time s and s (according to fault plane) are explained as the media effect (the fault plane is right on the basin edge). Trapped energy and reverberation inside the basin is observed after time s.

16. Uncertainty - Hypocentre
Velocity Profiles
Basin amplified effect on the wave fronts crossing the basin are apparent in one profile shown in Fig. up.

17. Uncertantity - Hypocentre
PGV characteristics
Two examples of the resulting PGVs in the LA Basin are shown in Fig. up2 for the hypocenter locations H1 (5km depth, located at SE fault edge) and H2 (15 km depth located towards the centre) as indicated . The shallow hypocentre with unilateral rupture propagation (H1, Fig. 6a) leads to a directivity-dominated distribution of PGVs towards the NW end of the fault, while the PGVs of the bilaterally propagating rupture from the deeper hypocentre (H2, Fig. 6b) show a clear distance dependence from the fault with dominant PGVs in the NW part. This is mainly due to the main slip occurring in the northern part of the fault (see Fig. 2). However, it is important to note that the deeper hypocentre illuminates the entire basin leading to considerable more basin-wide shaking compared to the shallower hypocentre.
The parameter study in the hypocentre space allows us to extract the PGVs of all 24 simulations (Fig. 6c) containing the dominant features of the previously shown two examples with basin wide shaking, fault-distance dependent ground motion, and peak motions above the fault area with the largest slip (asperity). The variations of the hypocentre-dependent ground motions can be expressed by relating the variance of the PGV to the mean PGV at each point of the surface grid. The resulting distribution illustrates the regions in which most variations of ground motions are to be expected from the hypocentre location. These variations are surprisingly symmetric around the fault edges with some amplification from the basin edges particularly on the SE end. It is interesting to note that – except at the fault edges – the variations are considerably larger inside the basin but at some distance from the fault.

18. Uncertantity - Hypocentre
Varying source depth
We investigate the relationship between PGV and source depth for all simulated scenarios and two receivers indicated in Fig. 7 (R1, 40 km from the fault, inside the basin; R2, above the centre of the fault). Horizontal velocity seismograms (fault-parallel component) are shown for receivers R1+2 and four different hypocentral depths (same epicentre) as indicated in Fig. 2 (inlet, white rectangle). The PGVs (and variance) for all 24 simulations at receivers R1+2 are displayed as a function of source depth in Fig. 7c+d, respectively. For the distant receiver (R1, Fig. 7c) the mean PGV increases slightly with source depth, while the variance is much larger for deeper events, indicating a stronger path-dependence for wave fields arriving from deep sources than from shallow sources. The opposite behaviour is observed for receiver R2 close to the fault (Fig. 7d). The mean PGV and its variance decrease with source depth indicating that the upward propagating rupture and the associated directivity effect dominates the PGV in this region.

19. 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

20. Uncertainty - Slip Outline Quasi-dynamic rutpure process generation
Outline
Quasi-dynamic rutpure process generation
Directivity effect
Slip variation effect
PGV characteristics
Guatteri presented one method to calculate the quasi-dynamic rutpure process. We use their method and created 20 different rutpure processes.
Directivity effect is paid special attention both from the theoretical and practical observation point view.
At last we show some pgv distribution corresponding to different static displacements and analyze the asperity properties effect on the pgv distribution.
Finally the statistic property of all 20 PGV distributions are shown.

21. Quasi-dynamic rutpure process
Uncertantity - Slip
Guatteri et al., 2005
Quasi-dynamic rutpure process

22. Uncertantity - Slip Wang et al., 2006, submitted to ESG 24.11.2018
Numbered slip histories used in the simulations. Red stars mark the hypocenters. White and black lines show the comparison of single cumulative slip to the mean cumulative slip (of all slip histories), respectively.
Wang et al., 2006, submitted to ESG

23. Uncertantity - Slip Directivity Somerville et al., 1997
Somerville et al., 1997
Directivity
Aki & Richards, 2002
Illustration of directivity in velocity pulses recorded in the 1992 Landers, California, earthquake. Rupture propagated north from the epicenter, away from the station at Joshua Tree (with the long, low amplitude velocity trace) and towards the Lucerne station (with the stronger, compact velocity pulse). (from Somerville et al., 1997)
From the S-wave radiation pattern of one double couple point source solution, we can see when pure strike slip is assummed the fault plane perpendicular component gets more contribution from the kinematic source than the fault parrallel component.

24. Uncertantity - Slip Different directivity on different components
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.
The area, with mean PGV of y-component larger than 0.8 m/s (black rectangular, Figure 3, middle), is the area towards which the rupture propagates and where directivity plays the most obvious role. We name that area A. The maximum value of mean PGV in this area A for the y-component (fault perpendicular) is around 1.7 m/s, and almost twice larger than that for the x-component (fault parallel) and almost three times larger than that for the vertical component (note the different color scale). At the same time elevated mean PGV is observed inside the basin but outside area A both in the x-component and the vertical component indicating the influence of basin structure and the slip variation.
Wang et al., 2006, submitted to ESG

25. Uncertantity - Slip Three individual slips
Three individual slips
To study the effects of various slip histories in more detail we take four different slip histories as example and show the resulting PGV distributions (Figure 4). These four slip histories are considered to be representative and their slip distributions are shown in the top. Slip 5 has a distinct asperity area right in the middle of the fault. Slip 7 has a smaller asperity area with very large slip close to the hypocenter. Slip 10 has a more uniformly distributed slip. Slip 16 has two asperity areas and the major part is located in the bottom half part of the fault. For slip 16, seismic motions have smaller amplitudes compared to the other three slip models because the most part of slip occurs in the bottom half part and further from the surface. Slip 5 gives a large PGV in the region close to its high slip asperity, especially in the x-component, indicating that large seismic motion is expected in the area close to asperities. This effect can also be seen in the results of slip 10 － there is a low PGV band between two high PGV areas along the fault plane that coincide with low cumulative slip as indicated in Figure 2.
Wang et al., 2006, submitted to ESG

26. Uncertantity - Slip
PGV characteristics: maximum value and standard deviation
Considering the complex PGV distribution on the surface due to different slip histories, it is instructive to present the possible range, namely maximum and variation (standard deviation), of shaking deduced from the 20 earthquakes for the NI fault. We show those ground motion characteristics.
To give a further illustration of the directivity effect, those shaking variations related to the two horizontal velocity components, x and y, are also shown.
The largest PGV standard deviation of the x-component is observed in the area near the epicenter. A directivity effect is not visible even in the far end area of the fault. The basin structure and the slip histories seem to control the seismic motion generation. Basin-structure dependent amplification can also be seen from both the mean value and standard value of the x-component PGV distributions. This further demonstrates that directivity does have different effects on the three seismic motion components.
The maximum PGV distribution of the modulus component, i.e. the length of the velocity vector, looks similar to the one for the fault perpendicular component both in terms of absolute maximum value and spatial pattern. We conclude that the maximum seismic motion variation on the surface is dominated by directivity. The source related variations, however, are different for the fault parallel component and the fault perpendicular component.
Wang et al., 2006, submitted to ESG

27. 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 dominated by directivity.

28. Conclusions
We investigate the ground motion variations due to sets of parameters using our new-developed method Numerical Green’s Function…
Horizontal hypocentre location variations influence the ground motion.
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.
Slip asperity elevates the ground motion in its nearby area.
The maximum seismic motion variation on the surface is dominated by directivity.

29. Future Works Investigation of rotational motions
Peak rotational motions
Attenuation relations for rotations
Source vs. 3D effects for rotations

30. End
Thanks