1. 2University of Southern California, 3San Diego Supercomputer Center
F3DT : A Computational Platform for Full-3D Waveform Tomography in Southern California
1En-Jui Lee, 1Po Chen, 2Thomas H. Jordan, 2Philip Maechling, 3Yifeng Cui, 2Scott Callaghan
1University of Wyoming,
2University of Southern California,
3San Diego Supercomputer Center
Good morning. Today I am going to present our full-3D waveform tomography in Southern California

2. Overview Motivation Methodology Results Future work Summary
In this talk, I will talk about our motivation of this research, the methods we used, our current results, future work and then summary.

3. Motivation Data Synthetic Blue: data Red: synthetic
First of all, the main motivation of this research is seismic hazard analysis purpose.
Advances in computer science allow us to simulate wave field in complex 3D structure model.
Accurate ground motion predictions depend both on the source that generate the wave and the velocity model which the wave propagated through.
In this example, we simulate an earthquake source close the SA fault.
The synthetic results could recover 3D complex effects quite well.
Such as the energy has been channeled into LA basin through a low velocity sediment valley and the basin amplification effect in LA basin area.
Most of synthetic waveforms are well agree with data, but still has room to improve the velocity model.
Synthetic
Blue: data
Red: synthetic
16 Jun 2005, ML4.9, Yucaipa earthquake

4. Study Area Ns : 172 earthquakes with ML≥3.5
Nr : 200 broadband 3-component stations
Over 3,500 selected phases
The map shows the stations and earthquakes we used in our first iteration.
So far, we used 172 earthquakes with magnitude greater than 3.5 and picked over 3,500 phases of body waves and surface waves.

5. Methodology Initial Model & Forward Computation Data Functional
SCEC Community Velocity Model 4.0
4th-order staggered-grid Finite-difference (Olsen 1994)
Data Functional
Generalized Seismological Data Functionals
(GSDF) of Gee & Jordan (1992)
Data Sensitivity Kernel
Scattering-integral (SI) method (Zhao et al. 2005)
Gauss-Newton optimization
LSQR (Paige and Saunders,1982)
We used the SCEC community velocity model version 4 as our 3D initial model.
For forward computation, we used finite difference method that developed by Olsen
For data functional, we used generalized seismological data functionals to capture the waveform differences between synthetic and observed seismograms.
We adopted the scattering-integral method to constrain our Data sensitivity Kernel.
The Gauss-Newton optimization was used to invert our velocity structures.

6. Reference model: SCEC Community Velocity Model 3.0
We used the SCEC CVM4 as our initial model.
This 3D velocity model already included basins structures in southern California, so this is a good initial model for inverting more accurate 3D structures.

7. Linearized Forward Problem
Tomography model
δm: model perturbation (δα, δβ …)
K: Fréchet kernel
Waveform differences
GSDF measurements
The problem we want to solve could be linearized.
The waveform differences may come from seismic source and/or the velocity model.
In this research, we used the GSDF measurements at different frequencies to capture the waveform differences.
Currently, we are using CMT solution as our source model.
We have another presentation of CMT source inversion at tomorrow afternoon, please come to our another talk.
The Fréchet kernel are computed by using 3D full-physics wave propagation method at initial model m0.
Source model
δμ¹: centroid moment tensor (CMT)
δμ²: finite moment tensor (FMT)

8. Linearized Forward Problem
source model
δμ¹: centroid moment tensor (CMT) perturbation
δμ²: finite moment tensor (FMT)
- temporal span
- spatial size
- rupture velocity (directivity)
The problem we want to solve could be linearized. The waveform differences may come from seismic source and/or the velocity model. In this research, we used the GSDF to capture the waveform differences. The CMT solution as our source model
tomography model
δm: model perturbation (δα, δβ …)
K: Fréchet kernel

9. Generalized Seismological Data Functionals (GSDF)
Windowed-Fourier analysis
10 numbers capture waveform difference
In our research, we used the GSDF measurements at different frequencies to capture the waveform difference.
It involved few steps. First, we isolate the part you want to model usually is a phase in data with high similarity with synthetic seismogram.
The cross-correlation between synthetic and data could give us the broad =band phase delay time and amplitude measurements .
By applying narrow band filtering at different frequencies, we can get phase delay and amplitude measurements at different frequencies.
Sometime we need to correct the circle skipping for phase delay measurements.
This kind of frequency dependent measurements can completely capture the waveform differences.
We adjusted the synthetic waveform based on our frequency dependent measurements could almost recover the data waveform

10. Scattering-Integral (SI) Method
Earthquake Wave Field (EWF)
Receiver Green Tensor (RGT)
Data sensitivity kernel
GSDF measurements
To constrain the data sensitivity kernel, we use the Scattering integral method.
This method involve the temporal integral between receiver green tensor from the receiver side and the earthquake wave filed from source side.
The seismogram perturbation kernel is a Fréchet kernel of GSDF measurements with respect to synthetic seismograms.
By storing the RGTs, we can save our computational time.
Seismogram Perturbation Kernel
Store RGTs for saving computational time
Chen, Jordan & Zhao 2007, GJI. Full 3D Waveform Tomography: A Comparison Between Scattering-Integral and Adjoint Wavefield Methods.

11. Scattering-Integral (SI) Method
Born Kernel
Seismogram Perturbation Kernel
To contract the kernel, we use the Scattering integral method.
This method involve the temperal convelution between receiver green tensor from the receiver side and the earthquake wave filed from source side.
This method involved
Receiver Green Tensor (RGT)
Chen, Jordan & Zhao 2007, GJI. Full 3D Waveform Tomography: A Comparison Between Scattering-Integral and Adjoint Wavefield Methods.

12. Full-3D Fréchet Kernels for Broadband Cross Correlation Travel-times
We will show some broadband cross correlation kernels examples that provide us better understanding for wave propagation in 3D Earth model
First, by looking the seismogram, we may not sure this is a P or Pnl phase.
But if we compute its kernel, we can know this part of waveform should be a P wave not a Pnl, because its kernel has significant sensitivity beneath the moho (the dash line is the moho in our initial model.

13. The 2nd example is mixed phases waveform.
This part of waveform has both S wave and surface wave in it.

14. If we look closely and compute the kernel separately.
The first part of waveform is a body wave kernel and the later part is a surface wave kernel.
This example shows linear super position between kernels.

15. (?) This kernel shows the more complex velocity structure.
In this kernel, the wave try to avoid the low velocity basin.
This kind of kernel could provide insight of how wave propagate in 3D velocity structure.

16. Again, this kernel shows an insight of wave propagate in 3D velocity structure.
The sensitivity of this kernels correlate to the shape of LA basin.
This kind of kernel is very useful to constrain the shape of the basin.

17. Kernels of Surface Waves
0.05 Hz
0.15 Hz
Source locates at surface
Ambient noise Green’s function data
The last example is frequency dependent kernels for Rayleigh wave with source locates at surface.
The kernels show frequency dependent effects: the lower frequency has deeper sensitivity.
This kind of kernel could be used for measurements made on ambient noise Green’s function data.

18. Results LAF3D 1st F3DT (up to 1 Hz) Chen, et al., 2007
Po has successfully applied this methodology to the LA basin region and improve the 3D initial model.
Results show the velocity in basin should increased and many significant improvement in waveforms for different paths from updated model.
It is small scale model but with high frequency up to 1 Hz.
Now, we extend our model to whole Southern California.
Chen, et al., 2007

19. Results for Southern CA
Computational parameters
# of stations (Nr)
200
# of earthquakes (Ns)
172
# of seismograms (Nu)
3,500
# of FD simulations (3Nr+Ns)
712
Grid spacing, time interval
500m , 0.3 sec
# of CPUs
2,048
Total disk space 3NrB
200T
(?)

20. Results Variance of phase delay measurements reduce 29%
After our first iteration.
The variance of phase delay measurements reduce 29% and also increase the waveform similarity between synthetic and observed seismograms.
Increase waveform similarity

21. We will show some waveform improvement examples for our updated model.
There are lots of examples, because the limitation of time we cannot go through all of them.
Please visit Po’s website for more examples.
This map shows the source & station path.
The first row velocity model cross section along source & receiver path for initial model.
The 2nd one is our updated model and the third row is natural log of difference.
We compared the 3 component waveforms of both models with data.
The black line is data and the red line is synthetic seismogram.
The upper pair is waveform from initial model with data; the lower pair is waveform from updated model with data.
This source & receiver path is almost along the SF. We can see marked waveform improvement.

22. In this example the source is close to the LA basin.
Our result also increase the velocity in basin area.
The waveform improvements are clear.

26. Future work
Use ambient noise Green’s function data improve data coverage
For 2nd iteration, we will use ambient noise Green’s function data to improve data coverage.
The black line is ANGF we get from GB’s group. This student Marine has a poster on tomorrow morning.
The red line is the synthetic seismogram computed based on our updated model.
Those are some examples with high similarity.
Ambient noise Green’s function data from Denolle et al., 2009

27. Future work Use more phase windows from original seismograms
Add more earthquake data
More iterations at 0.2 Hz
Increase frequency to 0.5 Hz
Since the model improved, we can use more phase from original seismograms.
We will also add more earthquakes to improve our model.
So for we just done our first iteration, we will run more iterations and then go to higher frequency.

28. Successful applications
Summary
A unified method
RGTs
GSDF
Source & structure inversion
Saving computational time
Individual kernels : 3D wave propagation
Successful applications
LA basin (up to 1 Hz)
CVM4SI1 : improve velocity model
(14:00) The methods we used for this research is a unified method for waveform inversion.
This methodology is based on calculation of RGTs and GSDF measurements to capture the waveform difference
This method could apply to both source and structure inversion. We have another talk about source inversion in tomorrow morning.
This method also save computational time and individual kernels provide insight for 3D wave propagation in complex structure.
It has been successfully applied in LA basin region at frequency up to 1 Hz.
We can also find the waveform improvements from our updated model in Southern California.

29. for PDF preprints and reprints
Thank You!
Go to
for PDF preprints and reprints
Rapid Centroid Moment Tensor (CMT) Inversion in 3D Earth Structure Model for Earthquakes in Southern California
Time: Dec :00 ~4:15 PM Location: 2007