CyberShake Source Filtering

As of February 2015, CyberShake runs show a damping effect at spectral acceleration periods close to the simulation period. If we perform a 0.5 Hz CyberShake run, we see a damping factor of 2 or more when we look at the 0.5 Hz/2 second hazard curves.

We are interested in examining the filtering we are using to see if we can improve this so that hazard curves at the simulation period do not show damping. This would be a big benefit, as a 1 Hz CyberShake run could produce undamped 1 second hazard curves, which are of broad interest.

Background

CyberShake only performs filtering when the source impulse is created for the SGTs. Neither the SGTs nor the seismograms are directly filtered. The source is produced as part of the Graves SGT code; since it is location-independent, we calculate it once for a given DT and NT and use it for all corresponding CyberShake runs. We decided to run some experiments by changing the filtering of the source. By default, the source is low-pass filtered with a 4th-order Butterworth filter at the frequency of the CyberShake run. For this experiment, we propose filtering the source at 2 times the frequency of the CyberShake run.

Spectral content of three sources, filtered with a 4th-order low-pass Butterworth filter at 0.5 Hz (blue), 1.0 Hz (green), and 2 Hz (red).

Experiment 1

We calculated a hazard curve for USC, ERF 35 (1000m fault surfaces), Graves & Pitarka 2010, with the AWP-ODC-GPU code and CVM-S4.26 using the 1 Hz filtered source and compared it to a run with all the same parameters, except for using a 0.5 Hz filtered source.

2 second SA. 0.5 Hz filtered source results are in magenta, 1 Hz filtered source results in black

3 second SA. 0.5 Hz filtered source results are in magenta, 1 Hz filtered source results in black

5 second SA. 0.5 Hz filtered source results are in magenta, 1 Hz filtered source results in black

10 second SA. 0.5 Hz filtered source results are in magenta, 1 Hz filtered source results in black

Experiment 2

We decided to run another test to compare 4 conditions:

1. 0.5 Hz simulation, 0.5 Hz filtered source (run 3837) - black
2. 0.5 Hz simulation, 1 Hz filtered source (run 3853) - green
3. 1 Hz simulation, 1 Hz filtered source, FP=1.0 (run 3842) - red
4. 1 Hz simulation, 2 Hz filtered source (run 3860) - gold
5. 1 Hz simulation, 1 Hz filtered source, FP=0.5 (run 3861) - blue

Results 1-5 are compared below.

2 second SA. 0.5 Hz sim/0.5 Hz filtered in black, 0.5 Hz sim/1 Hz filtered source results in green, 1 Hz sim (FP=1.0)/1 Hz filtered in red, 1 Hz sim/2 Hz filtered in gold, 1 Hz sim (FP=0.5)/1 Hz filtered in blue

3 second SA. 0.5 Hz sim/0.5 Hz filtered in black, 0.5 Hz sim/1 Hz filtered source results in green, 1 Hz sim (FP=1.0)/1 Hz filtered in red, 1 Hz sim/2 Hz filtered in gold, 1 Hz sim (FP=0.5)/1 Hz filtered in blue

5 second SA. 0.5 Hz sim/0.5 Hz filtered in black, 0.5 Hz sim/1 Hz filtered source results in green, 1 Hz sim (FP=1.0)/1 Hz filtered in red, 1 Hz sim/2 Hz filtered in gold, 1 Hz sim (FP=0.5)/1 Hz filtered in blue

10 second SA. 0.5 Hz sim/0.5 Hz filtered in black, 0.5 Hz sim/1 Hz filtered source results in green, 1 Hz sim (FP=1.0)/1 Hz filtered in red, 1 Hz sim/2 Hz filtered in gold, 1 Hz sim (FP=0.5)/1 Hz filtered in blue

We also plotted seismograms for the seismogram with the largest 3 second SA value, seen below:

Here are timeseries for the three sources. The 0.5Hz sim/1Hz filtering and 1Hz sim/1Hz filtering sources are practically identical, which is why you can only see 1 on the plot.

Spectral Response

Pseudo AA

Here are plots of the spectral response for the same two seismograms with the largest PSA values at 10 seconds, in an effort to understand why the 1 Hz/2 Hz hazard curves are elevated, even at low periods.

Note that the X axis is period, not frequency.

Fourier

These are plots of the Fourier response for the same two seismograms:

Seismogram Plots

Here are timeseries plots, low-pass filtered at 10 Hz, of two seismograms.