SAC Tutorial Six

6.1 Earthquake Source Properties

In today's activity we will take a closer look at what seismic sources look like on seismograms. These observations will provide us with information about the moment release during the earthquake (related to amount of slip and energy release), the length of the fault that ruptured, and the rate of rupture. I have collected a set of seismograms that record the initial P wave for a recent large earthquake: a magnitude 8.4 subduction thrust earthquake off the coast of Sumatra, Indonesia that happened on September 12, 2007. This earthquake represents the third in series of large events that began with the catastrophic Indonesian earthquake and tsunami in 2004 that killed over 200,000 people. The second event occured in 2005, immediately south of the original event, and this latest event is again south of the second event. In other words, the subduction fault has been progressively rupturing further south with each earthquake.

To start looking at this latest event, we will use sac. Please login to the linux server using the VNC viewer, open a terminal window, and create a directory called source. Enter this new directory and then copy the seismograms from the my database directory:

[username@linux source] cp /chiapas/mikeb/database/seismograms/*.SAC .

Now we can start sac and examine the seismograms:

[username@linux source] sac

SAC> r *.SAC
SAC> p1

There are a pretty large number of seismograms and they have varying arrival times because they are recorded at various different distances away from the earthquake. To help focus on the P wave arrival time for each seismogram, which I have already marked as time T1, we can set a limit for the X-axis to just plot 60 seconds before the P arrival time and 120 seconds after this time:

SAC> xlim t1 -60 120
SAC> p1 relative

Hopefully you can see the seismograms a little better now. The next step to improve our ability to interpret the source properties is to make sure we are examining the displacement time series. Do you recall what quantity digital seismometers actually record? Since they work via electro-magnetic induction, they record voltage that is proportional to velocity. So if our current seismograms are velocity, how would we convert them to displacement? Using our physics knowledge, we should know that since velocity is the derivative of displacment, we can integrate our velocity time series to get a displacment time series. SAC even has a command called int to perform the integration:

SAC> int
SAC> p1

So now that you are looking at displacment values, we can start to examine the polarity of the observed P waves. By that I mean whether the first arrivals are up or down. For this kind of analysis we want to sort the seismograms by azimuth (the direction they waves go out from the earthquake), and we want to look at each individual seismogram one at a time:

SAC> sort az
SAC> p1 perplot 1

Exercise 6.1

Hopefully, you recall that the polarity of first arrivals is important for determining the focal mechanism for an earthquake. We will not try to solve for the focal mechanism from the polarity of the first arrivals, but I do want you to identify which stations have positive (up motion) or negative (down motion) polarity. Open a file called source.txt and list which stations have positive polarities and which ones have negative polarities.

6.2 Source Duration

Now we want to look at how the source duration varies over the range of observations we have. The source duration tells us about the length of the fault that ruptures and the rate of rupture. The measurements we need to make on the seismograms are the shortest and longest apparent source duration. To help avoid issues with the variable polarity we just described in exercise 6.1, we can multiply each seismogram by it's polarity to show all observations with a common polarity:

SAC> mul 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1
SAC> p1 perplot off

Now we can look for the short and long source durations. For this event, I found it easiest to measure the time between the first arrival marking (T1) and the second big positive peak. I found that this duration varied from about 42 seconds on the first seismogram (recorded at azimuth ~5 degrees) to about 60 seconds on the 10th seismogram. Take a look at the seismograms and see if you agree with this estimate.

Exercise 6.2

Using the minimum, maximum, and mean source duration you measure and the equations we learned in lecture, please calculate the rupture length and the rupture velocity. You should use 12 km/s for the P wave velocity for this event. Store your answers in the source.txt file.

Summary

brudzimr@muohio.edu, 19th June 2007