Step 3: Determining a better location

You will use the measured arrival times from step 2 to determine a more accurate location. To be able to understand how this works, read section 7.2 of the book by Stein and Wysession, check your lecture notes or read about the general location problem here.

1. Write an elaborate paragraph on how earthquakes are localized using P arrival times.
Use the information of section 7.2 of the book, your lecture notes and/or the webpage accompanying this exercise.

The earthquake location program that you are going to use is written in the Matlab programming language.

• Download the file location.zip to the folder that you were working in save it in the directory on your home drive (for example: U:\eqlocation).

• Extract the files from the location.zip file.

• Read the contents of file LSQloc.m (by opening the file in Matlab), and try to understand how the earthquake localization program works.

Find an improved solution

• Start Matlab:

Start -> All programs -> Standard Applications -> Mathematics -> MATLAB -> MATLAB(version)

• In Matlab, go to the directory where you save your data file by typing in the Command Window:
  cd U:\ ....
  

2. Run the program LSQloc by typing

LSQloc

Enter the following answers to the options:

Maximum number of iterations:	10
Solve for depth:	n
Give fixed depth:	17
Use first arrival as initial guess:	n
Give lat of initial location:	The latitude that you found in Step 1
Give lon of initial location:	The longitude that you found in Step 1

Pay good attention to the output of the program. What information does the program supply to you?

3. Report all the relevant values that are given to you, such as what your initial values were, in how many iterations your solution converged, what the final location and origin time are.

4. Discuss the level of fit. Are any of the residuals particularly large? If so, find out whether some of your picks may have been wrong. Go back to Step 2 and look at that those particular trace(s) again. If it looks as if you didn't pick the onset correctly, repick it and modify your data file. Repeat the run that you just did and report the (improved) values.

5. When measurement errors are not known, it is common to assume that the Root Mean Square value of the residuals for the best model gives a good indication of the measurement error:

s² = S_i (T_i^obs - T_i^calc(best model))² / (ndata)

Compare the RMS value of your best solution to your measurement error estimate (Step 2, question 3). Are they similar? If not, which of the following possible factors contributed to the discrepancy:
- you over- or underestimated the measurement error
- the velocity model is not correct
- the seismograms may not have the correct time information

6. Run the script again, but now answer 'y' when it asks if you want to use the data of the first arrival as initial guess. Report the same things as before. Is your final location similar to the one you found in the first run? If not, which of the two is the better location? Is this result surprising to you?

7. Look at the official locations of this earthquake. Report how close your solutions were to the ones of the NEIC, EHB, and ISC (which are generally considered to be the best because they use the largest sets of arrivals). You can find these organisations in the 'Author' column of the page.

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