# GLG490 Assignment #6

Due by Friday, October 18 at the beginning of class.

## Regression exercise

This exercise is meant to give you some experience thinking about regression and its application to inference in geology.
These data relate earthquake rupture area to earthquake seismic moment magnitude based upon a global dataset from Wells, D.L., and K.J. Coppersmith (1994). New empirical relationships between magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seism. Soc. Am., 84, 974-1002.:
Table A.1.
Remember that the seismic moment of an earthquake is equal to the product of the shear modulus, the rupture area, and the mean slip (units of work). That can be converted to the Moment magnitude (Mw) by taking 2/3 times the log of the seismic moment and subtracting 6.0. That gives the magnitudes with which we are familiar and which are generally comparable to other means of describing earthquake magnitude based on the wave train (classically that would be the Richter magnitude).
However, we do not always know the total area, the shear modulus, or the mean slip, so if we can use regression to empirically determine a relationship between rupture area and magnitude determined by other means, we can apply that to the earthquakes in question.

1) Determine a relationship between earthquake rupture area and magnitude based upon the data in Table A.1.
Prepare the data for regression
a) You can find a Microsoft Excel version of those data (called regression eqs.ex) in the public folder on Caliente (Appleshare PSF zone).
b) Note that the Kaleidagraph that we have is not happy with Excel files unless they are of the oldest format. Open the regression eqs.ex and save it as a tab-delimited text format.
c) Use Kaleidagraph to do the regression.
d) Launch Kaleidagraph on the Macintosh side of the machines in our lab.
e) Open the tab-delimited text format version of the regression file.
f) Kaleidagraph will take you to a text input dialogue box. Make sure that it knows that you want to open a tab delimited file. It will put things into the right columns.
Linear scatter
g) Go to the Gallery menu and then choose the plot option of Linear Scatter. It will give you a dialogue box asking for the columns to put in the x and y axes. Give it the rupture area as the x axis column, and the magnitude as the y axis column. Plot it. What do you think the relationship between rupture area and magnitude is? Use the text tool on the Kaleidagraph tool bar (a big T) to write your answer briefly. Save that plot to a file.
Log scatter
h) Now go to the Plot menu and choose axis options. For the x axis, change the axis settings to log from linear. Now what do you think the relationship between rupture area and magnitude is? Use the text tool on the Kaleidagraph tool bar (a big T) to write your answer briefly. Save that plot to a file.
Curve fitting
i) Now let's do some curve fitting. Go to the menu option curve fit and choose linear. It will want you to click in the little box next to moment magnitude and then the fit will be tried. So is there a linear relationship between rupture area and magnitude?
j) Try a log curve fit. What do you think about the log curve fit? Show the equation for the fit by choosing display equation under the plot menu. What is the equation for the relationship between rupture area and magnitude? Save the plot with the fits and the equations to a file.

2) In 1992, the Landers earthquake occured. Here is a map view of the main rupture traces: Landers map.
Here is a black and white panorama of the main scarp at the Galway Lake field site: Panorama.
Go to see my buddy Brian Cohee's web page at Stanford and click on the Landers earthquake movie. It shows a simulation of the rupture development as if we were in teh earth looking side on to the rupture planes (from the southwest). The bottom of the movie is at about 18 km. The color intensity shows slip varying from 0 at blue to about 6 m at red. The actual rupture duration was probably more like a minute or so.

The depth of seismicity related to the earthquake was between 10 and 18 km. Determine the rupture length from the map and then select a meaningful depth, and then using your empirical equation, determine a magnitude for the event. What was the Landers event magnitude according to your analysis?

3) The moment magnitude of the event was determined to be about Mw7.3 by many different means. How does that compare to the number that you determined? What could be the difference if there is one?