Strike-Slip Dislocations Assignment
Using the discussion from the lecture: Long and short term deformation along the San Andreas Fault and
chapter 7 from this on line resource about the San Andreas Fault: U.S. Geological Survey, Professional Paper 1515 titled The San Andreas Fault System, California, do the following:
- Build a matlab set of functions and scripts (or build the equivalent functionality in Excel) that solves the dislocation equations for fault parallel displacement versus distance normal to the fault for a single, semi-infinite screw dislocation and for a pair of screw dislocations which represent a patch of finite strike slip along a vertical strike-slip fault.
- The Hector Mine earthquake occurred in 1999 in the Mojave Desert. It was a strike slip earthquake that occured along a northwest-striking fault zone in the eastern California shear zone.
- Here is a bit of background: http://earthquake.usgs.gov/regional/sca/hector/, nice pictures, and http://pasadena.wr.usgs.gov/hector/report.html.
- Here is a link to some INSAR data spanning the event: INSAR from SCRIPPS. Caption: A) line of sight displacements in ascending and descending orbits, B) azimuthal displacements, C) vertical displacements, and D) horizontal displacements.
This graphic shows the annotated horizontal displacement map. Note the horizontal scale at the bottom in kilometers and the vector scale in the upper portion of the graphic. Print this figure out and manually measure the fault normal displacement vector magnitude (choose one direction as positive and one as negative. Make the fault location 0 and measure the fault normal distance to the tail of each vector. Make a table of distance normal to the fault versus fault parallel displacement.
- Following the analysis demonstrated with respect to the 1906 earthquake in the Point Arena area (see lecture), plot the fault parallel observed displacements versus distance normal to the fault. Assume an average fault slip in the earthquake of 4 meters (displacement discontinuity). Compute the modeled fault parallel displacements versus distance normal to the fault. At what fault depth are the displacements best fit? Compute the RMS misfit* versus depth to rupture (slide 11) to justify your depth estimate. (*Where n is the number of observations and you compute the difference between an observation and a model calculation, square it, sum the squares, compute their mean, and then take the square of the mean).
- Seismic moment is defined as: M0 = μ A u_bar where
μ = 30 GPa (30x109 N/m2)
A = area of fault surface that slipped (length x depth)
u_bar = mean slip
Assuming that the u_bar = 4 m and that you know μ as above, measure the length of rupture from the faulting mapped on the figure (you are assuming it is a single plane, so just measure the straight line length). Use your best fit depth from the prior dislocation analysis and compute the seismic moment. Make sure that all the units are consistent and check that you get Nm. What is it?
- Moment magnitude is something we often can think of more easily than seismic moment. It is
Mw = (2/3) log10M0 - 6 where log10 is log base 10. What was the moment magnitude of the Hector Mine earthquake?
- In our lecture on Coordinate systems, displacements, and rotations, we reviewed the GPS-derived velocity field for the western US. This graphic shows a subset for the portion along the relatively simple (structurally) south-central San Andreas Fault (SAF):
- Here is a slightly nicer looking map with out the scale: gpssites.gif. Note that the last few stations are on the NE side of the Death Valley-Furnace Creek Fault zone and should probably bi ignored when looking at the San Andreas Fault slip rate.
- The displacement data are here: CMM3_CentralCA.xls.
- Rotate the data around their mean x,y position:
N = N-mean(N); %that would be AVERAGE in Excel
E = E-mean(E);
Eprime = -N.*sin(thetarads)+E.*cos(thetarads);
Nprime = N.*cos(thetarads)+E.*sin(thetarads);
Determine the local strike of the San Andreas Fault and use it as the rotation angle. Remember it will need to be converted to radians
One new component will be the position parallel to the SAF and one will be the position normal to it. Plot both data sets and make sure it seems like the rotated data look like an E-W swath (or N-W swath, depending on how you rotate it).
- Each of the velocities has to be rotated into the same fault parallel/fault normal directions.
- Plot fault parallel displacement versus fault normal distance. You will see that characteristic arctan pattern indicative of a buried dislocation.
- Translate the data so that the 0 position and 0 velocity is right in the middle of the peak of the displacement gradient (basically the surface trace location of the SAF).
- Looking at the depth of seismicity along the SAF in chapter 5 (look at Figure 5.8 for example) in U.S. Geological Survey, Professional Paper 1515 titled The San Andreas Fault System, California, estimate the typical maximum seismicity depth along the SAF in central California. Use that as the depth of the locked section of your fault (i.e., depth to top of your freely slipping, semi-infinite screw dislocation).
- Given that depth and the velocity data, use your dislocation model and the RMS approach to determine the most likely deep slip rate.
- How does that rate compare with the rate from Wallace Creek which is thought to be 34 mm/yr for the last 3700 years?
- At that rate, how long is it between earthquakes if the slip is 8 meters? If the last event were 1857, when do you expect the next with this rather crude method of estimation?
Assignment is due on Tuesday, March 17, 2008
Last modified: February 24, 2009