Fall 2012
GEOL 360
Lab 9
Geodesy and strain
Calculating and mapping incremental strain with GPS data
GPS data can be acquired from a variety of different research groups around the world, but some
the most accessible and easy to use GPS data comes from the EarthScope Plate Boundary
Observatory (PBO), which is managed by UNAVCO and is available online for free.
You will search for and collect data generated by three of the PBO’s permanent GPS stations
along the San Andreas fault in central California, near where you looked at offset streams.
1. Go to the interactive PBO map (http://pbo.unavco.org/network/gps) and zoom in to
southern California. You can see that there are LOTS of PBO sites in southern California,
where there are also lots of faults.
2. Search for Cholame, CA, to get you in the right vicinity, and then zoom out until you see
something like this:
3. You can see several green marker dots, indicating stations that are functioning normally.
Click on the one near the bottom center of the map. Clicking on the dot gives you a popup box that provides the name and location of the site (you should be looking at P538), as
well as a clickable link to more information (which you will need) at
http://pbo.unavco.org/station/overview/P538.
Fall 2012
GEOL 360
Lab 9
4. Near the bottom on the left side of the overview page is a box titled “GPS Monument
Coordinates.” Under the subtitle “SNARF Reference Frame,” the station location is
listed on the line that begins “WGS 1984 lat/log/elev (d/d/m).” The first number is the
site latitude with positive values indicating north latitude. The second number is the
longitude, with negative indicating west longitude. The third number is the elevation in
meters relative to the WGS84 ellipsoid – that is, it is not the elevation relative to mean
sea level, as might be indicated on a USGS topographic map. Carefully record the
latitude and longitude on your datasheet, with all of the decimal places. The sign of the
longitude is important. These data will be part of the input for the strain calculator that
we will use later in this process.
5. Now we need to acquire the velocity data for the site. Returning to the overview page for
site P150, mid-way along the left side of the page there is a box labeled “Station Position”
with three graphs. Clicking on the box causes the window to expand. The three plots
show the change in position as a function of time – that is, they are time-series plots. The
upper plot shows change in a north or south direction, the middle plot shows motion in an
east or west direction, and the lowest plot shows motion in the up or down direction.
These changes are measured relative to a reference frame that is computed relative to a
set of GPS sites established in the stable interior of North America – Stable North
American Reference Frame (SNARF). You can switch from the raw data view to a
“cleaned” view to a “detrended” view using either the navigation arrows on your
keyboard or by using the small control bar that should appear near the bottom of the plot
window. Both the cleaned and detrended plots provide a numerical estimate of the mean
velocity in each of the three directions along with the corresponding uncertainty. These
velocities are frequently updated as new data are collected. We can also access the daily
position data in a CSV spreadsheet file, and compute our own velocities and uncertainties.
Carefully record the three velocities (in mm/yr), their signs, and their uncertainties from
the cleaned data for Station P538. Keep in mind the following:



North: positive value indicate motion toward north, negative to south
East: positive values indicate motion to the east, negative to the west
Height: positive values indicate motion up, negative values indicate motion down
We can use these data and the Pythagorean Theorem to find the total site velocity and the
site mean horizontal velocity. These data will be used along with the site latitude and
longitude as input for the strain calculator we will use later in this process.
6. Follow the same procedure and record information for stations P539 and P541.
7. Once you have all of the information recorded on the datasheet, we can start to plot the
data on the graphs on the map and analyze the strain. On your map, for each station, plot
the two horizontal vectors using blue pen (and a ruler!).
8. Now plot the sums of each of the sets of the two vectors. You can do this graphically by
lightly redrawing your east vector starting from the end of the north vector, and marking
the endpoint. Then in red, draw the sum vector with an arrow precisely to that point.
Mark each endpoint with a black dot as well.
Fall 2012
GEOL 360
Lab 9
9. Now we want to see how the crust as a whole has deforms through this incremental strain.
Lay a piece of graph paper over your map. Make sure the edges of the pages line up, and
N is oriented up. Mark the locations of the three stations (the green dots) and connect
these points with a ruler.
10. Define the centroid of the triangle. Do this by lightly drawing three lines, one from each
vertex, that bisect each side of the triangle. The place where they intersect is called the
centroid.
11. Using this centroid as the origin, draw in an x- and y- axis (these should be oriented N-S
and E-W).
12. On your map, go through the same process with the endpoints.
13. Lay the graph paper over the map so that your centroids and axes line up perfectly. Trace
the endpoints and the deformed triangle onto the graph paper. By this process we are
removing the translation component of the deformation.
14. Lightly draw arrows from the station locations to the vertices on the deformed triangle.
How would you describe the type of deformation? Is there any rotation? Does it appear to
be pure shear or simple shear? Describe in a sentence or two on your graph paper what
you see.
15. Now we will actually calculate the deformation, using a spreadsheet and a set of formulas
where all you need to do is plug in your data. Download the GPS spreadsheet from
Blackboard and enter your data in the yellow boxes (note that this is in meters per year,
not mm/yr, so you need to convert). Once all of the data is entered, the blue boxes should
all have calculated values. Record some of these on your datasheet – you have now
quantified the deformation you described in words above.
16. On your graph paper, in the center of the triangle, plot the two strain axes that were just
calculated for you. Use the azimuth to do this, and don’t worry about the absolute length
of these lines. Show how they would differ in length relatively, however, and label them.
At the end of class, turn in your datasheet, map, and graph paper. Be sure to put your name on
everything and staple it together.
Fall 2012
GEOL 360
Lab 9
Map for plotting GPS velocity data
Name: ____________________________________________________________
On the map below, plot the two horizontal velocity vectors for your three stations. Plot the N and
E vectors in blue Sharpie and the total horizontal velocity vector in red Sharpie. Use a ruler to
draw your arrows, and mark the tips of the arrows with black points.
Fall 2012
GEOL 360
Lab 9
Datasheet for GPS location and velocity data from the
EarthScope Plate Boundary Observatory website
Name: ____________________________________________________________
Date on which the data were acquired from the PBO website: _________________________
Data from PBO website
Geographic coordinates using WGS 1984 datum, Stable North American Reference Frame
(SNARF)
Site
Latitude (decimal degrees)
Longitude (decimal degrees)
P538
______________________
_______________________
P539
______________________
_______________________
P541
______________________
_______________________
GPS site velocities relative to SNARF, expressed in mm/year
Site
N Velocity ± Uncert
E Velocity ± Uncert Height Velocity ± Uncert
P538
___________ _________
_________
___________ _________
___________
P539
___________ _________
_________
___________ _________
___________
P541
___________ _________
_________
___________ _________
___________
Deformation data from Excel spreadsheet calculations
Azimuth
Speed
________
___________
Degrees/yr
Direction
_________
___________
Magnitude (nano-strain)
Azimuth
Translation vector
Rotation
Max horizontal (e1)
________
__________
Min horizontal (e2)
________
__________