Geodesy and strain Calculating and mapping incremental strain with GPS data

Transcription

1 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 ( 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

2 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 P 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.

3 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.

4 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.

5 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 Translation vector Degrees/yr Direction Rotation Magnitude (nano-strain) Azimuth Max horizontal (e1) Min horizontal (e2)