Lab 6: GPS Geology 202 Earth s Interior. Due Thursday, March 4, 2004, and remember to sign out your GPS unit

Transcription

1 Lab 6: GPS Geology 202 Earth s Interior Due Thursday, March 4, 2004, and remember to sign out your GPS unit Introduction: Latitude and Longitude Any location on Earth is described by two numbers--its latitude and its longitude. If a pilot or a ship s captain wants to specify position on a map, these are the "coordinates" they would use. Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols (,,") e.g " means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (, ") for feet and inches!). Adegree contains 60 minutes of arc and a minute contains 60 seconds of arc. You may omit the words "of arc" where the context makes it absolutely clear that these are not units of time. To specify the latitude of some point on the surface of the earth, imagine a line extending from the earth s center to that point. Then the elevation angle of that point above the equator is its latitude (l) - northern latitude if north of the equator, southern (or negative) latitude if south of it. On a globe of the Earth, lines of latitude are circles of different size. The longest is the equator, whose latitude is zero, while at the poles - at latitudes 90 north and 90 south (or -90 ) the circles shrink to a point. On the globe, lines of constant longitude ("meridians") extend from pole to pole, like the segment boundaries on a peeled orange. Every meridian must cross the equator. Since the equator is a circle, we can divide it - like any circle - into 360 degrees, and the longitude of a point is then the marked value of that division where its meridian meets the equator. What that value is depends on where we begin to count--on where zero longitude is. For historical reasons, the meridian passing the old Royal Astronomical Observatory in Greenwich, England, is the one chosen as zero longitude. Geodesy and the Development of Plate Tectonics When Alfred Wegener proposed the theory of continental drift in 1915, the theory was skeptically received. The idea that continents drifted apart was an old one, rooted in the remarkable fit of the coasts of South America and Africa. Still, without compelling evidence for motion between continents, the idea that such motions were physically impossible prevented most geologists from accepting Wegener s ideas. We gener realized that proving continents moved apart was a formidable challenge. Although geodesy -the science of measuring the shape of and distances on the earth - was well established, standard surveying methods offered no hope of measuring the slow motions between distant continents. Wegener decided to measure the distance between continents using astronomical observations - an example of what

2 -2- we now call space-based geodesy. Using an extraterrestrial reference was not new. In about 230 BC, Eratosthenes found the Earth s size from observations of the sun s position at different sites. Since that time, navigators found their positions by observing the sun and stars. However, measuring the small changes in position caused by continental drift over a few years called for measurement accuracies far greater than ever before. Wegener s attempts failed, and the idea of continental drift was largely rejected. Space Geodesy with the Global Positioning System (GPS) Space geodesy uses space-based technologies to measure the positions of geodetic monuments to accuracies of better than a centimeter, even for sites thousands of kilometers apart. Hence measurements of positions over time yield relative velocities to precisions almost unimaginable during the early days of plate tectonic studies. Moreover, these studies cover much larger areas than would have been practical with traditional geodesy, which is restricted to sites which are in view ofeach other. Although various systems provide similar data, GPS is the system of choice for most tectonic applications. GPS was developed in the late 1970 s by the U.S. Department of Defense for real-time positioning and navigation. A constellation of satellites transmit coded timing signals on a pair of microwave carrier frequencies synchronized to very precise on-board atomic clocks. The timing signals are modulations of the carrier frequencies. By determining the ranges to a minimum of four satellites from the signal delays and the broadcast satellite orbit information, a single GPS receiver can determine its 3-dimensional position to a precision of 5 to 100 meters, depending on the level of signal degradation imposed by the military. This operation is conceptually the same as locating an earthquake from arrivals at multiple seismometers, which we discuss earlier. In fact, GPS positions are 2-3 times more precise in the horizontal than in the vertical, because radio signals arrive only from above, just as earthquake locations are less precise in depth because waves arrive only from below.

3 GPS Applications and Methods -3- Precision Method Science Typical Scale 2-5mm High-precision Plate motions, plate boundary s km geodetic (dualfrequency) deformation, glacial rebound, interseismic-, post-seismic deformation, volcanos 2-5mm High-precision Volcanos, fault zones, tide gauges, < 10km geodetic (singlefrequency) buildings and structures 1-10cm Real time kinematic, Very high-precision fault scarp and < 10km rapid static (use intersection mapping, uplifted terrace carrier phase) mapping, high-precision topography, volcanos, buildings and structures 10cm-1m Differential code, Precise geologic mapping, ice motions, < 100km high-end receivers GIS applications, topography (requires base station) 1-10m Differential code, Moderate precision mapping, seismic < 100km handheld receivers exploration surveying, navigation (requires base station) 100m Single GPS receiver Coarse locations of geological, biological, 100m to 1000 km (precision limited by archeological, etc. sample points, maps, selective availability) navigation The improvement to cm-level or better precision is obtained by using the phase delays of the microwave carriers. Because the carriers have higher frequencies than the modulations, their phase can yield more precise locations, much as higher-frequency seismic waves can reveal more detailed velocity structure. The carrier wavelengths are 19 and 24 cm, so precise phase measurements can resolve positions to a fraction of these wavelengths. The use of differential signals from multiple satellites recorded at multiple receivers reduces clock errors. Combining both transmitted frequencies removes the effects of the passage of the GPS radio signals through the ionosphere. Position errors due to signal delays from water vapor in the troposphere can be reduced by estimating the delays using an inversion process similar to solving for seismic velocity structure. The final element for high-precision surveys is provided by continuously operating global GPS tracking stations and data centers. These provide high-precision satellite orbit and clock information, earth rotation parameters, and a global reference frame. Using this information GPS studies can achieve positions better than 10 mm, so measurements over time yield relative velocities to precisions of a few mm/yr or better, even for sites thousands of kilometers apart. The uncertainty of the velocity estimate depends on the precision of the estimated positions and the time interval between them. Accuracy and Precision Geophysics uses data to estimate quantities that describe the earth. Ideally these estimates are both accurate and precise. Accuracy measures the deviation of the estimate from its true value, whereas precision measures the repeatability of individual estimates. Hence the accuracy depends on systematic errors that bias groups of estimates, whereas the precision depends on random errors that affect individual estimates. Estimates can be precise but inaccurate, or accurate but imprecise. Approaches to improving the accuracy and precision of estimates are often couched in terms of measuring a quantity like the length of a table. Accuracy is improved by using different measuring tools, ideally calibrated against each other. Precision is improved by making multiple measurements, ideally by different people. We follow such approaches for the earth when possible.

4 -4- Before you make the Measurements: i. Locate Chicago on a map and give its latitude and longitude (include an estimate of minutes). Give the latitude and longitude of our antipode (180 away). What s there? ii. Since you know the radius of the earth, compute approximately how many kilometers one degree of latitude represents. Does this value apply to longitude? Why orwhy not. iii. Assuming the earth is a sphere, compute the length of the parallel (line of constant latitude) that Chicago lies on. A parallel is a special case of a small circle, lines on the earth s surface defined by the intersection of a plane normal to a radius of the spherical earth. iv. As already stated, computing a precise velocity between two continents requires very accurate measurements of position. If we take all the GPS receivers used in this lab and lay them side-by-side, the latitudes and longitudes are different. Obviously the receivers are at the same location and this deviation represents a limitation in our measurement. In general, these GPS receivers locate themselves within minutes of each other. Compute how much this deviation is in meters. Is this a limitation in the accuracy or precision? Explain? v. Given the previous problem, how long do you need to wait to observe the relative motion between Europe and North America, and be sure it s not due to measurement errors? Assume the spreading rate between Europe and North America is ~20 mm/yr.

5 -5- The Measurements: vi. Locate the following locations and report their latitude and longitude. Complete the 4 sites assigned to the GPS unit you signed for on the sign-out sheet. Use the serial numbers: , , , , , , , The "Rock" The "Rock" The "Rock" Center of crosswalk in The Arch Front door of SPAC front of Burger King Main Norris entrance Flag by water plant No swimming/fishing sign by cooling pond (at north end of campu) North entrance of main library, near advertisement board Rock in front of Apts on NE corner of Sherman and Foster Top of steps outside of Kopy-Kat on Sherman vii. What is located at the following coordinates? Use the serial numbers to determine which 3 lat, long pairs apply to your group. Give a good description of what you think we located. Be as specific as possible! , , , , , , , ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) viii. Reoccupy asite from the lists above on a different day, ordifferent time of day, and record the coordinates. Are they different? Why orwhy not?

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