Introduction to Total Stations

8/8/2019 Introduction to Total Stations

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Infra-red radiation from a GaAs lasing diode

The source of the IR radiation for our instrument is a Gallium Arsenide (GaAs) lasing diode. This device is madefrom a small chip of semiconducting material, and is similar in size and appearance to other semiconductingdevices (Figure 7). Driven by a forward biased voltage and maintained by different electrostatic potentials in thetwo halves of the diode, an electron population inversion between the two halves of the diode will provide theenergy level transition for stimulated emission of photons by electrons as they fall to the lower energy state (Price,1989). The energy difference is emitted as radiation (and thus the process and device are called a laser--LightAmplification by the Stimulated Emission of Radiation). The process of stimulated emission enables the laser toemit an intense, monochromatic radiation that travels as a narrow beam for considerable distances before it spreadsout (Price, 1989). The intensity of the IR radiation is nearly linearly proportional to the current flow and withvirtually an instantaneous response (Burnside, 1991). If an alternating voltage is superimposed upon the normaloperating voltage of the GaAs diode, the intensity of its emitted radiation varies in sympathy with the alternatingvoltage (Figure 8, Price, 1989). This provides a simple and inexpensive means of directly modulating the infra-red

beam.

The GaAs diode is widely used in surveying. The small dimensions of the junction in which the radiation is emittedgives rise to poorer collimation of the radiation. Therefore, the GaAs laser emits a beam with a relatively largeelliptical spread and the brightness of the GaAs laser is lower than that of other lasers. The spectral width of theradiation emitted is usually 2-3 nm compared with 0.001 nm of the visible light, HeNe gas laser and thus the GaAslaser lacks the monochromacity of other lasers, contributing error to the effective propagation velocity. However,GaAs lasers can be made to operate at orders of magnitude greater efficiency than other lasers, can be made muchsmaller and more rugged, and are considerably less expensive than other lasers (Price, 1989).

Because of the relatively low power radiated, a beam of sufficient power will not be reflected from an unpreparedsurface. A special reflector is therefore used in order to ensure a good return signal. A plane mirror can beemployed, but it requires accurate setting, so in practice, a corner cube reflector is most often used. This reflector will return a beam along a path parallel to the incident path over a wide range of angles of incidence onto the frontsurface. A cube of glass is usually used with its edges ground into a corner with accuracies of grinding to within afew degrees of arc (Burnside, 1991). The path length of the signal within the reflector must be corrected for, and



that is the reason for the setting of the prism constant within the theodolite. The constant for Wild circular prisms is0. Note that over short distances, the "cat-eye" type reflector commonly used for bicycles will adequately reflecthighly oblique incident signals.

F igure 7. Gallium arsenide diode characteristics. F rom Burnside, 1991.

F igure 8. Modulation of a Gallium arsenide diode. F rom Price and Uren, 1989.

Selected Technical Data--Leica (Wild) DI4L

Standard deviation of distancemeasurement

5 mm + 5 mm/km

Breaks in beam result not affected

Range with one reflector 1.2 km in strong haze



2.5 km in average atmosphericconditions

(the maximum range I have shot is1.8 km)

Carrier wavelength 0.835 µm infra-red

Fine measurement 4,870,255 Hz = 30.7692 m

Coarse measurement 74,927 Hz = 2000 m

Weight--DI4L

Counterweight

Container

Total weight

1.1 kg (2.4 lb)

0.8 kg (2.0 lb)

3.8 kg (8.4 lb)

5 .7 kg (12.8 lb)

Beam width at half power 4' (12 cm at 100 m)

Theodolite

The Theodolite is an accurate horizontal and vertical angle measuring device with a telescope and on boardelectronics for data storage and EDM operation. Fortunately for us, the angles are measured and recordedaccurately and electronically, avoiding the need for us to read a vernier and record data manually as is typical ontransits and optical theodolites. This electronic theodolite contains circular encoders which sense the rotations of the vertical and horizontal spindles of the telescope, and converts those rotations into horizontal and vertical angleselectronically, and displays the values of the angles on a Liquid Crystal Display (LCD) (Moffitt, 1987).

The integrated EDM/Theodolite combination is often called a "Total Station" or "Total Geodetic Station." Outputfrom the horizontal and vertical circular encoders and from the EDM are stored in a data collector. The instrumentmay convert the data (horizontal and vertical angles and the slope distance) electronically into Easting and

Northing coordinates, height difference, and horizontal distance (Moffitt, 1987).

Selected Technical Data--Leica (Wild T-1000)

Standard deviation of angular measurement

3.0' (seconds of a degree) horizontaland vertical

Telescope Erect image

Magnification 30x

Shortest focusingrange

1.7 m

Field at 1000 m 27 m

Displays 2 LCD displays each for 8 digits,sign, decimal point and symbols for user guidance

Keyboard Weatherproof, 14 multiple functionkeys, contact pressure 30 g

Automatic power off About 3 minutes after last keystroke

Angle measurement Continuous, by absolute encoder



U pdates 0.1 to 0.3 seconds

Optical plummet (in tribrach) Focusing

Magnification 2x

Temperature Range -20°C to +50°C

Weight--T1000 4.5 kg (9.9 lb)

Container 3.9 kg (8.6 lb)

Total weight 8.4 kg (18. 5 lb)

Determination of Easting, Northing, and Elevation

The actual observations made by the Total Station are the horizontal and vertical angles ( Hz and V ), and the slopelength ( D )--these are called fundamental measurements. Clearly, from these data, one can determine the relativecoordinates of the instrument and reflector (Figure 9). The instrument makes its own reductions based only uponthe fundamental measurements. The horizontal angles are made relative to a backsight or reference azimuth or known orientation. This may be determined by a careful compass sighting to a distant, but stable and easilyidentifiable landmark, or it may be arbitrary. Once the backsight is made, the reference azimuth, (h z0 ) may be set

on the Theodolite. The vertical angle may be called a zenith angle and is measured in a vertical plane down fromthe upward direction of a vertical or plumb line (Moffitt, 1987).

Instrument Station Reference Location

The point over which the Total Station is set up is called an instrument station. Such a point should be marked asaccurately as possibly on some firm object. On many surveys, each station is marked by a wooden stake, spike, or

piece of REBAR driven flush with the ground and into the top of which a small (~ mm diameter) dimple is marked(a tack may be put in the wooden stake) (Moffitt, 1987). The Total Station measurements and reductions are maderelative to the instrument station ( E 0 , N 0 , and H 0 --where E refers to distance East, N distance North, and H elevation, and the subscript 0 indicates a reference value). These values must be predetermined by other means(triangulation, previous survey location, Global Positioning System, etc., or they may be arbitrary). In fact, for most local surveys, with only one survey set up, the instrument station is commonly taken to be (0, 0, 0).

Determinations in the vertical plane

In the lower portion of Figure 9, the geometric reductions in a vertical plane are indicated. From the fundamentalmeasurements and a few more observations, the horizontal distance ( HD ) and elevation ( H ) may be determined:

(9)

H * is the elevation difference between instrument and reflector, IH is instrument Height, and PH is the PrismHeight.

(10)

F igure 9. Surveying geometry.



Determinations in the horizontal plane

In the upper portion of Figure 9, the map view reductions from the fundamental measurements are shown. Becausewe are interested in the map relations of the surveyed objects or observations, the distances East ( E ) and North ( N

may be determined in the following way:

(11)

(12)

Foresight and Backsight: the traverse

One other thing that people have trouble with and that I have only recently gotten to the bottom of is the traverse or how you move your station to a new position. The figure below shows how one starts of at the reference positionE0, N0, H0, works, and then moves to the new station with a reference position E1, N1, H1. What you have to dois shoot from the first location to the second (foresight) and record the E1, N1, H1, and the bearing Hz0. Then,



move to the new location, set up, tell the total station you are at E1, N1, H1, and set the horizontal circle to Hz1 or Hz0+180 degrees (backsight). Then shoot to the reflector set up at the first station and record the position. It should

be within a few mm of the original E0, N0, H0.

Precision

The angular accuracy at one standard deviation of the Theodolite is 3", and the linear accuracy at one standarddeviation of the EDM is 5 mm ± 5 ppm of the slope length. The upper portion of Figure 10 shows a map view of the 1 standard deviation error volume (remember that the horizontal and vertical angles have the same precision).In reality, this volume is really an ellipsoid if we assume that the errors are normally distributed. The significance

of this figure and the plot in the lower portion of Figure 10 is that one can anticipate the precision and its changeswith slope length, and consider them accordingly. For example, for a 100 m shot, or slope length D = 100 m, thelinear error, l, is 5.5 mm, and the angular error, a, is 1.5 mm, and therefore, the error volume is 11 mm along theshot, and 3 mm wide along horizontal and vertical arcs. Note that this is much smaller than reflector placementerror.

Planning and executing a surveying/mapping project

The important concern when planning a mapping project is the question that is being asked, or problem beingaddressed. While mapping and surveying may be intrinsically fascinating and interesting of themselves, unless youwant to become a surveyor, they are only methods used to collect data in order to address a geologic problem.



Therefore, the technique and methods should be appropriate for the problem. You should collect data at theappropriate scale and precision that will most efficiently shed light upon the problem. Check (Compton, 1985) for an inspiring and essential text to guide you in the field.

Basic detailed mapping procedure

This technique is appropriate for outcrop to kilometer scale mapping (1:10 to 1:1000 scale) for which no adequate base map exists. The basic idea is to shoot in control points with the Total Station, establish a base map, and thenuse tape and compass and triangulation to interpolate and locate features between the control points.

F igure 10. Surveying precision.

1) Recon the area. Consider the problem, and instrument locations.



2) Flag points. Place flags (numbered) on important features (along large fractures or contacts for example). Thedensity depends upon the scale of the problem and the map. If the flags are too close, you will spend a long timeshooting them in and then may be confused while mapping. If they are too far apart, you will spend a long timemeasuring off distances and bearings between points. I suggest a radial distance between flags of 5 to 10 m.

3) Shoot points with Total Station. Make sure that the point number corresponds either directly or in some notedway with the flag numbers.

4) Produce basemap. This may be done in several ways. It may be done in the field or the office by manually plotting the location and recording the elevation of the point on grid paper. Be sure to use metric grid paper. Theother way to produce the basemap is to download the data as described above, and contour and plot the points withtheir numbers. Print the contour map out to an appropriate size for your mapping. I do this step in Deltagraph Pro

by importing a four column (point number, E, N, H) Excel file, and then plot an XYZContour chart (select the data by using the arrow in between the two label words:

c Label

Label

Show symbols, and adjust the size of the chart by selecting Axis Attributes under the Axis choice under the Chartmenu. Make sure that the X and Y (E and N) axes are the same scale. Choose an appropriate contour interval.Show the labels of the points (point numbers, for example) by selecting the chart, and then under the Chart menu,select Show Values, and choose a location besides None, and the Text should be Category. This will plot the itemsin the corresponding cell in the Labels Column adjacent to the symbol.

5) Mapping. The above method should provide a basemap with the control points displayed and labeled. Tape the base map or a portion of it to your map board and overlay a piece of vellum or mylar. Mark the control points and afew more index marks, especially if you will use more than one page for the base map. As you map, observe thelocations and orientations of objects and features by noting the bearing and distance (using a Brunton Compass anda tape measure or a well calibrated pace) from one or more control points. You may also shoot a bearing to two or more control points, plot the angle on the map and triangulate your location. Mark your observations carefully witha sharp pencil. As you map, record the topography. If you plotted contour lines, trace and modify them in the fieldand include the subtleties that you can. In the evenings or whenever you are at a stable point, trace your lines in ink using a very fine pen.

Examples

Below are a few examples of different mapping projects our members of our group have completed recently. Theseare meant to illustrate the different solutions to different problems that have been achieved.

Topography

My own interest in the geomorphic responses to active faulting provides the following example. During the June28, 1993 Landers California earthquake, spectacular faulted landforms were produced all along the surface rupture.These landforms provided an important opportunity to document the original shapes and initial modification of faulted landforms. This project posed several interesting survey challenges: 1) producing detailed scarp profilesand longitudinal profiles of gully main and tributary channels, and detailed topographic contour maps of faultedknickpoints; 2) establishing a cheap but hopefully stable control network; and 3) reoccupying the network.



Scarp profiles--coordinate transformation by rotation

These profiles are made perpendicular to the fault scarp and are ideally planar. In thefield, we marked the upper and lower ends of the profiles with steel rods, and walk

between, shooting points about every 50 cm until we are at the free face of the scarp,where points are shot about every 10 - 20 cm. These data are down loaded as describedabove, and then the profile is projected to a plane perpendicular to the scarp. Thecoordinates are transformed by a rotation about the origin so that one axis is thedistance along the profile and the other is the deviation from the plane of the profile.The equations for such a coordinate transformation are as follows:

(13)

(14)

The figure above and to the right illustrates this geometry.

The following two figures illustrate the initial and rotated coordinate systems for a scarp profile. In the lower plot,the coordinate system has been rotated by -36° (counterclockwise), and the horizontal axis used as the horizontaldistance along the profile. The vertical axis indicates that the deviation from a plane is a maximum of 5 m over 30m.



Reoccupation

There are three types of errors: random errors, systematic errors, and blunders (Kennie, 1990). Random errorsresult from the random normally distributed probability of a

measurement. Systematic errors cannot be detected by redundant measurements because they effect allmeasurements similarly. However, they can be addressed by making more observations; for example the scaleerror due to atmospheric changes that is explained above is a type of systematic error that can be minimized bymaking observations of temperature and pressure and making the appropriate scale adjustment. Blunders arehuman errors that hopefully are minimized or large enough to be noticed and removed from the data.

Errors within a single survey are rather small. Reoccupation of a survey network in order to repeat measurementsmay be desirable, but it incorporates greater error. The best way to adjust two sets of data measured of the same



network during successive occupations of a survey network is by least squares. In this technique, the squares of theresiduals of the observations are minimized:

(15)

where V = l i¶ - li, in which l i is the observation and l i¶ is the adjusted observation, and W is a weight matrixconsisting of the inverse of the covariance matrix of the observations. If the data are not correlated, the matrix will

be diagonal, and if the variances of all the data are the same, the W matrix may be dropped from the determination(Kennie, 1990).

Detailed F racture Mapping

Finally, as an example of the mapping technique I described above, I will briefly discuss the method by which wemade a detailed fracture map of a portion of the surface rupture of the Landers earthquake (Antonellini, 1992). SeeFigures 12 and 13. First, we made a reconnaissance of the area, and noted the important features and discussed the

problem and the pertinent observations. Second, we determined the approximate size: ~700 m long by ~250 mwide. We considered the mapping scale by determining the basemap size for various mapping scales: 1:250--theultimate scale chosen--would result in a basemap approximately 2.8 by 1 m in size. We divided into four mappinggroups, so each would have a base map approximately 0.7 by 1 m--probably the maximum comfortable size for a

single sheet. Third, we flagged numbered control points along fractures and other obvious and important features.Fourth, the southeastern third of the control points were located using a conventional plane table set up. Thenorthwestern two-thirds of the control points were located using the Total Station in approximately the same timeas that for those done with the plane table. We did not have a means of automatically plotting our data in the field,so we did it manually. Here we made things difficult by having grid paper ruled in English units: inches and tendivisions. This made it necessary to convert the measurement read off of the Total Station LCD in metric units tothe quirky and irregular English scale. With metric ruled paper, and such a regular mapping scale of 1:250, itwould have been much easier to lay off the base map control points. The points were plotted with the point number and elevation adjacent to the symbol, and then four basemaps generated by overlaying sheets of mylar on thecontrol point map, marking the control points (including some shared by the adjacent maps to help with futurecompilation). With the control points marked in pen on the basemaps, we were ready to do our mapping of the

surface fracturing. Each mapping group had a measuring tape and compass, and recorded observations relative tothe control points within the mapping area (Figure 12). As mapping proceeded, topography was recorded, andcontours generated. The contours generated varied in their precision depending upon the effort of the mappers. Themost successful contour generation technique was for one member of the mapping group to put his eye level at thelevel of a contour and site along a level line determined by the Brunton compass toward the landscape, and thecontour continued and mapped in by communication with the mapping partner who interpolated between thecontrol points in a manner similar to that used for mapping other features (Cooke and Christiansen, Figure 12). Asmapping progressed, observations and contour lines were inked. The final map was compiled and drafted by KenCruikshank (Figure 13). It was presented at the Fall, 1992 AG U meeting (Antonellini, 1992).

F igure 12. Reduced portions of original basemaps from landers earthquake surface rupture mapping

(Antonellini and others, 1992). Note the different styles and representations of fractures, topography,landforms, and human impacts.



F igure 13. F inal analytical fracture map from Landers study (compiled by Ken C ruikshank)..



Bibliography

Geologic mapping

Compton, R. R., 1985, Geology in the Field: New York, John Wiley and Sons, 398 p.

The best fiel d geology book available. Cove r s all of the basics f r om r ock i d en tificatio n thr ou gh basic o u tcr op pr oce dur es to ae r ial photog r aphy. Yo u shou l d own it.



Electromagnetic distance measurement

Burnside, C. D., 1991, Electromagnetic distance measurement: Boston, Blackwell Scientific Publications, 278 p.

G ood r efer en ce o n the s u bject. A bit a r ca n e in the expla n atio n of the basics, b u t tho r ou gh. I n cl ud es a n ice d esc r iptio n

d iffer en t eq u ipme n t (3 rd ed ition , TA6 01 .B87 1991 , E n gin ee r in g Lib r a r y).

Price, W. F., and U ren, J., 1989, Laser surveying: London, Van Nostrand Reinhold (International), 256 p.

Con tai n s a goo d d esc r iptio n of the basics of lase r s, pa r ticu la r ly G aAs d iod es, a nd a clea r d esc r iptio n of the basics of EDM s. Cove r s othe r types of lase r equ ipme n t as well (e.g., time d pu lse d ista n ce meas ur emen t, alig n men t lase r s, a nd lase r Theo d olites a nd levels), a nd lase r safety (TA57 9 . P94 19 89 , E n gi n ee r in g Lib r a r y).

Basic Surveying

Moffitt, F. H., and Bouchard, H., 1987, Surveying: New York, Harper and Row, 876 p.

G ood r efer en ce o n the s u bject. This o n e has it all (8th e d ition , TA5 4 5.B7 19 87, E n gin ee r in g Lib r a r y).

Advanced Surveying

Kennie, T. J. M., and Petrie, G., editors, 1990, Engineering surveying technology: New York, John Wiley and Sons (Halsted Press), 485 p.

Tho r ou gh ove r view of latest a d van ces. Co n tai n s n ice d iscu ssio n s of elect r on ic d ista n ce a nd an gle meas ur emen t, s ur ven etwo r k e rr or s, photog r ammet r y, a nd d igital te rr ai n mod elin g

Mapping reference

Antonellini, M., Arrowsmith, R., Aydin, A., Christiansen, P., Cooke, M., Cruikshank, K., Du, Y., and Wu, H., 1992, Complex surfacerupture associated with the North Emerson Lake fault zone, caused by the 1992 Landers, CA earthquake: results of detailed mapping:EOS Transactions AG U , v. 73, p. 362.

Comments? e-mail Dr. Ramón Arrowsmith [email protected]

Introduction to Total Stations

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