Department of Geology

Surveying Procedures

Surveying Procedures

Instructions for Precise Surveying of a Quadrilateral

Details on procedures for measuring angles and distances. Methods involve multiple measurements of the same angle, and averaging / checking procedures.

You should be familiar with various methods for obtaining the angle between two stations. To survey a quadrilateral (e.g. for strain measurements) you should follow the method outlined below. The objective is to determine angles as accurately as possible. Sometime this may require taking more readings than is suggested below (other time, less readings are required). The order in which the readings are taken is important! For example, you should not take three F1/F2 readings to B, then three to C and three to D (from point A).  You should use the order shown in part 3 below.

The corners of the quadrilateral should be labeled A, B, C, D, in a clockwise direction. That is, if you are standing at A, looking at the opposite corner – C –, D will be on your right, and B on your left.

http://web.pdx.edu/~i1kc/courses/Surveying/Handouts/Quadrilateral.gif

1) Make a sketch of the quadrilateral in your notebook. Record project, time, date, name of survey crew. All of this is important. Since we are looking for changes in angles and lengths over time, we need to know when the readings were made.

2) If you are using a SDR33 notebook, you should still make a sketch in a notebook. You should record the point numbers used in the SDR for each round of readings. I suggest that you do not use the point averaging in the SDR33 — that is, never change a point number, only change the label. The more advanced users of SDR33 notebooks may wish to use the set collection program.

3) Set the instrument at A. Use the 0-SET on the instrument to set zero just counterclockwise of point B (this helps make life simple!).

  • Check that B, C, & D are level and over the benchmarks
  • Measure the height of all tripods
  • Take a F1 reading to B – check that the label and tripod height are correct
  • Take a F2 reading to B – check that the label and tripod height are correct
  • Take a F1 reading to C – check that the label and tripod height are correct
  • Take a F2 reading to C – check that the label and tripod height are correct
  • Take a F1 reading to D – check that the label and tripod height are correct
  • Take a F2 reading to D – check that the label and tripod height are correct
  • On the first cycle record the readings in your notebook. You can use this to check your other readings as they are taken. You should also use the first set of readings to check that the sum of the angles is correct for the various triangles in the quadrilateral. This may help you detect a bust.

Repeat the above procedure two more times (for a total of 9 pairs of readings)

4) Move the instrument to station B. Make measurements to A, D, and C as described above. Before starting, make sure that all reflectors are level and exactly over your points.

5) Move the instrument to station C. Make measurements to D, A, and B as described above. Check reflectors are level and over the points.

6) Move the instrument to station D. Make measurements to A, B, and C as described above. Before starting, make sure that all reflectors are level and exactly over your points.

7) When done you should have eight angles and six lengths. From here you can check the quality of your measurements and make any necessary adjustments. You should see the web page on adjusting quadrilaterals.

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Methods for Balancing a Traverse

Some ways in which you can adjust distances to 'close' a traverse (e.g., a quadralteral)

A traverse is a survey where you have occupied each station and measured each angle and distance between points. An example of a strong shape often used for studying deformation, such as on a landslide (Baum and others, 1988; Johnson & Baum, 1987) or for from an earthquake (Cruikshank and other, 1996; Johnson and others, 1997), is a braced quadrilateral. This is where all the angles and distances in a quadrilateral are measured repeatedly and averaged for accuracy. The quadrilateral is then measured at some later date and strain calculated from the change in shape of the quadrilateral.

The sum of the interior angles for a quadrilateral should be 360°. Any deviation from that is a measure of error. Also, the triangles that make up the quadrilateral should all obey the laws of sines and cosines - any deviation is a measure of error. Needless to say, either the distance measurements or the angles could be in error. We also have an over-determined system. For example, measuring two angles and one side of a triangle is sufficient to construct the whole triangle (although there would be no error control). If we measure all three sides and angles we have much more information than we need, and could possibly construct several different triangles using the data. Probably the best method for solving over-determined systems is the methods of least-squares.

Least Squares Adjustment

An outline of the method of general least squares is given in the following PDF format document 

Since we know that the quadrilateral should have no error, and we have convinced ourselves that there is no obvious bad data in our data set, we can adjust the angles and distances so that out shape meets all the geometric criteria. The most complete adjustment methods uses least-squares to adjust angles and distances so that you make the smallest possible changes (Moffitt, and Bouchard, 1992; Wolfe and Ghilani, 1997). One method for adjusting quadrilaterals is given by Smith & Varnes (1987).

Coordinate Adjustment

Simpler ways of adjusting traverses are shown in many Geology field methods texts. A sense of error in a traverse can be obtained by calculating coordinates for each point following the path of your traverse. After completing the traverse, you should return to the starting coordinates, any difference is a measure of your total error. For a quadrilateral you would perform the following calculations:

  • Fix one corner of quadrilateral, say the SW corner. This will have coordinates of (0,0,0). Assign the direction from the SW to the SE corners to be "east". Use your data to calculate the coordinate of the SE corner.
  • From the SE corner, use the angle between lines from the SE to SW corner and SE to NE corner to calculate the coordinates of the NE corner.
  • From the NE corner, use the angle between lines from the NE to SE corner and NE to NW corner to calculate the coordinates of the NE corner.
  • From the NW corner, use the angle between lines from the NW to NE corner and NW to SW corner to calculate the coordinates of the SE corner. The difference between this calculated coordinate and (0,0,0) is your error of closure.

This closure error can then be adjusted to zero using either the compass rule or the transit rule. An Excel workbook showing these correction methods is available here.

Compass Rule

In this method the coordinate error is distributed in proportion to the length of traverse lines. The assumption is that the greatest error will come from the longest shots.

  • Northing adjustment = Length of traverse line to point / Total length of traverse × Northing closure error
  • Easting adjustment = Length of traverse line to point / Total length of traverse × Easting closure error
  • Elevation adjustment = Length of traverse line to point / Total length of traverse × Elevation closure error

Transit Rule

In this method, the coordinate error is distributed in proportion to the amount that various coordinates change between points.

  • Northing adjustment = Change in Northing for traverse line to point / Sum of absolute values of all changes in northing for all traverse lines × Northing closure error
  • Easting adjustment = Change in Northing for traverse line to point / Sum of absolute values of all changes in northing for all traverse lines × Easting closure error

References

Baum, R. L., Johnson, A. M., and Fleming, R. W., 1988, Measurement of slope deformation using quadrilaterals, United States Geological Survey, Bulletin 1842B, p. 23.

Cruikshank, K. M., Johnson, A. M., Fleming, R. W., and Jones, R., 1996, Winetka deformation zone. Surface expression of coactive slip on a blind fault during the Northridge earthquake sequence: Denver, CO, United States Geological Survey Open-File Report 96-698, p. 70.

Johnson, A. M., and Baum, R. L., 1987, BASIC programs for computing displacement, strains, and tilts from quadrilateral measurements: United States Geological Survey Open-File Report 87-343, Reston, Virginia, p. 19.

Johnson, A. M., Fleming, R. W., and Messerich, J. A., 1997, Growth of a tectonic ridge, United States Geological Survey Open-File Report 97-153, p. 94.

Moffitt, F. H., and Bouchard, H., 1992, Surveying: New York, New York, Harper Collins, 848 p.

Smith & Varnes (1987), Least-squares adjustment of triangles and quadrilaterals in which all angles and distances are observed: Surveying and Mapping, v. 47, no. 2, p. 125-142.

Wolf, P. R., and Ghilani, C. D., 1997, Adjustment computations: Statistics and least squares in surveying and GIS, Wiley Series in Surveying and Boundary Control: New York, John Wiley & Sons, 564 p.

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Instructions for Using an Electronic Total Station as a Plane Table

This document assumes that you are familiar with the operation of Total Stations.

Modification to Short Instructions for SDR33 Setup

The instructions for setting up a SDR33 are given here. For control-point mapping we use the following settings under "Configure Reading"

Configure Reading

  • Type: Total Stn
  • Auto pt num: The number displayed here is the next automatic point number that will be used. For control-point mapping it is usually set to 2. Point 1 will be your first instrument point.
  • Topo view stored: Set to "OBS". This stores the observations - horizontal angle, vertical angle, and slope distance.
  • Combine F1/F2: Generally set to "No". If it is set to yes, the SDR33 will force you to take a F1 reading, then a F2 reading. It will then average the values and inform you if the difference between reading is greater than any tolerances you have set.
  • # dist rdgs: Generally leave as "1". This is the number of distance reading the instrument will take. If greater than one, the distances are averaged. If you are only measuring angles then you can set this value to 0. This disables the EDM for normal readings.
  • Tracking: Generally "No". If set to "Yes" then the EDM constantly takes measurements.
  • Code list active: Generally "No", unless you have developed a code list.
  • Info blocks: Set to "0". This is the number of comment block associated with each reading.
  • Code fields: Set to "0".
  • Recip Calc: Set to "Prompted"
 

Procedure for 'shooting-in' points

Case I. Starting a New Map

If you are starting a new job this is the time to set up your coordinate system. If you are making a control-point map then you will want to orient "North" along the long axis of your mapping project. Point the total station along the long axis and use the instrument control panel to set the direction to zero (see instructions below). Then, when the SDR33 prompts you for the instrument station number, enter any number (usually 1). When prompted for a backsight reading, just press OK, and then confirm that you want to skip the backsight. The SDR will not reset the instrument under these conditions.

  • At this point you should have the Total Station setup over your first point, and the SDR33 should be configured.
  • Set the zero direction in the Total Station. Do this by pointing the total station along the long axis of the intended map. Press the ENT and then 0 SET keys on the instrument,
  • Start by pressing 'Clear' until you have the main SOKKIA screen
  • Press Clear one more time
  • At this point you should see a screen with space for a job name, station, and backsight.
  • Select SURV (F2 key)
  • Select Topography and press the OK key
  • At this point, if you will enter the Job Creation screen.
  • Select the appropriate job parameters and press OK. Press OK to pass the screen that allows you to type a descriptive paragraph
  • You will now enter a screen asking you for
    • Stn: Enter 1, since this is your first station (press enter)
    • North: For the first station I usually use 0 (press enter)
    • East: For the first station I usually use 0 (press enter)
    • Elev: For the first station I usually use 100 (press enter)
    • Theo Ht: (press enter)
    • Cd: This field allows you to type a text identifier. (press enter)
    • Press OK when done
  • You will now enter a screen asking you to confirm the backsight
  • Press OK
  • Press F1 to confirm that you are not entering a backsight
  • You are now ready to start taking readings.
  • To take a reading, align the crosshairs on the target, and press the large blue key in the bottom right corner of the SDR33. This will take a reading and display the angles and coordinates on the screen. You can move about this screen with the cursor arrows.
  • Enter some text. For most points I just use the text "Point"
  • Enter the reflector height.
  • Press OK to save the data.
  • The SDR33 will remember both the point name and reflector height from now on, although you can change them at any time.

Case II. Continuing an Existing Map

If you are continuing a job where it is important to orient the instrument, you should set up the instrument over a known point, and set up a reflector over a second known point. When starting to use the SDR33 specify the station number where the instrument is located. If the point number exists in the current job, then the SDR will display the stations coordinates and ask you for a instrument height. If the point number is not found in the current job then you will need to enter the coordinates of the current instrument station and the instrument height.

After specifying the location of the instrument you have to indicate the backsight point number. Again, if this point exists in the current job, you will asked to point the instrument at a target over this point and take a reading. If the point does not exist, you are given the choice of either entering the coordinates of the backsight point, or the direction to that point. Once you have entered the information about this point, then you will be asked to take a reading to this point

The SDR will set the horizontal circle to value you entered, or from it’s record of point. It will then take a reading to the point and verify that the range and elevation difference match what is has in the job database (if it is a pre-existing point).

At this point you should have the Total Station setup over your first point, and the SDR33 should be configured.

  • When you start the SDR33 it will take you to a screen displaying Job, Stn, and BS point. These should have been the last points you occupied.
  • Press the F2 (SURV) key
  • Select Topography
  • Enter the point number you are occupying
  • You will enter the Point coordinate definition screen. Check these values, and change the descriptive text if needed. Press OK
  • You will now be asked for a backsight point. Enter the BS point number and press OK
  • Align the crosshairs on the target at the backsight point and take a reading. The SDR33 will set the correct orientation in the instrument
  • Proceed as normal to get more points. They will be in the same coordinate system as previously surveyed points.

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Using Surfer to Plot Base Maps for Control-Point Mapping

For this project, we suggest you keep all files in the same directory. This will make it easier to move between computers.

You should start the process with an Excel worksheet containing the following information:

  1. Point Number
  2. Elevation
  3. Easting
  4. Northing

Step 1. Create a Surfer Data file

The simplest way to get this information into Surfer, without using intermediate files, is to use the Windows copy (Ctrl+c) and paste (Ctrl+v) commands.

  • With your Excel worksheet open, start Surfer
  • Use the File … Worksheet menu item to open a Surfer worksheet
  • Switch to Excel
  • Highlight an entire column of data (click on the letter at the top of the worksheet). If the data columns are next to one another in the Excel worksheet you can highlight adjacent cells.
  • Copy the column (use either the Edit … Copy menu or Ctrl+c)
  • Switch to the Surfer worksheet
  • Paste the column into the worksheet (use the Edit … Paste menu or Ctrl+v)
  • Repeat the above sequence until you have all four columns transferred.
  • Make sure that the first row for each column contains text identifying the contents of the column
  • Save the Surfer worksheet using the File … Save As command (note where you are saving the file!)
  • You can now exit Excel
  • Switch to the Surfer plot window using the Window … menu

Step 2. Create a Map of Points

There are two parts to this step. You need to create a map of points with point numbers, and then overlay a second map that has elevations.

  • At this point you should be in a Surfer plot window
  • Choose the Map … Post menu item
  • You will not get a File Open dialog box. Find and open the data file you created in Step 1
  • You will now get the Post Map dialog box
  • Select the correct columns for the E (or x), and N (or y) columns (the list boxes will contain the column names you used in the Surfer worksheet in step 1)
  • For the label, Select the point number
  • Click on the symbol button to select the symbol you want to use
  • Select the correct symbol size (0.1 inch is good)
  • Select the "Format" button to change the format to zero decimal places
  • Select the "Font" button and change the font size to 8 points
  • The label position should be "Above"
  • When all is done, select OK
  • Click on the map that appears
  • Go to the Edit … Object ID menu item, and identify the map with the name "Point Numbers"
  • Now repeat the above procedure, but this time:
  • For the point label use the elevation column
  • Under "format" use 2 decimal places
  • The label position should be "Below"
  • When you click OK a second map will be generated
  • Skip the Edit … Object ID step. This layer will have the default name of "Post"
  • Now press the F2 button (or use the Edit ... Select All menu item)
  • Use the Map … Overlay Maps menu item to make a single map out of the two layers.
  • Should you want to change the properties of one of these layers, select the map and use the Map … Edit Overlays command to select which layer you want to edit (one will be called "Point Numbers", the other "Post").

Step 3. Scale the Map

The next step is to work out the map scale you want to use. Surfer works in inches, and the total station data we have is in meters. The conversion factor is 1 inch = 2.54 cm. So, if we want a scale of 1:100, or 1 cm represents 1.00 m, this is the same as 2.54 cm represents 2.54 m, or 1 inch represents 2.54 meters.

  • Click on the map to select it
  • Use the Map … Scale menu item to get the Scale dialog box
  • The dialog box is in terms of 1 inch on the paper = units on the ground. Our ground units are meters. So, for a map of scale 1:100 enter 2.54 in the dialog box. Surfer will calculate the size of the map for you.

Common map scales are given in the table below.

Map Scale

Surfer Scale

1: 100

1 inch represents 2.54 meters

1: 200

1 inch represents 5.08 meters

1: 250

1 inch represents 6.35 meters

1: 500

1 inch represents 12.70 meters

You should add a scale bar to your map using the Map … Scale bar menu item. This will let you check your map scale.

Step 4. Print the Map

  • When you have created your map and it is at the correct scale, save the Surfer file.
  • You can then use the Epson 1500 to plot your map.
  • Use the File … Page Layout menu item
  • Select a paper size of "Ledger" (11 x 17 inches) and select OK
  • Use the View … Page menu item to see if the plot fits on this size paper. If the paper is too small, select the File … Page Layout menu item and change the paper size to "Other" and set the size to a width of 22 inches and a height of 17 inches. This is the largest size paper we have available.
  • Surfer can "Tile" plots. That is, if the map is bigger than the paper specified it will print the map on several overlapping sheets.

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