UNITED STATES 

DEPARTMENT OF THE INTERIOR 

]. A. KRUG, Secretary 

GEOLOGICAL SURVEY 

W. E. WRATHER, Director 

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CIRCULAR 12 

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GEOLOGIC MAPPING 

by means of 

GRAPHIC LOCATOR 

By 

D. ]. VARNES 

WASHINGTON 

1946 
GEOLOGIC MAPPING BY MEANS OF 

GRAPIDC LOCATOR 

By D. J. Varnes 

CONTENTS 

Page Page 

Introduction. . . . . . . . . . • . • . . . . . . . . . . . . . . . . . . . . 1 

Description of the graphic locator.. . . . . . . . . . . . . 1 

Procedure for using the graphic locator. . . . . . . 2 

Inherent errors and advantages. . . • . . . . . . . . . . . 2 

ILLUSTRATIONS 

Page 

Figure 1. Graphic locator technique . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

2. Range of observed errors. . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . 4 

INTRODUCTION 

The writer has designed a graphic locator for 

rapid and accurate preparation of geologic maps. 

He describes it and how it is used, and enumerates~ 

the inherent errors and advantages of its use. 

The preparation of a detailed geologic map of any 

particular area implies that a geologist observes the 

vertical and horizontal patterns and relationships of the 

various rock formations that are present at or near the 

surface within the boundaries of the area being mapped. 

He determines by visual evidence and logical deduction 

the geologic composition of all physical features within 

the area, from the bottom of the lowermost valley to the 

top of the highest hill or mountain. As he progresses in 

his survey he sketches the geologic detail on a topographic 

map base that has been prepared in advance of the geologic 

survey. Thus, the geology is superimposed on the topographic map in contrasting colors that depict the extent, 

thickness,and "lay" of individual bedrock units at each and 

every point within the area being mapped. 

The accuracy of the geologic map depends not 

only upon the accuracy of the topographic base, but 

upon the ability of the geologist to determine correct 

locations on the map in tracing the contacts of the 

different rock formations across country. In areas of 

low relief, few difficulties arise unless the rock surface is greatly obscured by blanketing surface materials. 

In rugged or mountainous terrain, it is often impossible 

to plot accurately all geologic information on topographic maps because of inaccessibility of certain 

critical positions that can be neither reached on foot 

nor determined by standard instrum.ental.survey methods. In such places it is possible only to 'estimate the 

vertical and horizontal position of the points in plotting 

them. 

To overcome this inherent deficiency in orthodox geologic mapping technique, the writer and Arthur H. Frazier 

of the Geoloqical Survey have constructed a "grG.phic 

locator" for field use in geologic mapping. The graphic 

1 

locator eliminates the need of a stadia rod in determining the position on a topographic map of any point 

within the range of visibility of the observer. Used 

in conjunction with a surveying alidade it will not only 

locate points that are inaccessible with a rod, but will 

greatly speed the accurate mapping of loose surface 

materials that do not justify tedious rod shots but would 

otherwise be difficult to sketch accurately. 

Properly used, the graphic locator technique allows 

the preparation of geologic maps that are automatically 

adjusted to the topographic base map, though it does not 

effect the absolute delineation of certain special features 

such as mineral veins and igneous dikes. With the graphic 

locator the intersection of a line of sight with the surface 

of the ground can be plotted directly on the topographic map, 

thus fixin.g any desired point within the limits of accuracy of 

the map itself. 

The technique has been successfully used in the field 

by the writer. It has been fountl to give locations that are 

sufficiently accurate for most geologic work. It is definitely a time -saving technique and makes possible much 

closer control of mapping in difficult terrain. Although the 

graphic locator was designed for use in rugged country, it 

can also be used in rolling terrain or in areas of moderate 

relief provided the line of sight makes an angle of more 

than 15° with the surface of the ground. 

DESCRIPTION OF THE GRAPIDC LOCATOR 

The graphic locator consists of a single rectangle 

of xylonite or other transparent plastic material, about 

3 inches square and 1/16 inch thick. 

Two scales, graduated in divisions corresponding 

to the contour interval of the topographic map with which 

it is to be used, are marked or engraved on the under 

side of the rectangle, one at the right and one at the 

left edge. Because of the simplicity of its construction, sets of these graphic locators can readily be made 

for use with maps having any specified contour intervals 
OI' horizontal scales. The accompanying drawing 

(fig. 1) illustrates the graphic locator used in mapping 

an area in the San Juan region, Colorado, on a topographic map having a contour interval of 25 feet and 

a horizontal scale of 1 inch to 1, 000 feet. The scale 

divisions on the mod~ computed from the equation 

25 x 12 x 1,

000 1

x 12 =1/40 inch, are 1/40 inch apart. The 

etched areas B and B 1 , on figure 1, between the major 

scale divisions, are used for recording with pencil 

the range of elevations for any particular setup. 

PROCEDURE FOR USlliG THE GRAPIDC LOCATOR 

The procedure for using the graphic locator 

(see fig. 1 for example) is as follows: 

1. Location of the plane table setup point A is 

plotted on the topographic map by resection or other 

suitable means. , 

2. Elevation of the alidade ("ID") is determined 

to be 12, 150 feet. 

3. Reference elevations are written in the 

opaque areas B and B 1 on the graphic locator, as suming that the range in elevations for the shot used in this 

example will be between 10,000 and 13,000 feet. 

4. Telescopic alidade is sighted at point to be 

plotted; ray A-Cis drawn on map, and the vertical 

angle read. If an open-sight alidade is used, the 

line of sight is drawn and the angle is read with a 

Brunton compass. 

5. From the ray A-C the vertical angle CAD is 

plotted with an 8-inch protractor and a segment &f the 

line A-D drawn. In the example the angle is 18 . 

6. The graphic locator is placed over the ray A -C 

so that the scale readings at both edges (E and E') 

correspond to them of the instrument (12, 150 feet). 

While held firmly in this position the straightedge of 

the alidade base is placed against either the top or 

bottom edge to serve as a guide for shifting the graphic 

locator laterally. 

7. The locator is then shifted along the straightedge until the edge of the scale atE intersects line A-C 

at the estimated position on the map of the point being shot. 

8. Next, it is noted whether the scale reading 

at F (the point where line A-D crosses the edge of 

the scale) is greater or less than the contour reading 

at E. If, for example, the contour elevation of the 

estimated position at E is 10,900 feet the scale 

reading at F would be approximately 10, 975 feet. This 

means that the line of sight has not yet intersected 

the ground surface at point E. A profile of the ground 

surface, G -G 1 , has been added to figure 1 to indicate 

the relation of the ground surface to the line of sight. 

9. If the graphic locator is moved farther to the left 

so that the scale reading at E is 11, 000 feet, then the scale 

reading at F will read approximately 10, 930 feet, meaning 

that the line of sight has penetrated the surface and the 

point as located by this second estimate lies beneath the 

ground surface. The point sought must, therefore, lie 

between the 10,900- and 11, 000-footcontour lines online 

A-C. The range between the tria). points is then quickly 

reduced by moving the graphic locator back and 

forth between the 10,900- and 11, 000-foot contour 

lines. 

10. When the positjon of the graphic locator is 

such that the contour elevation at E is the same as 

the scale reading at F (10, 950 feet in the example) 

the point of intersection at E is the point on the map 

that is sought. 

lliHERENT ERRORS AND ADVANTAGES 

The degree of accuracy with which points 

may be determined with the graphic locator depends upon the accuracy of the topographic map, 

upon the accuracy of manipulation of the instrument, 

and upon the relief of the terrain. 

In order to evaluate the combined errors 

that may be inherent in the construction and manipulation of the graphic locator, a number of shots 

were taken between points on a topographic map 

whose position and elevation had previously been 

determined by topographers. The contour map was 

therefore very accurate in the immediate vicinity 

of these known points and any error in relocating 

these points by the process described above would 

be inherent either in the instrument, the procedure, 

or a combination of both. The test was carried out 

in the office on 32 known points. Angles were computed from the horizontal and vertical distances as 

scaled from the map and plotted with an 8-inch 

protractor. The operation was thereafter completed 

in exactly the same manner as would normally have 

been done in the field. 

It was found that a major source of error 

between the measured distance and distance as 

determined by the graphic locator lies in the angle 

that the line of sight makes with the surface of the 

ground in the vicinity of the point that is being 

located. The distribution of points plott ~d on 

figure 2 shows that at low angles (grazing shots) large 

errors may occur because the point at which the 

line of sight intersects the ground surface is generally difficult to determine. Conversely, at higher 

angles location becomes increasingly more accurate. 

The solid line in figure 2 represents approximately 

the upper limit of error at any angle of the line 

of sight with the ground surface, and the dashed 

line the approximate mean error. It can be seen that 

for angles greater than 25°-30° the error is consistently less than 1 percent and that for angles 

greater than 15° the mean error is less than 1 percent. 

Although the absolute error in feet may tend 

to increase with length of shots, owing to possible 

errors in plotting the vertical angle, the percentage 

error showed no definite relation to the length of 

shot. The 32 shots plotted on figure 2 range from 

1, 220 feet to 5, 900 feet; they average 3, 100 feet 

in horizontal distance. Accurate results cannot be 

expected with a 13-foot rod at such a distance. 

The graphic locator cannot be used effectively if 

the line of sight makes an angle of less than 15° 

with the surface of the ground in the vicinity of 

the point being located. This circumstance generally limits the use of the graphic locator to regions 

of moderate to great relief. 
25 foot contour lines omitted 

except near set-up and point 

bein9 located 

Bose of alidode 

Figure 1. -Graphic locator technique. 

Scale of mop 

0 1000 2000 3000 4000 FEET 
0/o Error in horizontal distance= measured distance minus distance by graphic locator 

measured distance x 100 

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Figure 2. -Range of observed errors. 

4 
The field tests made with the graphic locator 

indicate that the following advantages may be expected 

through its use: 

1. Familiarity with the use of the graphic 

locator makes possible the fixing of a location within 

3 minutes after the alidade is set up and the position 

and elevation of the point of observation are determined. 

2. Results obtained with the graphic locator 

have been checked with actual rod determinations in 

the course of geologic mapping and have been found 

to be approximately the same. Where the rod cannot 

be used, the graphic locator offers an equally reliable 

alternative. 

5 

3. The graphic locator is especially suited for 

long shots, beyond the range of the rod. 

4. The locator is valuable for checking rod shots. 

5. The instrument is useful for determining from 

a topographic map alone the area visible from any selected point. 

6. Use of the graphic locator results in a 

great saving of time in mapping rough terrain 

because the number of rod shots required is 

reduced. The services of a rodman are not 

required. 

INT.-DUP. SEC., WASH., D.C.Iflf7&l