> Direction of Movement of 

Jasperoidizing Solution

By T. S. LOVERING

^

< CONTRIBUTIONS TO ECONOMIC GEOLOGY

GEOLOGICAL SURVEY BULLETIN 1222-F

Petrofabric analysis of asymmetric zonal 

" overgrowths on quarts crystals in jasperoid shows direction mineralizing solutions 

" moved information of both theoretical and 

 f practical value

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1966
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington. D.C. 20402 - Price 15 cents (paper cover)
CONTENTS

Abstract. ____.____._______-__^__.______-,__._.___.

Introduction. _____________________________________

Theoretical considerations._________________________

Petrographic technique.._______-______--___--_____.

c-axes of quartz.______________________________

a-axis elongation and zonal overgrowth_._.___.. 

Procedure and interpretation_____.______.._______.

Mathematical analysis of vectors__-____-_-_--__-___.

Cave and Coolidge prospect, Oilman district, Colorado. 

Tintic Standard mine, East Tin tic district, Utah_____.

Conclusions. ______-______--__---____-_-_-_-_-___.

References cited-__-___-_-__-__--____-__-----____.

Page.

Fl

1

3

5

6

7

8

11

14

20

25

25

ILLUSTRATIONS

Pago 

FIGURE 1. Photograph of jasperoid from J stope, 900 level, Tintic Standard

mine, showing asymmetrically zoned quartz crystal________ F3

2. Diagram of c-axes of quartz in samples from the Cave and Coolidge prospect, Oilman, Colo ___________________________ 10

3. Composite contour diagrams of quartz c-axes from Cave and

Coolidge prospect plotted on lower hemisphere.____________ 12

4. Contoured patterns of descending and ascending solution movement vectors from Cave and Coolidge jasperoid---_________ 16

5. Diagram of solution movement as interpreted from figure 4. ___ 18

6. Diagram of resultants calculated from various groups of solution

movement vectors from Cave and Coolidge jasperoid_-__-_ 19

7. Contoured patterns of solution movement vectors from J stope

jasperoid, 900 level, Tintic Standard mine..--_-_---__---__ 22

8. Calculated resultants of various solution movement vector

groups, J stope jasperoid, 900 level, Tintic Standard mine. _ _ . 24

TABLE

Page 

TABLE 1. Calculation of resultant of ascending vectors within ±15° of

bedding plane, Cave and Coolidge prospect....__-_____ _- F13

CONTRIBUTIONS TO ECONOMIC GEOLOGY

DIRECTION OF MOVEMENT OF JASPEROIDIZING

SOLUTION

By T. S. LOVERING

ABSTRACT

Experimental work has shown that crystals nourished by moving solutions 

commonly grow asymmetrically with overgrowths facing upstream, toward the 

stoss direction. This feature suggests that hydrotherinal jasperoids show zonation which indicates the direction of movement of the hydrothermal solutions. 

Petrographic examination of jasperoids from the Oilman district, Colorado, and 

the East Tintic district, Utah, showed that asymmetric zonal overgrowth perpendicular to the c-axis of quartz is common in the jasperoidized limestones and 

dolomites examined. A special type of petrofabric analysis was devised to determine the direction of asymmetric zonal growth perpendicular to the c-axes. 

Directions of overgrowth were plotted as unidirectional vectors on a lower hemisphere equal-area projection. Contoured concentrations of overgrowth vectors 

similar to the usual contoured petrofabric diagrams were made and compared 

with the significant structural conditions in the two areas sampled. The vectors 

were also analyzed mathematically to obtain resultants for all vectors and for 

selected groups of vectors. The resultant for the Oilman district, which has a 

relatively simple geologic setting, and the resultant for the Tintic Standard 

mine in the East Tintic district, which has a very complex structural setting, 

agree in indicating a statistically significant concentration of vectors pointing in 

the direction of the most probable source of hydrothermal solutions. Additional 

vector concentrations in the Oilman district suggest that the jasperoidizing solution deposited jasperoids where convective circulation took place in cells at right 

angles to the main direction of updip motion of the hydrothermal solutions. In 

the East Tintic district the resultant of all the vectors points downward from 

the jasperoid area directly toward the main ore body in the Tintic Standard 

mine, and thus could have been used as a guide to exploration. The jasperoid at 

the Tintic Standard mine is closely associated with ore, whereas that in Oilman 

has a much more tenuous association with the actual ore. The technique developed seems worthy of additional investigation both as an exploration tool and 

because its use can throw additional light on the genesis of jasperoid bodies 

themselves.

INTRODUCTION

The experimental work by Newhouse (1938,1941) showed that crystals nourished by moving solutions in unobstructed channels grew 

most rapidly on the upstream, or stoss, faces. He noted that crystals

Fl
F2 CONTRIBUTIONS TO ECONOMIC GEOLOGY

close to and on the lee side of other obstructing crystals might receive 

more nourishment on the sides or on the downstream faces, and thus 

grow more rapidly on the lee sides. Asymmetric crystal growth is 

shown best by zonal structure that makes visible the asymmetric overgrowth; it also may be recorded in abnormal elongation parallel to 

certain crystallographic directions, by groups of crystals piled in 

oriented stacks, or by "hollow crystals" whose lee sides were 

undernourished.

Experimental work by the author, using copper sulfate solution, 

checked the results of Newhouse and added little that was new; it was 

found, however, that where crystal growth was rapid the zonal overgrowth was far less unidirectional and the crystals much smaller than 

where the growth was slower. The speed of the current was also an important factor; as the speed dropped below about 1 cm per minute the 

zonal overgrowths of chalcanthite tended to become more and more 

random. At higher current rates the overgrowths were more and more 

consistently directed upstream except for those on crystals in the lee 

of obstructions. In a current moving 5 cm per minute almost all the 

crystals showed overgrowth on the stoss sides. The degree of preferred 

orientation reflects the relative amount of nourishment received 

through physical transport of the solute as contrasted with that provided by diffusion; the speed of current required to produce a marked 

preferred orientation of stoss-side overgrowths depends on the concentration and kind of solute that was precipitating. The behavior of 

copper sulfate illustrates only the tendencies of crystal growth in an 

easily crystallized compound; the rates of movement of solution and 

degree of supersaturation of a solution depositing quartz would be 

entirely different, but crystal growth nevertheless would similarly 

reflect relative rates and precipitation gradients.

Petrographic study of jasperoids from the Oilman district, Colorado, and the East Tintic district, Utah, shows that zonal overgrowth 

perpendicular to the c-axis of quartz is common in the jasperoidized 

limestones examined (fig. 1.) and that statistically significant concentrations of overgrowth directions can be found by detailed petrofabric 

study.

After the author had developed theory and petrofabric technique 

and applied them to the study of the Tintic Standard mine jasperoids, 

the petrofabrics were rechecked independently by Dr. Bronson 

Stringham when he was the author's assistant in 1945, and later the 

work on the Cave and Coolidge jasperoid was carried on by graduate 

students at the University of Michigan under the author's direct supervision. The data presented later in this paper thus are believed to be 

free from operator bias.
MOVEMENT OF JASPEROIDIZING SOLUTION F3

FIGURE I. Jasperoid from J slope, 900 level. 

Tintic Standard mine, showing asymmetrically 

zoned quartz crystals, zQ. Crossed nicols. 

X 285.

THEORETICAL CONSIDERATIONS

The conversion of large masses of rock to jasperoid probably involved the pervasive movement of substantial quantities of solution, 

but the small size of the openings available for the fluids suggests 

that the flow would be relatively slow even though a strong pressure 

differential existed. Solutions moving through the complex of minute 

interconnecting openings of the host rock might have an overall movement in a definite direction but still follow tortuous channels in detail. 

The pattern and the dimensions of the open spaces would determine 

the size of the block required to give a representative sample of the 

overall direction of flow in a given spot. In a thick bed made up of 

1-mm spheres, the average direction of flow in a 2-cm cube might 

be expected to approximate closely that in the aggregate for several 

meters in any direction, but in an aggregate made up of 1-m spheres, 

the average direction of flow in a random 2-cm cube would have little 

meaning. To get the same relative sampling would require a cube 

2,000 cm on a side.

The characteristics of replaceable rocks probably differ greatly from 

district to district, but some acceptable generalizations can be made. 

The more widely spaced the network of openings traversed by moving 

solutions, the less the chance of consistent directions of flow in small
F4 CONTRIBUTIONS TO ECONOMIC GEOLOGY

volumes of the mass chosen at random. Whatever their dimensions, 

irregular channels would not favor tis high a degree of preferred 

orientation of zonal overgrowths as would straight parallel channels. 

If the solution movement were sufficiently slow or changed direction 

many times, a completely random orientation might result regardless 

of the space pattern of the channels.

Even under favorable conditions, overgrowths in many directions 

inevitablv would be present in jasperoidized rocks, but the concentration of overgrowth directions should be significantly greater on 

the stoss sides of the crystals than on other sides.

If the orientation of the c-axes of quartz seed crystals were completely random, slight deflections from the general current direction 

could nourish opposite sides of crystals with their c-axes nearly parallel 

to the direction of flow; such crystals would show the least agreement 

in a-axis overgrowth. Because quartz crystals grow most rapidly 

along the c-axis, the crystals whose c-axes are nearly parallel to the 

current have less tendency to obstruct the passage of solutions as a 

result of crystal growth than do the crystals disposed at right angles 

to the current. Thus the largest and best zoned crystals in the jasperoid might be those that show the smallest degree of asymmetric 

zonation. Conversely, the crystals whose c-axes lie perpendicular to 

the direction of solution movement would be expected to exhibit the 

most conspicuous asymmetric zonal overgrowth and the greatest degree of preferred orientation of a-axis elongation.

A statistical picture of the orientation of c-axes and &-axis elongations should be analyzed with these considerations constantly in mind. 

Porous jasperoids that formed from relatively fast moving solutions 

should provide a minimum of conflicting data; dense jasperoids 

formed by diffusion through nearly stagnant solutions might have 

completely random orientations of c-axes and a-axis overgrowth. Furthermore, investigations in regions of geothermal power potential 

show that in hyperthermal areas convection currents are commonly 

present and give rise to oppositely directed currents, which change 

position from time to time. Convection currents probably existed also 

in jasperoidizing solutions where thermal waters mingled with cooler 

ground waters. Here some opposing directions of overgrowth would 

be expected. Evaluation of a petrofabric analysis of such material 

requires that the overgrowths having a downward component be separated from those having an upward component, and that each group 

be interpreted with reference to the local geology. A plot of the 

directional vectors representing crystal overgrowths, together with 

contours showing their relative concentrations, is essential to a meaningful interpretation.
MOVEMENT OF JASPEROIDIZING SOLUTION F5 

PETROGRAPHIC TECHNIQUE

With a Federov universal stage the direction in space of the c-axis 

of a quartz grain can be determined regardless of the grain's orientation, but limitations are imposed on the usable orientations of grains 

where the direction of zonal overgrowth and elongation parallel or 

approximately parallel to the a-axes is to be determined; these elements can be observed and measured accurately only when the c-axis 

of the crystal can be moved to a vertical position. The horizontal 

axes of the universal stage are limited to a rotation of 55° in either 

direction, and only those grains whose <?-axis makes an angle of more 

than 35° with the plane of the thin section can be turned into position 

for measurement of asymmetric overgrowths parallel to the &-axes. 

It thus is necessary to study three mutually perpendicular sections 

of the jasperoid to include all possible orientations of. a-axis overgrowth. If the three slides.>8to?.e a ..horizontal section, an east-west 

vertical section, and a north-south vertical section, the angles turned 

for complete coverage of all orientations must include the solid sections of a sphere included between the intersection of mutually perpendicular planes making angles of 45° with the a?, y, and z axes of the 

sphere. In the horizontal section the angles sought would range from 

45° in east-west and north-south directions through 50° in N. 35° W., 

N. 55° W., N. 35° E., and N. 55° E. directions to 55° in northeast 

and northwest directions. In the vertical sections corresponding 

angles would range from 45° for the horizontal and vertical directions 

to 55° for the intermediate 45° directions (p. F9; fig. 2).

The specimens of jasperoid chosen for such a study should be 

porous rather than dense, and the grain size of the quartz crystals 

should average not less than 75/* (0.075 mm). The orientation of 

the specimen must be noted in the field so that each of the three 

mutually perpendicular thin sections made from it can be properly 

marked with its orientation. Commonly, one section is made parallel 

to the bedding, if that useful reference plane is known, but the plotting of results is somewhat simpler if one section is cut parallel to the 

horizontal plane, another to the north-south vertical plane, and a third 

to the east-west vertical plane.

The technique of measuring the orientation of crystallographic 

directions in a thin section by using a universal stage was well 

explained by Ingerson (Knopf and Ingerson, 1938) and more recently 

by Turner and Weiss (1963). As some readers may not have access 

to published information, the method for obtaining the orientation 

of the c-axis of quartz is summarized below, together with an extension of the method to include the problem of asymmetric crystal 

overgrowth.

791-596 O - 66 - 2
F6 CONTRIBUTIONS TO ECONOMIC GEOLOGY

c-AXES OP QUARTZ

The following discussion assumes the measurements are made witn 

a Federov universal stage and that the results are plotted in lower 

hemisphere projection on a Schmidt equal-area net. A stereographic 

net is almost as satisfactory.

The Federov universal stage has four axes of rotation two vertical 

and two horizontal when all are in the 0° positions. The vertical 

axis of the inner ring is commonly designated the A1? that of the outer 

ring the A3 , and that of the microscope stage on which the universal 

stage is mounted the A5 . The horizontal axis of the intermediate 

ring is the A2 and the horizontal axis of the outer ring is the A4 .

A3 need not be used in the jasperoid investigation and can be set and 

clamped with A2 in the north-south position. Because of the limitations of movement of the universal stage two methods are used to 

determine the position of the c-axis lying at angles above and below 

45°. If the £-axis makes an angle of less than 45° with the plane of 

the thin section the axis is turned to the horizontal and made parallel 

to A4 ; if the c-axis is inclined at a steeper angle the axis is turned to 

a vertical position. It is usually difficult to judge whether the c-axis 

lies at an angle above or below 45°, and many grains may have to be 

tried by first one method and then the other.

If the c-axis is not steep, the measurement is made as follows: A2 

and A4 are set at 0° and A5 is clamped so that A4 is in an east-west 

position, A! is then rotated to extinction and A2 is turned; if extinction is not maintained the c-axis is in a north-south position and A! 

must be turned 90° at which position extinction will be maintained 

during rotation of A2 . The c-axis is now in an east-west position but 

not necessarily horizontal. A2 is set at 0° and A4 is rotated; if 

extinction is maintained the c-axis is horizontal. If extinction is not 

maintained, A4 is tipped about 35° and A2 is rotated until extinction 

is achieved. The c-axis is now horizontal and parallel to A4 and the 

grain remains dark when A4 is rotated.

Aj and A2 are read and recorded and the data plotted on transparent 

paper superimposed but free to turn on the Schmidt net. A mark 

is made on the paper at 0° and the sheet is then turned until this mark 

is at the A! reading. The A2 reading is then plotted by placing a 

mark over the east-west line of the Schmidt net at the point corresponding to the number of degrees from the horizontal indicated by 

A2 , measured from the edge of the net on the same side that the A2 

reading was taken. When the oversheet is turned so that the zero 

mark is again at 0°, the point plotted indicates where the c-axis of 

the observed grain will fall when all axes of the stage are turned back 

to 0° and the section is horizontal.

If the <?-axis is steep, the procedure differs somewhat. A2 and A4 

are set at 0° and A5 is clamped with A4 in an east-west position. Ax
MOVEMENT OF JASPEROIDIZING SOLUTION F7

is turned until the grain is at extinction and A2 is then rotated. If 

the grain remains at extinction the <?-axis is in the desired east-west 

position, but if the extinction is relieved the <?-axis is north-south and 

Aj must be turned 90°. After the <?-axis is placed in the eastwest direction, A5 is undamped and the microscope stage is 

turned to 45° to obtain maximum birefringence and A2 is then rotated 

until the grain becomes extinct. The c-axis is now vertical and AI 

and A2 are read and recorded. These data are plotted by turning the 

plotting paper to the reading of At as before and placing the point 

on the equator, but this time the degrees must be counted from the 

center of the net toward the opposite side from which the A2 reading 

-was made.

a-AXIS ELONGATION AND ZONAL OVERGROWTH

As stated on page F5, the directions of a-axis elongation and zonal 

overgrowth can be observed and measured only when the c-axis of the 

grain has been turned vertical. In this position the plane of the &-axis 

is parallel to the microscope stage, and zonal growth lines and differences in dimension can be most easily seen. For measurement of these 

elements after the c-axis has been made vertical, A5 is turned until 'the 

greatest dimension of the grain is parallel to the east-west cross hair 

The upper nicol is then removed and the zoning of the crystal observed 

If the zones are wider on the right side, the apparent direction of solution flow indicated is from right to left. The actual direction, however, is from left to right because the microscope reverses the field. 

An arrow pointing to the right is drawn in the notes to indicate that 

the solutions feeding that particular grain were probably moving to 

the right.

Four notations should now be available: Ax and A2 which orient the 

c-axes to the vertical, A5 , and an arrow which gives the direction of 

zonal overgrowth

A! and A2 are then plotted, according to the procedure just described 

for fixing the position of the <?-axis when turned to the vertical. With 

the c-axis point over the equator of the net, the plane of the a-axes )' 

marked on the net by a north-south great circle (meridian) '9P°:.awa^ 

from the c-axis. The direction of elongation lies in this .plane .for 

plotting this direction, the A5 reading is noted and without movement 

of the paper this value is counted off on the circumference of the net 

from the equator as the zero point, and measured clockwise if A5 ,had 

been turned counterclockwise, and measured counterclockwise if As 

had been turned clockwise. A straightedge is placed from this point 

to the center of the net. The point where the straightedge crosses the 

great circle made by the plane of the. a-axes represents the direction 

of #-axis elongation. From this point, an arrow is then drawn parallel
F8 CONTRIBUTIONS TO ECONOMIC GEOLOGY

to the straightedge and pointing either right or left as recorded in the 

notes. This arrow indicates the direction of solution movement as 

shown by zonal overgrowth, and points either toward or away from the 

center of the hemisphere. An arrow pointing toward the center indicates a vector appropriate to rising solutions, and an arrow pointing 

away indicates a vector for descending solutions. These downwardand upward-directed vectors should be separated ultimately and 

plotted in separate hemispherical projections.

The data for the vertical sections should ultimately be transposed to 

the horizontal and a composite of all three sections made for the final 

step in the study. This transposition to the horizontal requires rotating all points and arrows 90° and tracing these points on the horizontal 

projection. The rotation is accomplished by turning the oversheet, on 

which the data from a vertical section are plotted, until the desired 

axis of rotation is parallel with the north-south line of the net and 

shifting all point 90° on parallels. Particular care should be given 

to the arrows when transferring them from the vertical to the horizontal section, for not only should they be properly placed but their 

direction either upward or downward must be correctly plotted. It 

should be remembered that although all arrows pointing outward on 

the horizontal projection are descending directions, similarly pointing 

arrows on the vertical projections may point either upward or downward ; all outward-pointing arrows in the lower half represent descending directions, but in the upper half they are ascending directions.

PROCEDURE AND INTERPRETATION

A preliminary step in the study of a jasperoid is to measure and plot 

from the horizontal thin section the c-axis of 150-300 grains selected 

at random and without regard for the angle the axis makes with the 

section. Both methods of c-axis determination, as previously outlined, should be employed so that any orientation may be measured. 

Figures 2 and 3 illustrate how the relative concentration is accented by 

contouring. The pattern of the contours should determine whether 

a preferred orientation or a random one is present.

A small circle superimposed on an equal-area net represents a conical 

angle. The magnitude of this angle can be approximated by measuring its diameter in degrees, according to the degree scale on the equalarea net. The size of the circle may be changed according to the number of axes plotted (Turner and Weiss, 1963, pp. 61-64). A 16° circle 

enclosing 1 percent of the net is a satisfactory size for bringing out the 

pattern of concentration when 100 points or more are plotted. The 

circle is placed above the paper containing the plotted points over a 

high concentration of them and then moved until all the space in 

which contiguous or overlapping groups containing the same number
MOVEMENT OF JASPEROIDIZING SOLUTION F9

is covered; contours are drawn to include these groups, using the center 

of the circle to limit the distance of the contour from the points at the 

outside of the group being contoured. Alternatively, the circumference of the circle can be used to give a coarser pattern, and all overlapping circles be joined to form contours. Several areas may show 

similar concentrations and contours are drawn around them. Decreasing concentrations are then sought in increments of 1 or 2 percent. 

These areas commonly are adjacent to the larger concentration areas, 

but some may be in independent positions. A preferred orientation 

commonly causes a girdle or spot pattern.

The plot of the c-axes can be used in selecting grains in the three 

mutually perpendicular sections to be measured for o-axis elongation 

and zonal overgrowth. If random orientation is apparent no selection 

is necessary, but if preferred orientation is evident the grains for o-axis 

elongation and zonal overgrowth measurement should be selected so 

that their c-axis pattern approximates that obtained in the general caxis sampling. This selection requires an analysis of the proportion 

of c-axes that lie in the visibility zones of each of the three perpendicular sections to be studied.

Since only those grains inclined more than 35° to the section will 

now be used, the net containing the plotted c-axes is divided into 

reference segments and used as a guide in the selection of zoned crystals 

for study (see fig. 2). Thin solid lines are drawn through the center 

of the net in the same direction as the vertical thin sections. These 

lines will be termed "section lines." Light dashed lines are then 

drawn through the center at 45° angles to the section lines. These 

represent two limits for c-axis observation in each vertical thin section. 

The traces of four intersecting planes (2 north-south and 2 east-west) 

that dip at 45° are then plotted on the net (fig. 2), and the area that 

they enclose is shown by heavy solid lines having a slight outward 

curvature between the 45° light dashed lines; heavy dashed lines are 

drawn from the circumference of the net to the points along the light 

dashed lines where the planes intersect on the hemisphere. If for 

.the moment we consider the net as a projection of a complete sphere, 

the heavy solid lines then divide the sphere into three double and 

slightly distorted complementary solid cones whose cross sections 

approach a circle but are rudely tetragonal in outline.

The &-axes overgrowth of crystals, the c-axes of which plot as points 

within the central area of figure 2, may be measured in the horizontal 

thin section; for c-axes falling in the outer areas the overgrowth can 

be measured in the vertical sections represented by the appropriate 

section line (fig. 2). The section lines together with the periphery 

of the net divide each "cone" into quadrants. The percentage of 

points lying within each quadrant is calculated and used as a guide in 

further sampling. In the final composite of the three sections, the
F10 CONTRIBUTIONS TO ECONOMIC GEOLOGY

N

200 AXES, SYSTEMATIC SAMPLING 

OF HORIZONTAL PLANE

Axes in east-west 

vertical section

Axes in north-south 

vertical section

Axes in horizontal section

150 AXES HAVING ZONAL OVERGROWTHS

FIGUKE 2. c-axes of quartz in samples from the Cave and Coolidge prospect, 

Oilman, Colo. Schmidt net projection, lower hemisphere, showing two 

north-south and two east-west planes at 45° to vertical axis. Heavy lines 

outline the area enclosed by these planes. Light dashed lines represent limits 

of c-axis observation in north-south and east-west vertical planes. Heavy 

dashed lines lead from circumference of net to points where the 45° planes 

intersect the hemisphere.
MOVEMENT OF JASPEROIDIZING SOLUTION Fll

percentages of plotted c-axes should agree with the percentages found 

in the preliminary measurements. Attention therefore must be given 

to every measurement to make sure that the proper number of c-axes 

fall within the appropriate quadrants. Contours drawn on these 

points, though showing some divergence from those drawn on the 

original c-axis plot, should have the same general pattern (fig. 3).

Greater accuracy can be achieved by dividing the quadrants into 

octants for better guidance in the selection of crystals to be measured, 

but in the author's work division into quadrants was found to be 

satisfactory.

The completed composite plot of the c-axis elongations and of thezonal overgrowths parallel to the a- axes results in three separate hemispherical projections, two of AVhich correspond to the unidirectional 

vectors and either have dots representing the upward-directed vectors 

in one plot and downward-directed vectors in another, or show arrows 

in the net pointing toward or away from the center. The vector concentrations are then contoured in the same way as for the c-axes 

(figs. 4, 7).

The pattern of the contoured vectors must first be studied to ascertain randomness or possible anisotropy; if anisotropic, any localized 

high concentrations of vectors should be interpreted in relation to 

geologic factors such as bedding, joints, and fractures. The technique described was applied to analysis of jasperoid samples from two 

contrasting geologic environments: one, a relatively simple geologic 

environment the Cave and Coolidge prospect in the Oilman district, 

Colorado and the other, a highly complex structural setting the 

Tintic Standard mine in the East Tintic district, Utah.

MATHEMATICAL ANALYSIS OF VECTORS

In addition to the graphic representation of a vector population 

described and interpreted above, a mathematical statistical analysis 

of the geological vectors is possible (Fischer, 1955; Steinmetz, 1962; 

Watson, 1956). The essence of this type of attack is the computation 

of a vector that represents the most probable angle and direction of 

the best resultant of the group of vectors plotted. This group can 

include all the vectors, or the vectors may be considered in various 

groups as dictated by the logic of the problem or the bias of the operator. For each resultant a "circle of confidence" can be computed, 

which is a circle that represents the area on the hemisphere where the 

probability that the true resultant direction falls outside it is less 

than some specified amount, usually taken as less than 5 percent (95 

percent confidence) or less than 10 percent (90 percent confidence). 

The sines and cosines of both the azimuth and the plunge of the vectors
F12 CONTRIBUTIONS TO ECONOMIC GEOLOGY

N

wwPERCENTAGE 

OF AXES

150 AXES HAVING ZONAL OVERGROWTHS 

SELECTIVE SAMPLING

FIOUBE 3. Composite contour diagrams of quartz c-axes 

from Cave and Coolidge prospect plotted on lower hemisphere. Contours show percentage of axes per 1 per* 

cent of the area.
MOVEMENT OF JASPEROIDIZING SOLUTION F13

are obtained and are then manipulated mathematically so as to give 

the azimuth and plunge of the resultant of the vectors used.

The formulas used and illustrative data from the Cave and Coolidge 

prospect are shown on a typical work sheet in table 1.

TABLE 1. Calculation of resultant of ascending vectors (in lower hemisphere) 

within ±15° of bedding plane, Cave and Coolidge prospect

N= number of samples 

A=azimuth of m6vement vectors 

A,=azimuth of resultant vector 

D=lnclination of movement vectors

D,=inclination of resultant vector 

a=cos DXsin A; 6=cos DXcos A; c=sin D 

or =cos DrXsin A,\ 6r =cos DrXcos A,; cr=sin D,

Sample

1.. 

2. . ......

3.... .

4.. -

5... 

6.. 

7.. .

8.-- 

9........

10. 

11. 

12.. 

13.. -

14........

15..-..-..

16.-- 

17.. 

18.. -

19.- 

Tota 

Total

A 

(azimuth 

of dip)

343° 

352°45' 

0° 

18°30' 

19°45' 

21°15' 

24°30' 

29°30' 

37°45' 

49°30' 

54°45' 

56° 

67°45' 

73°15' 

82°15' 

94° 

121°30' 

125°45' 

317°15'

...... 

(squared)

D (inclination 

of dip)

07° 

09°30' 

17° 

12°30' 

16° 

16° 

23°30' 

12° 

21<> 21° 

13° 

11° 

11° 

10° 

04° 

11° 

02° 

01° 

0°

sin^l

-0. 2924 

-. 1262 

0 

+. 3173 

+. 3379 

+. 3624 

+. 4147 

+. 4924 

+. 6122 

+.7604 

+. 8166 

+. 8290 

+. 9255 

+. 9576 

+. 9909 

+. 9976 

+. 8526 

+. 8116 

-. 6788

+9. 3813 

88.0088

cos A

+0.9563 

+. 9920 

+1. 0000 

+.9483 

+. 9412 

+. 9320 

+.9100 

+. 8703 

+. 7907 

+.6494 

+. 5771 

+. 5592 

+. 3786 

+.2882 

+. 1348 

-. 0698 

-. 5225 

-. 5842 

+. 7343

+10. 4859 

109. 9541

cos-D

0. 9925 

.9863 

.9563 

.9763 

.9613 

.9613 

.9171 

.9781 

.9336 

.9336 

.9744 

.9816 

.9816 

.9848 

.9976 

.9816 

.9994 

.9998 

1. 0000

17.9862 

323. 5034

cosJ5X 

cos A 

(6)

+0. 9491 

+. 9784 

+.9563 

+.9258 

+. 9048 

+. 8959 

+. 8346 

+. 8513 

+. 7382 

+.6063 

+.5623 

+.5489 

+. 3717 

+.2838 

+. 1345 

-. 0685 

-. 5222 

-. 5841 

+. 7343

+11. 2697 

127. 0039

cos-DX 

sin A 

(a)

-0. 2902 

-. 1245 

0 

+. 3098 

+. 3248 

+. 3484 

+. 3803 

+. 4816 

+. 5715 

+. 7099 

+. 7957 

+. 8737 

+. 9085 

+. 9430 

+.9885 

+. 9792 

+.8521 

+. 8114 

-.6788

+9. 1249 

83. 2638

sinD 

(c)

0. 1219 

.1650 

.2924 

.2164 

.2756 

.2756 

.3987 

.2079 

.3584 

.3584 

.2250 

.1908 

.1908 

.1736 

.0698 

.1908 

.0349 

.0174 

0

3.7634 

14. 1632

Checked '

I

V

V 

V 

VV

V

V 

V

IfV V V

}V 

V

i Check &2+c2+a2=1.000±0.003.

Direction cosines of resultant: 6r = +0.7522; or= +0.6099; cr= +0.2512. 

Resultant of movement vectors:

N=W R= 14.9810

cr = sin Dr= 0.2512 sin .4 ,= % - =0.6293

COS-Dr

X>r=14°33' Ar=W> 

Circle of confidence: 

(N- R) =4.0190 0=spherical radius cos 0=c

X= (-) 1 where p is deviation factor, arbitrarily picked as 0.05 or 0.1

(N-R) (X) C ~ l R 

for p=0.1, 

AT=(10)-1=U365-1

(4.0190) (0.1366) 

14.9810

c=0.»634 e=15827'
F14 CONTRIBUTIONS TO ECONOMIC GEOLOGY

If the population of vectors is to be divided into groups that, for one 

reason or another, seem more significant than the totality, it is apparent that many choices as to grouping are possible. The contoured patterns for the two hemispheres are used as a guide in making such a 

choice.

The value of using analytical methods to obtain precise figures for 

azimuths and slopes of resultants of several groups of vectors for 

solution movements is questionable. The interpretation of the directions of movements becomes progressively less confident as more vector 

clusters are tested for separate resultants. The resultant for all of the 

vectors gives the direction and slope with the least subjective bias, but 

it entirely ignores the geologic setting. It should, however, indicate 

a general ~ direction of flow within the "circle of confidence" calculated.

CAVE AND COOLIDGE PROSPECT, OILMAN DISTRICT,

COLORADO

Five specimens of jasperoid were obtained from the Cave and 

Coolidge prospect in the Gilman district, Colorado, through the 

courtesy of Mr. Frank Meloit, General Manager, Empire Zinc Co. at 

Gilman. The jasperoid is a replacement of hydrothermally dolomitized Leadville Limestone about half a mile northwest of the No. 1 ore 

body of the Eagle mine at Gilman. The Leadville Limestone throughout this area has a regional northeasterly dip of about 15° with only 

minor local deviations in strike and dip. Although the rocks in the 

Cave and Coolidge prospect are inadequately exposed, the structural 

control of alteration and ore deposition in the Eagle mine, where geologic relations are similar, was well shown on washed walls underground and was carefully studied during the 1930's in the No. 1 ore 

body and the nearby area by the author and Mr. Ogden Tweto of the 

U. S. Geological Survey. The sequence of hydrothermal events includes several periods of hydrothermal dolomitization followed by the 

introduction of jasperoid, and, later, of the manganosiderite and sulfide ores exploited in the mine. Both the altered zones and the ore 

bodies show a pronounced structural control, chiefly by joints and 

bedding. The most prominent trends in the No. 1 ore zone are controlled by joints striking N, 70°-75° E., N. 20°-35° E., and N. 60°-70° 

W., and by minor faults striking N. 55° E. Altered rock and preore 

solution channels follow the joints, especially the intersections of 

northeast-trending joints and bedding planes.

Hydrothermal dolomite, jasperoid, and ore are largely confined to 

the Leadville Limestone, but ore has been found also in older rocks. 

Mineralized northeasterly faults are common in the Precambrian 

rocks and in the Paleozoic rocks between the Precambrian and the 

Mississippian Leadville.

Three thin sections of each of the five jasperoid specimens from the
MOVEMENT OF JASPEROIDIZING SOLUTION F15

Cave and Coolidge prospect were studied, and the composite of fifteen 

sections is shown in figures 2-5. The pattern of the long or c-axes of 

the quartz shows little anisotropy but instead is fairly random (fig. 3). 

The pattern of the a-axes, on the contrary, shows a marked anisotropy. 

The pattern of the upward-pointing vectors in figure 4 corresponding 

to upward-moving solutions or downward-pointing overgrowths is 

contoured to show concentrations of 3,4, or 5 percent within unit areas 

(16° circles) of the hemisphere; the strike and dip of the beds and 

some prominent joint systems in the Eagle mine are also plotted on 

the hemispherical projection. The concentration of upward-directed 

vectors subparallel to the bedding is as notable as the absence of downward vectors in this part of the companion projection. Such a coincidence is unlikely to be fortuitous and suggests a major hydrothermal 

current moving updip parallel to the bedding. The greatest concentration of upward vectors in the bedding centers around a vector 

directed 15° upward at about S. 25° W.

The greatest concentration of upward vectors apart from £he bedding 

is bimodal. The heaviest concentration corresponds approximately 

to a vector directed upward N. 25° E. at an angle of 75°, the other 

is directed upward S. 75° E. at about 10°. When these three maxima 

are considered relative to the joint systems that obviously control the 

movement of hydrothermal solutions in the nearby Eagle mine, it is 

apparent that all three could represent solution movement along intersections of joint systems and the bedding plane or along the joint 

systems themselves.

The downward-directed vectors also have an anisotropic pattern 

which, however, is less apparent than that of the upward-directed 

vectors. They too show a trimodal distribution of maxima, the heaviest concentration clustering around an axis directed S. 70° E., downward at 45°; the two other maxima comprise one sloping N. 60° W. 

downward at 55° and another one directed N. 85° W. downward at 

10°. These down-ward vectors could be controlled by joint systems but 

not by bedding. The high concentration near the western edge of the 

hemispheres for both the ascending and descending vectors is of special interest because of the opposite directions indicated for the 

ascending and descending solutions. This opposition of directions 

may reflect the mixing of rising and descending solutions. Ascending 

and descending vectors in the same area could also be explained as 

asymmetric overgrowths on crystals parallel to the general direction 

of movement of a silica-saturated solution. Lack of a girdle pattern 

perpendicular to the general direction of updip solution movement, 

however, suggests a different explanation, such as periodic changes in 

direction of a convective circulation that was at right angles to the 

general updip movement of the hydrothermal solution (fig. 5).
F16 CONTRIBUTIONS TO ECONOMIC GEOLOGY

The contoured vector patterns seem best explained by hydrothermal 

solutions that rose southwesterly along bedding planes, especially 

along intersections of bedding planes with the northeasterly joint system. Locally and from time to time, however, the solutions apparently 

moved almost vertically upward along the intersections of northeast 

and west-northwest joints which dip steeply south; cooler water apparently moved down along the intersection of nearly vertical westnorthwest joints and N. 60° E. joints to mix with water rising to the 

southwest along bedding planes. This mixing presumably produced 

local convection cells which changed position and direction from time 

to time (figs. 5, 6).

w- -E

DESCENDING

FIGURE 4 (above and right). Solution movement vectors plotted on lower hemisphere, Cave and Coolidge prospect, Oilman, Colo. Contours show percentage 

of vectors per 1 percent of area. Joint planes and bedding shown by hachured 

areas; intersections by heavy lines.
MOVEMENT OF JASPEROIDIZING SOLUTION F17

The general technique devised by Fischer (1955) and modified by 

Steinmetz (1962) as described earlier in this paper was used on the 

Cave and Coolidge prospect data, which have been analyzed in various 

ways so that the advantages and limitations of the mathematical 

method are illustrated.

A mathematical analysis shows that the resultant of all the vectors 

in both hemispheres is directed upward at only 1° with an azimuth 

of 213° (S. 33° W.). But the fact that the circles of 95 percent and 

of 90 percent confidence have radii of 45° and 39°, respectively, indicates that the resultant of a much larger number of vectors could be 

tens of degrees different in both azimuth and slope. If the geologist

wASCENDING 

PERCENTAGE OF 75 VECTORS
F18 CONTRIBUTIONS TO ECONOMIC GEOLOGY

is satisfied with a 90 percent "circle of confidence," the chances are 

9 out of 10 that regardless of how many vectors were plotted, for the 

Cave and Coolidge jasperoid the ultimate resultant of the entire 

population would be less than 40° away from the S. 33° W. resultant 

sloping up at 1°; this limitation would allow for an angle of inclination parallel to the dip of the bed (to agree with the geological bias 

of the author) pointing in an updip direction and would indicate 

that the jasperoid was formed by rising dominantly hydrothermal 

solutions.

Figure 4 suggests that the downward-directed vectors have a 

bimodal distribution separated by a line having an azimuth of N. 55° 

E. (fig. 5). The resultants in the two areas are calculated to be 

downward-directed vectors N. 44° W. at 42° and S. 38° E. at 45°. 

The obvious choice for a bimodal division for the ascending vectors 

Avould be along a line parallel to the strike of the bedding, namely 

N. 45° W., and here we find that the resultant of the vectors in the 

northeast half slopes S. 50° W. upward at 33° and the resultant of 

the vectors in the southwest half slopes N. 51° E. upward at 50°.

FIGURE 5. Resultants of various vector groups plotted on lower hemisphere, 

Cave and Coolidge prospect, Gilman, Colo. Resultants for halves of hemispheres shown by dashed arrows; resultants for indicated concentration 

clusters by solid arrows.
MOVEMENT OF JASPEROIDIZING SOLUTION F19

Because many asymmetric overgrowths are definitely random and 

caused by chance factors not directly related to the major directions 

of solution movement, the use of only those vectors that cluster in 

statistically or geologically significant areas can be justified. If calculations of ascending vectors in the northeast half of the hemisphere 

are restricted to the wedge that is within 15° of the bedding plane, 

a resultant is found that slopes upward at 15° in a S. 39° W. direction, 

which is parallel to the bedding. (See table 1 for calculation.) If 

we next consider resultants for groups of vectors containing more than 

3 percent concentrations per unit area, three resultants can be calculated for the southeast half of the hemisphere: S. 70° E. up at 10°, 

N. 40° W. up at 18°, and N. 20° E. up at 73° (fig. 5).

The direction of the resultant calculated for all the vectors, together 

with the pattern of crystal overgrowths, shows such a striking relation 

to the geologic factors that the overgrowths obviously reflect an overall updip movement of jasperoidizing solutions toward the southwest. 

If the source of the jasperoidizing solutions were to be sought by 

exploration, it would be expected to lie N. 35°-40° E. of the Cave and 

Coolidge prospect, and to be a mineralizing center separate from that 

which gave rise to the zinc mantos exploited by the New Jersey Zinc Co.

The multimodal concentration pattern of quartz overgrowths may 

have a bearing on the genesis of the jasperoids. Such a pattern suggests that locally and from time to time both steep- and low-angle 

lateral currents influenced crystal growth, and this inference, in turn, 

suggests that jasperoid was deposited where convection currents 

formed as rising silica-bearing hydrothermal solutions mingled with

DESCENDING ASCENDING

FIGUBE 6. Diagram of solution movement, Cave and Coolidge prospect,

Oilman, Colo.
F20 CONTRIBUTIONS TO ECONOMIC GEOLOGY

descending cooler ground water (fig. 6). Many of the asymmetric 

overgrowths, however, undoubtedly represent chance interference 

caused by local irregularities in the changing crystal mesh, and many 

more specimens will have to be analyzed before this hypothesis can be 

satisfactorily evaluated.

TINTIC STANDARD MINE," EAST TINTIC DISTRICT,

UTAH

The East Tintic district, Utah, is about 60 miles south of Salt Lake 

City, and in contrast to the Gilman mining district, it has an extremely 

complex geologic setting. The three specimens of jasperoid examined 

were collected from the J stope area of the 900 level of the Tintic 

Standard mine, which exploited a large lead-zinc ore body in highly 

altered, faulted Cambrian limestone and shale adjacent to a steeply 

folded contact with the underlying Cambrian quartzite. The southernmost specimen was taken about a yard from the quartzite and 

jasperoid contact which here strikes N. 60° E. and dips about 45° N. 

A few yards farther east, however, the contact turns due north and 

dips 35° W.; about 35 feet farther north it turns abruptly west-southwest and dips about 40° S. Two other specimens were taken at 10 

and 15 feet respectively south of the west-southwest part of the contact and 10 and 40 feet respectively west of the north-trending part. 

There is thus a gentle southwesterly dipping trough in the quartzite 

f ootwall below one of the specimens, and the other two were taken on 

the northwest and southeast sides of the trough.

The J stope ore body plunges southwest subparallel with the footwall trough for some distance, but the major ore body is northwest of 

the J slope area. The limestone was much fractured, before jasperoidization, by both steep- and low-angle faults, but only the main 

directions of the nearby quartzite-footwall contact with the jasperoid 

are indicated in figure 7. This figure also shows the contoured pattern of solution-movement vectors as interpreted from quartz overgrowths in nine oriented thin sections of the three specimens noted. 

The pattern shows a strong bimodal concentration for ascendingsolution vectors; one maximum is virtually parallel to the trough 

between the north-trending and west-southwest-trending f ootwall contact, and the other slants S. 35° E. up at 45°, almost directly parallel 

to the dip of the N. 60° E. contact adjacent to the southernmost sample
MOVEMENT OF JASPEROIDIZING SOLUTION F21

locality. This latter maximum is of special interest, because the opposite direction, which presumably should point down toward the 

source of the solution, points downward toward the main ore body of 

the mine.

The mathematical resultant computed for the entire sphere of projection points even more specifically to this large ore body as the source 

area for the jasperoidizing solution and has an azimuth of 112°29' 

slanting upward at 31°43'; the reverse direction and slope angle 

(N. 68° W. down at 32°) would intersect the major ore body of the 

Tintic Standard mine about 200 feet below. The ascending and 

descending vectors for the J stope jasperoid are unevenly distributed: 

88 slant downward and 114 slant upward. There are thus 30 percent 

more crystals showing overgrowths indicating upward movement than 

downward movement. The pattern of the downward vectors could 

result largely from chance growths on crystals that were parallel to the 

direction of flow or so related to obstructions and to solution-carrying 

interstices as to favor growth in random directions. The pattern 

slightly resembles a girdle arrangement normal to the two directions 

of flow indicated by the major concentration of vectors and their 

resultants in the lower hemisphere, but the pattern is also suggestive 

of solution movement along north-northeast fractures dipping 

about 50° E. No such fractures were mapped, although premineralization fractures that strike N. 10°-20° E. and dip 65°-70° are not uncommon. Resultants for various vector groups were also calculated 

(fig. 8); those for descending vectors are almost symmetrically distributed about the vertical axis and those representing rising solutions 

suggest the configuration shown in figure 7. The calculated resultant 

of all the vectors, however, seems much more relevant than resultants 

of the arbitrarily chosen groups.

Although the investigation of the jasperoids was made after the J 

stope and main ore bodies were found, it is of interest to note that 

exploration toward the sources of jasperoidizing solutions as indicated 

by this petrofabric study would have led into ore bodies; exploration 

to the southwest parallel to the trough vector maximum would have 

disclosed an excellent moderate-sized ore body whereas exploration 

west-northwest, parallel to the resultants calculated from all the overgrowth vectors and also subparallel to the source indicated by the 

second concentration maxima in the northwestern quadrant (fig. 7), 

would have led into the ma j or ore body of the mine.
F22 CONTRIBUTIONS TO ECONOMIC GEOLOGY

W - -E

DESCENDING

FIGURE 7 (above and right). Solution movement vectors plotted on lower 

hemisphere, J stope jasperoid, 900 level, Tin tic Standard mine, East Tintic 

district, Utah. Contours show percentage of vectors per 1 percent of area. 

Contact surfaces between jasperoid and quartzite shown by a hachured area ; 

intersections by light solid lines; movement vectors by heavy arrows.
MOVEMENT OF JASPEROIDIZING SOLUTION F23

w -

ASCENDING 

'PERCENTAGE OF 100 VECTORS
F24 CONTRIBUTIONS TO ECONOMIC GEOLOGY

N

wDESCENDING

w- -E

ASCENDING

FIGURE 8. Calculated resultants of various solution 

movement vector groups, J stope jasperoid, 900 

level, Tintic Standard mine.
MOVEMENT OF JASPEROIDIZING SOLUTION F25 

CONCLUSIONS

Studies by petrofabric methods of jasperoid overgrowths in specimens from two very different geologic environments led to unexpectedly significant results. In both instances the general direction of 

flow indicated by the petrofabric diagrams and by. the resultant of all 

overgrowths is surprisingly compatible with the geologic interpretation of the probable source of the jasperoidizing solution. At the 

Tintic Standard mine such a petrofabric analysis could have been 

used as a guide to exploration for ore deposits. At the Cave and 

Coolidge prospect, the area downdip from the jasperoids has been 

little explored, but the relation of jasperoids to ore is less intimate 

than in the Tintic district. Nevertheless this technique has sufficient 

mer^t to warrant its use in other areas where jasperoid is of the 

"productive type" and likely to be an updip expression of ore deposits 

(Levering and Hamilton, 1962), especially in much fractured or permeable beds where a hydrothermal current could be expected to maintain a generally uniform direction for some distance.

REFERENCES CITED

Fischer, R. A., 1953, Dispersion on a sphere: Royal Soc. [London] Proc., ser.

A, v. 217, p. 295-306. 

Knopf, E. B., and Ingerson, F. E., 1938, Structural petrology: Geol. Soc. America

Mem. 6,270 p.

Levering, T. G., and Hamilton, J. C., 1962, Criteria for the recognition of jasperoid associated with sulfide ore, in Short papers in geology and hydrology:

U.S. Geol. Survey Prof. Paper 450-C, p. C9-C11. 

Newhouse, W. H., 1938, Direction of solution flow and the formation of minerals:

Science, new ser., v. 88, p. 109. 

 1941, The direction of flow of mineralizing solutions: Econ. Geology,

v. 36, p. 612-629. 

Steinmetz, Richard, 1962, Analysis of vectorial data: Jour. Sed. Petrology, v. 32,

p. 801-812. 

Turner, F. J., and Weiss, L. E., 1963, Structural analysis of metamorphic tectonites: New York, McGraw-Hill Book Co., Inc., p. 46-75. 

Watson, G. S., 1956, A test for randomness of direction: Royal Astronomical

Soc., Monthly Notices Geophys. Supp., v. 7, 160-161.

U.S. GOVERNMENT PRINTING OFFICE: 1966 p 791-596