UNITED STATES

DEPARTMENT OF THE INTERIOR

GEOLOGICAL SURVEY

TRUE LOCATION AND ORIENTATION OF FRACTURES LOGGED WITH THE ACOUSTIC

TELEVIEWER (INCLUDING PROGRAMS TO CORRECT FRACTURE ORIENTATION)

By R. A. Kierstein

Water-Resources Investigations Report 83-4275

Denver, Colorado

1984
 UNITED STATES DEPARTMENT OF THE INTERIOR

JAMES G. WATT, Secretary

GEOLOGICAL SURVEY

Dallas L. Peck, Director

For additional information write to

U.S. Geological Survey

Water Resources Division
Mail Stop 403, Box 25046
Denver Federal Center
Denver, Colorado 80225

For purchase, write to:

Open-File Services Section

U.S. Geological Survey
Box 25425
Denver Federal Center
Denver, Colorado 80225
(303) 234-5888; FTS 234-5888
 CONTENTS
Page

Abstract 1
Introduction 1
Hole-survey methods 3
Minimum-curvature method 3
Radius-of-curvature method 5
Tangential method 5
Geometric rotation 6
Magnetic effect 10
Test results 16
Hand-held-calculator program 18
Example 1 Simple-dip increase 18
Example 2 Multiple-survey stations 21
Fortran programs 27
Example 3 Single-fracture version 27
Example 4 Single-well version 28
Stereographic solutions 33
Stereographic solution of a simple-dip increase 33
Stereographic solution of a rotation off the net 33
Stereographic solution including a magnetic-declination angle 36
Stereographic solution including a magnetic-inclination angle 36
Conclus ions 41
Selected references 42
Supplemental data 43
Table 1. Storage-register assignments 45
2. Hand-held-calculator program listing 46
3. Fortran program listing Single-fracture version 59
4. Fortran program listing Single-well version 62
5. Fortran variables 70
6. Theta values 72
7. Theta program listing 73

ILLUSTRATIONS

Figure 1. Three-dimensional sketch of borehole with intersecting

planar fracture (a), and the corresponding
two-dimensional televiewer log (b) -
2. Sketch of directional-survey parameters
3. Sketch of coordinate-system relationships: surface-
coordinate system; borehole-coordinate system (a);
an intersecting fracture (b) with the corresponding
log (c) -
4. Three-dimensional sketch of a fracture plane, the unit
normal, and the directional cosines defining
that normal
5. Graph of different borehole orientations in the north-
south plane, illustrating a 180° reversal in the
triggering component 11

ill
 ILLUSTRATIONS Continued

Page

6. Televiewer log of casing with switch triggering (a); the

same casing shown with magnetic triggering (b) 12
7. Map view of inclined holes at different hole azimuths 14
8. Sketch of angles used in the geometric rotation 16
9. Televiewer sweeps at 'a hole azimuth of 90° 17
10. Example problem in east-west plane 19
11. Stereographic projection 1 Dip increase 34
12. Stereographic projection 2 Rotation off net 35
13. Stereographic projection 3 Including magnetic-
declination angle 37
14. Stereographic projection 4 Including magnetic-
inclination angle 39

CONVERSION FACTORS

For use of readers who prefer to use metric units, conversion

factors for terms used in this report are listed below:

Multiply By To obtain

feet (ft) 0.3048 meters (m)

iv
 TRUE LOCATION AND ORIENTATION OF FRACTURES LOGGED WITH THE ACOUSTIC
TELEVIEWER (INCLUDING PROGRAMS TO CORRECT FRACTURE ORIENTATION)

By R. A. Kierstein

ABSTRACT

The attitude of fractures measured on acoustic-televiewer logs may

be misorientated by as much as 180° in a drill hole that is deviated
significantly from vertical, because of the effect of the vertical
component of the magnetic field on the tilted magnetometer that is used
to orient the log. A method has been developed to correct for the
misorientation by analyzing the orientation of the magnetometer with
respect to the magnetic-field vector at the magnetometer's center.
Computer programs were written to correct the attitude of fractures for
both magnetic effects and.hole deviation. For the reorientation of a
single fracture, a stereographic solution is illustrated. Test results
indicate that the fracture orientation can be corrected to plus or minus
5° of true orientation, provided there are no other magnetic effects,
such as magnetite in the rocks.

INTRODUCTION

The location, orientation, and characterization of fractures are

important in reservoir engineering, waste disposal, and other
geosciences. The acoustic televiewer is a geophysical well-logging
device used to provide the location and orientation of fractures and
other planar features that intersect a drill hole. Televiewer logs can
be misoriented if the hole logged is deviated from vertical. This
misorientation error has geometric and magnetic components. This report
shows how these logs can be corrected with the aid of a hole survey.

The acoustic televiewer (Zemanek, 1969) produces an image of the

borehole wall in two.dimensions. Planar fractures that are
perpendicular or parallel to the borehole appear as straight lines;
other angles of intersection produce sinusoids (fig. 1). The triggering
of the televiewer is sensitive to the component of the Earth's magnetic
field that is perpendicular to the axis of the tool. When the
instrument is tilted, changes in the vertical component of the magnetic
field affect the direction in which the magnetometer detects magnetic
north. For this reason, holes that are deviated to the north may
produce televiewer logs with as much as an 180° error in fracture
orientation; holes deviated to the south may cause little or no
magnetic error. To correct for the magnetic effect, the location and
orientation of the borehole needs to be described mathematically; this
is the subject of the next section.
 Magnetic north
trigger line

Planar
fracture

N S N
(a) (b)

Figure 1. Three-dimensional sketch of borehole with intersecting planar fracture (a),

and the corresponding two-dimensional televiewer log (b).
 HOLE-SURVEY METHODS

Several different methods are used to mathematically describe the

path of a deviated borehole (Craig and Randall, 1976). However, the
programs in this report were written to use only one of the following
methods: minimum-curvature, radius-of-curvature, or tangential.
Variables used in the programs and the corresponding equations are
illustrated in figure 2. For further information on the derivation of
the following formulas, consult Wilson (1968) and Turner (1980).

Minimum-Curvature Method

The minimum-curvature method fits a circular arc between two

stations, by using a dogleg angle (an angle representing the curvature
of the borehole's path between two survey stations) and a ratio factor.
The following equations define the dogleg angle (D), the ratio factor
(RF), the difference in latitude between survey stations (AN), the
difference in depth between survey stations (Av) , and the difference in
departure between survey stations (AE):

D= arccos{cos(l2-Il)-[sin(Il)sin(I2)][l-cos(A2-Al)]}, (1)

RF = [2/D] [tan(D/2>], (2)

AN = [AMD/2] {[sin(Il)cos(AD] + [sin(I2)cos(A2) ]} RF, (3)

AV = [AMD/2] [cos(ll) + cos(I2)] RF, and (4)

AE = [AMD/2] {[sin(Il)sin(Al)] + [sin(I2)sin(A2)]} RF. (5)

The programs assume that the borehole is straight throughout the

length that the fracture intersects the hole. The new azimuth, A(new),
and new inclination, I(new), of this straight segment are calculated by
interpolation between two bounding stations, 1 and 2:

Knew) = II + {[MD(new) - MD(1) ] [(I2-Il)/AMD]}, and (6)

A(new) = Al + {[MD(new) - MD(1) ] [(A2-AD/AMD]}, (7)

where MD = measured depth.

Al, A2, II, 12, and MD are defined in figure 2. New angles, I(new) and
A(new), are used to calculate the location of the fracture center,
(depth to bottom of sinusoid - depth to top of sinusoid)/2 + depth to
top of sinusoid, as well as to find the true orientation of the fracture
plane as explained in the following section on geometrical rotation.
Specifically I(new) and A(new) are used as 12 and A2 in equations (1)
through (5) to calculate the differences in latitude, departure, and
depth between the fracture center and the station above it (station 1).
The differences are then added to the values at station 1 to obtain the
latitude, departure, and depth to the fracture center.
 (Upward)
-Z

EXPLANATION

AMD MEASURED DISTANCE BETWEEN SURVEY STATION 1

AND STATION 2.
(South) - +X (North)
Al AZIMUTH AT STATION 1 MEASURED FROM MAGNETIC
NORTH.

11 MEASURED INCLINATION ANGLE AT STATION 1

(FROM VERTICAL OR +Z AXIS).

A2 AZIMUTH AT STATION 2,

12 INCLINATION AT STATION 2.

AN DIFFERENCE IN LATITUDE: = LATITUDE (2)

MINUS LATITUDE (1).
AMD AV DIFFERENCE IN DEPTH: = DEPTH (2) MINUS
(Borehole path)
DEPTH (1).

AE DIFFERENCE IN DEPARTURE BETWEEN THE UPPER

AND LOWER STATION: = DEPARTURE (2) MINUS
DEPARTURE (1).

Figure 2. Directional-survey parameters,

 Radius-of-Curvature Method

The radius-of-curvature method also fits a circular arc between two

bounding-survey stations. The following equations define AN, AV, andAE
between the stations:

AN = MD[cos(ll)-cos(l2)] [cos(Al)-cos(A2)]/[(12-11)(A2-A1)], (8)

AV= MD[sin(l2)-sin(Il)]/(l2-Il), and (9)

AE = MD[cos(ll)-cos(I2)] [sin(A2)-sin(Al)]/[(12-11)(A2-A1)].' (10)

Note that the quantities (12-11) and (A2-A1) of the above equations need
to be in radians, which are dimensionless. The new angles, I(new) and
A(new), and new coordinates at the fracture center are calculated in the
same manner as shown in the minimum-curvature method.

This method is sensitive to small changes in angles. If the change

in inclination or azimuth is too small, a division by zero will occur in
equations (8) through (10), which will lead to significant errors in
both the location and attitude of the fracture. In such cases, the
minimum-curvature method needs to be used.

Tangential Method

The tangential method assumes the borehole to be a straight,

inclined line, with an azimuth (A) and an inclination (I). AN, AV, AE
are then expressed as:

AN = AMD[sin(l)cos(A)], (11)

AV = AMD[cos(l)], and (12)

AE = AMD[(sin(l)sin(A)]. (13)

The tangential method is provided with these programs to give the

user flexibility. It should be reiterated that borehole surveys are
reported from true north, and televiewer logs are referenced to magnetic
north. Therefore, the programs subtract the declination angle from
station azimuths, and further calculations are made with angles that are
referenced to magnetic north, but the final results are reported with
respect to true north.
 GEOMETRICAL ROTATION

After determining the azimuth and inclination of the borehole with

respect to magnetic north, the strike and dip of the fracture needs to
be described in terms of a surface-coordinate system (X, Y, and Z in
fig. 3). The relationship between the acoustic-televiewer log, the
borehole-coordinate system (x, y, and z in fig. 3), and the parameters
needed to calculate the attitude of the fracture in the surface-
coordinate system are illustrated in figure 3. The five angles needed
to perform this conversion are:

A = hole azimuth (between 0° and 360°),

D = hole dip (between 0° and 90°),

P = apparent dip of fracture,

Dp = apparent down-dip azimuth of the fracture, and

K = apparent strike of fracture (K = Dp - 90°).

The adjective "apparent" is used to describe angles that are referenced

to the skew borehole-coordinate system. Conventionally, strike is
referenced to the northern quadrants; however, for this paper, the
strike is the azimuth (between 0° and 360°) of the feature, so that the
down-dip direction of the feature is always given by the strike-azimuth
angle + 90°. In other words, the down-dip direction of a fracture is
always in a clockwise direction from the given strike azimuth, never in
a counter-clockwise direction.

Using the televiewer log illustrated in figure 3(c), the important

parameters Dp, K, and P are calculated in the following manner. First
the lowest point of the sinusoid is located [shown in fig. 3(b) and 3(c)
as a*], and the azimuth of this point is read from the log. This
azimuth is (Dp), the apparent down-dip azimuth; in this case it equals
135°. Next, the apparent strike of the fracture (K) is determined by
subtracting 90° from (Dp), apparent down-dip azimuth of the fracture; in
this case it equals 45°. Finally, the apparent dip angle (P) is
calculated by taking the inverse tangent of (h), (the total height of
the sinusoid), divided by the hole diameter. It is important to note
that both the height (h) and the hole diameter needs to be in the same
units. The apparent dip angle (P), therefore, equals the arctan(3/0.25)
or 85°. To summarize:

Dp = apparent down-dip azimuth = 135°,

K = Dp - 90° = 45°, and

P = arctan(h/hole diameter) = arctan(3/0.25) = 85°.

 ~-t-X (Magnetic North)
This point is in the X-Y plane

-f-x (In the X-Z plane

pointing north)

-f-z (Down hole)

(a)

p = Apparent K = Apparent strike

dip of
fracture of fracture

Dp = Apparent down-dip azimuth

-f-z of fracture (c)
(b)

Figure 3. Coordinate-system relationships: surface-coordinate-syste.m (in capitals);

borehole-coordinate system (in small letters) (a); an intersecting fracture (b)
with the corresponding log (c).
 For calcuation purposes, the fracture plane is described in terms
of its,unit normal. This unit normal is expressed as three directional
cosines <rf t gf, and Yf (fig. 4). These directional cosines are defined
by the-following equations:

B = \/tan 2 (D) + cos 2 (A), (14)

ocf = -[cos(P)cos(A)cos(D)]

- [sin(P)/B]{[sin(K)tan(D)] + [cos(K)sin(A)cos(A)cos(D)]> , (15)

$f = [Bsin(P)cos(K)cos(D)] - [cos(P)sin(A)cos(D)] , and (16)

Yf = [sin(P)/B]{[sin(K)cos(A)] - [cos(K)sin(A)sin(D)]>

- [cos(P)sin(D)]. (17)

Once the directional cosines are known, the surface-coordinate

fracture dip, surface-coordinate down-dip azimuth, and the
surface-coordinate fracture strike are defined by the following
relations :

Surface-coordinate fracture dip = arccos

Surface-coordinate down-dip azimuth = arctan (ftf/^f)* and

Surface-coordinate fracture strike = arctan ($f/ocf) - 90°.

As shown in figure 4, these relationships are only valid if the unit

normal is in the upper hemisphere, which corresponds to a negative Yf.
If a positive Yf i- s obtained when rotating a fracture, the programs
choose the other normal by reversing the signs of ccf, ^f, and yf» The
program also checks for limiting cases, such as a vertical fracture,
when Yf = 0 > °r when ftf/^f approaches infinity (an east-west dip line).
In these cases, the program makes the appropriate substitutions.

To this point, all the calculations made have assumed that the
televiewer triggers in the north-south plane. This is not necessarily
an accurate description of the triggering mechanism, as shown in the
next section called magnetic effect. However, when the hole is nearly
vertical, the tool is triggering correctly, and there is no need to make
a magnetic correction. Therefore, the programs include an option to
make no magnetic-effect correction. In such a case, the programs would
report the true strike as the surface-coordinate fracture strike plus
the declination angle; in a similar manner, true down-dip azimuth would
be reported as the surface-coordinate down-dip azimuth plus the
declination angle. This addition of the declination angle references
the angles to true north rather than to magnetic north.
 -Z (Upward)

Fracture
plane

Unit
normal

Down-dip 1 .0
L
a z imuth
+X (North)

Figure 4. Three-dimensional sketch of a fracture plane, the unit

normal, and the directional cosines defining that normal,
 MAGNETIC EFFECT

The effects of the vertical component of the magnetic field on the

orientation magnetometer, and the corrections for these effects in the
programs are explained in this section. The orientating magnetometer in
the acoustic televiewer is sensitive to the component of the earth's
magnetic field that is perpendicular to the axis of the tool. When the
instrument is tilted, the vertical component of the magnetic field also
affects the direction in which the televiewer detects north; hence, that
component changes the position at which each sweep on the televiewer log
is started. The effect of the magnetometer for different borehole
orientations is illustrated in figure 5. The components shown in this
figure are all in the north-south plane. Vector F is at the center of
the magnetometer.

An 180° reversal in triggering direction is illustrated in

figure 5. In figure 5(a), the borehole is perpendicular to the
magnetic-field vector. The triggering component of each sweep, R (the
component of the magnetic-field vector perpendicular to the borehole),
has the same magnitude and direction as the magnetic-field vector;
therefore, no misorientation of the log occurs. No misorientation
occurs when the borehole is inclined to the south, as shown in figure
5(b). When the borehole is inclined in such a manner, the
magnetic-field vector can be represented by two components: a vector Q
that is parallel to the borehole axis and a vector R that is
perpendicular to the borehole axis. Note that if figure 5 were not in
the north-south plane, the small change in direction of the vector R
from figure 5(a) to figure 5(b) would cause a small change in the
triggering of each sweep. When the borehole is vertical, the
magnetometer is triggering each sweep correctly at the northern-most
position as shown in figure 5(c). Note that as the orientation of the
borehole approaches the direction of the magnetic-field vector, the
magnitude of the triggering component is decreased. The borehole and
magnetic-field vectors coincide in figure 5(d); therefore, the
triggering component is zero. In this case, the magnetometer cannot
correctly trigger, and the logs are misorientated. As the hole dip
becomes smaller, the direction of the triggering component changes from
north to south. It is this change in the triggering component that
produces an incorrectly orientated log. This 180° change is shown in
figure 5(e). In this case, a fracture actually dipping to the north
would be shown as dipping to the south on the televiewer log.

Steel casing or a concentration of a magnetic mineral such as

magnetite also can cause orientation errors. Two logs of the same hole
are shown in figure 6. The sweeps were triggered by the magnetometer in
figure 6(b), but they were not in figure 6(a). Note the wandering lines
in figure 6(b); these lines indicate changes in the orientation of the
trigger pulse from the magnetic effects of casing.

10
South
North

(b) (c) (d) (e)

Borehole perpen- Borehole inclined Borehole vertical. Borehole and Borehole inclined
dicular to the to the south. magnetic-field to the north more
magnetic-field vector parallel, than the magnetic'
vector. field vector.

EXPLANATION

MAGNETIC-FIELD VECTOR AT MAGNETOMETER'S CENTER.

Q = $
r
COMPONENT OF THE MAGNET1C-FIELD VECTOR PARALLEL TO THE BOREHOLE.
~a
R- ^ COMPONENT OF THE MAGNETIC-FIELD VECTOR PERPENDICULAR TO THE BOREHOLE (TRIGGERING COMPONENT)

,_ BOREHOLE AXIS.

Figure 5. Different borehole orientations in the north-south plane, illustrating a 180° reversal
in the triggering component; reversal has occurred in (e).
Figure 6. Televiewer log of casing with switch triggering (a); the
same casing shown with magnetic triggering (b).

12
 A map view of the triggering component (R) and a due north
component (N) is shown in figure 7. The vector N is defined by the
intersection of a north-south plane, and a plane perpendicular to the
hole axis at the center of the fracture. Holes deviated to the south
are less susceptible to orientation errors, as indicated in figure 7.

To correct for these errors, consider the vectors involved:

1. The vectors in figure 5(c) are

a. Magnetic field vector (given an arbritary magnitude of 1) is

"? = cos(V)i + sin(V)k, (18)

where V = magnetic inclination angle,

b. Component parallel to hole axis is

Tf - [(a)cos(A)cos(D)i] +[(a)sin(A)cos(D)j] +[(a)sin(D)k], (19)

where a = an arbitrary amplitude of the vector R,

A = the azimuth of the hole, and

D = the hole dip.

c. Component perpendicular to the hole axis is

It = xi + yj + zk. (20)

2. The magnetic-field vector has two components,

F = 7f + R, which yields by equating parts, (21)

cos(V) = [(a)cos(A)cos(D)] + x,

0 = [(a)sin(A)cos(D)] + y, and

sin(V) = [(a)sin(D)] + z,

which implies that

x = cos(V) - [(a)cos(A)cos(D)],

y = -[(a)sin(A)cos(D)],

z = sin(V) - [(a)sin(D)].

13
 North

45°
315

270

225°

^ Hole azimuth
= 180°

180" South
EXPLANATION

N PROJECTION OF MAGNETIC FIELD VECTOR.

R TRIGGERING COMPONENT.

Figure 7. Map view of inclined holes at different hole azimuths. The center
ring of ellipses is inclined at 37°, the middle ring at 53°, and
the outer ring at 66°. The azimuth of the hole is indicated by
the axis passing through the center of the ellipse. Magnetic
inclination of F is 60° (V = 60°).

14
3. Solving for the amplitude (a),
|f| - pol + |R| =1, (22)
= [(a) 2 cos 2 (A)cos 2 (D)] +[(a) 2 sin2 (A)cos 2 (D)] +[(a) 2 sin2 (D)]

+ [cos(V) - (a)cos(A)cos(D)] 2 + [(-a)sin(A)cos(D)] 2

+ [sin(V) - (a)sin(D)] 2 .

which when solved for (a) yields

(a) = [cos(V)cos(A)cos(D>] + [sin(V)sin(D)]. (23)

4. Solving for the magnitude of Q,

"Q = [cos(V) - (a)cos(A)cos(D)]i - [(a)sin(A)cos(D)]j (24)

+ [sin(V) - (a)sin(D)]k, or

"Q = /I - (a) 2 . (25)

5. The vector N shown in figure 8 is defined as

"N = [tan(D)/B]i - [cos(A)/B]k, (26)

where N = 1, and

B = \/tan 2 (D) + cos 2 (A).

6. The star (*) in figure 8 indicates the position of an important

feature, such as the low point of a sinusoid (fig. 3). When the
televiewer is tilted, N and R are not coincident, as illustrated in
figure 8. The tool triggers on R, not N. Before the corrections
mentioned in the geometrical-rotation section can be made, the
angle 6 between N and R needs to be known and appropriately added or
subtracted. The angle between N and the important feature (*) is
6-6, where 6 is the angle between N and K (fig. 8). The angle
8 needs to be added to apparent azimuths for hole azimuths between
180° and 360°, and subtracted for hole azimuths between 0° and 180°
(fig. 8). The angle 6 is obtained by taking the dot product of R
and N:
"R»"N = | If | [R|cos 9 = RxNx + RyNy + RzNz; (27)

solving for 6 yields

0 - arccos{[cos(V) - (a)cos(A)cos(D)]tan(D) (28)
- [sin(V) - (a)sin(D)]cos(A)}/(B|R|).

15
 EXPLANATION

Dp = APPARENT DOWN-DIP AZIMUTH OF THE FRACTURE.

9 = ANGLE BETWEEN N AND If.
6 =8 + Dp.
=» ____v COMPONENT OF FIELD VECTOR PERPENDICULAR
_^ * TO THE BOREHOLE.
N PROJECTION OF MAGNET1C-FIELD VECTOR.

Figure 8. Angles used in the geometric rotation.

Maps showing the magnetic inclination and declination in the United

States can be purchased through the U.S. Geological Survey (1976 for
magnetic inclination, and 1980 for magnetic declination). Moffitt and
Bouchard (1975, p. 196) give a interpolation technique that can be used
between publication of two old maps.

TEST RESULTS

Calculated triggering errors were compared with experimental

results. The experiment was conducted in a open field sufficiently
removed from power lines and the logging truck to eliminate extraneous
magnetic effects. The televiewer was centered in a plastic tube filled
with water, and the tube was fastened to a wooden platform that could be
tilted to simulate the inclination of a borehole and prevent the tube
itself from rotating. The recording instruments were set to examine
each 360° sweep of the televiewer signal. A nonmagnetic rod was fixed
to the side of the plastic tube. It was the position of this rod that
was monitored.

A series of individual sweeps taken at different inclinations for a

hole azimuth of 90° are shown in figure 9. The arrows indicate the
acoustic response of the televiewer to the rod. Note that as the tool
is inclined from vertical the arrows move to the right. The difference
between the position of the arrows in figures 9(b) through 9(d) and in
figure 9(a) is a measure of the angle 0 in equation 28. There were 36
records made with 24 in the northern quadrants. These data indicate
that the difference between experimental and calculated orientations is
within ±5°, which is an error of 2.8 percent.

16
 OQ
cI-J
I
I
i-J <-n 1-3
CD O (t>
X) h-1
i-S O. (t)
n> H- <
en < H-
(T> H- (t>
P co S3
rt H- (t)
cn o i-J
3
**i w w
o s] o>
o H- 0>
rt X)
3T1 CO
09
rt
03
H- O
0 h-1
(t) fD (a) Inclination = 0°. (b) Inclination =15°.
CO
» The rod is at 30 divisions or 216°, The rod is at 34 divisions or 245°.
(t) N
< H-
Theoretically, the rod should be at 24?'
SI
Ui
o
CL HI
H-
^ >sO
H. o
CO O
H-
O
CO W
O
CL rt
H- O
< 0<3
H- i-t
CO P
H* X)
O V
0
P
CO
(c) Inclination = 43°. (d) Inclination =67°.
The rod is at 37.5 divisions or 270°. The rod is at 39 divisions or 281°.
Theoretically, the rod should be at 274°, Theoretically, the rod should be at 281°
 HAND-HELD-CALCULATOR PROGRAM

The purpose of the calculator program is to allow the user to

reorientate a fracture without having to access a large computer. The
program is user-oriented; after completing several examples, the user
can run the programs without written instructions. The program requires
hole-survey data, such as measured depth, angle of inclination, azimuth
angle, and the type of calculation technique. All length measurements
need to be entered in the same units, and all depths need to be measured
from the same reference. All angles need to be entered in degrees,
minutes, and seconds. For example, an azimuth of 123°, 36 minutes, and
24 seconds would be entered as 123.3624. The hole azimuth needs to be
referenced to true north.

The program was written for a Hewlett-Packard(HP)-4lCV and was

designed to run with the peripheral printer. However, with the
following modifications, the program can be run without the printer.
The program requires almost the entire memory; therefore, all other
programs first need to be cleared. Set the size to 41 and clear all key
assignments and all flags. If you wish to run the program without the
printer, delete the following lines in order: 687, 425, 59, and 17.
All of these steps are "ADV", the command for advancing the printer
paper. Next, insert a stop after the following "AVIEW" (alpha view)
commands: 388, 361, 353, 347, 282, 279, 276, 273, 269, 266, 166, 158,
and 149. After running the program several times, the user might desire
to change some of the "STOP" commands to "PSE" or pause commands. The
"STOP" commands inserted above are now on the following lines: 150,
160, 169, 270, 274, 279, 283, 287, 291, 357, 364, 373, and 401. If only
one of the three borehole-survey methods is needed, the following lines
may be deleted for any given method: tangent (1-49) , minimum-curvature
(420-598), or radius-of-curvature (628-832). These are line numbers
prior to the changes listed above. If a mistake is made, or it is
desired to change to a different survey method, turn the calculator off
and then back on; this is done to clear all of the user flags (11-20)
and some of the error flags. If the fracture under consideration has an
apparent horizontal orientation, then enter zero to the down-dip azimuth
prompt when running the program. A listing of register assignments is
in table 1 (Supplemental data section); a listing of the program is in
table 2 (Supplemental data section). Two examples using this program
follow.

Example 1 Simple-Dip Increase

Problem: A hole inclined 30° due west (A = 270°) has a diameter of

0.25 ft. The top of the fracture intersects the borehole at a
depth of 100 ft, and the bottom of the fracture intersects at
100.25 ft. The fracture dips due east (Dp = 90°). In this
example, all the angles are referenced to true north
(fig. 10).

_!/ The use of trade names in this report is for identification only and
does not constitute endorsement by the U.S. Geological Survey.
18
 :rue dip = 180°-45°-60° = 75° to the east;

hole inclined 30° to the west.

West 4-

45

Fracture plane

Down

Figure 10. Example problem in east-west plane

Solution: Press Display Comment

XEQ XEQ__

ALPHA XEQ_

TANG XEQ TANG_

ALPHA HOLE NAME? ENTER AS MANY AS SIX

ALPHANUMERIC CHARACTERS
HOLE 1 HOLE 1

R/S HOLE NAME = HOLE 1

DECL? +FOR E ENTER MAGNETIC DECLINATION;
POSITIVE FOR DECLINATION
EAST OF TRUE NORTH.

0.0 0.0

R/S WITH THETA? DO YOU WISH TO INCLUDE

THE EFFECT OF THE VERTICAL
COMPONENT OF THE MAGNETIC FIELD?
ENTER Y FOR YES OR N FOR NO.
19
 N N_

R/S HOLE DIA? HOLE DIAMETER?

0.25 0.25_

R/S HOLE AZIMUTH?

270.0 270.0_

R/S INC.? HOLE INCLINATION?

30.0 30.0_

R/S FRAC. TOP? CALCULATOR WILL BEEP AND

ASK FOR MEASURED DEPTH
TO FRACTURE TOP.

100.0 100.0_

R/S FRAC. BOTTOM? FRACTURE BOTTOM?

100.25 100.25_

R/S DOWN DIP AZ? DOWN DIP AZIMUTH?

90.0 90.0

R/S

ANSWERS: TOP DEPTH= 100.0000

BOTTOM DEPTH= 100.2500
CENTER DEPTH= 100.1250
TRUE DEPTH= 86.7108 TO FRACTURE CENTER
TRUE DEPARTURE5*-50.0625
TRUE LATITUDE= 0.0000
DIP= 75.0000 TRUE STRIKE AND DIP,
DIP DIRECTION= 90.0000 DIP DIRECTION
INDICATES THE
DOWN-DIP AZIMUTH
OF THE PLANE.
STRIKE= 0.0000
FRAC. TOP? PROMPT FOR NEXT FRACTURE.

ON TURN CALCULATOR OFF AND ON

AGAIN TO CLEAR ALL FLAGS
FOR NEXT EXAMPLE.

20
 Example 2 Multiple-Survey Stations

Problem: A hole was surveyed by the minimum-curvature method and

the following data were reported:

DEPTH AZIMUTH INCLINATION TRUE DEPTH DEPARTURE LATITUDE

(feet) (degrees, minutes) (feet) (feet) (feet)

0 N72 08 E 14 30 0.0 0.0 0.0

100 N69 07 E 14 40 96.78 23.74 8.36

200 N70 05 E 15 00 193.45 47.74 17 .27

300 N69 21 E 15 20 289.96 72.28 26.34

400 N71 01 E 15 35 386.34 35.38 97.35

Azimuth angles are from true north.

Magnetic declination is 7°, 30 minutes east.
Magnetic inclination is 76°, 50 minutes, and 6 seconds.
Hole diameter is 0.25 ft.

You wish to know the true orientation of three fractures

given the following information:

Fracture 1 Fracture 2 .Fracture

Fracture top 50 ft 225 ft 376 ft

Fracture bottom 51 .08 ft 225.20 ft 406 ft

Down-dip azimuth 90 o 45° 231°

29 minutes 30 minutes
56 seconds

Solution:

Press Display Comment

XEQ XEQ_

ALPHA XEQ_

MINC XEQ MINC_

ALPHA HOLE NAME?

HOLE 2 HOLE 2
21
R/S DECL? + FOR E

7.30 7.30_

R/S WITH THETA?

Y Y_

R/S MAG. INC? MAGNETIC INCLINATION ANGLE?

76.5606 76.5006_

R/S HOLE DIA?

0.25 0.25_

R/S STAT. 1 D? DEPTH TO TOP STATION

0.0 0.0_

R/S STAT. 1 A? AZIMUTH AT STATION 1?

72.08 72.08_

R/S STAT. 1 I INCLINATION AT STATION 1?

14.30 14.30_

R/S VERT. DEP 1? TRUE VERTICAL DEPTH TO STATION 1?

0.0 0.0_

R/S DEPART. TO 1? TRUE DEPARTURE TO STATION 1?

0.0 0.0_

R/S LAT. TO 1? TRUE LATITUDE TO STATION 1?

0.0 0.0_

R/S STAT. 2 D? MEASURED DEPTH TO STATION 2?

100.0 100.0_

R/S STAT. 2 A? AZIMUTH AT STATION 2?

69.07 69.07_

R/S STAT. 2 I? INCLINATION AT STATION 2?

14.40 14.40

22
R/S FRAC. TOP? CALCULATOR BEEPS AND PROMPTS FOR
FRACTURE TOP?

50.0 50.0_

R/S FRAC. BOTTOM? FRACTURE BOTTOM?

51.08 51.08_

R/S DOWN DIP AZ? DOWN DIP AZIMUTH?

90.2956 90.2956

R/S

ANSWERS

TOP DEPTH= 50.000

BOTTOM DEPTH= 51.0800
CENTER DEPTH=50.5400
TRUE DEPTH= 48.9210
TRUE DEPARTURES2.0241
TRUE LATITUDE= 4.0538
DIP= 65.1360
DIP DIRECTION 32.3004
STRIKE= 302.0004

SAME STAT.? SAME STATIONS FOR NEXT FRACTURE

ENTER N FOR NO, Y FOR YES

R/S STA 2 NOW 1? IS STATION 2 NOW THE TOP STATION.

IN OTHER WORDS IF WE HAD A FRACTURE
LOCATED AT 103 FT THE ANSWER WOULD
BE YES BUT SINCE THE NEXT FRACTURE
IS AT 225 FT THE ANSWER IS NO
ENTER Y FOR YES OR N FOR NO

N N_

R/S STAT. 1 D?

200.0 200.0_

R/S STAT. 1A?

70.05 70.05_

R/S STAT. 1 I?

23
15.00 15.00_
R/S VERT. DEP 1?

193.45 193.45_

R/S DEPART. TO 1?

47.74 47.74_

R/S LAT. TO 1?
17.27 17.27_

R/S STAT. 2 D?
300.0 300.0_

R/S STAT. 2 A?

69.21 69.21_
R/S STAT 2 I?

15.20 15.20_

R/S FRAC. TOP?

225.0 225.0_

R/S FRAC. BOTTOM?

225.2 225.2_
R/S DOWN DIP AZ?
45.0 45.0_

R/S

TOP DEPTH= 225.0000

BOTTOM DEPTH= 225.2000
CENTER DEPTH* 225.1000
TRUE DEPTH= 217.6900
TRUE DEPARTURE=53.8609
TRUE LATITUDE" 19.4989
DIP= 39.0124
DIP DIRECTION= 329.0504
STRIKE= 239.0504
SAME STAT.? PROMPT FOR NEXT FRACTURE

24
N N_

R/S STA 2 NOW 1?

Y Y_

R/S STAT. 2 D?

400.0 400.0

R/S STAT. 2 A?

71.01 71.01_

R/S STAT. 2 I?

15.35 15.35_

R/S FRAC. TOP?

376.0 376.0_
R/S FRAC. BOTTOM?

406.0 406.0_

R/S DOWN DIP AZ?

231.30 231.30_

R/S

TOP DEPTH= 376.0000

BOTTOM DEPTH= 406.0000
CENTER DEPTH= 391.0000
TRUE DEPTH= 377.6799
TRUE DEPARTURE=95.0698
TRUE LATITUDE= 34.5850
DIP= 87.0232
DIP DIRECTION= 353.2245
STRIKE= 263.2245

SAME STAT.? PROMPT FOR NEXT FRACTURE.

TURN THE CALCULATOR OFF AND BACK ON
(THIS CLEARS ALL THE FLAGS), THEN
EXECUTE RCUR INSTEAD OF MINC AND
REPEAT THE ABOVE PROCEDURE. THIS
YIELDS SIMILAR RESULTS:

25
FRACTURE 1 TOP DEPTH= 50.0000
BOTTOM DEPTH= 51.0800
CENTER DEPTH= 50.5400
TRUE DEPTH= 48.9209
TRUE DEPARTURES2.0249
TRUE LATITUDE= 4.0536
DIP= 65.1360
DIP DIRECTION 32.3004
STRIKE= 302.3004

FRACTURE 2 TOP DEPTH 225.0000

BOTTOM DEPTH= 225.2000
CENTER DEPTH= 225.1000
TRUE DEPTH= 217.6900
TRUE DEPARTURE=53.8609
TRUE LATITUDE= 19.4989
DIP= 39.0124
DIP DIRECTION= 329.0504
STRIKE= 239.0504

FRACTURE 3 TOP DEPTH= 376.0000

BOTTOM DEPTH= 406.0000
CENTER DEPTH= 391.0000
TRUE DEPTH= 377.6795
TRUE DEPARTURE=95.0711
TRUE LATITUDE= 34.5860
DIP= 87.0232
DIP DIRECTION= 353.2245
STRIKE= 263.2245

26
 FORTRAN PROGRAMS

Two Fortran programs were written for a Digital Equipment

Corporation PDF 11/34 computer. The first program is the simpler
version that requires only mimimum data to correct the orientation of a
single fracture. The second program uses different hole-survey
methods; it was written to reorient many fractures in one well. All
parameters are entered in the same format as the calculator program;
however, the output is reported only to the nearest degree. The
single-fracture version is listed in table 3 (Supplemental data
section); the single-well version is listed in table 4 (Supplemental
data section). Variable names used in the Fortran programs, with their
corresponding definitions, are listed in table 5 (Supplemental data
section).

The single-fracture version requires data for eight paramters;

magnetic declination, magnetic inclination, hole diameter, hole azimuth,
hole inclination, measured depth to fracture top, measured depth to
fracture bottom, and apparent down-dip azimuth of fracture. This
version reports both the orientation of the fracture corrected for the
attitude of the hole, and the orientation of the fracture corrected for
both the attitude of the hole and the magnetic effect.

The single-well version of the Fortran program needs similar input.

Documentation at the beginning of the program listing describes the
format under which input data needs to be entered. When data are
entered for the single-well version, care needs to be taken to not enter
a fracture at or above the first station. For example, if a fracture
centered at 0.0 was entered between line 160 and 170, in the single-well
version, this entry would cause the program to stick in an infinite
loop. Care also needs to be taken when the hole survey indicates no
change in hole direction or inclination for a given segment, as
indicated by equations 8 through 10; this would cause a division by
zero. Examples of both versions follow.

Example 3 Single-Fracture Version

Note that input to this program is the same as input to the first
example in the hand-held-calculator section. Therefore, the first set
of answers is the same as those obtained with that program; however the
second set shows the large difference in answers obtained when the
magnetic effect is considered.

RUN DL1:SHORT

MAGNETIC DECLINATION?
DEGREES (NEGATIVE FOR WEST): 0.
MINUTES: 00.
SECONDS: 00.

27
 MAGNETIC INCLINATION?
DEGREES: 67.
MINUTES: 00.
SECONDS: 00.

HOLE DIAMETER? 0.25

HOLE AZIMUTH?
DEGREES: 270.
MINUTES: 00.
SECONDS: 00.

HOLE INCLINATION?
DEGREES: 30.
MINUTES: 00.
SECONDS: 00.

MEASURED DEPTH TO FRACTURE TOP?

(IN SAME UNITS AS DIAMETER): 100.00

MEASURED DEPTH TO FRACTURE BOTTOM? 100.25

DOWN DIP AZIMUTH OF FRACTURE?

DEGREES: 90.
MINUTES: 00.
SECONDS: 00.

WITHOUT VERTICAL INCLINATION CORRECTION:

TOP BOTTOM STRIKE DIP DOWN DIP AZIMUTH

100.00 100.25 0. 75. 90.

WITH VERTICAL INCLINATION CORRECTION:
TOP BOTTOM STRIKE DIP DOWN DIP AZIMUTH

100.00 100.25 35. 68. 125.

TT5 STOP

Example 4 Single-Well Version

In this example, the second Fortran program is used. An example of

the input file that needs to be created prior to running the program
follows. A simplified explanation of the input is on the right. An
explanation of the input parameters is given in the beginning of table 4
(Supplemental data section).

28
Input data:

Line
No.

10 0.0000 0000.0 0.000 Line 10 contains the true depth,

20 0.0 0000000 0000000 true departure, and true latitude
30 200.0 1633900 151500 of the first station.
40 299.0000 1642200 152300
50 499.0000 1684200 154300 Line 20 contains the depth
60 600.0000 1695300 162100 measured along the borehole, the
70 800.0000 1732700 172600 azimuth, and the borehole
80 899.0000 1760400 175200 inclination at station 1.
90 984.0000 1783900 182500
100 1099.000 1811000 190800 Lines 30 to 150 contain the
110 1152.000 1811800 193200 remaining station data, as in
120 1201.000 1815600 194800 line 20.
130 1250.000 1820400 201000
140 1850.000 1874100 225700
150 1900.000 1870600 232300
160 -1.0 Line 160 indicates the end of the
170 299.00 299.00 station data with a -1.
180 499.00 499.00
190 600.00 600.00 Lines 170 to 360 contain fracture
200 800.00 800.00 data. The first value indicates
210 899.00 899.00 the depth measured along the
220 984.00 984.00 borehole to the top of the
230 1099.00 1099.00 fracture; the second value
240 1152.00 1152.00 indicates the depth measured along
250 1201.00 1201.00 the borehole to the bottom of the
260 1250.00 1250.00 fracture. Note that if these
270 1850.00 1850.00 first two values are the same,
280 1900.00 1900.00 there is no third value; this is
290 214.40 214.79 74.0 because the fracture is horizontal
300 214.40 214.79 63.0 with respect to the hole. The
310 1098.31 1098.79 133. third value indicates the down-dip
320 1132.23 1132.84 140. azimuth of the fracture.
330 1132.23 1132.84 132.
340 1233.12 1233.32 160. Line 370 indicates the end of the
350 1868.68 1868.94 172. file.
360 1868.34 1868.72 151.
370 -1.0

29
The following are two options of the program with the input data given
on page 29. A copy of the program's output for each option follows.
Note that decimals need to be entered with all responses except for the
hole-survey method and the integer number of pages.

Option 1:

RUN ROMCUR

HOLE SURVEY METHOD?

ENTER 1 FOR RADIUS OF CURVATURE
2 FOR MINIMUM CURVATURE OR
3 FOR TANGENTIAL: 1

HOLE NAME? URL 1

MAGNETIC DECLINATION:
DEGREES (NEGATIVE FOR WEST): 7.
MINUTES: 50.
SECONDS: 00.

DO YOU WISH TO INCLUDE THETA? (ENTER 1 FOR YES OR 2 FOR NO) 1

MAGNETIC INCLINATION?
DEGREES: 77.
MINUTES: 00.
SECONDS: 00.

HOW MANY LINES PER PAGE (ENTER INTEGER)? 66

HOLE DIAMETER? (ENTER 0. IF VARIABLE) 0.25

Option 2:

RUN ROMCUR

HOLE SURVEY METHOD?

ENTER 1 FOR RADIUS OF CURVATURE,
2 FOR MINIMUM CURVATURE OR
3 FOR TANGENTIAL: 2

HOLE NAME? URL 1

MAGNETIC DECLINATION?
DEGREES (NEGATIVE FOR WEST): 7.
MINUTES: 50.
SECONDS: 00.

DO YOU WISH TO INCLUDE THETA? (ENTER 1 FOR YES OR 2 FOR NO) 2

HOW MANY LINES PER PAGE (ENTER INTEGER)? 66

HOLE DIAMETER? (ENTER 0. IF VARIABLE) 0.25

30
 Option 1 Output

HOLE NAME: URL 1 RADIUS OF CURVATURE' MAG. DEC. = 7. 50. 0. MAG. INC. = 77. 0. 0. PG

* *
MEASURED DEPTH TO FRACTURE * COORDINATES OF FRACTURE CENTER * TRUE ORIENTATION OF FRACTURE *
* * * *
***(***************.*.*.********************* *****:**X***************M*********M*******X *** ****************************************)***
* * * *
* * TRUE DEPARTURE LATITUDE * STRIKE * DIP- DOWN DIP *
* CENTER TOP BOTTOM * DEPTH + FOR EAST + FOR NORTH * IN DEGREES * IN DEGREES DIRECTION *
s * * * *
^ ^-^ r<£^^^*^^^<^^^4
**i I************'*******.**.***** *f *r ^ ^ ^ '*********** ^^^^^4t^^^*^i^t^^^»
*** * * £****** *****
>*************4>************ ************ ******* *******!k&** ********** *** ^*f ^ ************* ************>K**
^ ^ ^ ************* ***
* * * * *
* 299.00 299.00 299,00 * 293.13 25.36 -22,53 * 74. * 15. 344. *
* 499.00 499.00 499.00 * 485,81 37,85 -74.65 * 79. * 16, 349. *
* 600.00 600.00 600.00 * 582.88 43.03 -102,06 * 80. * 16. 350. *
* 800.00 800.00 800.00 * 774.25 51.46 -159.55 * 83. * 18, 353. *
* 899.00 899.00 899.00 * 868.59 54,20 -189.44 * 86. * 18. 356. *
i * * * * *
* 984.00 984.00 984.00 * 949.36 55.42 -215,88 * 89. * 19. 359. *
* 1099.00 1099.00 1099.00 * 1058.24 55.48 -252.89 * 91. * 19. 1. *
* 1152.00 1152.00 1152.00 * 1108.25 55.10 -270.43 * 91. * 20. 1. *
* 1201.00 1201.00 1201.00 * 1154.39 54.63 -286.91 * 92 . * 20. 2. *
* 1250.00 1250.00 1250.00 * 1200,44 54.05 -303.65 * 92. * 20. 2. *
* * * * *
* 1850.00 1850.00 1850.00 * 1758.42 35.32 -523.21 * 98. * 23. 8. *
* 1900.00 1900.00 1900.00 * 1804.38 32.79 -542.72 * 97. * 23. 7. *
* 214.60 214.40 214,79 * 211.73 19.23 -1.08 * 150. * 60. 60. *
* 214.60 214.40 214,79 * 211.73 19.23 -1.08 * 140. * 63. 50. *
* 1098.55 1098.31 1098.79 * 1057.82 55.48 -252.74 * 37. * 50, 127. *
* * * * *
* 1132.54 1132.23 1132.84 * 1089.90 55.24 -263.95 * 46. * 53. 136, *
* 1132.54 1132.23 1132.84 * 1089.90 55.24 -263.95 * 38. * 55 « 128. *
* 1233.22 1233.12 1233.32 * 1184.69 54,26 -297.89 * 59. * 21. 149. *
* 1868,81 1868.68 1868.94 * 1775.73 34.35 -530.51 * 83. * 24. 173. *
* 1868.53 1868.34 1868.72 * 1775.47 34.37 -530.40 * 56. * 38. 146. *
* * * * *
 Option 2 Output

HOLE NAME: URL i MINIMUM CURVATURE' MAG. DEC. = 7, 50. 0. MAGNETIC EFFECT EXCLUDED PG

* * * *
* ME/
MEASURED DEPTH TO FRACTURE * COORl
COORDINATES OF FRACTURE CENTER
:ENTER * TRUE ORIENTATION OF FRACTURE *
* * *
Jf*f*p*if&*f*ififr \ ******»i'^^**^'»*'*i.'****^*
*** ********;( ***'.^*Y*****J ,^^^^^^^*^^^ T>* 41 *»*^^^<T**>*****
£&££££&&&£ *** **)|f**3|r*J|'**)j'***^*^***>i'i 4t4k^4>4.^*4>^^4k4k4 K*>*

* * * *
* TRUE DEPARTURE LATITUDE * STRIKE * DIP DOWN DIP *
* CENTER TOP BOTTOM * DEPTH + FOR EAST FOR NORTH * IN DEGREES * IN DEGREES DIRECTION *
* * * *
********i r&^*f*fik^*Jt<Af^<*f
*** ******»*' . **i
4^4;********) t^JVLJJL*;**^^*^ *** ************ ***
^^*p ************* ************Jk**
* * * * *
* 299.00 299.00 299,00 * 293.13 14,65 -50.53 * 74. * 15. 344, *
* 499.00 499.00 499.00 * 485.82 27.12 -102.64 * 79. * 16. 349. *
* 600.00 600.00 600.00 * 582.89 32.30 -130.05 * 80. * 16. 350. *
* 800.00 800.00 800.00 * 774.26 40.66 -187.53 * 83, * 18. 353. *
* 899.00 899.00 899,00 * 868.60 43.39 -217.41 * 86, * 18. 356. *
* * * * *
* 984.00 984,00 984.00 * 949.38 44.61 -243.84 * 89. * 19. 359. *
* 1099.00 1099.00 1099.00 * 1058.26 44.65 -280,85 * 91. * 19, 1. *
* 1152.00 1152.00 1152,00 * 1108.27 44.27 -298.39 * 91, * 20. 1. *
* 1201.00 1201.00 1201.00 * 1154.41 43.81 -314,87 * 92. * 20, 2, *
* 1250.00 1250.00 1250.00 * 1200.46 43.22 -331.61 * 92. * 20. 2. *
* * * * *
* 1850.00 1850.00 1850.00 * 1758,49 23,85 -550.96 * 98. * 23. 8. *
* 1900.00 1900.00 1900.00 * 1804.46 21,32 -570.47 * 97. * 23. 7. *
* 214.60 214.40 214.79 * 211.73 8.53 -29.08 * 161. * 57. 71. *
* 214.60 214.40 214.79 * 211.73 8.53 -29.08 * 151. * 60. 61. *
* 1098.55 1098.31 1098,79 * 1057.83 44.65 -280.70 * 41. * 49. 131. *
* * * * *
* 1132,54 1132,23 1132.84 * 1089.92 44,42 -291.91 * 50. * 52, 140. *
* 1132,54 1132.23 1132.84 * 1089,92 44.42 -291.91 * 41. * 54. 131. *
* 1233.22 1233.12 1233,32 * 1184.70 43.43 -325.85 * 64. * 20, 154. *
* 1868.81 1868.68 1868.94 * 1775.80 22.88 -558.26 * 83. * 24. 173. *
* 1868.53 1868.34 1868.72 * 1775.55 22.89 -558.15 * 56 . * 38. 146. *
* * * *
 STEREOGRAPHIC SOLUTIONS

The orientation of a fracture also can be corrected by using the

angle theta (fig. 8) and a stereonet. It is assumed that the reader is
familiar with stereographic projections on a Wulff net (Goodman, 1976).
The following plots use the lower hemisphere unless otherwise specified.
Note that the position of the planes in the following illustrations are
sometimes shown after the overlying trace paper has been rotated to a
second position. This section will illustrate the stereographic method
by using the examples in the previous program sections.

Stereographic Solution of a Simple-Dip Increase

The solution of the example given in figure 10 is stereographically

solved in figure 11. The bottom one-half of a plane perpendicular to
the hole axis (henceforth referred to as the hole-reference plane) at
the position that the fr-acture intersects the borehole is shown in
figure ll(a). This hole-reference plane is then rotated out to the edge
of the net, as indicated by the dashed arrows in figure ll(a). The
apparent strike and dip of the fracture is then plotted on the net, as
shown in figure ll(b). Then, both the fracture and the hole-reference
plane are rotated back to the original position in figure ll(a), which
is shown in figure 11(c) by the dashed arrows. The new position of the
fracture plane is shown with a dotted line. This new plane has the
proper dip and strike, as shown in figure ll(d).

Stereographic Solution of a Rotation Off the Net

The procedure to be used when the apparent-fracture plane is

rotated off the net is shown in figure 12. Using the same hole
orientation as described in figure ll(a), the hole-reference plane is
plotted and rotated out to the periphery in figure 12(a). A rotation
problem occurs, as illustrated in figure 12(b), when the hole-reference
plane and a fracture (apparent attitude N 20° E/12° W) rotate back to
the original position. The fracture rotates off the net. This occurs
because the stereographic-projection technique uses only the lower
hemisphere, and, therefore, the lower one-half of the fracture plane.
By plotting the upper one-half of the fracture plane, rotation can be
successfully accomplished. The upper and lower halves of the
apparent-fracture plane (a plane representing the fracture with an
apparent attitude) is shown in figure 12(c). The movement of a point A
on the upper one-half of the apparent-fracture plane, as it is rotated
with the hole-reference plane back to its correct position is depicted
in figure 12(d). First, the point is rotated down 20° from the upper
one-half of the projection to the edge, Al. Next, it is rotated the
remaining 10° in the normal manner on the lower one-half of the
projection to the point A2.

33
 tated hole reference 7>^Zl^gv^^^ ( Rotated
plane (Hole azimuth - 270°^"^^ hole
Hole reference Hole inclination = 30°) ^Apparent fracture plane reference
plane (strike - 0°, dip - 45** plane
due east)
(a) (b)

Rotated hole reference rue

plane fracture
plane
Apparent
fracture
plane

Hole
reference
plane

True fracture plane

Stereographic projection 1 Dip increase,

34
 Rotated hole Rotated
reference plane hole
Hole reference plane Apparent fracture £>lane reference
(attitude = N20°E/12°W) plane
(b)

le
reference
ane

Upper tated
apparent apparent half of 1 hole
fracture plane fracture plane apparent 1 0" reference
plane

(c) (d)

Figure 12. Stereographic projection 2 Rotation off net.

35
 Stereographic Solution Including a Magnetic-Declination Angle

The effect of a +20° magnetic declination on a fracture, with an

apparent attitude of N 60° E/45° S (the attitude of the fracture is
referenced from magnetic north), is represented in figure 13. The hole
has an azimuth of 60° and an inclination of 30°. The hole-reference
plane and a rotation axis indicated by the line CD is shown in figure
13(a). The rotation axis corresponds to the strike of the
hole-reference plane. The magnetic-north marker (MN) is plotted 20°
clockwise from north.

Because the magnetic-north marker does not lie along the axis of
rotation, a new rotated magnetic-north marker needs to be determined.
This is done by finding the point at which the hole-reference plane
intersects the magnetic north-south line. The magnetic-north marker is
alined with the vertical-stereonet line in figure 13(b). The point A is
the intersection point of the north-south line and the hole-reference
plane. A line from the center of the stereonet to the point A indicates
the magnetic-south direction in the hole-reference plane.

The rotation axis is alined with the vertical-stereonet line, as

shown in figure 13(c). The hole-reference plane is rotated 30° out to
the edge, and the point A is rotated out to the point Al. This new
point, Al, represents the rotated magnetic-south marker (MSr). The
rotated magnetic-north marker (MNr) is 180° from the magnetic-south
marker.

The rotated magnetic-north marker is alined with the

vertical-stereonet line in figure 13(d). From this point, the fracture
(apparent attitude N 60° E/45° S) is plotted. The rotation axis is
alined with the vertical-stereonet line; the rotated hole-reference
plane and the apparent-fracture plane are rotated back 30° to their true
positions in figure 13(e). The fracture plane is shown to have a true
attitude of S 47° E/62° W in figure 13(f).

Stereographic Solution Including a Magnetic-Inclination Angle

The rotation of a fracture (apparent attitude S 10° W/45° N) found

in a hole with a 50° azimuth and a 30° inclination is shown in figure
14. The magnetic inclination is 67°. The hole-reference plane,
rotation axis (CD), the true-north marker (N), and the magnetic-north
marker (MN) are shown in figure 14(a). The magnetic-north marker is
alined with the vertical-stereonet line, and the intersection of this
line with the hole-reference plane is marked by the point A. This point
(A) and the plane are rotated out 30° to the edge in figure 14(b). The
point Al establishes the rotated magnetic-south marker (MSr) and its
complement, the rotated magnetic-north marker (MNr).

36
 Rotation
axis
Hole reference plane
Hole reference plane
(b)

MNr

^ m-.^m+im
Rotated Hole reference Rotation
,
plane axis
hole refer
ence plane Apparent fracture
D ^Rotation axis plane ^-Rotated hole
reference plane
(c)
(d)

Figure 13. Stereographic projection 3 Including magnetic-declination angle.

37
 Apparent
fracture
plane S
True
Rotated fracture
hole refer- plane
ence plane (SA7°E/62°W)
Hole reference plane

Figure 13. Stereographic projection 3 Including magnetic-declination angle Continued.

38
 Pxr
|D Dotation axis
Hole reference plane

(a) (b)

Hole azimuth
mark

Rotated hole
reference ('Rotation Rotated
axis holt
reference
plane

Figure 14. Stereographic projection 4 Including magnetic-inclination angle,

39
 parent fracture plane True fracture
(attitude - S10°W/45°N) plane

MNr

parent
Rotation axis fracture
Rotated plane
hole reference hole reference
plane plane
(e) (f)

Figure 14. Stereographic projection 4 Including magnetic-inclination angle Continued.

 The 30° separation between the hole-azimuth marker (50° from N) and
the magnetic-north marker is illustrated in figure 14(c). This
clockwise distance, in degrees from magnetic-north to the hole-azimuth
marker, is the value of the hole azimuth to be used in table 6
(Supplemental data section). In this table, the theta-correction values
in an area with a magnetic inclination of 67° for hole inclination
varying from 5° to 85° are indicated. A short calculator program to
calculate the absolute value of theta for any hole azimuth (referenced
from magnetic north) and any inclination is listed in table 7
(Supplemental data section). This program does not supply the correct
sign; it needs to be obtained as explained in the section on magnetic
effect. The formula used to calculate theta is given in equation 28.
The program reports theta in degrees not degrees, minutes, and seconds.
A 30° hole azimuth and a 30° hole inclination yields a -104° theta
correction (the negative indicates counterclockwise direction) in figure
14(d). The position of the triggering point (TP) also is indicated in
figure 14(d). It is located theta degrees from MNr; in this case, 104°
counterclockwise from MNr.

The apparent-fracture plane is plotted after alining the triggering

point with the vertical-stereonet line in figure 14(e). The rotation
axis is realined with the vertical-stereonet line in figure 14(f). The
rotated hole-reference plane and apparent-fracture plane are then
rotated back 30° to their true positions. The fracture has a true
attitude of N 62° W/72° S.

CONCLUSIONS

The acoustic televiewer is a logging device that produces images of

fractures that intersect a borehole. The attitude of planar fractures
seen with the acoustic televiewer can be corrected for hole geometry and
magnetic-field effects. Correcting the fractures for hole geometry
requires only a hole survey. An additional correction for the magnetic
effect requires knowledge of the inclination of the Earth's magnetic
field at the logging site. Maps showing the magnetic inclination and
declination in the United States can be purchased from the
U.S. Geological Survey. The corrections due to the magnetic field can
be as large as 180°. Tests were conducted to verify the magnetic-effect
correction. These tests indicated an accuracy of corrected fracture
attitude of 2.8 percent. The also illustrates how to correct the
orientation of fractures through stereographic projection.

41
 SELECTED REFERENCES

Bateman, R. M., 1979, The log analyst and the programmable pocket
calculator: Log Analyst, v. 20, no. 2, p. 3-6.

Craig, J. T., Jr., and Randall, B. V., 1976, Directional survey

calculation: Petroleum Engineer International, March, 1976,
p. 38-54.

Fabiano, E. B., and Peddie, N. W., 1980, Magnetic declination in

the United States Epoch 1980: U.S. Geological Survey Map 1-1283,
Scale 1:5,000,000.

Goodman, R. E., ed., 1976, Methods of geological engineering in

discontinuous rocks: New York, West Publishing Co., 466 p.

Logan, M. H., and others, 1968, Computer determination of true dip

and strike for planar structures intersected by an inclined drill
hole: Denver, Colo. , U.S. Bureau of Reclamation Report 109573,
40 p.

Moffitt, F. H., and Bouchard, Harry, 1975, Surveying: New York,

Harper and Row, 879 p.

Peddie, N. W., Jones, W. J., and Fabiano, E. B., 1976, Magnetic

inclination in the United States Epoch 1975.0: U.S. Geological
Survey Map 1-912, Scale 1:5,000,000.

Turner, W. J., 1980, Hand-held calculator programs for frequently used

formulas: Petroleum Engineer International, June, 1980,
p. 102-114.

Wilson, G. J., 1968, An improved method of computing directional

surveys: Journal of Petroleum Technology, v. 21, no. 8,
p. 871-876.

Zemanek, Joseph, 1969, The borehole televiewer A new logging concept

for fracture location and other types of borehole inspection:
Journal of Petroleum Technology, v. 21, no. 6, p. 762-774.

42
SUPPLEMENTAL DATA SECTION

43
44
 Table 1. Storage-register assignments

00 Calculation register - variable content.

01 Hole name.
02 Magnetic declination.
03 Hole diameter.
04 Hole azimuth.
05 Hole dip.
06 Depth (as measured along the hole) to the top of the
sinusoidal fracture.
07 Depth (as measured along the hole) to the bottom of the
sinusoidal fracture.
08 Depth (calculated from 06 and 07 above) to the center of the
sinusoidal fracture.
09 Positive difference in depth between top and bottom of the
fracture = h.
10 Apparent fracture dip (calculated from 09 and 03 above) = P.
11 Apparent fracture strike = apparent down dip
azimuth -90° = K. __________
12 Computational factor = tan2 (05) + cos2 (04) = B.
13 Directional cosine = af.
14 Directional cosine = (3f.
15 Directional cosine = yf.
16 Well depth to station 1 = Dl .
17 Azimuth at station 1 = Al .
18 Inclination at station 1 = II .
19 True vertical depth to station 1.
20 True departure to station 1.
21 True latitude to station 1.
22 Well depth to station 2 = D2.
23 Azimuth to station 2 = A2 .
24 Inclination at station 2 = 12 .
25 Difference in well depth between stations
(station 2-station 1) = AD.
26 Difference in well azimuth between stations
(station 2-station 1) = AA.
27 Difference in well inclination between stations
(station 2-station 2) = AI.
28 True vertical depth to center of fracture = AtV.
29 True departure to center of fracture = AtE.
30 True latitude to center of fracture = AtN.
31 New inclination angle at fracture center.
32 New or old dogleg angle for minimum curvature method.
33 Calculation register - variable content - usually = RF .
34 Difference in true depth between stations = AV.
35 Difference in true latitude between stations = AN.
36 Difference in true departure between stations = AE .
37 Magnetic inclination angle = V.
38 Amplitude of the vector Q.
39 Amplitude of the vector R.
40 Angle between vector R and the vector N = 0 .

45
 Table 2. Hand-held-calculator program listing

01 LBL "TANG" 26 RCL 31 51 AON

02 XEQ 01 27 SIN 52 "HOLE NAME? "

03 "HOLE AZIMUTH?" 28 RCL 04 53 PROMPT

04 PROMPT 29 COS 54 ASTO 01

05 HR 30 * 55 "HOLE NAME= "

06 STO 04 31 RCL 08 56 ARCL 01

07 LBL 15 32 * 57 AVIEW

08 "INC.?" 33 STO 30 58 AOFF

09 PROMPT 34 RCL 31 59 ADV

10 HR 35 SIN 60 "DECL? +FOR E"

11 STO 31 36 RCL 04 61 PROMPT

12 CHS 37 SIN 62 HR

13 90 38 * 63 STO 02
64 "N"
14 + 39 RCL 08

15 STO 05 40 * 65 ASTO Y

16 LBL 03 41 STO 29 66 AON

17 ADV 42 FS? 12 67 "WITH THETA?"

18 XEQ 04 43 GTO 60 68 PROMPT

19 FS?C 11 44 RCL 02 69 ASTO X

20 XEQ 94 45 ST- 04 70 AOFF

21 RCL 08 46 FS? 17 71 X=Y?

22 RCL 31 47 XEQ D 72 GTO 16

23 COS 48 XEQ "R" 73 SF 17

24 * 49 GTO 03 74 "MAG. INC.?"

25 STO 28 50 LBL 01 75 PROMPT

46
 Table 2. Hand-he Id-calculator program listing Continued

76 HR 101 / 126 "YOU GOOFED"

77 STO 37 102 RCL 06 127 AVIEW

78 LBL 16 103 + 128 RTN

79 "HOLE DIA?" 104 STO 08 129 LBL 13

80 PROMPT 105 RCL 09 130 XEQ 12
81 STO 03 106 RCL 03 131 GTO 04
82 X<=0?
107 / 132 LBL 14
83 XEQ 17 108 ATAN 133 "YOU DO IT"
84 RTN 109 STO 10 134 AVIEW
85 LBL 04 110 "DOWN DIP AZ?" 135 BEEP
86 TONE 1 111 PROMPT 136 PSE

87 "FRAC. TOP?" 112 HR 137 GTO 70

88 PROMPT 113 90. 138 LBL 17

89 STO 06 114 - 139 XEQ 12

90 "FRAC. BOTTOM?" 115 X<0? 140 GTO 16

91 PROMPT 116 XEQ 92 141 LBL 94
92 STO 07 117 STO 11 142 SF 12
93 -
118 RTN 143 XEQ 93
94 CHS 119 LBL 92 144 RTN
95 STO 09 120 360 145 LBL 93
96 X<0? 121 + 146 RCL 31
97 XEQ 13 122 RTN 147 HMS

98 X»0?
123 LBL 12 148 STO 00
99 SF 11 124 SF 20 149 "DIP= "

100 2 125 BEEP 150 ARCL 00

47
 Table 2. Hand-held-calculator program listing Continued

, 7, 201 RCL 10
151 AVIEW 1/b ~
177 DTM 202 SIN
152 RCL 04 177 RTN
153 180 178 LBL " R "

154 + 179 RCL 31 204 RCL 12

155 XEQ 91 18 ° X=0?

156 HMS 181 GTO 14

1 R9 QF 9A 207 RCL 10
1 57 STO 00 z bi? /4
1 QO VTTA 13 208 COS
158 "DIP DIRECTION- " x BJ XE Q B
1 RA RTT 1 1 209 RCL ° 4
159 ARCL 00 184 RCL X1
21 ° cos
160 AVIEW

161 RCL 00 186 RCL ° 4

1 ft?
187 STN
SIN 212 RCL ° 5
162 90
188 * 213 COS
163 +

164 XEQ 91 189 RCL ° 4

165 STO 00 * 90 COS

i Q1 * 216 STO 13
166 "STRIKE* " 191 *
109 RTT ns 217 RCL 10
167 ARCL 00 192 RCL ° 5

174 RTN 199 *

 Table 2.--Hand-held-calculator program listing Continued

276 "TRUE DEPTH* "

226 RCL 10 251 *
277 ARCL 28
227 SIN 252 +
278 AVIEW
228 RCL 11 253 RCL 10
279 "TRUE DEPARTURE*"
229 COS 254 SIN
280 ARCL 29
230 * 255 *
281 AVIEW
231 RCL 05 256 RCL 12
282 "TRUE LATITUDE* "
232 COS 257 /
283 ARCL 30
233 * 258 RCL 05
284 AVIEW
234 RCL 12 259 SIN
285 FS?C 12
235 * 260 RCL 10
286 GTO 03
236 + 261 COS
287 FS?C 13
237 STO 14 262 *
288 GTO 96
238 RCL 11 263 -
289 FS?C 14
239 COS 264 STO 1 5
290 GTO 98
240 RCL 04 265 CF 24
v 291 RCL 15
241 SIN 266 "TOP DEPTH* "
292 X<0?
242 RCL 05 267 ARCL 06
293 GTO 37
243 SIN 268 AVEIW
294 RCL 13
244 * 269 "BOTTOM DEPTH* "
295 CHS
245 * 270 ARCL 07
296 STO 13
246 CHS 271 AVIEW
297 RCL 14
247 RCL 11 272 LBL 60
298 CHS
248 SIN 273 "CENTER DEPTH* "
299 STO 14
249 RCL 04 274 ARCL 08
300 RCL 15
250 COS 275 AVIEW

49
 Table 2. Hand-held-calculator program listing Continued

301 CHS 326 RCL 02 351 HMS

3 02 STO 1 5 327 + 352 STO 00

3 03 GTO 3 7 328 STO 00 353 "DIP D]

3 04 LBL 7 0 329 X<0? 354 ARCL OC

3 05 RTN 330 XEQ 56 355 AVIEW

3 06 LBL 3 7 331 STO 00 356 RCL 00

3 07 RCL 1 4 332 360 357 90

3 08 X=0 ? 333 "X<Y? 358 -

3 09 GTO 51 334 GTO 58 359 x<o?

3 10 SF 25 335 CLX 360 XEQ 56

3 11 RCL 1 4 336 LBL 66 361 "STRIKE

3 12 RCL 1 3 337 RCL 15 362 ARCL X

3 13 / 338 ACOS 363 AVIEW

3 14 FC? C 25 339 CHS 364 GTO 70

3 15 GTO 3 8 340 180 365 LBL 38

3 16 ATAN 341 + 366 RCL 13

3 17 STO 00 342 .5 367 X=0?

3 18 X<0 7 343 XOY 368 GTO 53

3 19 XEQ 5 7 344 X<Y? 369 SF 24

3 20 LBL 50 345 GTO 52 370 RCL 14

3 21 RCL 1 4 346 HMS 371 RCL 13

3 22 X<Q ? 347 "DIP = " 372 /

3 23 XEQ 5 7 348 ARCL X 373 CF 24

3 24 LBL 63 349 AVIEW 374 ATAN

3 25 RCL 00 350 RCL 00 375 STO 00

50
 Table 2. Hand-held-ealculator program listing Continued

376 X<0? 401 STO 00 426 XEQ ° 4

377 XEQ 57 402 GTO 63 427 XEQ ° 7

378 GTO 50 403 LBL 54 428 FS?C 20

379 LBL 51 404 270 429 GTO ° 8

380 RCL 13 405 STO 00 43 ° RCL 26

381 X»0? 406 GTO 63 431 COS

382 GTO 52 407 LBL 56 432 CHS

383 X<0? 408 360 433 * -°

384 GTO 55 409 + 434 +

385 0 410 RTN 43 5 RCL 24

386 STO 00 411 LBL 57 436 SIN

387 GTO 63 412 RCL 00 437 *

388 LBL 52 413 180 438 RCL 18

389 "DIP= 0.0000" 414 ST+ 00 43 9 SIN

390 AVIEW 415 RTN 44 ° *

391 GTO 70 416 LBL 58 441 CHS

392 LBL 55 417 360 442 RCL 27

393 180 418 ST- 00 443 COS

394 STOP 00 419 GTO 66 444 +

395 GTO 63 420 LBL "MINC" 445 ACOS

396 LBL 53 421 XEQ 01 446 STO 32

397 RCL 14 422 LBL 08 447 XE Q 18

398 X<0? 423 XEQ 05 448 RCL 24

399 GTO 54 424 LBL 09 449 ST0 31

400 90 425 ADV 45 ° RCL 23

51
 Table 2. Hand-held-ealculator program listing Continued

451 STO 04 476 / 501 *

452 XEQ 19 477 RCL 27 502 RCL 19

453 RCL 25 478 * 503 +

454 * 479 RCL 18 504 STO 28

455 STO 34 480 + 505 XEQ 20

456 XEQ 20 481 STO 31 506 RCL 08

457 RCL 25 482 CHS 507 RCL 16

458 * 483 90 508 -

459 STO 35 484 + 509 *

460 XEQ 21 485 STO 05 510 RCL 21

461 RCL 25 486 RCL 08 511 +

462 * 487 RCL 16 512 STO 30

463 STO 36 488 - 513 XEQ 21

464 RCL 32 489 RCL 25 514 RCL 08

465 RCL 08 490 / 515 RCL 16

466 RCL 16 491 RCL 26 516 -
467 - 492 * 517 *

468 RCL 25 493 RCL 17 518 RCL 20

469 / 494 + 519 +

470 * 495 STO 04 520 STO 29

471 STO 32 496 XEQ 18 521 FS?C 11

472 RCL 08 497 XEQ 19 522 GTO 95

473 RCL 16 498 RCL 08 523 RCL 02

474 - 499 RCL 16 524 ST- 04

475 RCL 25 500 - 525 FS? 17

52
 Table 2. Hand-held-calculator program listing Continued

526 XEQ D 551 LBL 19 576 2

527 XEQ "R" 552 RCL 31 577 /

528 LBL 96 553 COS 578 RTN

529 ,, N n 554 RCL 18 579 LBL 21

530 ASTO Y 555 COS 580 RCL 31

531 AON 556 * 581 SIN

532 "SAME STAT.7" 557 RCL 33 582 RCL 04

533 PROMPT 558

:>:)0 * 583 SIN

534 AS TO X 5592
J3» * 5 84 *

535 X=Y? 56 ° > 585

536 GTO 25 561 RTN 5 86

537 AOFF 562 LBL 20 58?

538 STO 09 563 RCL 31 588 SIN

539 LBL 18 564 SIIJ 589 *

540 RCL 32 565 RCL ° 4 59 ° *

541 2 566 COS 591 RCL 33

542 / 567 * 592 *

543 TAN 568 RCL 18 593 2

544 2 369 SIN 594 '

545 * 570 RCL 17 595 RTN

546 RCL 32 571 COS 596 LBL 25

547 D-R 572 * 597 XEQ 28

548 / 573 + 598 GTO 09

549 STO 33 574 RCL 33 599 LBL 28

550 RTN S7S

5/:> * 600 "N"

53
 Table 2. Hand-held-calculator program listing Continued

601 ASTO Y 626 "STAT. 1 D?" 651

602 "STA 2 NOW 1 ? 627 PROMPT 652 STO 25

603 PROMPT 628 STO 16 653 "STAT. 2 A?"

604 ASTO X 629 "STAT. 1 A?" 654 PROMPT

605 AOFF 630 PROMPT 655 HR

6 06 X=Y? 631 HR 656 STO 23

6 07 GTO 0 8 632 STO 17 65 7 RCL 17

6-33 "STAT. 1 I?" 65 8 -

6 08 XEQ 2 6

6 09 RTN 634 PROMPT 65 9 STO 26

6 10 LBL 26 635 HR 660 "STAT. 2 I?"

6 11 RCL 22 636 STO 18 66 1 PROMPT

6 12 STO 1 6 637 "VERT. DEP 1?" 66 2 HR

6 13 RCL 23 638 PROMPT 663 STO 24

6 14 STO 1 7 639 STO 1 9 66 4 RCL 28

6 15 RCL 24 640 "DEPART. TO 1?" 66 5 -

6 16 STO 1 8 641 PROMPT 666 STO 27

6 17 RCL 3 4 642 STO 20 66 7 RTN

6 18 ST+ 1 9 643 "LAT. TO 1?" 66 8 LBL 07

6 19 RCL 3 5 644 PROMPT 66 9 RCL 22

6 20 ST+ 2 1 645 STO 21 67 0 RCL 08

6 21 RCL 36 646 LBL 27 67 1 X>Y?

6 22 ST+ 20 647 "STAT. 2 D?" 67 2 XEQ 12

6 23 XEQ 2 7 648 PROMPT 67 3 RCL 16

6 24 RTN 649 STO 22 67 4 RCL 08

6 25 LBL 0 5 650 RCL 16 67 5 X< = Y?

54
 Table 2. Hand-held-calgulator program Us ting--Continued

676 XEQ 12 701 RCL 25 726 RCL 26

677 RTN 702 * 727 D-R

678 LBL 95 703 STO 35 728 *

679 SF 13 704 XEQ 83 929 R-D

680 XEQ 93 705 RCL 25 730 RCL 17

681 GTO 60 706 * 731 +

682 LBL "RCUR" 707 STO 35 732 STO 04

683 XEQ 01 708 RCL 08 733 XEQ 80

684 LBL 10 709 RCL 16 734 RCL 08

685 XEQ 05 710 - 735 RCL 16

686 LBL 11 711 RCL 25 736 -

687 ADV 712 / 737 STO 33

688 XEQ 04 713 STO 33 738 *

689 XEQ 07 714 RCL 27 739 RCL 19

690 FS?C 20 715 D-R 740 +

691 GTO 10 716 * 741 STO 28

692 RCL 24 717 R-D 742 XEQ 81

693 STO 31 718 RCL 18 743 RCL 33

694 RCL 23 719 + 744 *

695 STO 04 720 STO 31 745 RCL 20

696 XEQ 80 721 CHS 746 +

697 RCL 25 722 90 747 STO 29

698 * 723 + 748 XEQ 8l

699 STO 34 724 STO 05 749 RCL 33

700 XEQ 81 725 RCL 33 750 *

55
 Table 2. Hand-held-calculator program lasting Continued

7 51 RCL 21 776 SIN 801 -

7 52 f 777 802 D-R

7 53 STO 30 778 RCL 31 803 /

7 54 FS?C 11 7 79 RCL 18 804 RCL 04

755 GTO 97 7 80 - 805 RCL 17

7 56 RCL 02 7 81 D-R 806 -

7 57 ST- 04 7 82 / 807 D-R

758 FS? 17 7 83 RTN 808 /

759 XEQ D 7 84 LBL 81 809 RTN

7 60 XEQ "R" 7 85 XEQ 82 810 LBL 83

761 LBL 98 7 86 RCL 17 811 XEQ 82

762 "N" 7 87 COS 812 RCL 04

7 63 ASTO Y 7 88 RCL 04 813 SIN

764 AON 7 89 COS 814 RCL 17

765 "SAME STAT.?" 7 90 - 815 SIN

7 66 PROMPT 7 91 * 816 -

7 67 ASTO X 7 92 RTN 817 *

768 X=Y? 7 93 LBL 82 818 RTN

769 GTO 85 7 94 RCL 18 819 LBL 86

820 "N"
770 AOFF 7 95 COS

771 GTO 11 7 96 RCL 31 821 ASTO Y

772 LBL 80 797 COS 822 "STA 2 NOW 1?"

7 73 RCL 31 798 - 823 PROMPT

774 SIN 799 RCL 31 824 ASTO X

775 RCL 18 800 RCL 18 825 AOFF

56
 Table 2. Hand-held-calculator program listing Continued

826 X=Y? 851 RCL 31 876 RCL 38

827 GTO 10 852 X=0? 877 X?2

828 XEQ 26 853 RTN 878 CHS

829 RTN 854 XEQ B 879 1.0

830 LBL 85 855 RCL 37 880 +

831 XEQ 86 856 COS 881 SQRT

832 GTO 11 857 RCL 04 882 X=0?

833 LBL 97 858 COS 883 GTO 77

334 SF 14 859 RCL 05 884 STO 39

835 XEQ 93 860 COS 885 RCL 37

836 GTO 60 861 * 886 COS

837 LBL B 862 * 887 RCL 05

838 SF 24 863 RCL ° 5 888 COS

839 RCL 04 864 SIN 889 RCL 04

840 COS 865 RCL 37 890 COS

841 xt2 866 SIN 891 *

842 RCL 05 867 * 892 RCL 38

843 TAN 868 + S93 *

844 xt2 869 STO 38 S94 -

845 + 870 1.000000000 895 RCL 05

846 SQRT 871 X<=Y? S96 TAN

847 STO 12 872 STO 38 897 *

848 CF 24 873 CHS 898 RCL 37

849 RTN 874 X>Y? 899 SIN

850 LBL D 875 STO 38 900 RCL 05

57
 Table 2. Hand-he Id-calculator program listing Continued

901 SIN 926 RCL 40

902 RCL 38 927 -

038 * 928 STO 11

904 - 929 LBL 72

905 RCL 04 930 360.000000

906 COS 931 X>Y?

907 * 932 GTO 75

908 - 933 -

909 RCL 12 934 STO 11

910 / 935 GTO 73

911 RCL 39 936 LBL 75

912 / 937 0

913 ACOS 938 RCL 11

914 STO 40 939 X<Y?

915 180.00000 940 360

916 RCL 04 941 +

917 X<=Y? 942 STO 11

918 GTO 71 943 LBL 73

919 RCL 11 944 RTN

920 RCL 40 945 LBL 77

921 + 946 "FUNNY Q=0"

922 STO 11 947 AVIEW

923 GTO 72 948 STOP

924 LBL 71 949 .END.

925 RCL 11

58
 Table 3. Fortran program listing Single-fracture version

C ************* FORMAT STATEMENTS *********************************

400 FORMAT (/,1X,' MAGNETIC DECLINATION?'»/,5X»'DEGREES
* (NEGATIVE FOR WEST)? ',*)
425 FORMAT (5X»'MINUTES! '»*>
450 FORMAT (5Xr'SECONDSJ ',*)
500 FORMAT (/»1X,' MAGNETIC INCLINATION?'»/,5X,'DEGREES: '*>
600 FORMAT (F)
2300 FORMAT (/,1X>' HOLE DIAMETER? '»*>
2380 FORMAT (/,2X,'HOLE AZIMUTH?'>/,5X,'DEGREESJ 'f*>
2382 FORMAT (/,2X,'HOLE INCLINATION?',/,5X,'DEGREES: ',*>
2384 FORMAT (/,2X,'MEASURED DEPTH TO FRACTURE TOP?'f/»lX»
* ' (IN SAME UNITS AS DIAMETER): ',*>
2386 FORMAT (/,2X,'MEASURED DEPTH TO FRACTURE BOTTOM? 'f$>
2388 FORMAT (/,2X,'DOWN DIP AZIMUTH OF FRACTURE?'»/»
* 5Xf'DEGREES: '»$>
2389 FORMAT (1X,/,/,IX,'WITHOUT VERTICAL INCLINATION CORRECTION:')
2390 FORMAT (1X,/,/,IXf'WITH VERTICAL INCLINATION CORRECTION:')
2391 FORMAT (2X,'TOP',7X,'BOTTOM',4X,'STRIKE'»4X>'DIP',7X»
$ 'DOWN DIP AZIMUTH'»/>
PI=3,14159265
C ******************* INPUT OF DATA *****************************
TYPE 400
ACCEPT 600, DECD
TYPE 425
ACCEPT 600 f DECM
TYPE 450
ACCEPT 600» DECS
DEC=(PI/180,>*(DECD+DECM/60.+DECS/3600,>
TYPE 500
ACCEPT 600» RINCD
TYPE 425
ACCEPT 600»RINCM
TYPE 450
ACCEPT 600» RINCS
RINC=(PI/180. )*(RINCD-fRINCM/60.+RINCS/3600.)
TYPE 2300
ACCEPT 600, DIA
TYPE 2380
ACCEPT 600rWHAZD
TYPE 425
ACCEPT 600fWHAZM
TYPE 450
ACCEPT 600»WHAZS
HELP=(PI/180.)*(WHAZD+(WHAZM/60.) + <WHAZS/3600.))
HZI=HELP
TYPE 2382
ACCEPT 600rWHICH
TYPE 425
ACCEPT 600, WHICM
TYPE 450
ACCEPT 600T WHICS
HINC=(WHICD-KWHICM/60.)+(WHICS/3600.))*(PI/180.)
TYPE 2384
ACCEPT 600, RMDEPT
TYPE 2386
ACCEPT 600, RMDEPB
TYPE 2388
ACCEPT 600,WDDAZD
TYPE 425
ACCEPT 600,WDDAZM
TYPE 450
ACCEPT 600,WDDAZS
DIPDIR=(WDDAZD-KWDDAZM/60.)+(WDDAZS/3600.))*(PI/180.)

59
 Table 3. Fortran program Us ting--Single-fracture version Continued

2900 RMDEP-(RMDEPT4RMDEPB>/2.0
1-1
TYPE 2389
TYPE 2391
CALL ROTATE (HELPtHINC»DEC»RINGfRMDEPtRHDEPT*RHDEPB»
* DIPDIRrDIArl)
1=2
TYPE 2390
TYPE 2391
CALL ROTATE (HZI»HINC»DECfRINCrRMDEP»RMDEPT,RMDEPB»
* DIPDIR»DIA»I)
STOP
END
C *************************************************************************
SUBROUTINE ROTATE (AZI, CLINAr DECLINf VERTC» DEPTHM»
$ DEPMT» DEPMB* DDIPAZF DIAMET» IJUDGE)
C ************************ FORMAT STATEMENTS **************************
4300 FORMAT (2X»'ERROR DETECTED IN INPUT')
4500 FORMAT (2X»F7.2»3X»F7.2»5X»'HORIZONTAL FRACTURE')
4550 FORMAT (2X»F7.2r3X»F7.2»5X»F4.0»6X»'VERTICAL FRACTURE')
4600 FORMAT (2X»'QMAG=0.0 - YOU ARE VERY FUNNY!')
4620 FORMAT (2X,F7.2,3X,F7.2,5X,F4.0»6X,F3.0r7X»F4.0>
C ******************** INITIALIZATION OF CONSTANTS ***************
DOUBLE PRECISION DIRECT* SDIP
PI=3«1459265
IF (CLINA «LT. .0087266) GO TO 5925
HDIP=PI/2.0-CLINA
AZI=AZI-DECLIN
IF (AZI .LT. 0.0000) AZI=AZI-f2.0*PI
IF (AZI .GT. 2.0*PI) AZI=AZI-2.0*PI
DELDEP=DEPMB-DEPMT
IF (DELDEP .EQ. 0.0000) DDIPAZ=AZI-PI
IF (DDIPAZ .LT. 0.0000) DDIPAZ=DDIPAZ42.0*PI
B=SQRT((TAN(HDIP»*(TAN(HDIP)) + (COS(AZI))*<COS(AZI»)
IF (IJUDGE .EQ. 1) GO TO 5300
C ********** CORRECTION FOR VERTICAL COMPONENT - TO LABLE 5300 ******
AMP=COS(VERTC)*COS(AZI)*COS(HDIP)+SIN(VERTC)*SIN(HDIP>
IF (AMP .EQ. 0.00000) GO TO 5000
IF (AMP .GT. 1.0000000000) AMP=1.00000000
QMAG=SQRT(1.000000000-(AMP*AMP))
IF (QMAG .EQ. 0.00000) GO TO 5100
4700 TEMP=((((COS(VERTC >-AMP*COS(AZI)*COS(HDIP)>
* *TAN(HDIP)>-((SIN(VERTC)-AMP*SIN(HDIP))
* *COS(AZI)))/(B*QMAG)>
IF (TEMP .GT. 1.000000000) GO TO 4800
IF (TEMP .LT. -1.0000000000) GO TO 4900
THETA=ACOS(TEMP)
GO TO 5200
4800 THETA=0.0000000000
GO TO 5200
4900 THETA=PI
GO TO 5200
5000 OMAG=1.OOOOOOOOO
GO TO 4700
5100 TYPE 4600
GO TO 6100
5200 IF (AZI .GE. PI) TDIPAZ=DDIPAZ4THETA
IF (AZI .LT. PI) TDIPAZ=DDIPAZ-THETA
DDIPAZ=TDIPAZ
IF (DDIPAZ .LT. 0.0000) DDIPAZ=DDIPAZ+2.0*PI
IF (DDIPAZ .GT. 2.0*PI) DDIPAZ=DDIPAZ-2.0*PI
5300 FSTRIK=DDIPAZ-PI/2.0
60
 Table 3. Fortran program listing Single-fracture version Continued

C ********************* CHECK OF FRACTURE STRIKE ****************

IF (FSTRIK .LT. 0.0000) FSTRIK=PI*2.0+FSTRIK
IF (FSTRIK GT. PI*2.0> GO TO 5400
IF (FSTRIK LT 0.0000) GO TO 5400
GO TO 5500
5400 TYPE 4300
GO TO 6100
C * GEOMETRICAL ROTATION OF FRACTURE PLANE TO SURFACE COORDINATE SYSTEM
5500 IF (DELDEP .LT. 0.0000) GO TO 5600
GO TO 5700
5600 TYPE 4300
GO TO 6100
5700 FDIP=ATAN2(DELDEP»DIAMET>
ALFAF=((-SIN(FDIP)/B)*(SIN(FSTRIK>*TAN(HDIP>+
f COS(FSTRIK)*SIN(AZI)*COS(AZI)*COS(HDIP)))-
$ (COS(FDIP>*COS(AZI)*COS<HDIP))
BETAF=(B*SIN(FDIP>*COS<FSTRIK)*COS(HDIP))-
$ (COS(FDIP)*SIN<AZI)*COS(HDIP>)
GAMMAF=«SIN<FDIP)/B)*(SIN<FSTRIK>*COS(AZI>-
$ COS(FSTRIK)*SIN(AZI)*SIN(HDIP»)-(CGS(FDIP)*SIN(HDIP»
IF (GAMMAF .LT. 0.0000) GO TO 5800
GAMMAF=-GAMMAF
BETAF=-BETAF
ALFAF=-ALFAF
5800 DIP=180.-((ACOS(GAMMAF))*180./PI>
IF (DIP .LT. .5) GO TO 6000
DIPAZ=(ATAN2(BETAFrALFAF»*180./PI
DIPAZ=DIPAZ+(DECLIN*180./PI>
C ************** DETERMINATION OF DOWN DIP DIRECTION ***********
5900 IF (DIPAZ .LT. 0.00) DIPAZ=360.+DIPAZ
IF (DIPAZ .GT. 360.00) DIPAZ=DIPAZ-360.
IF (DIPAZ .GT. 360.00 .OR. DIPAZ .LT. 0.00) GO TO 5400
5915 STRIKE=DIPAZ-90.00
IF (STRIKE .LT. 0.00) STRIKE=STRIKE+360.
IF (STRIKE .GT. 180.00) STRIKE=STRIKE-180.
IF (DIP .GT. 89.5) GO TO 5950
C ******************** OUTPUT OF RESULTS ***********************
TYPE 4620 j DEPMTr DEPMBr STRIKE» DlPr DIPAZ
GO TO 6100
5925 DIP=(ATAN2(DELDEP»DIAMET))*180./PI
DIPAZ=DDIPAZ*180./PI
GO TO 5915
5950 TYPE 4550f DEPMTr DEPMB» STRIKE
GO TO 6100
6000 TYPE 4500r DEPMT* DEPMB
6100 RETURN
END

61
 Table 4. Fortran program listing--Single-well version

C THIS PROGRAM CALCULATES THE TRUE ORIENTATION OF PLANAR STRUCTURES

C INTERSECTED BY THE BOREHOLE AS VIEWED WITH THE ACOUSTIC TELEVIEWER.
C
C **:m******************* DIRECTIONS *******************************
C DATA INPUT FILE:
C CREATE A FILE CALLED INDAT.DAT? THE FIRST LINE SHOULD CONTAIN
C THE TRUE DEPTH* TRUE DEPARTURE AND TRUE LATITUDE (IN THAT ORDER)
C FOR THE FIRST SURVEY STATION. THESE VALUES WILL BE READ WITH
C FORMAT STATEMENT 2000. THE NEXT LINE WILL BE READ WITH FORMAT
C STATEMENT 2100. THIS LINE CONTAINS THE MEASURED DEPTH* AZIMUTH
C AND INCLINATION OF THE FIRST STATION. THE PROGRAM AS WRITTEN
C WILL ACCEPT UP TO 100 STAIONS IF A LARGER NUMBER
C IS REQUIRED INCREASE THE DIMENSIONED SIZE OF ALL THE ARRAYS.
C TO TERMINATE STATION DATA INSERT -1.0 FOR THE FIRST VALUE OF
C THE LAST LINE. AFTER THE STATION DATA COMES THE FRACTURE DATA?
C IT IS READ WITH STATEMENT 2200. AS MANY LINES AS DESIRED MAY BE
C ENTERED. EACH LINE MUST HAVE THE FIRST TWO VALUES! MEASURED DEPTH
C TO FRACTURE TOP AND BOTTOM? BUT IF THESE VALUES ARE THE SAME,
C ENTRY OF THE THIRD VALUE (DOWN DIP AZIMUTH) MAY BE OMITTED.
C THE FOURTH VALUE IS AN OPTIONAL DIAMETER TO BE USED FOR THE
C IMMEDIATE FRACTURE AND ALL THAT FOLLOW UNTIL THE VALUE IS AGAIN
C CHANGED BY ENTRY OF SOME OTHER NON-ZERO NUMBER IN THE FOURTH
C SPOT. THE DIAMETER SHOULD BE ENTERED IN THE SAME UNITS AS THE
C DEPTH MEASUREMENTS. FOR EXAMPLE IF THE HOLE IS 3 INCHES IN
C DIAMETER BUT THE DEPTHS ARE IN FEET THEN THE DIAMETER SHOULD
C BE CHANGED TO 0.25 FEET. FRACTURE DATA IS TERMINATED IN THE SAME
C MANNER AS THE STATION DATA, WITH A -1 ON THE LAST LINE.
c NOTE: FRACTURE DATA SHOULD BE ENTERED NUMERICALLY
C WITH INCREASING DEPTH FOR RUNNING EFFICIENCY?
C HOWEVER IT IS NOT A NECESSITY, ANY FRACTURE
C OUTSIDE OF THE RANGE OF THE STATION DATA WILL
C BE IGNORED.
C
C DATA INPUT FROM TERMINAL:
C 1. HOLE SURVEY METHOD - THREE METHODS ARE AVAILABLE:
C RADIUS OF CURVATURE (1)
C MINIMUM CURVATURE (2) AND
C TANGENTIAL (3)
C FOR TANGENTIAL ENTER TWO SURVEY STATIONS ONE AT THE TOP DEPTH
C AND ONE AT THE BOTTOM DEPTH OF THE HOLE. BOTH WITH IDENTIAL
C AZIMUTH AND INCLINATION.
C 2. THE HOLE NAME MAY BE ANY 32 CHARACTER ALPHANUMBERIC STRING.
C 3. MAGNETIC DECLINATION - ENTER THE DESIRED PARAMETER INCLUDING
C THE DECIMAL POINT.
C 4. IF YOU WISH TO INCLUED THE EFFECTS OF THE VERTICAL COMPONENT
C OF THE MAGNETIC FIELD ENTER 1 FOR YES OR 2 FOR NO.
C 5. MAGNETIC INCLINATION - ENTER THE DESIRED PARAMETER INCLUDING
C THE DECIMAL POINT. NOTE THIS QUESTION WILL NOT BE ASKED IF
C THE RESPONCE TO QUESTION 4 IS NEGATIVE.
C 6. COUNT THE LINES PER PAGE THAT YOUR PRINTER IS SET AT OR GUESS
C (THE QUICK METHOD) AND ENTER A TWO DIGIT INTERGER NUMBER.
C 7. HOLE DIAMETER - ENTER IN CONSISTANT UNITS AS EXPLAINED ABOVE.
C MAY BE SET TO ANY INITIAL VALUE.
C
c DATA OUTPUT:
C THE RESULTS ARE WRITTEN TO THE FILE OUTDAT.DAT.
C
C
C **************** FORMAT STATEMENTS ******************:M************
100 FORMAT (X,lXr' HOLE SURVEY METHOD?',/,5X»'ENTER 1 FOR RADIUS
% OF CURVATURE»',/,!IX,'2 FOR MINIMUM CURVATURE OR ',/,llX,
* '3 FOR TANGENTIAL: ',*>
200 FORMAT (/rlX,' HOLE NAME? ',*>
62
 Table 4. Fortran program listing Single-well version Continued

300 FORMAT (4A8)

400 FORMAT (/,lXt' MAGNETIC DECLINATION?' >/f5X» 'DEGREES
1 (NEGATIVE FOR WEST): ',*>
425 FORMAT (5X, 'MINUTES! ',$>
450 FORMAT (5Xt 'SECONDS! '»$)
500 FORMAT (/,1X,' MAGNETIC INCLINATION?' ,/»5X» 'DEGREES: '$>
600 FORMAT (F)
800 FORMAT (/rlXr' HOW MANY LINES PER PAGE (ENTER INTEGER)? *>
900 FORMAT (12)
1000 FORMAT (/,1X»' DO YOU WISH TO INCLUDE THETA?
1 (ENTER 1 FOR YES OR 2 FOR NO) ',$>
1100 FORMAT (ID
1251 FORMAT <2X,'HOLE NAME! ' ,2X,4A8,2X, ' -TANGENTIAL' ' »2X»
'MAG* DEC* = 'f2X»3(lX»F3.0),2X» 'MAGNETIC EFFECT EXCLUDED', 2X
1252 FORMAT (4X, 7 HOLE NAME! ',2X,4A8,2X, "TANGENTIAL'',2X,'MAG* 'i
'DEC* = ',2X,3(1X,F3.0),2X,'MAG. INC. * ',2X,3(1X,F3.0) * 3X,
'PG ',15)
1253 FORMATC HOLE NAME! ' ,2X,4A8,2X, "MINIMUM CURVATURE" ,2X,'MA'
'G. DEC* = ',2Xf3(lX,F3.0),2X,'MAGNETIC EFFECT EXCLUDED',
2X,'PG ',15)
1254 FORMAT (' HOLE NAME! ', IX, 4A8,2X» "MINIMUM CURVATURE" ,2X,
'MAG. DEC. » ',1X,3(1X,F3.0),2X,'MAG. INC. = ',IX,3(1X,F3.0) t
2X»'PG ',15)
1255 FORMAT (2X,'HOLE NAME: ', 1X»4A8, IX, "RADIUS OF CURVATURE",
2X,'MAG. DEC. = ',IX,3(IX,F3.0),IX,'MAGNETIC EFFECT EXCLUDED')
2X,'PG ',15)
1256 FORMAT (' HOLE NAME! ', IX,4A8, IX, "RADIUS OF CURVATURE" , IX,
'MAG. DEC. = ',1X»3(1X,F3.0),2X,'MAG. INC. = ',1X,
3(1X,F3.0)»2X,'PG ',15)
1300 FORMAT (1X,131('*'))
1400 FORMAT (IX)
1450 FORMAT ('!')
1500 FORMAT (1X,'*',42X, / *',42X,'*',14X,'*',28X,'* / )
1600 FORMAT (1X, / *',42X,'*',42X,'*',43X,'* / )
1700 FORMAT (1X,'*'»8X,'MEASURED DEPTH TO FRACTURE',
8X,'*',6X,'COORDINATES OF FRACTURE CENTER',6X,
'*',7X,'TRUE ORIENTATION OF FRACTURE',8X,'*')
1800 FORMAT <IX,'*',42X,'*',5X,'TRUE',7X,'DEPARTURE',
6X»'LATITUDE',3Xi'*',4X,'STRIKE',4X,'*',5X,'DIP',
8X,'DOWN DIP ',3X,'*')
1900 FORMAT (IX,'*',4X,'CENTER',9X,'TOP',10X,'BOTTOM',
4X,'*',4X,'DEPTH',7X,' » FOR EAST',3X,'-I- FOR NORTH',
2X,'*',2X,'IN DEGREES',2X,'*',2X,'IN DEGREES',4X,
'DIRECTION',3X,'*')
2000 FORMAT (3F)
2100 FORMAT <7F)
2200 FORMAT <6F)
2300 FORMAT (/?iX,' HOLE DIAMETER? (ENTER 0. IF VARIABLE) ',$)
2310 FORMAT
DIMENSION STATEMENTS ***************************
DIMENSION ASD(IOO), ASA(IOO), ASI(IOO)
DIMENSION ASDEPT(IOO), ASPART(IOO), ASLAT(IOO)
C ****************** INITIALIZATION OF CONSTANTS ***********************
DOUBLE PRECISION ADDR1, ADDR2, ADDR3, ADDR4
INTEGER PAGE, ACOUNT
PI=3.14159265
ICOUNT=1
ACOUNT=1
PAGE=1
ITEST=0
C ***************** TERMINAL DATA ENTRY *******************************
2350 TYPE 100
63
 Table 4. Fortran program listing Single-well version Continued

ACCEPT llOOr MEANS

TYPE 200
ACCEPT 300F ADDRlr ADDR2* ADDR3* ADDR4
TYPE 400
ACCEPT 600» DECD
TYPE 425
ACCEPT 600 r DECH
TYPE 450
ACCEPT 600 f DECS
DEC=(PI/180.>*(DECD+DECM/60.+DECS/3600.)
TYPE 1000
ACCEPT 1100» METHOD
IF (METHOD .EQ. 2) RINC=0.0
IF (METHOD .EQ. 2> GO TO 2375
TYPE 500
ACCEPT 600i RINCD
TYPE 425
ACCEPT 600,RINCM
TYPE 450
ACCEPT 600» RINCS
RINC=(PI/180.>*(RINCD+RINCM/60.+RINCS/3600.)
2375 TYPE 800
ACCEPT 900» J
TYPE 2300
ACCEPT 600r DIA
TYPE 2310
J=J-14
M=J
C ********** ENTRY OF STATION DATA AND OPENING OF OUTPUT FILE **********
C ******************* INDIRECT LOOP TO LABLE 1200 **********************
OPEN <UNIT=1 1 NAME='INDAT.DAT',TYPE= ' OLD'»ACCESS='SEQUENTIAL')
READ (1>2000> SDEPTlr SPARTlr SLAT1
READ (1,2100) SDlrZl,Z2fZ3,Z4,Z5,Z6
SA1=(PI/180.>*(ZH-Z2/60.+Z3/3600.)
SI1=(PI/180.>*(Z4+Z5/60.+Z6/3600.)
ASD(1)=SD1
ASA(1)=SA1
ASI(1)=SI1
ASDEPT<1)=SDEPT1
ASPART(1)=SPART1
ASLAT(1)=SLAT1
OPEN (UNIT=2rTYPE*'NEW , NAME*'OUTDAT.DAT')
WRITE (2»1400)
WRITE <2>1400>
IF (MEANS »EQ, 3 .AND* METHOD .EQ. 2) WRITE (2»1251>
$ ADDR1> ADDR2 rADDR3 > ADDR4 rDECD , DCCM f DECS rPAGE
IF (MEANS .EQ. 3 .AND. METHOD .EQ. 1) WRITE (2»1252)
$ ADDR1»ADDR2 > ADDR3 r ADDR4»DECD»DECM»DECS»RINCD»RINCM»RINCS»PAGE
IF (MEANS .EQ. 2 .AND. METHOD .EQ. 2) WRITE (2»1253)
$ ADDR1r ADDR2 , ADDR3 rADDR4 rDECDiDECM»DECS > PAGE
IF (MEANS .EQ. 2 .AND. METHOD .EQ. 1) WRITE (2»1254)
$ ADDR1f ADDR2 r ADDR31ADDR4 > DECD , DECMiDECS > RINCD r RINCM»RINCSr PAGE
IF (MEANS .EQ. 1 .AND. METHOD .EQ. 2) WRITE (2»1255) i
$ ADDR1r ADHR2 r ADDR3 > ADDR4 > DECD»DECM > DECS > PAGE
IF (MEANS .EQ. 1 .AND. METHOD .EQ. 1) WRITE (2rl256)
$ ADDRltADDR2rADDR3»ADDR4»DECD»DECM»DECS*RINCD»RINCM»RINCS»PAGE
WRITE (2>1400>
WRITE (2»1300)
WRITE (2»1600)
WRITE (2»1700)
WRITE (2»1600)
WRITE (2rl300>
64
 Table 4. Fortran program listing Single-well version Continued

WRITE (2»1500)
WRITE <2fl800)
WRITE <2fl900>
WRITE <2»1500)
WRITE (2»1300>
WRITE (2»1500>
2400 READ (If2100) SD2» 27f Z8» Z9i Z10» Zllf Z12
IF <SD2 .LT. 0.0000) GO TO 2800
ACOUNT * ACOUNT +1
SA2=(PI/180.>*<Z7+Z8/60.+Z9/3600.>
SI2~(PI/180. )*(Z10+Z11/60. +Z12/3600.)
C ********* CALCULATION OF TRUE COORDINATES OF STATIONS ****************
DELI=SI2-SI1
DELA-=SA2-SA1
DELD=SD2-SD1
IF (MEANS .EQ. 3) GO TO 2600
IF (MEANS .EQ. 1) GOTO 2500
IF (MEANS .NE. 2) STOP
DOG=ACOS(COS(DELI>-SIN(SIl>*SIN(SI2)*(1.OOOO-COS(DELA)»
DOG2=DOG/2.0
RF=(2.0/DOG > *TAN(DOG2)
CD=((SD2-SD1)*RF)/2.0
SDEPT1=SDEPT1+CD*(COS(SI1)+COS(SI2)>
SPARTl=SPARTl-t-CD*(SIN(SIl)*SIN(SAl)iSIN(SI2)*SIN(SA2»
SLATl=SLATliCD*(SIN(SIl)*COS(SAl)-l-SIN(SI2>*COS(SA2)>
GOTO 2700
2500 SDEPT1=SBEPT1+(DELD*(SIN(SI2)-SIN(SI1>>/DELI>
SLAT1=SLAT1-KDELD*(COS(SI1)-COS(SI2))*
$ (SIN(SA2)-SIN(SA1)))/(DELI*DELA)
SPART1=SPART1+(DELD*(COS(SI1)-COS(SI2))*
$ (COS(SA1)-COS(SA2)»/(DELI*DELA)
GO TO 2700
2600 SDEPT1«SDEPT1+(DELD*COS(SI1)>
SPARTl«SPARTli(DELD*SIN(SIl)*SIN(SAl»
SLAT1=SLAT1-KDELD*SIN(SI1>*SIN(SA1»
2700 ASD(ACOUNT)=SD2
ASA(ACOUNT)=SA2
ASI(ACOUNT)=SI2
ASDEPT(ACOUNT)=SDEPT1
ASPART(ACOUNT)=SPART1
ASLAT(ACOUNT > =SLAT1
SA1=SA2
SI1=SI2
SD1=SD2
GO TO 2400
C ****************** ENTRY OF FRACTURE DATA ****************************
C ************** INDIRECT LOOP TO LADLE 3800 ***************************
2800 READ (1»2200) RHDEPTt RMDEPB» DIP1» DIP2» DIP3» RDIA
IF (RMDEPT *LT. 0.0000) GOTO 4200
DIPDIR=(DIPH-DIP2/60. +DIP3/3600.)*PI/180.
IF (RDIA .EQ. 0.0000) RDIA=DIA
2900 RMDEP=(RMDEPTiRMDEPB)/2.0
SD1=ASD(ICOUNT)
SI1=ASI(ICOUNT)
SA1=ASA(ICOUNT)
SDEPTl=ASr«EPT<ICOUNT)
SPART1=ASPAF<T(ICOUNT)
SLAT1=ASLAT(ICOUNT)
ICOUNT=ICOUNT-H
SI2=ASI(ICOUNT)
SA2=ASA(ICOUNT)
SD2=ASD(ICOUNT)
ICOUNT«ICOUNT-1
65
 Table 4. Fortran program listing--Single-well version-- Continued

IF (RMDEP .LE. SD1 .OR. RMDEP .GT. SD2) GOTO 3800

DELD=SD2-SD1
) ******** CALCULATION OF FRACTURE COORDINATES AND ORIENTATION *********
IF (MEANS .EG. 3) 00 TO 3100
HAZI*«(RMDEP-SD1>/DELD)*(SA2-SAl))+SAl
HINC=« (RMDEP-SD1 >/DELD)*(SI2-SIl) >+SIl
DELI=HINC-SI1
DELA=HAZI-SA1
IF (RMDEP .EQ. SD1) GOTO 3200
IF (RMDEP .EQ, SD2> GO TO 3250
IF (MEANS .EQ. 1) GO TO 3000
IF (MEANS .NE. 2) STOP
FDOG=ACOS(COS(DELI>-SIN(SI1>*SIN(HINO*(1.0000-COS(DELA^)>
IF (FDOG .EQ. 0.0000000000000) GO TO 3200
FDOG2=FDOG/2.0
FRF=<2.0/FDOG>*TAN(FDOG2>
TDEPTH=SDEPT1-K ((RMDEP-SD1)/2.0)*(COS(SIl)fCOS(HINC)))*FRF
TDEPAR=SPART1 -K FRF*(RMDEP-SD1)/2.0)*
% (SIN(SI1>*SIN(SA1>+SIN(HINC>*SIN(HAZI»
TLATIT=SLAT1-KFRF*(RMDEP-SD1>/2.0>*
S (SIN(SI1>*COS(SA1)+SIN(HINC)*COS(HAZI>>
GO TO 3300
3000 TDEPAR=SPART1+((RMDEP-SD1>*(COS(SI1)-COS(HINC»*
* (COS(SA1)-COS(HAZI)»/(DELI*DELA>
TLATIT=SLAT1-M (RMDEP-SD1)*(COS(SI1)-COS(HINC)>*
$ (SIN(HAZI)-SIN(SA1)))/(DELI*DELA)
TDEPTH=SDEPT1 -K (RMDEP-SD1)*(SIN(HINC)-SIN(SI1»/DELI)
GO TO 3300
3100 HAZI=SA1
HINC=SI1
TDEPTH=(RMDEP-SD1)*COS(SI1)
THEPAR=(RMDEP-SD1>*SIN(SI1>*SIN(SA1>
TLATIT=(RMDEP-SD1)*SIN(SI1)*COS(SA1>
3101 FORMAT (3F)
GO TO 3300
3200 TLATIT=SLAT1
TDEPTH=SDEPT1
TDEPAR*SPART1
GO TO 3300
3250 ICOUNT=ICOUNT-H
TLATIT=ASLAT(ICOUNT)
TDEPTH=ASDEPT(ICOUNT)
TDEPAR=ASPART <ICOUNT)
ICOUNT=ICOUNT-H
3300 HIA=RDIA
C *********** INTERNAL LOOP TO REGULATE OUTPUT FORMAT ***************
1=1+1
IF (I .EQ. 5) GO TO 3400
GO TO 3700
3400 WRITE (2»1500)
1=0
M=M-5
IF (M .LT. 7) GO TO 3500
GO TO 3700
3500 WRITE (2»1300)
WRITE (2fl450)
PAGE=PAGE-H
WRITE <2»1400>
WRITE (2»1400)
IF (MEANS .EQ. 3 .AND. METHOD .EQ. 2) WRITE (2»1251)
ADDR1» ADDR2 » ADDR3»ADDR4,DECD» DECM»DECS » PAGE
IF (MEANS .EQ. 3 .AND. METHOD .EQ. 1) WRITE (2»1252>
ADDR1»ADDR2»ADDR3 f ADDR4 t DECD > DECM»DECS»RINCD»RINCM»RINCS»PAGE
66
 Table 4. Fortran program listing Single-well version Continued

IF (MEANS .EQ. 2 4AND. METHOD .EQ. 2) WRITE <2fl253>

* ADDR1r ADDR2»ADDR3 , ADDR4»DECD r DECM r DECS,PAGE
IF (MEANS .EQ. 2 .AND. METHOD .EQ. 1) WRITE (2.1254)
% ADDR1,ADHR2,ADDR3»ADDR4,DECD,DECM,DECS,RINCD,RINCMrRINCS»PAGE
IF (MEANS .EQ. 1 .AND. METHOD .EQ. 2) WRITE (2rl255)
ADDR1,ADDR2 * ADDR3 r ADDR4 , DECD»DECM r DECS ,PAGE
IF (MEANS .EQ. 1 .AND. METHOD .EQ. 1) WRITE (2,1256)
$ ADDR1,ADBR2,ADDR3,ADDR4,DECDrDECM,DECS»RINCD,RINCM,RINCSrPAGE
WRITE (2,1400)
WRITE (2,1400)
WRITE (2,1300)
WRITE (2,1600)
WRITE (2,1700)
WRITE (2,1600)
WRITE (2,1300)
WRITE (2,1500)
WRITE (2»1800)
WRITE (2,1900)
WRITE (2,1500)
WRITE (2,1300)
WRITE (2,1500)
M=U
C **CALLING OF SUBROUTINE ROTATE TO CALCULATE NEW PLANAR ORIENTATION **
3700 CALL ROTATE (HAZI, HINC, DEC, RINCr RMDEP» RMDEPTr RMDEPB»
% TDEPTH» TDEPARr TLATIT» DIPDIRr DIA? METHOD)
GO TO 2800
C ****** BRANCH LOOP FOR CONTROLLING FRACTURE DATA CALCULATIONS *****
3800 ICOUNT=ICOUNT-H
IF (ICOUNT .GE. ACOUNT ) GO TO 4000
3900 IF (ITEST .EQ. 2) GO TO 4100
GO TO 2900
4000 ITEST=ITEST-H
ICOUNT=1
GO TO 3900
4100 ITEST=0
GO TO 2900
C **************************** CLOSING OF FILES ***************************
4200 WRITE <2»1500)
WRITE (2rl300)
CLOSE (UNIT-2»DISP= / SAVE / )
CLOSE (UNIT=lfDISP= / SAVE / )
STOP
END
C *************************************************************************
SUBROUTINE ROTATE <AZI» CLINA» DECLIN» VERTC> DEPTHMt
% DEPMTr DEPMBr TCDEPr TCDPT» TCLAT» DDIPAZt DIAMET» IJUDGE)
C ************************ FORMAT STATEMENTS **************************
4300 FORMAT (IX, '*', 9X,'ERROR DETECTED IN INPUT',10X,
$ '*',42X, / * / ,14X, / *',28X,'* / )
4400 FORMAT (IX,'*',2X,F8.2,6X,F8.2,6X»F8.2,4X,'*',
$ 2X,F8.2»6X,F8.2,6X,F8.2»4X, / *',5X,F4.0,5X,'* / ,4X,
$ F4.0,MX,F4.0,5Xr'*')
4500 FORMAT (IX,'*',2X,F8.2,6X,F8.2,6X,F8.2,4X,
$ '*',2X»F8.2,6X,F8.2,6X»F8.2,4X,'*',4X,
$ 'HORIZONTAL FRACTURE NO STRIKE OR DIP',3X,'*')
4550 FORMAT (IX,'*' f 2X,F8.2,6X,F8.2,6X,F8.2,4X,
$ '*'»2X,F8.2,6X,F8,2,6X,F8.2»4X,'*',5X,F4.0,5X,
$ '*',6X,'VERTICAL FRACTURE',5Xr'*')
4600 FORMAT (IX,'*',2X,F8.2,6X,F8.2,6X,F8.2,4X,'*',2X,F8.2
$ ,6XrF8.2,6XrF8,2,4X, / * / t2X» / QMAG=0.0',3X,'*',5X,
$ 'YOUR VERY FUNNY!!', 6X,'*')
C ******************** INITIALIZATION OF CONSTANTS ***************
DOUBLE PRECISION DIRECT, SDIP
67
 Table 4. Fortran program listing Single-well version Continued

PI«3.1459265
IF (CLINA .LT. .0087266) GO TO 5925
HDIP«PI/2.0-CLINA
AZI-AZI-DECLIN
IF <AZI .LT. 0.0000) AZI=AZI+2.0*PI
IF <AZI .GT. 2.0*PI) AZI=AZI-2.0*PI
DELDEP=DEPMB-DEPMT
IF (DELDEP .EQ. 0.0000) DDIPAZ=AZI-PI
IF (DDIPAZ .LT* 0.0000) DDIPAZ=DDIPAZ+2.0*PI
B=SQRT((TAN(HIiIP))*(TAN(HDIPm(COS(AZI»*(COS(AZI>»
IF (IJUDGE .EQ. 2) GO TO 5300
C ********** CORRECTION FOR VERTICAL COMPONENT - TO LABLE 5300 ******
AMP=COS(VERTC)*COS(AZI)*COS(HDIP>+SIN(MERTC)*SIN(HDIP>
IF (AMP .EQ. 0.00000) GO TO 5000
IF (AMP .GT. 1.0000000000) AMP=I.00000000
QMAG=SGRT <1.000000000-(AMP*AMP))
IF (OMAG .EQ. 0.00000) GO TO 5100
4700 TEMP=((((COS(VERTC)-AMP*COS(AZI)*COS(HDIP)>
$ *TAN(HDIP))-((SIN(VERTC)-AMP*SIN(HDIP»
$ *COS(AZI)))/(B*QMAG))
IF (TEMP .GT. 1.000000000) GO TO 4800
IF (TEMP .LT. -1.0000000000) GO TO 4900
THETA=ACOS(TEMP)
GO TO 5200
4800 THETA«0.0000000000
GO TO 5200
4900 THETA=PI
GO TO 5200
5000 QMAG=1.000000000
GO TO 4700
5100 WRITE (2t4600> DEPTHMfDEPMT»DEPMB»TCDEP»TCDPT»TCLAT
GO TO 6100
5200 IF (AZI .GE. PI) TDIPAZ=DDIPAZ+THETA
IF (AZI .LT. PI) TDIPAZ=DDIPAZ-THETA
DDIPAZ=TDIPAZ
IF (DDIPAZ .LT. 0.0000) DDIPAZ=DDIPAZ+2.0*PI
IF (DDIPAZ .GT. 2.0*PI) DDIPAZ=DDIPAZ-2.0*PI
5300 FSTRIK=DDIPAZ-PI/2.0
C ********************* CHECK OF FRACTURE STRIKE ****************
IF (FSTRIK .LT. 0.0000) FSTRIK=PI*2.0+FSTRIK
IF (FSTRIK .GT PI*2.0) GO TO 5400
IF (FSTRIK .LT 0.0000) GO TO 5400
GO TO 5500
5400 WRITE <2»4300)
GO TO 6100
C * GEOMETRICAL ROTATION OF FRACTURE PLANE TO SURFACE COORDINATE SYSTEM
5500 IF (DELDEP .LT. 0.0000) GO TO 5600
GO TO 5700
5600 WRITE (2t4300)
GO TO 6100
5700 FDIP=ATAN2(DELDEP,DIAMET)
ALFAF=((-SIN(FDIP)/B)*(SIN(FSTRIK)*TAN(HDIP)4
$ COS(FSTRIK)*SIN(AZI )*COS< AZI )*COS(HDIP) > )-
$ (COS(FDIP>*COS(AZI)*COS(HDIP»
BETAF= (B*SIN(FDIP >*COS( FSTRIK )*COS(HDIP) )-
* (COS(FDIP)*SIN(AZI)*COS(HDIP))
GAMMAF= ((SIN<FDIP)/B )* (SIN (FSTRIK )*COS( AZI )-
f COS(FSTRIK)*SIN(AZI)*SIN(HDIP) ) )- < COSCFDIP )*SIN<HDIP) )
IF (GAMMAF .LT. 0.0000) GO TO 5800
GAMMAF=-GAMMAF

ALFAF=-ALFAF
5800 DIP=180.-«ACOS(GAMMAF)>*180./PI)

68
 Table 4. Fortran program listing Single-well version Continued

IF (DIP .LT* .5) GO TO 6000

DIPAZ= < ATAN2 < BETAF f ALFAF)> *180./PI
DIPAZ«DIPAZ+(DECLIN*180./PI>
C ************** DETERMINATION OF DOWN DIP DIRECTION ***********
5900 IF (DIPAZ .LT. 0.00) DIPAZ=360.+DIPAZ
IF <DIPAZ .GT. 360.00) DIPAZ=DIPAZ-360.
IF <DIPAZ .GT. 360.00 .OR. DIPAZ .LT. 0.00) GO TO 5400
5915 STRIKE=DIPAZ-90.00
IF (STRIKE .LT. 0.00) STRIKE=STRIKE+360.
IF (STRIKE .GT. 180.00) STRIKE=STRIKE-180.
IF (DIP .GT. 89.5) GO TO 5950
C ******************** OUTPUT OF RESULTS ***********************
WRITE (2*4400) DEPTHMr DEPMTr DEPMBr TCDEPr TCDPT r
* TCLAT* STRIKE, DIP» DIPAZ
GO TO 6100
5925 DIP=(ATAN2(DELDEP»DIAMET))*180./PI
DIPAZ=DDIPAZ*180./PI
GO TO 5915
5950 WRITE (2»4550) DEPTHM, DEPMTf DEPMBr TCDEPf
$ TCDPT» TCLAT» STRIKE
GO TO 6100
6000 WRITE (2»4500> DEPTHMr DEPMTr DEPMB»TCDEPf
* TCDPT» TCLAT
6100 RETURN
END

69
 Table 5. Fortran variables

1. ACOUNT - integer variable representing the station number.

2. ADDR - 10 alphanumeric character variable for the hole name,
3. ALFAF - a directional cosine of the fracture plane normal.
4. AMP - amplitude of the vector Q.
5. ASA - array variable storing station azimuths.
6. ASD - array variable storing station measured depths.
7. ASDEPT - array variable storing station true depths.
8. ASI - array variable storing station inclinations.
9. ASLAT - array variable storing station latitude.
10. ASPART - array variable storing station departure.
11. AZI - hole azimuth.
12. B - computational factor.
13. BETAF - a directional cosine of the fracture plane normal.
14. CD - calculation factor.
15. CLINA - hole inclination at center of fracture.
16. DDIPAZ - apparent down-dip azimuth of the fracture.
17. DEC - magnetic declination in radians.
18. DECD - degree portion of magnetic declination.
19. DECLIN - magnetic declination in radians.
20. DECM - minutes portion of the magnetic declination.
21. DECS - seconds portion of the magnetic declination.
22. DELA - delta azimuth = HAZI-SAl or = SA2-SA1.
23. DELD - delta depth = SD2-SD1 or RMDEP-SD1.
24. DELDEP - the difference in measured depth between fracture
top and bottom.
25. DELI - delta inclination = SI2-SI1.
26. DEPMB - measured depth to fracture bottom.
27. DEPMT - measured depth to fracture top.
28. DEPTHM - measured depth to fracture center.
29. DIA - diameter used for input into subroutine rotate = RDIA.
30. DIAMET - diameter at fracture center.
31. DIP - true dip azimuth of fracture.
32. DIP1 - degree portion of the down-dip azimuth.
33. DIP2 - minutes portion of the down-dip azimuth.
34. DIP3 - seconds portion of the down-dip azimuth.
35. DIPAZ - true down-dip azimuth of fracture.
36. DIPDIR - apparent down-dip azimuth of fracture - converted
to radians.
37. DIRECT - alphanumeric variable for dip direction.
38. DOG - dogleg angle between stations.
39. DOG2 - = DOG/2.0.
40. FDIP - apparent fracture dip.
41. FDOG - fracture dogleg angle from station 1 to fracture.
42. FDOG2 - = FDOG/2.0.
43. FRF - ratio factor to fracture.
44. FSTRIK - fracture strike.
45. GAMMAF - a directional cosine of the fracture plane normal.
46. HAZI - hole azimuth in radians at point of interest.
47. HDIP - hole dip.
48. HINC - hole inclination in radians at point of interest.
49. I - integer used for controlling page output.
50. ICOUNT - integer variable for representing station number.
70
 Table 5. Fortran variables

51. IJUDGE - alphanumeric character representing the inclusion

or exclusion of the vertical component.
52. INDEX - integer to control loop.
53. ITEST - integer for station cheek.
54. J - integer number of lines per page.
55. M - integer used for controlling page output.
56. MEANS - alphanumeric letter representing the hole survey
method to be used.
57. METHOD - alphanumeric letter representing the inclusion and
exclusion of theta.
58. PAGE - integer variable for page number of output.
59. PI - constant equal to 3.14159265.
60. QMAG - the magnitude of the vector R.
61. RDIA - hole diameter at fracture center.
62. RF - ratio factor between stations.
63. RING - magnetic inclination in radians.
64. RINCD - degree portion of the magnetic inclination.
65. RINCM - minutes portion of the magnetic inclination.
66. RINGS - seconds portion of the magnetic inclination.
67. RMDEP - measured depth to fracture center.
68. RMDEPB - measured depth to fracture bottom.
69. RMDEPT - measured depth to fracture top.
70. SA1 - hole azimuth at station 1 (in radians).
71. SA2 - hole azimuth at station 2 (in radians).
72. SDEPTI - true depth to station 1.
73. SDIP - alphanumeric variable for dip direction.
74. SDl - measured depth to station 1.
75. SD2 - measured depth to station 2.
76. SI1 - hole inclination at station 1 (in radians).
77. SI2 - hole inclination at station 2 (in radians).
78. SLATI - true latitude to station 1.
79. SPARTI - true departure to station 1.
80. STRIKE - true strike of the fracture.
81. TCDEP - true coordinates of fracture depth = TDEPTH.
82. TCDPT - true coordinates of fracture departure = TDEPAR.
83. TCLAT - true coordinates of fracture latitude = TLATIT.
84. TDEPTH - true vertical depth to fracture center.
85. TDEPAR - true departure depth to fracture center.
86. TDIPAZ - temporary variable.
87. TEMP - temporary calculation factor.
88. THETA - 9
89. TLATIT - true latitude to fracture center.
90. VERTC - magnetic inclination.
91. Zl - degree portion of the azimuth at station 1.
92. Z2 - minutes portion of the azimuth at station 1.
93. Z3 - seconds portion of the azimuth at station 1.
94. Z4 - degrees portion of the inclination at station 1.
95. Z5 - minutes portion of the inclination at station 1.
96. Z6 - seconds portion of the inclination at station 1.
97. Z7 - degree portion of the azimuth at station 2.
98. Z8 - minutes portion of the azimuth at station 2.
99. Z9 - seconds portion of the azimuth at station 2.
100. Z10 - degrees portion of the inclination at station 2.
101. Zll - minutes portion of the inclination at station 2.
102. Z12 - seconds portion of the inclination at station 2.
71
 Table 6. Theta values

MAGNETIC INCLINATION : 67°

Hole inclination, in degrees
HOLE
AZIMUTH 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
(degrees)
********** ***************!******>******* ******* ******]********* ************ **************** ******* ******* ******* ******* ******* ********
10. -3. -7. -17. -46. -112. -143. -154. -159. -163. -165. -167. -169. -170. -171, -172, -174. -175.
20. -5. -14. -30. -58. -95. -119. -133. -141. -147. -151, -154. -157. -160. -163. -165. -167. -170.
30. -7. -19. -36. -61. -85. -104. -117. -126. -132. -138. -142. -147. -151. -154. -158. -161. -165.
40. -9. -22. -40. -59. -78. -93. -104. -113. -120. -126. -131. -136. -141. -146. -151. -155. -160.
50. -11. -24. -40. -57. -71. -83. -93. -101. -108. -114. -120. -125. -131. -137. -143. -149. -156.
60. -11. -25. -39. -53. -65. -74. -83. -90, -96. -102. -107. -113. -120, -126. -134. -142. -151.
70. -12. -25. -37. -48. -58. -66. -73. -79. -84, -89. -94. -99. -105. -113. -121. -132. -144.
80. -12. -24. -35. -44. -51. -58. -63. -67. -71. -75. -79. -83. -87. -93. -100. -112. -131.
90. -12. -22. -31. -39. -45. -50. -53. -57. -59. -61. -63. -64. -65. -66. -66. -67. -67.
100. -11. -20. -28. -34. -38. -42. -44. -46. -47. -47. -47. -46. -43. -39. -33. -22. -4,
110. -10. -18. -24. -29. -32, 35 » -36. -37. -37. -36. -34. -31. -27. -21. -14. -4. -8.
120. -9. -16. -21. -24. -27. -28. -29. -28. -28. -26. -23. -20. -16. -11. -4. -3. -11.
130. -8. -13. -17. -20, -21. -22. -22. -22. -20. -18. -16. -13. 9. -5. 0. -6. -12.
140. -6. -11. -14. -15. -16. -17. -17. -16. -14. -13. 11. -8. -5. _I -2. -6. -11.
150. -5. -8. -10. -11. -12. -12. -12. -11. -10. -8. -7. -5. -2. 0. -3. -6. -9.
-7. -7. -8. -8. -7. 5. -4. -3. 1 -1. -2. -4. -6.
160. -3. -5. -7. -6.
-3. -4. 4 -4. -4. -2. -2. -1 . 0, 0. 1 -2. -3.
170. -2. -3. -3, -3.
180, 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. o. 0. 0. 0.
190. 2. 3. 3. 4. 4. 4. 4. 3. 3. 2. 2. 1. 0. 0. 1. 2. 3.
200. 3. 5. 7. 7. 8. 8. 7. 7. 6. 5. 4. 3. 1. 1. 2. 4. 6.
J^ 210. 5. 8. 10. 11. 12. 12. 12. 11. 10. 8. 7. 5. 2. 0. 3. 6. 9.
220. 6. 11. 14. 15. 16. 17. 17. 16. 14. 13. 11. 8. 5. 1. 2. 6. 11.
230. 8. 13. 17. 20. 21. 22. 22. 22. 20. 18. 16. 13. 9. 5. 0. 6. 12.
240, 9. 16. 21. 24. 27. 28. 29. 28. 28. 26. 23. 20. 16. 11. 4. 3. 11.
250. 10. 18. 24. 29. 32. 35. 36. 37, 37. 36. 34. 31. 27, 21. 14. 4. 8.
260, 11. 20. 28. 34. 38. 42. 44. 46. 47. 47. 47. 46. 43. 39. 33. 22, 4.
270. 12. 22. 31. 39. 45. 50. 53. 57. 59. 61. 63. 64. 65. 66. 66. 67. 67.
280. 12. 24. 35. 44. 51. 58. 63. 67, 71. 75. 79. 83. 87. 93. 1OO. 112. 131.
290. 12. 25. 37. 48. 58. 66. 73. 79. 84. 89. 94. 99. 105. 113. 121. 132. 144.
300. 11. 25. 39. 53. 65. 74. 83. 90. 96. 102. 107. 113. 120. 126. 134. 142. 151.
310. 11. 24. 4O. 57, 71. 83. 93. 101. 108. 114. 120. 125. 131. 137. 143. 149. 156.
320. 9. 22. 40. 59. 78. 93. 104. 113. 120. 126. 131. 136. 141. 146. 151. 155. 160.
330. 7. 19. 36. 61. 85. 104. 117. 126. 132. 138. 142. 147. 151. 154. 158. 161. 165.
340. 5. 14. 30. 58. 95. 119, 133. 141. 147. 151. 154. 157. 160. 163. 165. 167. 170.
350. 3. 7. 17. 46. 112. 143. 154. 159. 163. 165. 167. 169. 170. 171. 172. 174. 175.
360. 0. 0. 0. 0. 180. 180. 180. 180. 180. 180. 180. 180. 180. 180. 180. 180. 180.
 Table 7. Theta program listing

01 LBL "THETA" 41 X=0?

02 "VERTICAL COMP?" 42 GTO 01
03 PROMPT 43 RCL 01
04 STO 01 44 COS
05 "HOLE INC?" 45 RCL 02
06 PROMPT 46 COS
07 CHS 47 RCL 03
08 90.000000 48 COS
09 + 49 *
10 STO 02 50 RCL 04
11 "HOLE AZI?" 51 *
12 PROMPT 52 -
13 STO 03 53 RCL 02
14 COS 54 TAN
15 RCL 02 55 *
16 COS 56 RCL 04
17 * 57 RCL 02
18 RCL 01 58 SIN
19 COS 59 *
20 * 60 CHS
21 RCL 01 61 RCL 01
22 SIN 62 SIN
23 RCL 02 63 +
24 SIN 64 RCL 03
25 * 65 COS
26 + 66 *
27 STO 04 67 -
28 1.0000000 68 RCL 02
29 X<=Y? 69 TAN
30 STO 04 70 Xi2
31 CHS 71 RCL 03
32 X>Y? 72 COS
33 STO 04 73 X+2
34 RCL 04 74 +
35 Xt2 75 SQRT
36 CHS 76 /
37 1.000000000 77 RCL 05
38 + 78 /
39 SQRT 79 ACOS
40 STO 05 80 LBL 01
81 .END.

73

£ U.S. GOVERNMENT PRINTING OFFICE: 1984 778-200/9186 REGION NO. 8