PB84-212711.
Geophysical Methods for
Locating Abandoned Wells v
(U.S.) Geological Survey, Denver, CO
Prepared for
Environmental Monitoring Systems Lab
Las Vegas, NV
Jul 84
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EPA-600/4-84-065
July 1984
GEOPHYSICAL METHODS FOR LOCATING ABANDONED WELLS
by
F. C. Frischknecht, L. Muth, R. Grette, T. Buckley, and
B. Kornegay
U.S. Geological Survey
Denver, Colorado 80225
Project Officer
J. Jeffrey van Ee
Advanced Monitoring Systems Division
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89114
This study was conducted in cooperation with
U.S. Geological Survey
Interagency Agreement No. AO-14-F-2-A092
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89114
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TECHNICAL REPORT DATA
(Ptetue read Instructions on the reverse before completing)
\. REPORT NO.
EPA-600/4-84-065
3. RECIPIENT'S ACCESSION NO.
IT-
«. TITLE ANOSUBTITLE
Geophysical Methods for Locating Abandoned Wells
5. REPORT DATE
July 1984
6. PERFORMING ORGANIZATION CODE
7.AUTHORISI F-C. Frischknecht, L. Muth, R. Grette,
T. Buckley, 8. Kornegay,
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
1O. PROGRAM ELEMENT NO.
U.S. Geological Survey
Denver, CO 80225
C104
11. CONTRACT/GRANT NO.
IAG #AD-14-F-2-A092
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency—Las Vegas, NV
Office of Research & Development
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89114
13. TYPE OF REPORT AND PERIOD COVERED
Project Report
14. SPONSORING AGENCY CODE
EPA 600/07
15. SUPPLEMENTARY NOTES
16. ABSTRACT .
A "preliminary study of the feasibility of using geophysical exploration methods to
locate abandoned wells containing steel casing indicated that magnetic methods
promise to be effective and that some electrical '-.chniques might be useful as
auxiliary methods. Ground magnetic measurements .:ade in the vicinity of several
known cased wells yielded total field anomalies with peak values ranging from
about 1,500 to 6,000 gammas. The anomalies measured on the ground are very narrow
aad, considering noise due to other cultural and geologic sources, a line spacing
on the order of 50 feet (15.2m) would be necessary to locate all casings in the
test area.
7.
KEY WORDS AND DOCUMENT ANALYSIS
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RELEASE TO PUBLIC
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UNCLASSIFIED
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23%
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22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS COITION is OBSOLETE
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ATTENTION
'PORTIONS OF THIS REPORT ARE NOT LEGIBLE,
HOWEVER, IT IS THE BEST REPRODUCTION
AVAILABLE FROM THE COPY SENT TO NTIS.
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NOTICE
The information in this document has been funded wholly or in part by the
United States Environmental Protection Agency under interagency agreement number
AD-14-F-2-A092 to U.S. Geological Survey. It has been subject to the Agency's
peer and administrative review, and it has been approved for publication as an
EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
ii
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PREFACE
The U.S. Environmental Protection Agency's (EPA) Environmental Monitoring
Systems Laboratory in Las Vegas has provided the funding for the research
effort described in the report. The mathematical model described in this
report of a magnetic anomaly for a steel-cased well indicates that an airborne
magnetic survey can theoretically locate abandoned wells. The EPA has enlisted
the help of the National Center for Groundwater Research at the University of
Oklahoma to identify areas around Oklahoma City where high-resolution aerial
magnetic surveys may be flown. The Environmental Monitoring Systems Laboratory
in Las Vegas has funded the U.S. Geological Survey (USGS) to perform these
field studies in 1983, and the results will be presented in a later USGS/EPA
report in IS'84.
M^e'"cooperative effort between the EPA and the USGS is aimed at providing
local, state, and Federal agencies with the methodology to determine if aban-
doned wells"exist in an area where the underground injection of wastes is
contemplated. Magnetometer surveys will likely be jus*" one of several methods
that can be utilized in locating abandoned wells. The record searches con-
ducted by the National Center for Groundwater Research and the historical
photographic searches conducted by the EPA's Environmental Photographic Inter-
pretation Center may provide alternative approaches to the problem of locating
ab?,ndoned wells. An examination of the costs and benefits of the various
methods will be available from the EPA in 1984 after the USGS has completed the
field studies in Oklahoma.
iii
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ABSTRACT
A preliminary study of the feasibility of using geophysical exploration
methods to locate abandoned wells containing steel casing indicated that mag-
netic methods promise to be effective and that some electrical techniques might
be useful as auxiliary methods. Ground magnetic measurements made in the
vicinity of several known cased wall s yielded total field anomalies with peak
values ranging from about 1,500 to 6,000 gammas. The anomalies measured on the
ground are very narrow and, considering noisa due to other cultural and geo-
logic sources, a line spacing on the order of 50 feet (15.2 m) would be neces-
sary to locate all casings in the test area.
The mathematical model used to represent a casing was a set of magnetic
pole pairs. By use of a nonlinear least squares curve-fitting (inversion)
program, model parameters which characterize each test casing were determined.
The position and .strength of the uppermost pole was usually well resolved. The
parameters of lower poles were not as well resolved but it appears that the
results are adequate for predicting the anomalies which would be observed at
aircraft altitudes. Modeling based on the parameters determined from the
ground data indicates that all of the test casings could be detected by air-
borne measurements made at heights of 150 to 200 feet (45.7-61.0 m) above the
ground, provided lines spaced as closely as 330 feet (100 m) were used and
provided noise due to other cultural and geologic sources is not very large.
Given the noise levels of currently available equipment and assuming very low
magnetic gradients due to geologic sources, the detection range for total field
measurements is greater than that for measurements of the horizontal or ver-
tical gradient of the total intensity.
Electrical self-potential anomalies were found to be associated with most
of the casings where measurements were made. However, the anomalies tend to be
very narrow; and, in several cases, they are comparable in magnitude to other
small anomalies which are not directly associated with casings. Measurements
made with a terrain conductivity meter and slingram system were negative.
However, from other work it is known that electrical resistivity and induced
polarization measurements can be influenced significantly by the presence of
a casing.
It is concluded that detailed ground magnetic surveys would be effective
in locating casings within relatively small areas. It would be very costly to
cover large areas with ground surveys, but it appears that airborne surveys may
be a cost-effective means of locting wells when the search area is on the order
of a few square miles or more. Also, airborne methods could be used in some
areas where access to the area on the ground is difficult or impossible.
iv
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Th:s.report was submitted in partial fulfillment of interagercy agreement
AD-14-F-2-A092 by '. .5. Geological Survey under the partial sponsorship of the
U.S. Environmental Protection Agency. This report covers a period from April
1982 to April 1983, and work was completed as of April 1983.
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CONTENTS
Preface iii
Abstract 1v
Figures viii
Tables xv
1. Introduction 1
Study objectives 2
2. Magnetic Methods 3
*. •" Magnetic field of the earth 3
; " Magnetometers 3
--,* '- Survey techniques 3
3. Application of Magnetic Methods to Abandoned Well Problem ... 7
Magnetic parameters 7
Mathematical model 7
Field measurements 11
* Qualitative analysis of results 14
Inversion of field data 16
Modelling and design of airborne surveys 22
Recommendations for further study of magnetic methods. . . 25
4. Electrical Methods and Their Application 27
Summary of electrical methods 27
Field measurements 29
Recommendations for further study of electrical methods. . 30
5. Summary ..... 31
References - 33
Appendices
I. Brief Synopsis and Listing of the "Casing" 188
II. Time and Cost Estimates for Magnetic Surveys 209
vn
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FIGURES
Number Page
1 Well locations and aeromagnetic map for test area east
of Denver 35
2 Well locations and aeromagnetic map for test area north
of Denver 36
3 North-south profile of total field over Well Number 1 37
4 East-west profile of total field over Well Number 1 38
5 North-south profile of total field over Well Number 2 39
6 East-west profile of total field over Well Number 2 40
*..
7 North-south profile of total field over Well Number 3 41
8 East-west profile of total field over Well Number 3 42
9 North-south profile of total field over Well Number 4 43
10 East-west profile of total field over Well Number 4 44
11 North-south profile of total field over Well Number 5 45
12 East-west profile of total field over Well Number 5 46
13 North-south profile of total field over Well Number 6 47
14 East-west profile of total field over Well Number 6 48
15 North-south profile of total field over Well Number 7 49
16 East-west profile of total field over Wel'i Number 7 50
17 North-south profile of total field over Well Number 8 51
18 East-west profile of total field over Well Number 8 52
19 North-south profile of total field over Well Number 9 53
20 East-west profile of total field over Well Number 9 ; . 54
viii
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FIGURES (Continued)
Number Page
21 North-south profile of total field over Well f:.!".n-r 10 55
22 East-west profile of total field over Well Number iO 56
23 North-south profile of total field over Vcli Number 11 57
24 East-west profile of total field ovor Well Number 11 58
25 North-south profile of total field over Well Number 12 59
26 East-west profile of total field over Well Number 12 60
27 North-south profile of total field over Well Number 13 61
28 East-west profile of total field over Well Number 13 62
29 North-south profile of total field over Well Number 14 63
30 East-west profile of total field over Well Number 14 64
31 North-south profile of total field over Well Number 15 N . . 65
32 East-west profile of total field over Well Number 15 N. 66
33 North-south profile of total field over Well Number 15 S 67
34 East-west profile of total field over Well Number 15 S 68
35 North-south profile of total field over Well Number 16 69
36 East-west profile of total field over Well Number 16 70
37 North-south profile of total field over Well Number 17 71
38 East-west profile of total field over Well Number 17 72
39 North-south profile of horizontal differences 73
40 East-west profile of horizontal differences 74
41 North-south profile of vertical differences 75
42 East-west profile of horizontal differences 76
43 North-south profile of horizontal differences 77
44 East-west profile of horizontal differences 78
1x
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FIGURES (Continued)
Number ' Page
45 North-south profile of vertical differences 79
46 East-west profile of vertical differences 80
47 North-south profile of vertical component 81
48 East-west profile of vertical component 82
49 North-south profile of horizontal component 83
50 East-west profile of horizontal component 84
51 Observed and calculated results for Well Number I .... 85
52 Observed and calculated results for Well Number 1 86
53 Observed and calculated results for Well Number 2 87
*,
».. •
54 Observed and calculated results for Well Number 2 88
•"•"»*
55 Observed and calculated results for Uell Number 3 89
56 Observed and calculated results for Well Number 3 90
57 Observed and calculated results for Well Number 4 91
9
58 Observed and calculated results for Well Number 4 92
59 Observed and calculated results for Well Number 5 . . ... 93
60 Observed and calculated results tor Well Number 5 94
61 Observed and calculated results for Well Number 6 95
62 Observed and calculated results for Well Number 6 96
63 Observed and calculated results for Well Number 7 97
64 Observed and calculated results for Well Number 7 98
65 Observed and calculated results for Well Number 8 99
66 Observed and calculated results for Well Number 8 100
67 Observed and calculated results for Well Number 9 101
68 Observed and calculated results for Well Number 9 . 102
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FIGURES (Continued)
Number Page
69 Observed and calculated results for Well Number 10 103
70 Observed and calculated results for Well Number 10 104
71 Observed and calculated results for Well Number 11 105
72 Observed and calculated results for Well Number 11 106
73 Observed and calculated results for Well Number 12 107
74 Observed and calculated results for Well Number 12 108
75 Observed and calculated results for Well Number 13 109
76 Observed and calculated results for Well Number 13 110
77 Observed and calculated results for Well Number 14 Ill
78 Observed and calculated results for Well Number 14 112
79a Observed and calculated results for Well Number 15 S 113
79b Observed and calculated results for Well Number 15 N 114
80a Observed and calculated results for Well Number 15 S 115
80b Observed and calculated results for Well Number 15 N 116
81 Observed and calculated results for Well Number 16. . . 117
82 Observed and calculated results for Well Number 16 118
83 Observed and calculated results for Well Number 17 119
84 Observed and calculated results for Well Number 17 120
85 Observed and calculated results for Well Number 6 . . . . 121
86 Observed and calculated results for Well Number 6 122
87 Observed and calculated results for Well Number 6 123
88 Observed and calculated results for Well Number 6 124
89 Calculated airborne total field contour map of logjo (F-Fmin) .... 125
90 Calculated airborne total field contour map of log^o (F-Fmin) .... 126
xi
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FIGURES (Continued)
Number Page
91 Calculated airborne total field contour map of logjo (F-Fmi-n) .... 127
92 Calculated airborne total field profile at 100 ft for Well Number 4 . 128
93 Calculated airborne total field profile at 100 ft for Well Number 4 . 129
94 Calculated airborne total field profile at 150 ft for Well Number 4 . 130
95 Calculated airborne total field profile at 150 ft for Well Number 4 . 131
96 Calculated airborne total field profile at 200 ft for Hell Number 4 . 132
97 Calculated airborne total field profile at 200 'ft for Well Number 4 . 133
98 Calculated airborne total field profile at 250 ft for Well Number 4 . 134
99* Calculated airborne total field profile at 250 ft for Well Number 4 . 135
IBS- Calculated airborne total field profile at 100 ft for Well Number 5 . 136
101 Calculated airborne total field profile at 150 ft for Well Number 5 . 137
102 Calculated airborne total field profile at 200 ft for Well Number 5 . 138
103 Calculated airborne total field profile at 200 ft for Well Number 5 . 139
104 Calculated airborne total field profile at 100 ft for Well Number 6 . 140
105 Calculated airborne total field profile at 150 ft for Well Number 6 . 141
106 Calculated airborne tots! field profile at 200 ft for Well Number 6 . 142
107 Calculated airborne total field profile at 100 ft for Well Number 12. 143
108 Calculated airborne total field profile at 100 ft for Hell Number 12. 144
109 Calculated airborne total field profile at 150 ft for Well Number 12. 145
110 Calculated airborne total field profile at 200 ft for Well Number 12. 146
111 Calculated airborne vertical gradient for Well Number 4 147
112 Calculated airborne north-south horizontal gradient for Well
Number 4 148
113 Calculated airborne east-west horizontal gradient at 200 ft for Well
Number 4 149
xii
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FIGURES (Continued)
Number Page
114 Calculated airborne vertical gradient at 150 ft for Well Number 4 . . 150
115 Calculated airborne north-south horizontal gradient at 150 ft
for Well Number 4 151
116 Calculated airborne east-west horizontal gradient at 150 ft
for Well Number 4 152
117 Calculated airborne vertical gradient at 200 ft for Hell Number 4 . . 153
118 Calculated airborne north-south horizontal gradient at 200 ft
for Well Number 4 154
119 Calculated airborne vertical gradient at 250 ft for Well Number 4 . . 155
120 Calculated airborne north-south horizontal gradient at 250 ft
for Well Number 4 156
*..
121 Calculated airborne vertical gradient at 150 ft for Well Number 5 . . 157
122 Calculated airborne north-south horizontal gradient at 150 ft
for Well Number 5 158
*.
123 Calculated airborne vertical gradient at 200 ft for Well Number 5 . . 159
124 Calculated airborne north-south horizontal gradient at 200 ft
for Well Number 5 160
125 Calculated airborne north-south profile of vertical gradient
at 150 ft for Well Number 12 161
126 Calculated airborne east-west profile of vertical gradient
at 150 ft for Well Number 12 162
127 Calculated airborne north-south profile of horizontal gradient
at 150 ft for Well Number 12 163
128 Calculated airborne east-west profile of horizontal gradient
at 150 ft for Well Number 12 164
129 Calculated airborne north-south profile of vertical gradient
at 200 ft for Well Number 12 165
130 Calculated airborne north-south profile of horizontal gradient
at 200 ft for Well Number 12 166
•
131 Calculated airborne north-south profile of vertical gradient
at 250 ft for Well Number 12 167
xiii
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FIGURES (Continued)
Number Page
132 Calculated airborne north-south profile of horizontal
gradient at 250 ft for Well Number 12 168
133 Calculated airborne total field at 150 ft for two
identical casings separated 200 ft 169
134 Calculated airborne totai field at 150 ft for two
identical casings separated 300 ft 170
135 Calculated airborne total field at 200 ft for two
identical casings separated 300 ft 171
136 Calculated airborne total field at 200 ft for two
identical casings separated 400 ft 172
137 Self-potential profiles over Well Number 2 173
138 Self-potential profiles over Well Number 3 174
139 Self-potential profiles over Well Number 6 175
140 Self-potential profiles over Well Number 7 176
141 Self-potential profiles over Well Number 10 177
142 Self-potential profiles over Well Number 11 178
143 Self-potential profiles over Well Number 14 179
144 Self-potential profiles over Well Number 15 N (not centered on well). 180
145 Self-potential profiles over Well Number 15 S (not centered on well). 181
146 Self-potential profiles over Well Number 16 182
147 Self-potential profiles over Well Number 17 183
148 Electromagnetic profiles over Well Number 2, using the EM-31 system . 184
149 Electromagnetic profiles over Well Number 3, using the EM-31 system . 185
150 Electromagnetic N-S profile over Well Number 3, using Slingram. . . . 186
151 Electromagnetic N-S profile over Well Number 3, using Slingram. . . . 187
xiv
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TABLES
Number Page
1 Locations and Casing Information for Wells Studied 12
2 Parameters Found by Inversion 17
3 Statistical Information for Inversion of Data for
Well Number 10 19
4 Statistical Information for Inversion of Data for.
Well Number 14 20
5" ^Effect of Fixing Parameters for Well Number 6 21
xv
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SECTION 1
INTRODUCTION
The Underground Injection Control Regulations (UIC), issued by the Envi-
ronmental Protection Agency, regulate injection wells for the protection of
actual or potential underground sources of drinking water as required by the
Safe Drinking Water Act. One provision of the UIC regulations establishes a
radius of review around proposed new injection wells, based on the hydrogeo-
logic properties of the subsurface, within which a search must be made for
possible conduits, such as abandoned injection wells, from the injection stra-
tum to overlying aquifers containing potable water. Geophysical methods orig-
inally developed for resource exploration may offer assistance in carrying out
these regulations. The U.S. Environmental Protection Agency in an interagency
agreement with the U.S. Geological Survey sponsored a preliminary study of the
feasibility of using geophysical exploration methods to locate abandoned wells
containing steel casing.
It was estimated in 1979 that there were some 500,000 municipal, indus-
trial, commercial, agricultural, and domestic wells in the U.S. injecting
fluids*below the surface, and that at least 5,000 new injection wells were
being constructed each year. Also, due to differential pressures, dormant
wells sometimes serve as conduits between aquifers containing brine or other
pollutants and fresh water aquifers. Location of existing wells is an impor-
tant task; it was estimated in 1979 that there were as many as 1,800,000 pro-
ducing, dormant, and abandoned wells in the United States. The problem pre-
sented by abandoned or unknown wells is especially acute in petroleum producing
regions where the total number of wells may reach densities as high as 2,000
per square mile. Particularly in the early days of petroleum production, the
locations of wells were not always recorded. Some recorded locations v/ere
erroneous or described only in broad terms and many old records are not readily
available.
Throughout the history of petroleum production, steel casings have been
used in drilling almost all petroleum wells; and, until recently, steel casings
were used in most water wells. In some cases, all or part of the casing h?s
been removed from the well. Magnetometer surveys offer a means of locating
abandoned wells which contain steel casing near the surface. Magnetometers are
used to map perturbations in the Earth's magnetic field such as those caused by
buried ferromagnetic objects. A steel casing causes a relatively large dis-
turbance in the magnetic field at distances on the order of tens to hundreds
of feet from its end. Magnetometers can be operated in low flying aircraft
thereby offering a rapid means for magnetic surveys of large areas.
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Steel casings are very good conductors of electricity relative to the
surrounding: earth and rocks. Therefore, some of the electrical methods of
exploration geophysics show promise of being useful in locating casings.
Seismic n>et.hods appear to be only very marginally useful. Remote sensing
methods which employ microwave, infrared, or other high frequency electro-
magnetic radiation are likely to be useful in detecting disturbances of the
soil whicn mark a well site.
STUDY OBJECTIVES
The primary objectives of the work described in this report were: 1) to
develop a mathematical model and representative parameters from which the
magnetic field of a casing can be calculated and 2) to use this model to study
the feasibility of using airborne magnetic methods to locate well casings.
Secondary objectives were to investigate the feasibility of locating casings by
means of ground magnetic surveys, to make a preliminary study of the usefulness
of electrical methods, and to provide a brief discussion of the principles of
magnetic and electrical methods.
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SECTION 2
MAGNETIC METHODS
MAGNETIC FIELD OF THE EARTH
The Earth possesses a magnetic field caused primarily by sources in the
core. The form of the field is roughly the same as would be caused by a dipole
or bar magnet located near the Earth's center and aligned subparallel to its
geographic axis. Near the equator, the magnetic field lines are directed
almost horizontally; but, over most of the conterminous United States, the
field is inclined at an angle greater than 60° with respect to the horizontal
(Fabiano et al., 1983). The direction of the horizontal projection of the
field lines (declination) ranges between about 20° east and 20° west of north
oveJ" gios.t of the conterminous United States. The intensity of the Earth's
field -is customarily expressed in S.Ij units as nanoteslas or in an older unit,
the*gamma;'numerically one gamma (10-5 oersted) equals one nanotesla. Except
for local perturbations the intensity of the Earth's field varies between about
50,000 and 60,000 gammas over the conterminous states (Fabiano and Peddie,
1981).
Many rocks and minerals are weakly magnetic or magnetized by induction
1j the Earth's field and cause spatial perturbations or "anomalies" in the
Earth's main field. With some notable exceptions (Donovan et al., 1979),
sedimentary rocks, which characterize essentially all of the world's oil fields,
are usually so weakly magnetized that they can be ignored in ordinary magnetic
studies. Man-made objects containing iron or steel are often highly magnetized
and locally can cause large anomalies.
The intensity and direction of the Earth's field varies on time scales
ranging from thousands of years to ?. microsecond and shorter times. The very
slow or secular variations are due to changes in the core. Variations having
periods ranging from tens of years to about one second are caused by processes
in the magnetosphere and ionosphere; the ultimate source of these variations is
electromagnetic radiation and particles from the sun. At periods corresponding
to frequencies between about one hertz and several megahertz, most of the
energy comes from lightening strokes.
MAGNETOMETERS
The magnetometer is a sensitive instrument which can be used to map spatial
variations in the Earth's magnetic field. Some magnetometers are highly portable
instruments which are operated manually. Other instruments are mounted in air-
craft or other vehicles and they produce a continuous recording as the vehicle
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moves. Currently, most measurements are made with one of three types of elec-
tronic magnetometers: the fluxgate, the proton precession, and the optically
pumped magnetometer. In the fluxgate magnetometer, the magnetic field is
sensed by the level of saturation it causes in a strip of special steel.
Inherently, the fluxgate magnetometer measures the strength of the component of
the field which is parallel to the strip or, so called, fluxgate. However,
fluxgate magnetometers have been adapted to measure the total intensity or
scalar field by vector summation of the fields measured by three orthogonal
sensors or by automatically and continuously orienting a single sensor so that
it is always parallel to the field lines. In the proton magnetometer, a mag-
netic field which is not parallel to the Earth's field is applied to a fluid
rich in protons causing them to partly align with this artificial field. When
the controlled field is removed, the protons precess toward realignment with
the Earth's field at a frequency which depends on the intensity of the Earth's
field. By measuring this precession frequency, the total intensity of the
field can be determined. The sensor for optically pumped magnetometers in-
cludes a cell filled with rubidium or cesium vapor or helium which is "pumped"
by a light source; the principles of operation are more complex than for a
proton magnetometer. Like the proton magnetometer, the optically pumped magne-
tometer measures the total intensity of the field.
Total field magnetometers are generally faster and easier to use than
component or vector magnetometers; and, except for very special purposes, all
"airborne surveys and most ground surveys are made with total field instruments.
The proton magnetometer is most commonly used. Optically pumped instruments
are sometimes used in high resolution airborne measurements and in gradient •
measurements where high sensitivity and continuous measurements are desired.
Currently, the primary use of fluxgate instruments is in measuring components
of the Earth's field and in operating in areas of extremely high gradients or
electrical noise. Hand-held fluxgate magnetometers are sometimes used for
measuring the vertical component of the field. The sensor is oriented by a
damped pendulum. Tripod-mounted fluxgate instruments are used for measuring
the inclination and declination of the Earth's field. By using this instrument
in conjunction with a portable proton magnetometer, the components of the field
can be determined.
For some purposes a close approximation of the gradient of the field is
determined by measuring the difference in the field between two closely spaced
sensors. In principle, the gradient of any component or of the total intensity
of the field can be measured in the vertical direction or arty horizontal
direction. In practice, the quantity measured most commonly is the vertical
gradient of the total field.
SURVEY TECHNIQUES
Ground magnetic measurements are usually made with portable instruments at
regular intervals along more or less straight and parallel lines which cover
the survey area. Often the interval between measurement locations (stations)
along the lines is less than the spacing between lines. Ordinary land survey-
ing methods are used to establish stations at which measurements are made; high
accuracy is rot usually required. Continuously recording instruments are
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sometimes mounted on trucks (Hildenbrand, 1982); measurements can be made along
road networks and in some areas where it is possible to drive off roads.
Most magnetic surveys are done from aircraft. Airborne measurements are
made along parallel flight lines which are normally spaced 1/8 mile (0.2 km) to
6 miles (9.7 km) or more apart. For some purposes, aeromagnetic surveys are
made at a fixed altitude above sea level; for other purposes they are flown at
a f'xed height above the surface. Usually the pilot navigates visually to fly
along lines drawn on maps or aerial photographs. A tracking camera or a video
camera and recorder is used to obtain a continuous visual record of the flight
path. The location of the aircraft is plotted at m^p locations where common
points on the map and on the tracking film are recognized; the magnetic data
are then adjusted to the flight path by assuming that the speed and direction
of the aircraft are constant between identified locations. Errors in location
are on the order of several tens of feet at low altitudes and several hundreds
of feet or more at high altitude. Where flights are over featureless terrain
or water, the flight path cannot be recovered at all using the photographic
method. Doppler radar, VLF, Loran-C, and inertial navigation systems are
sometimes used for pilot guidance or to supplement photographic recovery of the
flight path. Their use improves the accuracy of the flight path determination;
but, in general, does not provide the degree of accuracy needed for purposes
such as the location of abandoned wells. Microwave navigation systems can
provide locations accurate to several meters or better. These systems employ
two or more transponders placed at accurately surveyed sites. Position is then
determined by a transceiver and computer on the aircraft which determines the
range to each transponder. The chief disadvantage of these systems is that a
line-of-site path between the aircraft ana at least two transponders is re-
quired at all timis. Height of the aircraft is usually measured with a radar
altimeter.
To make accurate anomaly maps, temporal changes in the Earth's field dur-
ing the period of the survey must be considered. Normal changes during a day,
sometimes called diurnal drift, are a few tens of gammas but changes of hun-
dreds or thousands of gammas may occur over a few hours during magnetic storms.
During severe magnetic storms, which occur infrequently, magnetic surveys
should not be made. There are a number of methods of correcting surveys for
temporal variations. For ground surveys, one method is to establish a base or
reference station in the survey area and to repeat measurements at this base at
frequent intervals. All of the measurements at field stations are then cor-
rected by assuming a linear change of the field during the time interval be-
tween repeat base station readings. This method works well provided the field
is relatively quiet. In airborne surveying, the traditional method is to fly
"tie" lines across the rows of parallel flight lines during a quiet period.
Intersections of the regular flight lines with the tie lines are determined and
the difference in intensity between the two sets of measurements is calculated.
The results are thjn adjusted by linear interpolation of the data along flight
lir.es between tie lines so that the flight line data fit the tie line data.
Sometimes continuously recording magnetometers are used at fixed base sites to
monitor temporal changes. If time is accurately recorded at both base sits and
field location, the field data can be corrected by subtraction of the varia-
tions at the base site. This method works very well for surveys of small
areas, provided the base site is in or near the area. It does not work well
-------
for surveys of large areas since, over a large area, temporal variations vary
spatially in an unpredictable manner.
Intense fields from man-made electromagnetic sources can be a problem in
magnetic surveys. Most magnetometers are designed to operate in fairly intense
60 hertz and radiofrequency fields. However, extremely low frequency fields
caused by equipment using direct current or the switching of large alternating
currents can be a problem. Pipelines carrying direct current for cathodic
protection can be particularly troublesome. With great care, particularly in
accurate determination of the flight path, significant airborne anomalies on
the order of one garrnia or less can be mapped in areas of very gentle magnetic
expression. Although some modern ground magnetometers have a sensitivity of
0.1 gamrca, sources of cultural and geologic noise usually prevent full use of
this sensitivity in ground measurements.
After all corrections have been made, magnetic survey data are usually
displayed as individual profiles or as contour maps. Geologic interpretation
of magnetic anomalies is carried out by comparison with theoretical anomalies
calculated for idealized geologic models, comparison with anomalies over known
geologic features, and from constraints provided by other geophysical and geo-
logical results in the area. Identification of anomalies caused by cultural
features., -such as railroads, pipelines, and bridges is commonly made using
field observations and maps showing such features. There are no well-estab-
listfe?a analytical procedures to follow for identification and location of such
features. However, in many respects the problem of locating abandoned wells is
much simpler than the interpretation of most geologic features. Anomalies due
to wells are probably all very similar. Also, the objective is simply to
detect the anomaly and to identify its source as being a casing and not to
determine additional parameters of the well.
»
For more information on the principles of the magnetic method and survey
techniques, the reader may wish to consult some of the many papers and text-
books (for example, Hood et al., 1979; Nettleton, 1976; Telford et al., 1976;
or Parasnis, 1975) on the subject.
-------
SECTION 3
APPLICATION OF MAGNETIC METHODS TO ABANDONED-WELL PROBLEM
MAGNETIC PARAMETERS
The feasibility of locating abandoned wells with magnatic methods might be
established empirically by making measurments over known wells using all of the
promising airborne and surface techniques. This would be an inefficient ap-
proach so a combination of field measurements and numerical modeling are being
used to study the general problem, Field surveys provide data from which the
magnetic parameters of casings can be determined. Once the parameters are
established, numerical modeling provides a relatively fast and inexpensive
method for simulating the anomaly for any type of survey. For example, by
modeling it is possible to design and evaluate the potential usefulness of an
airborne survey in discovering abandoned wells prior to having flown such a
survey. *••
Few measurements of the magnetic fields around well casings have been
published. Barret (1931) published some results and referred to other unpub-
lished measurements. Van Weelden (1933) gave an analysis and summary of a
number of measurements. Both authors were concerned with th« question of
whether or not a group of casings could cause the overall magnetic minima which
has been observed over a number cf oilfields around 1930.
The magnetization of a steel pipe consists of two components, induced and
permanent. The induced magnetization depends on the intensity of the Earth's
field, the magnetic permeability of the pipe, and the attitude of the pipe with
respect to the Earth's field. The permanent magnetization depends on the
ability of the pipe to retain a permanent field, and on the magnetic fields
and the mechanical and thermal effects to which the pipe has been exposed.
Ideally, one might hope to calculate the induced component. However, this
calculation is not easy (Lam, 1977) since analytical solutions do not exist and
one would have to resort to numerical methods. Furthermore, there is consider-
able uncertainty in determining the effective magnetic permeability of a steel
pipe given the effect of joints, other flaws, and stresses. With these prob-
lems in mind, we decided to characterize the magnetization of steel well cas-
ings using actual measurements without trying to distinguish between induced
and permanent magnetization.
A number of different mathematical models could be used to represent a
magnetized casing. The component of magnetization transverse to the pipe could
be represented as a line of transverse dipoles. However, considering the
relatively small diameter of the pipe, the moment of these dipoles would be
very small due to demagnetization. Therefore, the transverse component is of
-------
little interest and, for our present purpose, only the magnetization along the
axis of the pipe need be considered. This axial magnetization could be repre-
sented by a continuous distribution of infinitesimal magnetic dipoles. However,
a finite number of dipoles or pole pairs is adequate to represent the field at
any appreciable distance from the casing. From the papers by Barret and Van
Weelden, it appeared that, to a good first approximation, a casing can be repre-
sented by a single pair of poles. This observation plus the simplicity of the
model led us to use sets of pole pairs to represent a casing. Barret gave an
equation for calculating the pole strength. However, this equation does not
account for the demagnetization effect which occurs at surfaces of highly
permeable bodies. Van Weelden discussed some of the assumptions which have
been made about the location of the poles in a bar of magnetic material and gave
an equation for the calculation of the vertical field of a casing using an
empirically established constant. Our approach is similar except that we have
made the problem more general by the use of computer curve-fitting or inversion
methods to determine the model parameters from field data.
MATHEMATICAL MODEL
We will use a right-handed Cartesian coordinate system with the z-axis
positive upwards and the x-axis positive south. Definitions of the symbols
used are as follows:
B - magnetic field vector,
¥x, By, B2 - magnetic field components,
f - total magnetic field intensity,
H - horizontal magnetic field,
m - monopole strength,
x,y,z - spatial coordinates,
xi>yi»zi " position of a pole m,
fj (x-Xi, y-y}, or z-z,) - j-th component of the vector from pole m;
to the point of observation,
r = [(x-Xj)2 + (y-y})2 + (z-z1-)2]1/'2 - magnitude of the vector from
a pole to the point of observation,
0 - the angle between the horizontal plane and the casing,
4> - the angle between the horizontal projection of the casing and
the x-axis; this is the usual $ in spherical coordinates,
u0 - the magnetic permeability of free space.
-------
The components of the magnetic field and r.omo of the derivatives due to a
single pole are:
By = m
* 4ir 3
By = m — —
y 4it 3
r
no z'zi
>z =
JB,
3X
= m —
1 3(x-Xl)'
_ _
r r
3mu0 (X-XT) (y-y,)
3mu
More generally, these expressions can be written as
m — —-, j=l,2,3, corresponding to x,y,z - components (1)
4n 3
r
3BJ ^o
—- " m —
ax . 4it
1,2,3; k = 1,2,3 (2)
where
ajk
0 1f
-------
The field caused by the second pole of a pair is given by the same
expressions using the opposite sign for the pole strength. After surmiation
over all pairs of poles, the horizontal, H, and total, F, fields are given by
H = (B2 + B2)l/2
x y
F = (E$2 + B2 -i- B2)1/2
x y z
(3)
The three spatial derivatives of F are calculated as
3F
The absolute position of one pole in each casing is given by the coordinates
(x-j, y-j , zO- Then all other pole positions in a casing are calculated
according to the relation
= x° +
6,
where
x} = the position of another pole a distance i from the first pole along
a casing oriented in the (e, ) direction. The components of L^
U, p, ) are:
Lx = l cos B cos
Ly = £ cos 8 sin $
f
Lz = SL sin B
To simulate realistic magnetic data, nonzero values for the Earth's mag-
netic field components must be entered into the problem. In the forward prob-
lem, the components are simply added at each point within the region of interest
to the corresponding component of the anomalous field. In the inverse problem,
the Earth's field components are treated as parameters to be determined by the
nonlinear least squares procedure.
Since the coordinates have been set up in the conventional sense, with
the unit vector x pointing from north to south, the unit vector y_ pointing from
west to east, and" the unit vector z_ pointing up, care must be taken when
10
-------
entering geomagnetic values that were specified within the usual geomagnetic
coordinate system. The transformation is straightforward:
Bx = -X
By = Y
Bz = -Z
where X, Y, and Z are the field values in geomagnetic coordinates. Details of
the computer programs developed are given in the appendix.
FIELD MEASUREMENTS
To obtain representative data which could be used for analysis of the
detection problem and the design of airborne surveys, measurements were made
near a number of wells in two oil fields near Denver. The first field (figure
1) is east of Denver and contains a nunber of producing, dry, and abandonad
wells which were drilled during the 1970's. The contours on figure 1 are
values^of total intensity with an arbitrary datum subtracted and are taken from
an aeroinagnetic map (Petty et al., 1966). It should be noted that the oil
fie^d is located in a region of fairly gradual magnetic variations. The second
field (figure 2) is north of Denver near Boulder and contains many abandoned
and a few producing wells. Development of this field began around the turn of
the century. Records on the wells are incomplete but the magnetic data are
still useful. Relevant information regarding the wells where we have records
is summarized in table 1.
In general, measurements were made along four radial lines, originating at
each well, in the magnetic north, south, east, and west directions. Measure-
ments were made directly above the well, at 5 feet (1.5 m) from the well and
then at 10 foot (3.05 m) intervals out to 100 feet (30.5 m) 20 foot (6.1 m)
intervals to 200 feet (61 m) and 50 foot (15.2 m) intervals to a maximum dis-
tance of 700-800 feet (213-244 m) along each line. Total magnetic field
measurements were made with proton magnetometers, one with a sensitivity of one
gamma and another with a sensitivity of 0.1 gamma. Up to four readings were
taken at each station. Obviously poor readings were rejected and the remaining
were averaged. In general, there was little scatter among readings except very
near the well where the magnetic gradient was high. Repeat readings were made
at a base station near each well, and the results were used to correct the
profile c"3ta for diurnal drift. At most sites, a continuous recording proton
magnetometer was used to ensure that data were not taken during magnetic storms
and to provide additional information for diurnal drift corrections.
The results were all obtained with the sensor placed 8.25 fest (2.51 m)
above the Earth's surface. Before making any readings, all visible steel
objects such as discarded oil drums, valves, or pipes, were removed from the
immediate vicinity of the traverses. In some cases, the traverses were near or
over steel objects which were partially buried and could not be readily removed.
11
-------
TABLE 1. LOCATIONS AND CASING INFORMATION FOR WELLS STUDIED
ro
Veil
Ruabsr Rase
I Vif
Lowryatate )-2)
J m
LoBryatate 1-3)
lowrjTftate )-36
4 Peneoll
State A tl
) Tesoeo
State of Colo.
w -7- 01
6 Tcveco
Ststa of Colo.
location
Sec. 2) . T. ) 9.. B. 6) V.
500' PH., 2110' PRL
See. 3), T. ) 3.. B. »5 V.
600* PCT., 600* PEl
See. 36. T. ) 9.. I. 63 H.
660* flft, 1761* Pfil
See. 36. T. ) 3., B. 6) «.
1930' PCL, 630' P[H
fee. 20. T. ) 9., B. 64 tt.
6SO* PSl, 660' m.
Set. >•„ T. ) 9., B. 64 V.
660* FBL, 1090' Ftl
7 Vnllalted, Ud. See. 19. T. ) 8., B. 84 H.
KoShcr Goote II 660' tSL. «60* FVL
• TBI
Elate 9-16
9 RjeCiy ct. ol.
State 13-21
10 RFC
State 7-20
EBI. IG, T. ) •.. B. *5 «.
1930' rSH. 660' PEt
Sac. II, T. ) B.. B. «4 V.
690' PSL. 660* FUl
Btc. 20, T. ) 9., B. 64 H.
I9BO' fWI., 1980' PEt
3/30/78
7/24/77
0/1S/72
9/72
2/17/73
2/24/74
and teo«cit
of Cueing
260* of 8 5/8' or 24 IWft
8,«JO' of ) 1/2* «t I).) Ik/ft
210* of 8 5/3' *t 74 Ib/ft
8.562' ot ) 1/2* «« I).) Ib/ft
292' of fl )/8- et 24 Ifc/ft
8,422* of ) 1/2* ot I).) Ib/ft
211* of 8 )/8* «t 24 Jb/ft
fl,J50' of ) 1/2* at 15.5 Id/ft
2«6' of 8 )/8* at 24 Ib/ft
264' of 8 )/8' at 24 Ib/ft
1,583' of ) 1/2- at I).) Ib/ft
etartano. at 7,000* e>pth
4/17/79 19ft' of 8 )/8' at 24 Ik/ft
11/16/72 170* of 8 )/8- at 24 Ib/ft
».058' of J 1/2* «t 15.5 Ib/ft
ctcrtlnj at 17/0' 4epth
4/14/74 221* of 8 5/8' at 24 Ib/ft
2/13/79 240* of 8 )/8* at 24 Ib/ft
Pipe above
Ground
No, cet below
groend, turfaee
Ra, rift off belov
Tvj» of
Role
Kg, etft off belov
earfece
T*». V of easing
above ground turf ace
Tea, 1' of eating
above jroumd tcrfcee
oil
Atia
oil
oil e^ll
Dry hole
Dry hole
No, c4t off below Dry hoi*
aurfaee
Ro, eilt off b*low Dry hole
groand *arfoe*
Tea, i' of eaeln| Dry itole
•bov« ground turfec*
Mo. cat off belov Dry hole
aurface
Bo, e«t off below Dry hole
turfoee
Reproduced from
best available copy.
(continued)
-------
TABLE 1. (Continued)
M*!l
Hunter
toot leu
Drill*
•«! Awant
of Citing
Ground
of
Holt
II tone* 8»c. 19. T. 9 9.. I. M «. 10/22/71 247' of • 3/8" *t J4 Ik/ft VM. 3' of eoci«« 8ry Kelt
Stito of Colo. 640' PVL. 1980' PW. 0.311* cf 3 l/2'«t 13.3 Ik/ft «bo*o ground ••rfoto
It Boeld.t
CxJ
I) Bowlder
tec. 9, T. IB., I. 70V.
tec. 9. T. I •., I. 70 ».
Eoforo
I950T
to for*
ItlOt
It* mil lofomtloa
MB "»ll lofomtlo* •••lUklo
14 VIlltKi BBIWOU toe. 13. T. 2 n., i. 70 «. 1/1932 J»* of » 3/8" «t 2« lk/«»
13 2030* Hit. 1710' PH.
19 lhy«t«ck DOM fcc. 3). T. 2 M., I. 70 V. 9/1932 200' of 0 3/8' «t 32 Ik/ft
(HI Co. »1 «48' IK., 973' rd. 1000' of 3 7/8- «t J4 Ib/ft
138 Is «j>>ro«to«t«lr 24 ft. l/onttt tat 4 ft. oaat ..* 13 *. M>ll data U «nel««r on th**« tin
lofomatloo on 13 • oey «r>Jy Inotaed or •!«« to 13 8.
It Hor»t«ck Ooo* Sec. 33. T. 2 R.. •. 70 ». IE/1931 309' of 10 3/4*
Oil Co. 116
17 Mllim teniratt tee. 13. T. 2 ».. 1. 70 K. II/IW2 JOO' of • 3/8" «t 32 IWft
ll-ii
T«*. 2 1/2' of Dry
citlr.g «bov« groand
••rf»c*
T... 2 1/2* of
citing nbo*t
•urfac*
Dry twU
Teo, 3* of coiiRt Ab«ndon*d
•bo*o (roand tvttftf ell wll
Ho, c«t off twtow
ground
Abcndonod
oil wll
7»», 2* of eMfnf Dry bol*f
•bow ground larfcco
Bo. eat off btlov
groohd iurf*c*
Dry hol«T
-------
Experimental gradiometer measurements were also made; for this purpose a
special nonferrous staff was used to hold two sensors at a fixed separation. A
switch between the magnetometer (0.1 gamma sensitivity) and the sensors made it
possible to alternate between sensors fcr successive readings to determine the
difference in field between them. Vertical gradient measurements were made at
wells number 14 and 16 using a 6.6 foot (2.0 m) separation between sensors with
the lower sensor about 4.9 feet (1.5 m) above the ground. Horizontal gradient
measurements were made at the same stations with the sensors about 4.9 feet
(1.5 m) above the ground and with a horizontal separation of 6.6 feet (2.0 m).
The inclination of the Earth's field was measured at a number of stations
near well number 7 using a "D-I" fluxgate magnetometer. The height of the
sensor was about 5.0 faet (1.52 m). Declination was not measured due to the
time required to establish an accurate azimuth reference. Total field measure-
ments were made at the same stations and heights so that vertical and hori-
zontal components of the field could be calculated.
All of the magnetic data were processed and plotted using a microcomputer
and programs which were modified for this purpose.
QtfAMTATIVE ANALYSIS OF RESULTS
*"** In general, the field results confirm the validity of the mathematical
model. All of the known casings produce sharp positive anomalies in the total
field indicating that they are magnetized along the axis of the casing, as
expected. According to the mathematical model, with directions measured from
magnetic north, the east-west profiles over or near a well should be symmetric
and the north-south profiles should be asymmetric with a low on the north side.
$Th.e reason for the asymmetry in the north-south direction is that on the north
side, the horizontal field of the upper pole opposes the horizontal component
of the Earth's field whereas on the south side these two horizontal fields are
additive. Most of the field results (figures 3-38) show this pattern.
The peak amplitude of the total field anomalies ranges from about 1,500
to 6,000 gammas. Since the depth to the upper end of a well casing is unknown,
except for those wells which extend above the sjrface, and since accurate
measurements directly over the well are hard to obtain because of the steep
gradients present, it is difficult to assass actual variations in magnetization
among wells directly from field measurements.
The form of the gradient curves (figures 39-46) is roughly as expected.
Profiles of horizontal gradient are asymmetric about the casing. East-west
profiles of vertical gradient are symmetric about the casing but north-south
profiles of vertical gradient are somewhat asymmetrical due to the asymmetry of
total field profiles in this direction.
Unlike the total field, the vertical component of the field is symmetric
about the casing in all directions (figures 47-50). The horizontal component
is asymmetric in the north-south direction. If half of the anomaly were re-
versed, vne two halves would nearly be mirror images for well number 7. Near
the casing, a small anomaly was observed in the east-west profile of the
14
-------
horizontal component. This indicates that the profile was located sli
south of the true east-west line directly over the casing.
At most sites, the main anomaly due to the well is distorted by separate
small anomalies which must be due to concealed steel objects. As expected,
the gradient measurements are more affected than the total field measurements.
These small anomalies seem to be concentrated near the wells as one would
expect. K. H. Johnston, et al., (1973) have written a very interesting manual
on how to locate abandoned wells using such miscellaneous discarded metal
objects as clues. However, they relied on the use of electromagnetic metal
detectors and other techniques rather than magnetometers. Given the existing
data, none of the anomalies studied by these authors could be mistaken for the
anomaly due to the well itself. However, if one were searching for unknown
wells for our study areas using a rather loose grid, some of these anomalies
would be identified as possibly being caused by casings. Detailed measurements
would be required to avoid such aliasing and to permit more positive identifi-
cation of casing anomalies. The gradual changes in the total field which occur
along the profiles away from the wells are probably due mostly to sources in
the crystalline basement rocks at considerable depth. Some small changes were
observed which may be due to slight magnetization of the near-surface rocks.
Gradual variations are not a limitation in the use of ground magnetic surveys
because the variations due to extraneous man-made objects are larger. However,
variations associated with geologic sources may be a serious source of noise in
airborne total field surveys. Such geologic noise is probably a less serious
problem in airborne gradient surveys.
For the test areas described, a fairly tight grid would be necessary to
make the..probabil ity of missing a well very small using ground measurements.
Total field measurements made at 25- or 30-foot (7.6-9.1 n) intervals along
lines spaced 50 feet apart would probably be adequate for most cases. Even
with this type of grid, it would probably be necessary to make a considerable
number of other detailed measurements to distinguish between anomalies due to
well casings and anomalies due to extraneous sources; however, the latter may
serve as a guide to the presence of a nearby well.
From the limited number of measurments made, it appears that in locating
wells there is no advantage in measuring gradients. In some cases, the width
of the zone where the anomaly is large enough to be easily recognized is larger
for gradient than for total field measurements; and, in some cases, it is
smaller. However, there is a small zone near the center of gradient anomalies
where the sign of the anomaly changes or is near zero. Considering the fact
that a grid point could fall in this zone, the grid for ground gradient measure-
ments should be even finer than the grid for total field measurements.
From a theoretical standpoint, there are advantages in measuring compon-
ents of the field, particularly if the objective is to determine the parameters
of casings. However, from a practical standpoint, it is more cost-effective to
measure the total field on a fine grid than to measure vertical and horizontal
components on a somewhat coarser grid. Consideration might be given to measur-
ing the vertical component only using a self leveling fluxgate magnetometer.
*
15
-------
INVERSION OF FIELD DATA
Using the pole pair model and the nonlinear least squares fitting programs
described in appendix I, parameters for all of the wells listed in table 1 were
found. Profiles comparing the actual data (circles) with the computed data
(solid line) are shown in figures 51-86 and the pole parameters which were
found are listed in table 2. For several wells, very good computer fits were
obtained using only a single pole pair. For other wells a somewhat better fit
was obtained using two pole pairs rather than one to represent the casing.
Models with two or more separate sets of poles (casings) were used to fit some
of the data where the anomaly due to the casing is distorted by anomalies from
other sources.
To make the nonlinear least squares algorithm function properly for this
kind of data, the "tuning" parameter, V(42), was set equal to zero. Also it
was usually necessary to constrain or to fix at 90° the angle & which gives the
inclination of the well from the horizontal. This is not an unreasonable
constraint because wells are not likely to deviate much from vertical in the
upper few hundred feet where both poles are usually found. In models where two
casings were assumed, 0 was not set 90° for the second casing; in some cases e
was found to be near zero for the second source, indicating that it is a nearly
horizontal length of pipe or similar object.
The components of the Earth's field are unknown parameters in the program.
However, Y was set to zero since measurements were along lines approximately
parallel or perpendicular to the horizontal component of the Earth's field.
Values of X and Z appropriate to the area were entered as starting values. In
some cases, the values of X and Z determined by computer fitting seemed satis-
factory in that their ratio deviated little from the initial values assumed.
However, in other cases, their ratio changed enough so that the inclination of
the field was changed by a few degrees. Although inclination was measured at
only one site, we know that, except locally near a well, inclination is un-
likely to change much over the study areas. Consequently, for wells where the
initial computed inclination varied by more than about 0.5° from the regional
values, the regional total field was obtained from a good fit to the flanks of
the profile with X and Z free to vary. Then X and Z, as computed from this
total field and the regional value for the inclination, were fixed in obtaining
the final solution.
In general, the depth to the upper pole and the separation between pole
pairs was not constrained. However, the separation was fixed or bounded in a
few cases where the depth to the second pole exceeded the known depth to the
bottom of the casing or where the sign of x. was negative thereby placing an
apparent pole in the air. For secondary sources, x. was allowed to be negative.
It must be noted that distances can be given in either feet.or meters in
the program provided proper numerical values for the pole strength, m, are
used. Field measurements were made in feet and were used as such in the
inversion program. The pole strengths given here are in hybrid units; they
must be divided by 1076.4 to obtain the results in SI units. If distances are
entered in meters, the pole strengths must be divided by 100 to obtain SI
units.
16
-------
TABLE 2. PARAMETERS FOUND BY INVERSION
•fell «,
M.i M.i
CMl<« I
tO.O O.I
to.o o.
M.O 0.
to.o o.
M.O 0.
50.0 0.
to.o o.
tl.w 111.
11. t J»8.
o to.o e.
i to.o .1.1
t *5.« «1.
i tn.o o.i
t to.o o.
t to.e <*.<
t 11. <• >»i.
> -Mini -0.1
-limit o.<
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-mitM 0.
-int6o -o.
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1 -400111 H).
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to.t io«.i -eontt it.i -i.) -it.t tu.<
J*IM Intnlw
•J.» ti.i -t«otti tt.t l.t -i.o i.o
Citing t
111.) It).I -tlJOlt 'IJl.t -l.t -1.5 -It.J
-tIMt 0 -tlOM
-------
Although measurements were made to distances of 700 (213 m) or 800 (244 m)
feet from the well along most lines, data beyond 400 feet (122 m) from the
wells were not used in inversion. The use of data from greater distances does
not add significant information and, if noisy, can degradate the inversion
process.
Visual inspection of figures 51-86 indicates that the casing anomalies can
be fit quite well using the pole-pair model. Attempts to fit other anomalies
due to other miscellaneous sources were often fairly successful; for example,
consider the east-west profile for well number 2 or the north-south profile for
well number 11. However, no attempt was made to fit all of the distortions of
the casing anomaly or all of the separate small anomalies. Wells number 15 N
and number 15 S are extreme examples in which the north-south profiles show
much distortion of the main casing anomalies and the east-west profiles are
almost undistorted.
Although the visual correspondence between the observed and model data is
good, the question naturally arises as to how well the parameters are actually
resolved. In nonlinear least squares curve fitting, estimates of the errors in
the parameters are obtained using linear statistics. Such estimates can be
very useful if employed with caution; the numbers can be used to compare the
relative errors among the parameters but a single error estimate is not
necessarily very accurate. In the version of the NLSOL program used in this
.study (Anderson, 1982), a correlation matrix as well as estimates for the
parameters are computed provided the covariance matrix is positively definite.
It must be noted that the occurrence of a nonpositive definite covariance
matrix does not imply that the parameters are not well defined.
The data for well number 10 appear to be only slightly affected by sources
other than the casing. The estimated errors in the parameters are quite small
(table 3); the largest percent error (15.47) is in the determination of i, the
separation between poles. The data for well number 14 contain a much larger
amount of noise due to sources other than the casing. The estimated errors
(table 4) are much larger than those for well number 10. For example, the
error in & for the first pole pair is 60.5% even though i is much smaller for
well number 14 than for v/ell number 10 and consequently should, from this
standpoint, be better resolved. Also, the root mean square (rms) error between
observed and calculated curves is larger for well number 14 than for well
number 10.
Study of the correlation matrix can provide useful information on the
relationships between parameters. For example, if two parameters are highly
correlated it is difficult to obtain accurate independent estimates, of both
parameters. Usually, the correlation between parameters 3 and 6 is high; this
is because these are the two most important parameters in determining the
magnitude of the anomaly. For instance, if in fitting the data, the depth to
the first pole is changed to provide a better fit to the shape of the curve,
then the pole strength must change to keep the magnitude of the anomaly correct.
Another way of assessing how well parameters are resolved is to compare
the results of unconstrained inversions with results obtained in which one or
more parameters are fixed. The data for*well number 6 (Table 5) were inverted
18
-------
TABLE 3. STATISTICAL INFORMATION FOR INVERSION OF DATA FOR WELL NO. 10
• 9 RfJSCRR- 9.mJ7S77E«02
A&YRII
3 9.
« e.
s o.
6 0.
7 0.
0 9.
10 -0.
9S27E900
77MEJ09
\o
9.S469E-02 O.I900E*01
9.2«S2E«90 e.3S46t>Qi 0.|809E«B1
9.&273i:«09 0,596 IE-OS 9.6846EI09 9.l09QCt9i
0.8J88K»e9 0.J72SE-02 9.77C2C-OI 0.2443E-0I •.I909C«9I
-O..OII2EIOO -5f,JSJDE-e2 -0.7372K-OS -8.143QE-9I -0.99V9E«89
«•
9.I009E«9I
3 -e.i
« -0.!
5 9.I07SCIOI
6 -5.1
7 0.
t -o.:
10 -0.!
9.2322E*03 -9.225&C-QI -«
9.I257000 -0.3J95E-OI -9.:
9.6&09E-OI O.Ji2«E-OI O.j
9,2ffl07E««JO -0, S5P5E-OJ •*., I595C4OI
O.IS75E902 0.85«JE600 e.lS<33E«02
0,1090EOOJ -0,5CiOaE-0| -0.36Q2£»01
-0.6I2JE-02 -0.(
•••" X
polo
coordinate of eo»lng
coor3ctcQt off vflrtt) • field
vertical coscKKtsnt of earth'* (leM
-------
TABLE 4. STATISTICAL IMFQRMATION FOR INVERSION OF DATA FOR WELL NO. 14
ro
o
** MSI«O«
entail
-t.usit.tt 0.«tm-ti 0.i«ozx-ti
t.*.»•* -t.ii«t[t«0 e.«c«sctc0 0.uiai«B0
10 -t.i»«»t-»i «.«kiiictt0 -t.iilirc'O ~0.i
51
IS
0.tl>ICotO
-0.»*ttC-01
-».«4(Jlt»
-t.saiie-st -t.
»0.ft«it-ti
-t.iantttt -t.i
C. MSSC«00 0.«tt4lMit> d Hurt CM!I^
CMC«lM4« Ol HIM CMlBt
I*
«il«»lh •!
•( •Mik'« HaM
Mlllcil in«v<.«ia •« ••tit,** (l«
-------
TABLE 5. EFFECT OF FIXING PARAMETERS FOR WELL NUMBER 6
Uncon-
strained P=73 P=173 Zp-14.6 Z^IO.6 ZplO.6
Pole strength -636,597 -726,640 -673,441 -855,514 528,619 523,895
North
coordinate -2.99 -3.01 -2.99 -3.11 -2.88 -2.88
*
East
coordinate 0.82 .82 ..81 .86 .78 .79
Depth to pole -12.62 -12.94 -12.51 -14.60* 10.60* 10.60*
Separation
between poles 122.96 73.00* 173.00* 123.00* 123.00* 36.78
RMS error 21.85 26.18 22.71 68.07 82.61 78.07
* Fixed parameters
with the separation * fixed at 73 feet (22 m) and 173 fpet (53 m); t was found
to be 123 feet (37 m) when it was unconstrained. From table 4 it is seen that
the rms error between observed and calculated data is not much larger for
l = 73 feet (22 m) than for a = 123 feet (37 m). However, the rms error is
significantly different for i, = 73 feet (22 m) than for s. = 123 feet (37 m) and
visually there is a significant difference in the quality of the fits (figures
62-63 and 85-86). From such studies, one might say that t is resolved with an
accuracy of about -10" to 40%. In fixing s. at 73 or 173 feet (22 or 53 m), the
pole strength changed by a few percent and the depth to the first pole changed
slightly. In another experiment, .«, was fixed at 123 feet (37 m) and the depth
Z was fixed at -10.6 and -14.6 feet (-3.2 and -4.5 m). In both cases, the rms
error is more than triple that for the unconstrained case; the pole strength
changes by about 25% and visually the fit is not very good (figure 87-88).
When the depth to the first pole was fixed, but the separation was uncon-
strained, a slightly better fit was obtained.
It is concluded that, for most of the walls studied, the parameters are
sufficiently well resolved to be used in predicting the response of those wells
at airborne survey altitudes. Actual variations in parameters between wells
probably are greater than the errors in the estimates of the parameters.
All of the casing and other pipe in wells number 1-11 are of the same
type. Therefore, one might expect to find for these wells a correlation be-
tween the amount of pips in the hole (table 1) and the pole strength and separa-
tion between poles (table 2). However, there is no clear correlation between
the amount of pipe and the parameters. It appears that neither the presence of
the inner casing nor the variations in length of the surface casing have much
21
-------
affect on the parameters. This suggests that remanent magnetization or olher
unpredictable parameters are most important in determining the magnetization of
a casing.
MODELLING AND DESIGN OF AIRBORNE SURVEYS
Using the parameters listed in table 2, results expected from airborne
surveys were calculated for wells number 4, 5, 6 and 12. Well number 4 is one
of the most strongly magnetized and well number 5 is one of the most weakly
magnetized of those studied. Well number 6 has typical parameters and the field
data are relativelly free from noise. The interpreted pole separation for the
vertical casing at well number 12 is only 10.1 feet (3.1 m). Results for all
of these wells were plotted in profile form, and results for well number 4 were
also plotted as contour maps. To generate the contour maps, the field was
calculated along many parallel profiles, the minimum value for the data set was
subtracted from the data, and log^g of the result was taken to permit display of
the flanks of the anomaly without too much crowding of contours near the peak.
Individual contours on figures 89-91 are approximately circular in form;
the center of the circle tends to move southward as the circle becomes larger.
The small low in the north side of the casing is clearly seen in the results
for 150 feet (45.7 m) (figure 89). The principal effect of varying the aircraft
altitude is to decrease the peak amplitude and to broaden the anomaly. On the
flanks of the curves, the two effects tend to cancel each other. For example,
on the maps for altitudes of 200 and 250 feet (61 and 76 m), the contours be-
tween 0.3 and 0.6 occur at almost exactly the same points along an east-west
line through the well. Similarly, there are regions where contours on the two
maps taken along a north-south line through the well are nearly the same value.
From examination of the profiles for well number 4 (figures 92-99), it is
apparent that the magnitude of the low on the north side of the well increases
relative to the main high as the altitude increases. For an altitude of 200
feet (61 m), the amplitude of the anomaly for well number 4 is about four times
as large as the anomaly for v/ell number 5 (figures 100-103) and nearly three
times as large as the anomaly for well number 6 (figures 104-106). The shapes
of the anomalies are similar except that the low on the north side of the well
is not as pronounced for well number 4 as for the other two.
The pole strength for well number 12 is the highest that was determined
for any well, but the short spacing between poles causes the anomaly to atten-
uate rapidly with height (figures 107-110) so that at an altitude of 150 feet
(45.7 m) the anomaly is about the same as that for well number 5; and, at
greater altitudes, it is smaller. The model parameters for the subsidiary
anomaly at well number 12 were included in the airborne modeling. As a result,
a small secondary anomaly is observed, particularly in the profiles for alti-
tudes of 100 and 150 feet (30.5 and 45.7 m).
Vertical and horizontal gradients of the total field were calculated to
investigate the feasibility of using an airborne gradiometer. The contour map
of the vertical gradient over a casing (figure 111) has a similar "Bullseye" to
that of the total field (figure 90). A map of the horizontal gradient taken in
22
-------
the north-south direction has a low and a high of nearly the same shape and
nearly equal amplitudes (figure 112). A map of the horizontal gradient taken
in the east-west direction shows a low and a high (figure 113) which are
antisymetrical about a north-south line through the casing. The width of the
vertical gradient anomaly is somewhat less than the total width of the hori-
zontal gradient anomaly.
As expected, the gradient anomalies are much smaller and slightly narrower
for well number 5 (figures 121-124) and especially for well number 12 (figures
125-132) than for well number 4 (figures 114-120). The existence of a second
small anomaly is apparent in the profile at a 150 foot (45.7 n) altitude for
well number 12 but can scarcely be discerned in the profile for a 250 foot
(76.2 m) altitude.
To the extent that the wells studies in this report have typical magnetic
properties and that the parameters found by inversion are reasonably accurate,
the model results discussed above should be very valuable in designing airborne
surveys for locating abandoned wells. In designing a survey, one would like to
know, in addition to the expected anomalies, the noise level or errors in the
magnetic readings and navigation, magnetic variations due to geologic sources
and cultural features, and the density of wells in the area to be flown.
*, •"
By nfag'netlc compensation of the aircraft and by recording and correcting
for th£ motions of the aircraft, the noise level of an airborne system can be
reduced to about 0.2 gamma or better for the total field as measured by sensors
mounted in wing-tippods or tail stingers. The noise level of the difference in
signals between two sensors can be 0.2 gamma or less depending on where the
sensors are located. Considering the separations between sensors, noise levels
of about 0.007 gamma/feet (0.023 gemma/m) or better in the horizontal direction
and 0.003 gamma/feet (0.0098 garama/m) or better in the vertical direction can
be achieved.
An educated guess about anomalies due to geologic sources can be made if
surface and subsurface geologic information is available. However, the only
way to obtain quantitative information on either geologic or cultural sources
is to make magnetic measurements at the study sites.
If the density of wells in an area is very high, it may be difficult to
Identify individual wells using airborne surveys. Use of a small spacing
between lines will of course help to resolve anomalies due to individual wells.
Calculations of the total field were made for two identical wells separated by
200, 300, and 400 feet (61.0, 91.5, 122 m). Parameters of the wells were:
m = 1,000,000, zi = -20, t = 100 and & = 90°. From the results it is apparent
(figures 133-136) that the resolution at altitudes of 150 and 200 feet (47.7
and 61 m) is rather poor. Of course, even if individual peaks due to the two
casings are not recognized, the width and shape of the composite anomaly differ
from the anomaly caused by a single casing. If, for instance, the density of
wells were 2000/mis as mentioned in the introduction, the average spacing
between wells would be only about 118 feet. In such an area, an airborne
survey would have to be made at a height of 50 feet (15.2 m) or less with a
line spacing on the order of 50 feet (15.2 m) or less tc be able to resolve
most of the individual anomalies. If the density of wells is extremely high
23
-------
and all wells must be identified and located, it might be much more practical
to use ground measurements rather than airborne measurements. Of course, if
the density of wells is extremely high, it may not be necessary to identify
separately all of the wells in the cluster.
If the density of wells in an area is low, the primary concern in design
of an airborne survey is to be sure that one or two of the lines passes near
enuugh to the well that an identifiable anomaly is obtained. The worst case is
when adjacent lines intersect either side of an anomaly at the same level of
intensity or gradient. In the absence of geologic sources and cultural sources
other than casings, one might define an identifiable anomaly to be twice the
maximum noise excursions. To illustrate the design of a survey using the
results of this study, we will assume that the smallest identifiable total
field anomaly is about five times the expected noise level, or one gamma, and
that the smallest identifiable gradient is about five times the expected noise
level, or 0.03 gamma/foot (0.098 gamma/m) for horizontal gradients and 0.015
gamma/foot (0.049 gamma/m) for vertical gradients. These assumptions allow for
the presence of "noise" due to geologic and cultural sources.
Total field anomalies are slightly broader in the east-west direction than
in the north-south direction. Also, magnetometer system noise is likely to be
slightly less on north-south lines than on east-west lines. Therefore, there
is a small edvantage in flying total field surveys in a north-south rather than
an east-west direction.
To find well number 5 using a total field survey and assuming the worst
case, figures 100-103 can be used to estimate that the spacing must be about
480 feet (146 m) for an altitude of 150 or 200 feet (45.7 or 61.0 m). Under
the same conditions, the line spacing to find well number 12 would be about 330
feet (101 m) and to find well number 4 it would be about 900 feet (274 m).
Because of the zero line in the horizontal gradients near the well, a
single component gradiometer measuring dF/dx along east-west lines or one
measuring dF/dy along north-south lines would miss detecting the well if the
line passed almost directly over the well. However, commercially used hori-
zontal gradiometer systems measure the intensity and direction of the total
horizontal gradient so the zero line in one component would not be a problem
for such a system. If two horizontal gradients or the total horizontal gra-
dient are measured, the line spacing can be considerably larger than if only
the vertical gradient is measured. To find well number 12 using the vertical
gradient, the line spacing must be about 220 feet (67 m) for altitudes of 150
and 200 feet (45.7 or 61.0 m). To find well number 12 using horizontal gra-
dients, a line spacing of about 300 feet (91.3 m) could be used for an altitude
of 150 feet (45.7 m) but at an altitude of 200 feet (91 m) the well cannot be
detected. Using the vertical gradient, well number 4 can be detected at an
altitude of 150 feet (45.7 m) with a line spacing of about 360 feet (109.7 m)
or at an altitude of 200 feet (61.0 m) with a line spacing of about 4?0 feet
(128 m). If horizontal gradients are used, the line spacing can be increased
to about 590 feet (179.8 m) for altitudes of 150 or 200 feet (45.7 or 61.0 m).
From this discussion, it is apparent that for the assumptions used the
line spacing can be somewhat larger for total field than for gradient
24
-------
measurements. It is also apparent that, if the assumptions used are valid, it
would be possible to find all of the wells in this study with airborne surveys.
Although the actual flight path of the aircraft can be recovered very accu-
rately with a microwave navigation system, there are significant deviations
between the desired path and the path the pilot is able to fly. These devia-
tions are estimated to be aoout ±60 feet (18 m) or less. Consequently, the
line spacing should be reduced somewhat from the numbers given in the preceding
paragraph. To cover the worst case, the spacing should be decreased by 120
feet (36.6 m). A reduction of 80 feet (24.4 m) is probably reasonable since
the probability of maximum deviations occurring in opposite directions at
adjacent localities on adjacent lines is small. The line spacing necessary to
locate well number 5 is then 400 feet (121.9 m) if total field measurements are
made at an altitude of 200 feet (61 m). This spacing is used in making some of
the cost estimates in appendix II. It may be unrealistic to plan and conduct
surveys to detect all wells, such as number 12, which apparently contains only
a very short length of casing.
Measurements of the total field are usually obtained as a byproduct of
gradient measurement. Thus, it might be effective in some cases to design a
survey based on criteria for a total field survey but to use a gradiometer
system.-- The horizontal gradient information might be very useful in identify-
ing individual wells where several wells occur in a cluster.
•"•V " .. .
RECOMMENDATIONS FOR FURTHER STUDY OF MAGNETIC METHODS
Little further study of the application of the ground magnetic method is
needed at this time. However, if the ground method is applied in a routine
way, the results should be periodically evaluated to see if changes in proce-
dtires or further research is needed. A test and demonstration of airborne
methods is needed: 1) to evaluate the modeling described in this report, 2)
to discover any unforeseen problems in the application of airborne magnetic.
methods to this problem, and 3) to evaluate and demonstrate their effectiveness
in locating wells. Plans have been made to conduct a pilot airborne total
field survey over some of the wells studied in this report and to conduct more
extensive tests in areas near Oklahoma City where there are more than 15 known
wells per square mile (2.59 km^). The results of these surveys should be
carefully evaluated and reported. Gradients should be calculated from the
total field data to help estimate the effectiveness of using airborne gradi-
ometers. Complete evaluation of the airborne results may require a consider-
able amount of ground magnetic surveying and a careful visual examination of
areas. Some of the necessary examination can, no doubt, be done using aerial
photographs. In addition to the planned tests, it would be very useful to
study proprietory and other aeromagnetic data taken over oil fields to obtain
additional information on typical levels for geologic noise.
There are a number of other unanswered questions which have a bearing on
the use of geophysics. An estimate needs to be made of the percentage of holes
in which all or part of the casing was removed and the importance of such holes
in causing pollution should be studied. As additional data are collected, the
magnetization parameter of casings should be determined. The results contained
in this report may not be typical, and, if so, this additional data may be
25
-------
needed to guide the design of future surveys. The effect of corrosion on the
magnetization of old casings should be studied; possibly some wells are no
longer detectable because the casings are too corroded.
26
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SECTION 4
ELECTRICAL METHODS AND THEIR APPLICATION
SUMMARY OF ELECTRICAL METHODS
Many different geophysical methods and techniques comprise what are com-
monly called electrical or electromagnetic methods. Electrical methods often
are defined to include only those methods using direct currents; but, within
tt.is report, we use the term electrical methods to include geophysical tech-
niques using both stationary electrical fields and time-varying magnetic or
electrical fields. These fields may be of.natural or man-made origin.
In resistivity methods, electric currents are driven into the ground and
the resultant electric field or potential difference between two points is
measured. Usually, two electrodes are used for current injection and another
two electrodes are used for measuring potential differences. Commonly, the
current and potential electrodes are placed in one of several standard con-
figurations or arrays, depending upon survey objectives. The potential dif-
ference measured between two electrodes is divided by the current injected into
the ground and then multiplied by a geometric factor calculated from the spac-
ing and direction between electrodes. The results are thus expressed in units
of resistivity, ohm-meters. This "apparent resistivity" would be equal to the
true resistivity of the earth in the vicinity of the electrode array if the
earth were homogeneous. The earth is seldom homogeneous so the measured value
of apparent resistivity reflects a weighted average of earth resistivities in
the vicinity of the array. To map the resistivity of an area, one or more of
the electrodes are moved about to enhance or decrease the relative effect from
various parts of the electrical section. Basically, two survey schemes are
used: in "depth sounding" the spacing between the electrodes is increased
while keeping the center of the array fixed; in "horizontal profiling", all of
the electrodes are moved while maintaining a constant separation between elec-
trodes. Often depth sounding and horizontal profiling are combined by alter-
nately changing the separation and advancing the array. In interpreting
resistivity data, the objective is to define the boundaries between regions of
contrasting resistivity and to determine the intrinsic or true resistivity of
each region.
The magnetometric resistivity method is a hybrid technique in which the
static magnetic field resulting from direct current driven through the ground
is measured. With this method, spatial variations ir> the magnetic field are
used to deduce the relative resistivity of various regions of the subsurface.
In both resistivity and magnetometric resistivity methods, very low frequency,
time-varying currents are used, but the frequency is so low that electromag-
netic induction effects are negligible.
27
-------
A number of earth processes, such as the flow of water through porous
media and chemical reactions between bodies such as metallic ores or steel
pipes and the surrounding rocks and soil, generate static or very slowly
varying currents and electric fields. Such sources are the basis for the
self-potential or SP methods. In the SP method, the potential differences
between two electrochemically stable electrodes placed at different locations
are measured. Usually, one electrode is kept at a fixed position and the other
is moved about to explore the region. There is no way to establish the abso.-
lute value of the potential at the base electrode so each SP survey has its own
base level. The SP method is used for purposes such as studying the flow of
ground water and the exploration for metallic ore bodies and sources of geo-
thermal energy. Variations in the resistivity of the earth influence self-
potential values, but resistivity cannot be determined directly from SP
surveys.
In electromagnetic methods, time-varying magnetic or electric fields or
both are measured. The fields nay be of man-made or natural origin. Induc-
tion coils or sensitive magnetometers are used to measure electromagnetic
fields. At low frequencies, two electrodes are used to measure the electrical
potential differen'.es which, if the electrode spacing is small, are a good
approximation to the electric field.
»,
"A large variety of electromagnetic techniques exist in which artificial
sources, are-used. One type of source is an insulated loop or coil driven by a
harmonic or other time varying current. The time-varying magnetic field
induces eddy currents in the earth which have an associated secondary magnetic
field. The pattern of eddy currents and the secondary magnetic field are
dependent on the resistivity of the earth in the vicinity of the system. For
certain applications, time-varying current is driven into the earth using a
£air of electrodes. Such a source is more complex than the simple loop; the
total current in the earth is a superposition of the "galvanic" current flowing
between electrodes, eddy currents induced by the galvanic currents, and eddy
currents induced by the current flowing in the wire which feeds the electrodes.
Usually, when artificial or controlled sources are employed, one or more
components of only the magnetic field are measured. However, in other tech-
niques, both electric and magnetic fields are measured as in the "controlled
source" magnetotelluric method. In this latter technique^ which employs a
grounded wire source, the ratio of the electric field to the orthogonal mag-
netic field is measured. The results are rsadily expressed in units of
resistivity.
Many electromagnetic surveys are made to locate highly conductive (very
low resistivity) regions which could represent metallic ore bodies or other
features of interest. In interpreting such surveys, one usually tries to
estimate the resistivity of conductive features but not of the'region as a
whole. Electromagnetic methods are also used for depth sounding. By varying
the frequency, the depth of exploration is varied. In interpreting such sound-
ings, the objective is to determine the variation of resistivity with depth.
When current is driven through the earth using electrodes, it has both
vertical and horizontal components. The presence of a vertical steel casing
can locally cause a large change in the distribution of the vertical currents
28
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and corresponding changes in the electric and magnetic fields at the surface.
The magnetic field from a loop or other time-varying source causes eddy cur-
rents t:- flow directly in a steel casing. However, the dimensions of the eddy
current paths in a casing are so small that the secondary magnetic field asso-
ciated with these eddy currents cannot be detected at an appreciable distance
from the casing. In a horizontally layered earth, loop sources cause eddy
currents which flow only in horizontal paths. Horizontal pipelines can sig-
nificantly influence the distribution of these eddy currents. Thus, loop-loop
electromagnetic methods are very sensitive to horizontal pipelines but are
relatively insensitive to vertical casings.
The induced polarization or IP method is, in some respects, a hybrid of
resistivity and electromagnetic methods, but it depends on the ability of the
earth to become electrically polarized. In the IP method, a low frequency
sinusoidal or pulse waveform is driven into the ground with electrodes. Usu-
ally, the resulting potential difference between the electrodes is measured
although in one variation of the technique the magnetic field is measured. If
the earth exhibits polarization, the measured apparent resistivity will de-
crease with frequency and a phase shift between the received voltage and the
injected current will occur. Sulfide minerals, graphite, and some clay min-
erals are sources of polarization. Also, buried metallic objects including
vertical casings can locally cause strong IP anomalies. The direct current
resistivity* is usually obtained as a "byproduct" In making IP surveys. Induced
polarization results and their interpretation are often complicated by the fact
that the frequencies used are high enough to cause electromagnetic induction so
that the effects of the two phenomena are superimposed.
»,
"FIELD MEASUREMENTS
Self-potential surveys were made in the vicinity of 11 wells using a fixed
base electrode and a roving electrode. The SP nonpolarizing electrodes were of
lead-lead chloride construction. Potential differences were measured with a.
high impedance voltmeter. Distinct and fairly large anomalies were found in the
vicinity of four wells, numbers 7, 11, 15 N, and 15 S (figures 140, 142, 144,
145). Small, distinct, short-wavelength anomalies were observed in the im-
mediate vicinity of some of the other wells; for example numbers 14, 16, 17
(figures 143, 146, 147). Small anomalies which appear to be related to the
casing were observed for all other wells except number 6; however, many of
these anomalies are too small and too similar to other features along the
profiles to be diagnostic of a casing. At this time, we have no explanation
of why significant anomalies were observed for some of the wells and not the
others. The anomalies for wells number 7, 11, 15 S and 15 N are quite narrow,
measurements would have to be made on a grid having a spacing of about 10 or 15
feet (3,05 or 4.57 m) in both directions to be reasonably certain of identify-
ing the anomaly. Even then, much additional detailed work would be necessary
to identify the anomalies due to wells and those due to other causes.
Electromagnetic measurements were made using two different systems. One
system, the EM 31, uses a small transmitting and receiving coil operating at a
frequency of about 39 kHz with a looj:> separation of 12 feet (3.66 m). The in-
strument is designed so that it measures apparent conductivity (=l/resistivity)
29
-------
directly. Measurements were made over two casings with the coils in line with
the traverse and perpendicular to the traverse. No anomalies were observed
which could be attributed with certainty to the wells (figures 148 and 149).
Other anomalies which are probably due to buried horizontal pipes or cables
were observed.
Slingram measurements using a Max-Min II system were made in the vicinity
of well number 3 (figures 150 and 151). Slingram systems are similar to the
EM 31 except that the loop spacing is much greater, the frequencies used are
much lower, and the response is not proportional to earth conductivity. No
indication of the well is seen in profiles run with either the horizontal
coplaner or vertical coplaner configurations with a loop spacing of 400 feet
(121.9 m). The results are typical for flat-lying, conductive, sedimentary
rocks and could be inverted to determine the resistivity of the rocks.
RECOMMENDATIONS FOR FURTHER STUDY OF ELECTRICAL METHODS
Neither of the two electromagnetic techniques used, the EM 31 and sling-
ram, are well-suited for the detection of vertical pipe-like bodies. However,
it would be worthwhile to experiment with an electromagnetic method using a
grounded wire source.
It is known from the work of Holladay and West (1981) and others, that
vortical steel casings can cause strong distortion of resistivity and IP
measurements when an electrode is in the vicinity of the casing. At high
frequencies, some of the distortion may be due to electromagnetic coupling.
Due to present interest in the use of IP and resistivity methods in exploration
for oil, a considerable amount of proprietary data exist which show these
effects and which would have been useful in this study. Further evaluation of
any of these data which become available would be worthwhile. However, it must
be noted that IP/resistivity surveying is relatively expensive compared with
magnetic or SP surveying. Therefore, IP/resistivity might be useful in special
circumstances, such as when the upper part of the casing has been removed, but
would probably not be economically practical for more routine problems.
30
-------
SECTION 5
SUMMARY
Initial consideration of the problem of locating abandoned well casings
using geophysical exploration methods indicated that magnetic methods would
generally be most useful and that some electrical techniques might be useful.
Ground magnetic measurements were made over 18 wells in two oil fields near
Denver to develop information which could be used in modeling and in the design
of magnetic surveys. Anomalies having peak amplitudes ranging from about 1,500
to 6,000 gammas were found over all of the known wells tested. Horizontal and
vertical gradients of the total field were measured near some of the wells; the
results suggest that gradient measurements are not as useful as total field
measurements in the areas tested.
?he model chosen to represent a casing is a set of pole pairs. By use of
ajTonlinear least squares curve-fitting (inversion) program, the strength and
locations of'sets of pole pairs, which provide a close fit to the observed
data, were determined. Using this procedure, the position and strength of the
uppermost pole is determined with an accuracy of a few percent, but the error
in the position of lower poles may be much greater. The parameters which were
determined are adequate for predicting results at airborne altitudes and for
other modeling.
t
Using the parameters determined from the ground measurements, it appears
that all of the casings in the test area could be detected from airborne
measurements made at altitudes of 150 to 200 feet (45.7 to 61 m) above the
surface, provided the flight lines are spaced as close as 330 feet (100 m) and
provided noise due to other cultural and geologic features is not too severe.
More data over typical oil fields is needed to establish realistic noise levels.
If the gradients due to geologic sources are not too high, it appears that the
detection range tor total field measurements is greater than for gradient
measurements, given the instrumental noises of present equipment.
Self-potential anomalies were found to be associated with most of the
wells where measurements were made. However, the anomalies tend to be narrow
and low in amplitude so it is suggested that use of this method be considered
only in cases where magnetic data are inadequate or cannot be acquired.
Test wells were not detected using two loop-loop electromagnetic methods.
However, theory suggests that electromagnetic methods using loop sources would
not be effective and that only those methods employing grounded wire sources
should be used. Theoretical studies and field data, which have been obtained
by private contractors and most of which is proprietory, indicate that the
resistivity and induced polarization methods are sensitive to the presence of
31
-------
steel casings. These methods would be much more expensive to use than magnetic
methods but might be useful in special circumstances. In particular, the depth
range of these methods may be greater than that of magnetic methods in cases
where the upper part of a casing has been removed.
32
-------
SECTION 6
REFERENCES
Anderson, W. L. 1982. Adaptive nonlinear least-squares solution for con-
strained or unconstrained minimization problems: U.S. Geological Survey
Open-File Report No. 82-68.
Barret, W. M. 1931. Magnetic disturbances caused by buried casings: The Bull.
of the Amer. Assn. of Pet. Geol. Vol. 15, reprinted in Early Papers of the
Society of Exploration Geophysicists, Tulsa, Oklahoma, pp. 89-105.
Donovan, T. J., R. L. Forgey, and A. A. Roberts. 1979. Aeromagnetic detection
of diagenetic magnetite over oil fields: Am. Assoc. Pet. Geol. Bull.,
Vol. 63, Ho. 2, pp. 245-248.
Fabiano, E. B., N. W. Peddie, D. R. Barraclough, and A. K. Zunde. 1983.
International Geomagnetic Reference Field 1980 - Charts and Grid Values
(IAGA Bulletin No. 47): U.S. Geological Survey Circular 873, 142 pp.
Fabiano, E. B., and N. W. Peddie. 1981. Magnetic total intensity in the
United States - Epoch 1980: U.S. Geological Survey Map 1-1370.
Hildenbrand, f. G. 1982. Model of the southeastern margin of the Mississippi
Valley graben near Memphis, Tennessee, from interpretation of truck-
magnetometer data: Geology, Vol. 10, pp. 476-480.
Holladay, J. S., and G. F. West. 1981. Effect of well casings on surface
electrical surveys (abs): Geophysics Vol. 47, No. 4, p. 439.
Hood, P. J., M. T. Holroyd, and P. H. McGrath. 1979. Magnetic methods applied
to base metal exploration: Geological Survey of Canada Economic Geology
Report 31, pp. 77-104.
Johnston, K. H., H. B. Carroll, R. J. Heemstra, and F. E. Armstrong. 1973.
How to find abandoned oil and gas wells: U.S. Bureau of Mines Information
Circular 8578, 46 pp.
Lam, J. 1977. Introduction of a rectangular ferrite slab with magnetic field:
AFWL-TR-76-199 available from NTIS ADA041944.
Nettleton, L. L. 1976. Gravity and Magnetics in Oil Prospecting: New York,
McGraw-Hill, 464 pp.
33
-------
Parasnis, D. S. 1975. Mining Geophysics (2nd ed.): New York, Elsevier, 395 pp.
Petty, A. J., J. L. Vargo, and F. C. Smith. 1966. Aeromagnetic map of the
Denver area, Colorado: U.S. Geological Survey Geophysical Investigations
Map GP-557.
Senti, R. J. 1982. Special report on geophysical activity in 1981: The
Leading Edge, Vol. 1, No. 4, pp. 30-55.
Telford, W. M., L. P. Geldart, R. E. Sheriff, and D. A. Keys. 1976. Applied
Geophysics, Hew York, Cambridge University Press, 860 pp.
Van Weelden, A. 1933. Magnetic anomalies in oil fields: Proc. World Congress,
London, Vol. I, pp. 86-90.
34
-------
Reproduced from |f
best available copy. %,,!;l
EXPLANATION
Memettc eowtour* »B«wffi8 tot«l Intensity
moenooe ««»« of &• asrtn In g«»m««
foi»o»« t» OfWtr»r» eetum
lecmlen ol martyred m»«im«m of minimum
a
Figure 1. Well locations and aeromagnatic map for test area east of Denver.
35
-------
Reproduced from
best available copy.
z^-x^^^-^
—^ • ,-^^?y i°_>
ITVoPSr ' C 0^
•V.
scAte uwcoo
10 II _
19
EXPLANATION
fc9ae*«tlc contours af.ovn
Rieanonc ntia of tn* cartti m
re<«ttv« to ifDitrvry datum
Locnton e< f»«nur«e
intontity •itnin cieuo nifn of ;io»«o >0w
of «J»B«
m Taew 1
Figure 2. Well locations and aeromagnetic map for test area north of Denver.
36
-------
CO
ra
1/1
3
ID
We 11*1 LOWY STATE 5-25 T5S-R85¥ S2S 8/11/82
I ,
'S
a
en
5
*»«
in
-60 -40 -20 0
DISTANCE ( x 10 ft )
20
40
N
Figure 3. North-south profile of total field over Well Number 1.
-------
1 LOVRY STATE 5-25 T5S-RG5V SC5 E-H LINE
CO
00
-30 0
DISTANCE ( K 10 ft >
Figure 4. East-west profile of total field over Well Number 1.
-------
co
VD
Well*2 LOWY STATE 1-SS T5S-R8SY S3^M-S LINE
-30 -43
-20 0 20
DISTANCE ( M 10 ft )
40
N
60
Figure 5. North-south profile of total field over Well Number 2.
-------
Welt*2 LOtfRY STATE 1-35 T5S-R6SU 535 E-Y LIKE
8
o> r-
fc
w
Si
•-63
-23 0
OISTAHCE ( M 10 fi )
63
Figure 6. East-west profile of total field over Well Number 2.
-------
LOBBY STATE 5-38 T5S-R6SV 533 K-S LINE
1
•9—• »•
N
-60
-23 B
DISTANCE: (« 10 ft >
Figure 7. North-south profile of total field over Well Number 3.
-------
ro
UOY STATC«5-38 T5S-R3SN .538 E-¥ LIME
* *•
8
E
-------
Wel!*4
. STATE A-I TSS-RGSV saa M-S LINE
N
9
S!
Ci!
CO
in
-60
-40 -20 0
DISTANCE < x 10 fl )
Figure 9. North-south profile of total field over Well Number 4.
-------
Weil* 4 PEWG01L STATE A-l T5S-R8SV S38 E-V LINE
w
9
L'i
8i
»-»
fc
K
&
a
-40 -20 0
DISTANCE ( M 10 fi )
23
40
60
Figure 10. East-west profile of total field over Well Number 4.
-------
tn
i
t
Well#5 TEXACO STATS Y-l T5S-R84V S20 H-S LINE
* r-
N
-00 -40
-20
DISTAMCE ( M 10 fl )
Figure 11. North-south profile of total field over Well Number 5.
-------
w
Si
«-«
L'i
-80
TEXACO STATE Y-l T5S-R64W S2B E-tf LINE
-23 B|
DISTANCE ( K 10 ft )
60
Figure 12. East-west profile of total field over Well Number 5.
-------
SI
•-•
ft
CO
ta
We!l*6 TEXACO STATE 2-1 T5S-R64H SIB N-S LINE
-63 -
-------
Well#6 TEXACO STATE Z-l TSS-R84V SIB E-¥ LIkE
oo
a
VI
1
«a
*-4
K
w
I!)
-23 0
DISTANCE ( x 13 ft )
20
40
68
Figure 14. East-west profile of total field over Well Number 6.
-------
WHHER GOOSE ft T5S-R84V SiO H-S LINE
•J
i
* K
-60 -40
40
N
( K 10 ft)
Figure 15. North-south profile of total field over Well Number 7.
-------
01
o
w
A'l
IR
-60
HBTIER UH1SE 01 T7SHR04U S1U E-V l.lltK
-40
-29 0
DISTANCE ( x 18 ft )
68
Figure 16. East-west profile of total field over Uell Number 7.
-------
HUB H-S Ll»r
K
h
n
o:
N
Figure 17. North-south profile of total field over Well Number 8.
-------
01
ro
8
w
to i-
oo
in
O)
In
Si
Ol
C'J
ui
if)
P
!n
In
hti.18 t-v nrr
rf""! I » i"l • i t 1 « i i I
I I I I
480 -280 0
UIST/JICI-: (x i
Figure 18. East-west profile of total field over Well Number S.
-------
VH.19M-SL1NE
Ol
CJ
s
Br-
10
in
m
to
CJ
U)
'9 to
Ol
o
2
in
n>
tl
P
hi
HI 1 1
N
•—I—t-
1 9-
-4m
400
600
6(12
( v I fl )
Figure 19. North-south profile of total field over Well Number 9.
-------
Will9 E-V LINE
01
w
00
in r-
ro
in
8
O)
In
S
&
o
tit
oo
CD
L'i
CJ
* I
CJ
li]
•6S0 -400 -200 0 200
Disuucr (x i ri >
-------
VEIL 10 N-S t IKE
en
en
N
O!
in
en
(O
in
H
Ol
N-*
II
in
in
li!
DISTANCE ( x I ft )
Figure 21. North-south profile of total field over Well Number 10.
-------
w
01
o>
in
BELL 19 E-V LINE
-223 0
DISTANCE ( x 1 ft >
Figure 27.. East-west profile of total field over Well Number 10.
603
-------
I) N-S LINE
en
-.4
8
IO
CD
en
-------
w
E
un
CO
a
KLL II E-V LINE
i
-2(99 0
DISTANCE ( x I fI )
400
Figure 24. Fast-west profile of total field over Well Number 11.
-------
Ul
El
CD
><
O)
[n
(M
IM
U)
3 a
In
tit
in
(M
CD
PI
*•**
li!
!2 N-S LINE
N
0a -200
HIS1ANCF ( x 1 fl )
200
Figure 25. North-south profile of total field over Well Number 12.
-------
Will 12 E-V t lilt
en
o
w
tj
In
c,
in
m
0)
fc
CJ
GO
no
if)
*-•
H
lit
_
.
-
J{ '
•- » • •-*/ fc *^^ J .
t
A __ . n • • it • • • « a • i • • • • •
D1ST/JCK ( x 1 fl )
Figure 26. East-west profile of total field over Well Number 12.
-------
WELL 13 M-S LINE
to
u>
-I
CO
tn
CD
• •
f. &{
3 •"
R
8,
o
•sc.
IM
"
in
If I
N
_L
-IRU
fl 100
JJISUflLL ( x I fl )
?Cl3
300
Reproduced from
bosl available copy.
Figure 27. North-south profile of total field over Hell Number 13.
-------
tt-Ll 13 E-V LI HE
er>
ro
GO
to
Ul
CD
U>
CJ
w
1»"
£
CD
I/}
(I)
in
s
Ft
* •
«M
•\m
v*,****-*-*-
4 oa
Gffil
603
7BO
801!
DJSTAHCR ( w 1 fl )
Figure 28. East-west profile of total field over Well Number 13.
-------
BELL #14 «-Sl 1/1/82
V
' . , J
1 1 1
j#(******* • * ° — •—•--• — •• • • • ^
f i . . .
-CC3 -400 -209 0 200 400 600 80C
DISTANCE ( x 1 Ft )
Figure 29. North-south profile of total field over Well Number 14.
-------
WELL fi4W-Ell/l/82
I
09
£
i
6
D
-
-
, vtf
A, .•-! i .......
1 1 1 1 1 1 I 1
« -600 -400 -200 0 200 400 800 80
DISTANCE ( x 1 ft )
Figure 30. East-west profile of total field over Well Number 14.
-------
MELLI1S4 N-S LINES 1-2 11/16/82
en
-600
-400
-200 0
DISTANCE ( x 1 ft )
Figure 31. North-south profile of total field over Well Number 15 N.
-------
en
YELLI15N «-E LltES 3-4 11/16/02
-600 -400 -200 0 200
DISTANCE ( x I ft )
400
600
BOC
Figure 32. East-west profile of total field over Well Number 15 N.
-------
WELLfflSS FPS LINES 1-2 111/16/82
» r
(O
_l
-800
-400 -200 0
DISTANCE ( x 1 ft )
400
60C
Figure 33. North-south profile of total field over Well Number 15 S.
-------
VELL015S V-E 11/16/92
CM
00
-600
-400
-200 0
ntSTANCE ( x 1 Ft )
Figure 34. East-west profile of total field over Well Number 15 S.
-------
WELL#18 M-S LINES 1-2 11/12/82
10
I
• • •" t i •
J_
-600 -400
-200 0
DISTANCE ( x 1 ft )
200 400 800 80C
Figure 35. North-south profile of total field over Well Number 16.
-------
VELL#18 W-E LINES 3-4 11612/82
5i in
IS
2 J8
fc
-600 -400 -200 0 200
DISTANCE ( x 1 ft )
400
600
80C
Figure 36. E&st-wcst profile of total field ovor Well Number 16.
-------
VELLfl? N-S LINES 1-2 11/19/82
8
• • •
• B
1
« - 0
0 - 1
1 - »
-600 -400 -200 0 200
DISTANCE ( x 1 ft )
400
600
BQC
Figure 37. North-south profile of total field over Well Number 17.
-------
WELU17 S-E LINES 3-4 11/13/82
ro
(n
2DO
400
600
UOC
Figure 38. East-west profile of total field over Well Number 17.
-------
S-H SOUTH FROM H 14($SM 11/10/82
i o a • • » t.
OJ
I I I I I
-150 -103
-50 8
DISTANCE ( M 1 f I >
50 108 ISfl 20E
Figure 39. North-south profile of horizontal differences.
-------
V14HC N-E VEST FROM EAST 14QWE 11/10/82
1
-------
V14VC S-N TOP FRQ4 BOTTOM 14GVSN 11/19/B2
in
en
§
m
i
I
-ISfl
-53 0
DISTAtCE ( x 1 ft >
150
Figure 41. North-south profile of vertical differences.
-------
V14VG V-E TOP FROM BOTTGH )4GW£* ,11/10/82
1
I
-150
-50 0
DISTANCE ( x I fl )
100
150
222
Figure 42. East-west profile of horizontal differences.
-------
Y1GKG S-N SOUTH FROM N 18GHSN 11/10/82
• • • •
-lea -53
53
1E3
( M i f I >
• ' •
150
20*
Figure 43. North-south profile of horizontal differences.
-------
V18HG
FW* EAST U»«E
oo
(9
I
-isa
-IB;
-sa
DISTANCE ( x I ft >
50
168
-------
ea
*-4
V1BVG 5-N TOP-FROM BOTTOM ifecVSN 11/19/62
VO
«r >i~i i • > «. i
-iss -tea
-se e
DISTANCE ( « 1 f t )
153
1B8 159
Figure 45. North-south profile of vertical differences.
-------
oc
o
V1BVG V-E TOP FROM BOTTOM 18CWE 11/19/02
-153 -1GB -50 0
DISTANCE < * 1 ft >
1B3
158
Figure 46. East-west profile of vertical differencns.
-------
VELUF7 VERT. COUP. M-S 7DHVC 12/
00
I
Jh '
i !_..._
-103 0
DISTANCE ( x 1 ft )
308
402
Figure 47. North-south profile of vertical component.
-------
KLLI7 VERT.COMP.U-C 70MYCT 12/3/82
ro
M
r
-5 8
in
1
-203
-100 0 100
DISTANCE < x 1 ft )
2ft)
383
Figure 48. East-west profile of vertical component.
-------
03
CO
-------
f !
HOR.COW.V-C 7DMHCV 12/3AJ2
co
v r
(M !
Ol
(M
f
1
•
-309
-200 -tea 0 ico
DISTANCE ( x 1 ft >
I
200 303
Figure 50. East-west profile of horizontal component.
-------
INVERSION OF WELL #1
00
in
87000.
0*800.
86600.
6C400.
— 86200.
W
X 86000.
is
"" 89800.
88600.
68400,
88200.
88000.
o
V
OOP Or»
g
in
I
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 51. Observed and calculated results for Well Number 1.
-------
INVERSION OF WELL #1
tMVW.
87BOO.
87000.
86500.
- «000.
2 83500.
a 3
BSOOO.
S4500.
84000.
85900.
53000.
<
c
'
1 ' 1 ' 1 ' 1 ' 1 ' I ' 1 ' 1 ' 1
-
- A ~
'~ A '•
~
o
-
1 . 1 . 1 . 1 . 1 . I . 1 . 1 . 1 .
• •****•*•*<
>oeoooooooo
>oooo o o o o o
>»H>W»-' *-WW*-«
DISTANCE FROM WELL ALONG THE E-W PROFILE
Fiaure 5Z. Observed and calculated results for Well Number 1.
-------
INVERSION OF WELL #2
D2DUV.
99000.
98300.
59000.
- B7BOO.
| 97000.
U
23 "* 96300.
96000.
95500.
99000.
04800.
c
<
»
1
1 • 1 • 1 • 1 • 1 • 1 • 1 ' 1 • 1 •
i
— . —
-
-
-
;
>
-
-
1 :
Jl
» *
• i . i • i . i . i . i . i , i . i
»oooooooooc
20000 ooooe
>»rtw*- *-wro^ai
I i i I
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 53. Observed and calculated results for Well Number 2.
-------
INVERSION OF WELL #2
oo
oo
89000.
99000.
33000.
37500.
~ 37000.
V)
(J
96300.
36000.
35SOO.
33000.
94300.
84000.
I . I
'00 O 00
o
o
CM
DISTANCE FROM WELL ALONG THE E-V PROFILE
Figure 54. Observed and calculated results for Well Number 2.
-------
oo
<£>
INVERSION OF WELL
asm.
ESSSfl.
6S5S3.
SS7930.
6S5S3.
02039.
84SM.
I . I . I . I
I . I
f
DISTANCE FROM WELL ALWC THE N-S PROFILE
• m V
§ I i
Figure 55. Observed and calculated results for Well Number 3.
-------
INVERSION OF WELL 03
ve>
o
07000.
BC800.
B6COO.
BS4CO.
- BCOO.
|| ccooo:
u
~ B9800.
BB500.
68400.
S0200.
BS300.
I
8
g
7
§
7
8
i i
DISTANCE FROM WELL ALONC THE E-V PROFILE
Figure 56. Observed and calculated results for Well Number 3.
-------
H INVERSION OF WELL *4
vo
£0000.
89000.
6SOOO.
fiasco.
— (M»oo.
CO
X B7BOO.
2
~ 87000.
OCSOO.
66000.
Besoe.
80000.
g
f
O Q o Q
s
DISTANCE FROM WELL ALCNS THE N-S PROFILE
S
S
Figure 57. Observed and calculated results for Well Number 4.
-------
INVERSION OF WELL *4
ho
csooo.
C2000.
«IOOO.
crooo.
~ 89000.
CO
«J
MCOO.
07000.
86000.
BOOM.
84000.
63000.
I
s
n
i
o o o o o o
So o o o
— —MM
I I
DISTANCE FROM WELL ALONG THE E-V PROFILE
S
a
S
Figure 58. Observed and calculated results for Well Number 4.
-------
INVERSION OF WELL
VO
cooco.
8S3CO.
BSSOO.
6CSOO.
— GCSOO.
Q7EM.
87080.
(KSflO.
85000.
o
GESSO.
S
DISTANCE FROM WELL ALONG THE N-S PROFILE
S
ro
Figure 59. Observed and calculated results for Well Number 5.
-------
INVERSION OF WELL #5
ID
CC380.
P33C3.
BS8M.
6I2&0.
S •"«>•
I 67300.
~ 07000.
fiSQOO.
ssm.
63SOO.
a o—a
-e-o-e>o-e3
S
f
§
7
s
DISTANCE FROM VEIL ALONG THE E-W PROFILE
Figure 60. Observed and calculated results for Well Number 5.
-------
H INVERSION OF WELL #6
to
in
MOOO.
69000.
89000.
09600.
~ BtOOO.
(0
£ 87600.
87000.
BSOOO.
GCOOO.
CGGOO.
60CCO.
S
8
7
8
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 61. Observed and calculated results for Well Number 6.
-------
INVERSION OF WELL #6
en
09800.
63WM).
66800.
MOOO.
— B7BOO.
in
07000.
86600.
BGOOO.
66300.
BOOM.
B4000.
v
?
ooo e
S S S ° 8
DISTANCE FROM WELL ALONG THE E-U PROFILE
o
8
S
Figure 62. Observed and calculated results for Well Number C.
-------
N INVERSION OF WELL #7
VO
£0000.
esses.
83000.
acsso.
600C9.
67800.
87000.
83500.
esooo.
S33SO.
S
X
±rf . 1
S
V
I I
DISTANCE FROM WELL ALONE THE N-S PROFILE
m v
i §
Figure 63. Observed and calculated results for Well Number 7.
-------
INVERSION OF WELL »7
00
O30WJ.
89000.
83300.
eaooo.
- 67000.
£ 6/000.
~ KWO.
BGOOO.
86BOO.
68000.
64500.
<
«
• 1 ' 1
-
-
-
-
*•
-
1 . I
. • •
> o o
» o p
T 7
1 • 1 • 1 • 1 • 1 • 1 • 1 •
n "
"
II "
1 "
1 1 '•
i \
•
• l«ltlalilil«ti
«•*•*•• i
S80SgggS
77 - M K> •»• *
DISTANCE FROM WELL ALONG THE E-V PROFILE
Figure 64. Observed and calculated results for Well Number 7.
-------
„ INVERSION OF WELL #8
to
VO
B3OOV.
05000.
BOSOO.
88000.
— 87BOO.
<
H 87000.
~ 86800.
SSOOO.
85800.
08000.
ff/fUUl
OCOilv.
c
1
-
-
-
_
-
-
-
1 . 1 • 1 • 1 1
> O O O p «
» 0 O O O
7777
1 1 • I • 1 • 1 •
'
• -
_
•
-
-
-
l^_ _ :
1 1 • 1 . 1 . 1 .
3 O O 0 0 C
O 0 0 O C
•• W M ^ V
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 65. Observed and calculated results for Well Number 8.
-------
INVERSION OF WELL #8
o
o
6SOW.
68080.
8
-------
H INVERSION OF WELL
BS350.
SC333.
•» BPC80.
X B7CSB.
«^
U.
czsu.
CIS50.
B4SS3.
I
I
I
f I
I I
DISTANCE FROM WELL ALOW THE N-6 PROFILE
t t ii i
Figure 67. Observed and calculated results for Well Number 9.
-------
o
ro
INVERSION OF WELL
B70B3.
G53S9.
i . t . 1.1
S
7
1 .__.! t . I . ...-J
§ i § i
DISTANCE FRTO< WELL ALCWC THE E-W PROFILE
Figure 68. Observed and calculated results for Well Number 9.
-------
o
OJ
H INVERSION OF WELL
69000.
raooo.
88300.
— B73C9.
o>
Si B7DCO.
GC909.
8*009.
068GO.
98000.
64SOO.
o
n
i
S
-O ' 000*6"
S
n
a
8
DISTANCE FROM VELL ALONG THE N-S PROFILE
Figure 69. Observed and calculated results for Well Number 10.
-------
INVERSION OF WELL #10
B9000.
B5000.
6S600.
rooco.
— B7500.
5 07000.
t «"*«•
MOW.
K5BOO.
05000.
84BOO.
a
V
e o o
s
DISTANCE FROM WELL ALONG THE E-V PROFILE
Figure 70. Observed and calculated results for Well Number 10.
-------
INVERSION OF WELL *1t
o
en
89000.
89000.
88500.
6MOO.
— 87BOO.
(I)
X 07000,
06000.
53500.
09000.
O O O O
•oeooo o • o
o
»
I
DISTANCE FROM WELL ALONS THE N-S PROFILE
Figure 71. Observed and calculated results for Well Number 11.
-------
„ INVERSION OF WELL #11
GSOOO.
8C3SO.
03030.
G7ESO.
07CDO.
ESOCO.
eosoo.
53000.
B4S99.
o • o o o ..oooooeasss
OOOOO' O O O O
o
o
I
S
7
M
DISTANCE FROH HCLL ALO^ THE E-M P.XOFILE
Figure 72. Observed and calculated results for Well Number 11.
-------
INVERSION OF WELL *12
B3SCO.
85880.
OC500.
ES889.
07039.
O&COO.
03900.
65889.
BBOG6.
64GOO.
|
9
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 73. Observed and calculated results for Well Number 12.
-------
INVERSION OF WELL
o
oo
6S3S9.
B23CO.
BC253.
B33I8.
*• 678*9.
£ C7EC3.
" E3838.
cssso.
CS399.
E3BC3.
&CS39.
U.
59-00000 o e o e
§
7
DISTANCE FROH WELL ALONG THE E-W PROFILE
I
S
n
Figure 74. Observed and calculated results for Well Number 12.
-------
N INVERSION OF WELL #13
C1000.
(0099.
MOOO.
08000.
- 87000.
X 6COOO.
"* B8BOO.
84000.
85000.
82000.
81000.
OOCOOOa
8
S
7
S
DISTANCE FROM WELL ALONG THE N-8 PROFILE
Figure 75. Observed and calculated results for Well Number 13.
-------
INVERSION OF WELL #13
BMOO.
69000.
BCGCO.
MOOO.
07300.
67000.
HOMO.
06000.
8B300.
BBCC-9.
e
-------
» INVERSION OF WELL f14
83600.
BttOO.
(M800.
BSOW.
~ 07800.
«n
87000.
06500.
86000.
BSOOO.
58000.
84000.
0-0-000-
o
^
I
H
s
o
D
DISTANCE FROM VEIL ALOW THE N-S PROFILE
Figure 77. Observed and calculated results for Well Number 14.
-------
INVERSION OF WELL *14
ro
O7OV0.
69000.
58000.
MCOO.
— B7VOO.
5 B7009.
C3
KOOO.
B8SOO.
BBOOC.
B4SOO.
<
c
i
: i :
: t
-
_
1
-
I
t .
:
\
1 o -
• •
i . i . i i i . i . i . i . i . i
• **««*•••*
10000000000
XOOOO O^'^OC
•I7V7 .«•.»«
DISTANCE FROM WELL ALONG THE E-W PROFILE
Figure 78. Observed and calculated results for Well Number 14.
-------
INVERSION OF WELL #15
63000.
C2000.
etooo.
coooo.
- 59000.
in
X 98000.
C5
U.
97000.
96000.
99000.
94000.
93000.
o
•r
I
O
o
tn
•ooooo o o o o
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 79a. Observed and calculated resuUs for Well Number 15 S.
-------
N
INVERSION OF WELL
63000.
62000.
61000.
60000.
- 69000.
SBOOO.
57000.
86000.
09000.
84000.
83000.
u.
o
o
n
-e—o
o
o
*
I
g
DISTANCE FROM WELL ALONG TltE N-S PROFILE
Figure 79b. Observed and calculated results for Well Number 15 N.
-------
INVERSION OF WELL #15
««000.
£3900.
£2000.
CIOOO.
- £0000.
I
3
59000.
S9000.
97000.
3£000.
33000.
94000.
a
n
oooo-o
onoeeoou—»•
o
7
o
o
o
o
o
o
IM
DISTANCE FROM WELL ALONG THE E-W PROFILE
Figure 80a. Observed and calculated results for Well Number 15 S.
-------
INVERSION OF WELL #15
BJUUU.
62000.
61000.
60000.
- SSOCO.
U)
a! 3COOO.
U
*" 87000.
05000.
53030.
31000.
Binno.
1 1 • 1 ' 1 ' 1 ' 1 ' : 1 ' 1 ' ! • 1 '
-
-
**
C
o/
^Jft/
0
1 :
\ "
V "
_
. 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 .
DISTANCE FROM WELL ALONG THE E-W PROFILE
Figure 80b. Observed and calculated results for Well Number 15 N.
-------
,, INVERSION OF WELL #16
csooo.
C2000.
coeoo.
— SSOOO.
0>
H B6000.
is
.** 07000.
BS090.
C500D.
S1009.
05000.
o
?
o o u • e OOOCH>
^-oooo • o o o e
oooo
o o o o
T 7 7 7
DISTANCE FR(W WELL ALONG THE N-S PROFILE
Figure 81. Observed and calculated results for Well Number 16.
It::'
-------
INVERSION OF WELL
00
60000.
osaoo.
B9900.
03SSO.
-» 60000.
to
i vow.
S6&00.
86OTO.
3S300.
68090.
ooooo
DISTANCE FROM WELL ALONG THE E-W PROFILE
Figure 82. Observed and calculated results for Well Number 16.
-------
INVERSION OF WELL #17
esroo.
flSOOO.
ocoeo.
•» 67800.
OT
070C9.
BOT50.
B30C3.
553CD.
63CC4.
O O O O
»0000
O
O
s
7
O
7
DISTANCE FROM WELL ALONS THE N-S PROFILE
Figure 83. Observed and calculated results for Well Number 17.
-------
INVERSION OF WELL 017
ro
a
C0009.
89800.
09000.
86800.
~ BMOO.
-------
WELL #6 HOLDING L=73» CONSTANT
coooo.
BJSOO.
09000.
80000.
"> 08000.
in
87500.
07000.
BC300.
B6000.
85500.
BBOOO.
? ? ? °
^? ????.'
S
7
7
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 85. Observed and calculated results for Well Number 6.
-------
WELL *S HOLDING L«73' CONSTANT
IN)
ro
B9600.
89000.
0*300.
- 07800.
X. 07000.
I K800'
86000.
73900.
BSOOO.
04000.
S
o- e e e ooeoooo
oooeo o—e e o
§
7
DISTANCE FROM tfELL ALONG THE E-V PROFILE
Figure 86. Observed and calculated results for Well Number 6.
-------
WELL 06 HOLDING Z=-10.6'.L=123' -
fNJ
CO
CONSTANT
N
DISTANCE FROM WELL ALONG THE N-S PROFILE
Figure 07. Observed and calculated results for Well Number 6.
-------
ro
WELL #6
CONSTANT
u
69000.
6SCOO.
BG8OT.
08009.
67809.
B7000.
sseoo.
86900.
85300.
esaoo.
81800.
HOLDING Z=-10.6'.L«123'
o
o
eeeoo
j
oo ooe
j_
e oo
s
I I I
DISTANCE FROM WELL ALONC THE E-W PROFILE
Figure 08. Observed and calculated results for Well Number 6.
-------
MAP OF WELL #4, 150 FT. ABOVE GROUND
Figure 89. Calculated airborne total field contour map of
10910 (F-Fmin)-
125
-------
I I I I I I I I I
1 II 1 I I
-600 -
-700.
o o o o o a
o o o o o o o
K u> n
-------
-700.
ooooo
OOOOO
r\ v> n •*• to
I i i i I
MAP OF WELL #4. 250 FT. ABOVE GROUND
Figure 91. Calculated airborne total field contour map of
*
127
-------
VELLiM CALC N-S PROFILE. 100 FT.
55278.3
ro
oo
1 r \ i • i • • i • i • i • i
DISTANCE (FEET)
Figure 92. Calculated airborne total field profile at 100 ft for Well Number 4.
-------
VELUM CALC E-V PROFILE. 100 FT.
ro
vo
55276.6
55267.6
to
<
C9
o o
o in
•*• to
o
o
to
I
o
in
CM
o
o
M
I
O
tn
o o
o tn
*- \
o
in
o o o
o in o
— — CM
o o o
in o in
CM to to
o
o
DISTANCE (FEET)
Figure 93. Calculated airborne total field profile at 100 ft for Well Number 4.
-------
WELL#4 CALC K-S PROFILE. 150 FT
55229.8r-r
I • I ' I ' I ' I ' I *!
55221.4
~ 55212.3
09
Z
< 55204.4
o:
o
o
551S5.9
55187.3
T^yK^
o o o
o to o
to jo •*
DISTANCE (FEET)
Figure 94. Calculated airborne total field profile at 150 ft for Well Number 4.
-------
VELLiM CMC E-V PROFILE. 150 FT.
55228.6
CO
DISTANCE
-------
VEU.JM CALC N-S PROFILE. 200 FT.
LO
ro
CO
<
3
55211.2
55209.3h
55204.6 -
z 55199.8
•-«
a
5
* 55195.1h
ui
g 55190.4 -
55187
P • I ' J ' I ' I ' I • I
I • ' M ' ' '
o
o
00
I
o
o
rs
I
o
o
o
o
in
i I
o
o
o
o
ro
o
o
o
o
o
o
o
o
o
o
o o
o o
*- in
o
o
o
o
o
o
oo
DISTANCE (FEET)
Figure 96. Calculated airborne total field profile at 200 ft for Well Number 4.
-------
CO
VELUM CALC E-V PROFILE. 200 FT.
_i.
55210.9
to
a:
is
o
z
CJ>
55205.7 -
55201.1 -
55196.5 -
55192.0 -
55188.1
' I ' [ ' 11
o
a
00
I
O
o
10
O
O
in
o o
o o
o o
o o
w •-
I I
oooooooo
OOOOOOOQ
— cviroTinvorxoo
DISTANCE 1FEET)
Figure 97. Calculated airborne total field profile at 200 ft for Well Number 4.
-------
VELL*4 CALC N-S PROFILE. 250 FT.
55202.9
i
t
55200.0
~ 55197.0
to
*-«
*g 55193.9
U
I ' Jr\t ' I ' I ^1 ' l1 I ' I '
DISTANCE (FEET)
Figure 98. Calculated airborne total field profile at 250 ft for Well Number 4.
-------
WELL#4 CALC E-V PROFILE. 250 FT.
CO
in
55202.6 r-r
55199.8 -
x
- 55196.9
19
2
>•*
< 55194.1
o
P 55191.2H
uj
C5
55168.1
o
o
09
I
O
O
O
u>
I
o
o
Cs
O
o
7
O
O
O
T
O O
o o
— CM
O
o
O
O
o
o
in
o
o
o
o
o
o
00
DISTANCE (FEb'T)
Figure 99. Calculated airborne total field profile at 250 ft for Well Number fl.
-------
VELL#3 CALC N-S PROFILE. 150 FT.
OJ
V)
55225.2
55224.6
CO
| 55222.4
55220.2 -
55218.1 -
ta
>-«
a
UJ
cc
o
»-•
z 55215.9 -
o o o
o in o
ro •«•
DISTANCE (FEET)
Figure 100. Calculated airborne total field profile at 100 ft for Well Number 5.
-------
VELU5 CAUC E-V PROFILE. 150 FT.
55225.0
to
-4
ooo
o in o
*. — (M
DISTANCE (FEET)
Figure 101. Calculated airborne total field profile at 150 ft for Well Number 5.
-------
t€LL#5 CALC N-S PROFILE. 200
CO
00
x
55220. 3 f-
55219.2h
I ' I ' I ' I ' I ' f
~ 55218.0
is
< 55216.9
hi
CC
u
z
U)
55215.7h
o
o
to
g
o o
o o
r>. w>
I
I
o
o
in
o o o o
o o o o
•"?•
I
^ CVJ «-
o o o o
o o o o
— CM K> T
O
o
in
o o o
• • •
o o o
000
«jQ fx CO
I
I
I
DISTANCE (FEET)
Figure 102. Calculated airborne total field profile at 200 ft for Well Number 5.
-------
<*>
VELL#5 CALC E-V PROFILE. 200 FT.
55220.3
z
t-«
a
uj
a:
o
2
CD
55219.1
55217.9
55216.8
55215.7
=rT*r I ' I ' I ' I ' I
I ' I ' I ' I "I ' I '"
o
o
o
o
o
o
ID
I
o o
o o
to -«•
I I
o
o
o
o
o
o
o
•
o
O
o
O
o
o
o
o
o
to
o
o
u>
o
o
o
o
00
DISTANCE (FEET)
Figure 103. Calculated airborne total field profile at 200 ft for Hell Number 5.
-------
VELL*6 CALC N-S PROFILE, tOO FT.
CO
ac
o
L9
z
t-t
a
a:
o
55213.9
55204.4 -
55196.2 -
55188.1 -
w 55179.9
CJ
55173.0
o o o
o in o
— — CM
o
in
CM
o
o
O
in
to
o
o
DISTANCE (FEET)
Figure 104. Calculated airborne total field profile at 100 ft for Well Number 6.
-------
VELLJ6 CALCULATED N-S PROFILE. 150 FT.
£ 55191.
21
<
CD
Z
a
LJ
a:
o
•—4
J-
UJ
U)
3C
55188.
55185.
55181.
55178.
55174.
-T-J-I l^n^^l1^ I T
O Ct O
(O O U)
— — . i
DISTANCE (FEET)
Figure 105. Calculated airborne total field profile at 150 ft for Well Number 6.
-------
VELU6 CALC N-S PROFILE. 200 FT.
ro
55183.3
55182.3
< 55180.6
15
O
5 55178.8
a
<
Ul
a:
o 55177.0
55175.2
55174.4
o
o
CO
I
1 I ' I ' I ' I ' I
c,
o
o
o
to
i
o
o
in
i
o o
o o
*
-------
VELL#12 CALC N-S PROFILE. 100 FT.
CO
55347.5
~ 55343.9
tn
ac
o 55338.9
z
S 55333.9
hi 55328.9
u
CD
55323.8
55322.4
I "I
I ' I " I ' I '
. t . I . I . I . 1 . Ill .1.1.
o
o
o
in
o
o
ro
o
in
(M
o o o
o in o
CNJ •- —
i i i
o o
in
o
in
o o o
o in o
— — w
o
in
CM
o
o
ro
o
in
o
o
DISTANCE (FEET)
Figure 107. Calculated airborne total field profile at 100 ft for Well Number 12.
-------
VELUM 2 CALC E-V PROFILE. 100 FT.
to
<
X
o
<
UJ
CK
o
55347.4
55345.4
55340.5
2 55335.7
55330.0
UJ
g 55325.9
55323. 0
o
o
I ' I • I ' I ' I ' I ' I
o
•
o
o
o
ro
I • I ' I ' I^ I T
o
in
M
o
o
I , I
O
in
O
o
O
in
o
*
o
o
.
o
in
o o o
O (O O
— —
-------
VELLKH2 CALC N-S PROFILE. 150 FT.
55332.3
55330.6 -
ac
- 5S32&.8 -
o
< 55327.! -
a:
L9
<
55325.3 -
55323.5
o o o
o in o
ro T
DISTANCE (FEET)
Figure 109. Calculated airborne total field profile at 150 ft for Well Number 12.
-------
CALC N-S PROFILE. 200 FT.
tn
55327.2
| 55326.4
<
C9
•z.
•-«
a
«<
UJ
K.
O
»-«
UJ
2
CJ)
<
£
55325.6
55324.8
55324.0
55323.5
\ it I 1 I I
H , I i I
a
o
a>
I
o
o
vo
I
o
o
o
in
i
o
o
o
o
o o
o o
CM •-
I I
o o
o o
»- CM
o
o
O
O
IT
O
o
in
O
o
o
o
o
o
a>
DISTANCE (FEET)
Figure 110. Calculated airborne total field profile at 200 ft for Well Number 12.
-------
700
£00
COO
400
300
200
100
0
100
200
300
400
300
500
-700
V
T 1 I i I I I I I I I 1
I I I I ! I I 1 I I I 1
o o o o
o o o o a
oooQooooeo
o o o a a o o o o
\
MAP OP VELL «4. 200 FT. ABOVE CRCCM)
VERTICAL CRAOIENT (OF/02)
Figure 111. Calculated airborne vertical gradient for Well Number 4.
147
-------
700
! t ! 1 I I I I t I I
MAP OF WELL $4, 200 FT. ASOVE GROUND
HORIZONTAL SRADIENT (DF/DX)
Figure 112. Calculated airborne north-south horizontal gradient
for Well Number 4.
148
-------
700
MAP OF WELL #4, 200 FT. ABOVE CROUND
HORIZONTAL GRADIENT (DF/OY)
Figure 113. Calculated airborne east-west horizontal gradient
at 200 ft for tfell Number 4.
149
-------
VELUM CALC N-S PROFILE. 150 FT.
en
O
0. 033
o
o
u.
N
a
u.
a
-0.116
-0.231
-0.347
-0.462
-0.545
-J-H
'
I ' I ' I ' I • I ' I ' I
I . I . I . I . I . I .
i . i . I . I . ! . I . I
o
o
o
•
o
o
o
o
o
•
o
in
ro
i
o
o
o
•
o
o
o
o
o
•
o
in
(M
o
o
o
«
o
o
CM
8
O
O
o
•
o
in
o
o
o
«
o
o
o
o
o
•
o
in
o
o
o
o
o
o
•
o
in
o
o
o
*
o
o
o
o
o
•
o
in
o
o
o
•
o
o
o
o
o
«
o
in
(VJ
o
o
o
•
o
o
o o
o o
o o
O
in
o
o
DISTANCE (FEET)
Figure 114. Calculated airborne vertical gradient at 150 ft for Well Number 4.
-------
VELL#4 CALC N-S PROFILE, 150 FT.
O
o
u.
N.
to
<
a:
3E
<
13
X
a
u.
a
I I! ' J ' I ' I ' I '
DISTANCE CFEET)
Figure 115. Calculated airborne north-south horizontal gradient at 150 ft for Well Number 4.
-------
IN)
WELL04 CALC E-W PROFILE. 150 FT.
0.231 ft—y 'i 'I »"| » | 'i
0.185
o
o
u.
s:
3C
a
u.
a
0.092
0.000
-0.092
-0.185
-0.231
I . I . \ . I . 1 . I . I . I . I
i I • I • I _i_l il
o
o
«
o
o
o
o
•
o
in
to
o
o
•
o
o
ro
o
o
*
o
in
(M
o
o
•
o
o
(M
O
O
•
O
in
o
o
.
o
o
o
o
.
o
in
o
o
o
o
•
o
in
o
o
»
o
o
o
o
•
o
in
o
o
«
o
o
o
o
.
o
HI
CM
O
O
.
o
o
o
o
«
o
in
ro
o
o
o
o
o
DISTANCE (FEET)
Figure 116. Calculated airborne oast>west horizontal gradient at 150 ft for Well Number 4.
-------
in
VELLlM CALC N-S PROFILE. 200 FT.
0.014
0.000
O
O
u.
(ft
<
M
a
\
u.
a
-0.049 -
-0.098 -
-0.147 -
-0.196 -
-0.230
DISTANCE (FEET)
Figure 117. Calculated airborne vertical gradient at 200 ft for Well Number 4.
-------
VELL04 CALC N-S PROFILE. 200 FT.
O
O
u.
tn
<
s:
3:
X
a
\
u.
a
111111
-,1,1,1,1,1,1
-0.041 -
-0.089
o
O
?
o
O
o
o
to
I
o
o
to
o
o
o
o
o o
o o
CM —
I I
o o
o o
—
-------
WELL04 CALC N-S PROFILE. 250 FT.
en
ui
O
O
u.
V)
13
M
O
X
U.
a
0.008
0.000
-0.025 -
-0.051 -
-0.076 -
-0.102 -
-0.120
"1"!"' I ' I ' I
DISTANCE (FEET)
Figure 119. Calculated airborne vertical gradient at 250 ft for Well Number 4.
-------
in
CM
VELLJT4 CALC N-S PROFILE. 250 FT.
0.061
0.043 -
O
O
LL
CO
<
<
13
X
a
v.
u.
a
DISTANCE (FEET)
Figure 120. Calculated airborne north-south horizontal gradient at 250 ft for Well Number 4.
-------
en
VELL#5 CALC
^»
0
o
u.
X
to
X
2:
M
a
X
u.
a
0.011
Onnn
.000
H'
-0.031
i
-0.062
-0.093
-0.123
— fl 1 AT
1
MMW
-
—
-
.
"•
"
—
• 1
-0. 1 43Q
o
o
0
0
CO
1
N-S PROFILE, 150 FT.
s
-j-1-y-rj i^j^r-jvj-j-T f i j'l-j i -|- * I ' | ' 1 ' 1 '
\ /"
\ /
\ 1
\ 1
\
\ /
\ /
\ /
\ /
\ /
\ /
\ J ~~
\ /
1 . 1 . 1 . 1 . ! . 1 . 1 . I/. 1 . 1 . 1 . 1 . 1 . 1 . I . -
oooooooooooooooc
oooooooooooooooc
oooooooooooooooc
oooooooooooooooc
ooooooo oooooooc
rxurio^rotM— »-MM-*-tf>u)N,a
1 1 1 1 1 1 1
DISTANCE (FEET)
Figure 121. Calculated airborne vertical gradient at 150 ft for Well Number 5.
-------
06
VELL*5 CALC N-S PROFIUE. 150 FT.
o
o
u.
X
I
X
o
u.
a
0.073r-r-r-
0.052H
DISTANCE (FEET)
Figure 122. Calculated airborne north-south horizontal gradient at 150 ft for Well Number 5.
-------
WELL05 CAUC N-S PROFILE. 200 FT.
in
to
CJ
O
u.
x
X
<
19
M
a
U.
a
0.005
0.000
-0.013
-0.026
-0.039
-0.052
-0.060
I . I . I t I . \ . I .
. I I J I I I I I I •
I . I . I . i . i . I . I
o
o
o
•
o
o
CO
I
o
o
o
•
o
o
o
o
o
.
o
o
o
o
o
•
o
o
en
i
o
o
o
•
o
o
o
o
o
•
o
o
to
o
o
o
»
o
o
o
o
o
«
o
o
o
o
o
o
o
o
o
o
o
o o
o o
— CM
o
o
o
o
o
o
o
•
o
o
o
o
o
•
o
o
in
o
o
a
o
o
o
o
o
•
o
o
CD
DISTANCE tFECT)
Figure 123. Calculated airborne vertical gradient at 200 ft for Well Number 5.
-------
VELL#5 CALC N-S PROFILE. 200 FT.
0.030i-i~
•
0'.021 -
O
O
IL
cn
C9
X
u
UU
a
DISTANCE (FEET)
Figure 124. ra1cu1ated airborne north-south horizontal gradient at 200 ft for Well Number 5.
-------
VELL012 CALC N-S PROFILE. 150 FT.
o
o
u.
(O
a
u.
a
0.014
0.000
-0.033
-0.066
-0.099
-0.132
-0.151
I ' I ' I
-.1.1.1.1.1.1
I ' I
I '
I . I . I i I . I t I . I
i .
o
o
o
o
o o
o in
-a- to
i i
o
o
.
o
o
ro
o
o
•
o
en
CM
I
O
O
.
O
o
CM
O
O
O
O
o
o
o
o
o
o o o
to o to
T T '
o
o
o
o
tn
o
o
«
o
o
o
o
•
o
ID
O
O
.
O
o
o
o
•
o
an
CM
o
o
.
o
o
M
o
o
.
o
m
ro
o
o
o
O
o
DISTAN-CE (FEET)
Figure 125. Calculated airborne north-south profile of vertical gradient at 150 ft for Well Number 12.
-------
Ol
ro
VELUM 2 CALC E-V PROFILE. 150 FT.
0.009
0.000
o
o
u.
<
C9
M
a
-0.031H
-0.063 -
-0.094 -
-0.126 -
-0.148
i
DISTANCE (FRET)
Figure 126. Calculated airborne east-west profile of vertical gradient at 150 ft for Well Number 12.
-------
WELL*!2 CM.C N-S PROFILE, 150 FT.
0.0811 - | ' | ' 1 ' 1 ' i ' I
to
o
o
u.
a:
X
a
u.
a
0.057
0.029
0.000
-0.029
-0.063
rr T T i ' i • i ' i • i
-. I . I . I . ! . I . I . ( ,1 , I
I i i i J i ! i I _•-
o
o
o
.
o
o
o
o
o
.
o
in
o
o
o
•
o
o
fO
o
o
o
.
o
en
CJ
o
o
o
*
o
o
(M
o
o
o
o
o
o
o
o
o
o
o
o
O O O
in o in
— .- i
o
o
o
.
o
to
o
o
o
.
o
o
o
o
o
•
o
in
o
o
o
o
o
o
(V
o
o
o
•
o
to
(M
o o o
o o o
o o o
o
o
o
tn
ro
o
o
DISTANCE (FEET)
Figure 127. Calculated airborne north-south profile of horizontal gradient at 150 ft for Well Number 12.
-------
M2 CALC E-W PROFILE. ISO FT.
a
o
cr>
a
u.
a
O.OS9
0.054
0.027
0.000
-0.027
-0.054
-0.065
^ I ' I ' I ' I ' I ' I
r I ' I rl ^ I ' I • I ' I • I '
o
o
o
in
o
o
ro
o
in
(M
o
o
(VI
o
in
o
o
T
.0
in
i
o
in
o
o
o
in
o
o
CM
O
in
CM
o
o
O
in
O
o
DISTANCE (FEET)
Figure 128. Calculated airborne east-west profile of horizontal gradient at 150 ft for Well Number 12.
-------
VELLUM 2 PALC N-S PROFILE. 200 FT.
0.002
O
O
u.
V
in
-0.011 -
-0.022 -
- -0.033 -
IM
Q
in
-0.044 -
-0.053
I ' I
I . I . I . I . I . I . I
o
o
o
*
o
o
o
o
o
o
in
o
o
o
•
o
o
o
o
o
•
o
o
o
o
o
*
o
o
00
DISTANCE (FEET)
Figure 129. Calculated airborne north-south profile of vertical gradient at 200 ft for Well Number 12.
-------
VELUM2 CALC N-S PROFILE. 200 FT.
o
o
in
<
x
X
a
li.
a
-0.010 -
-0.020
-0.023
r
I ' I T I ' I ' I1! f I ' I ' .
DISTANCE (FEET)
Figure 130. Calculated airborne north-south profile of horizontal gradient at 200 ft for Well Number 12.
-------
VELLUM2 CALC N-S PROFILE. 250 FT.
o>
a
o
u.
10
<
<
C9
0.001
-0.005 -
-0.010 -
~ -0.014 -
a
u.
a
-0.019 -
-0.023
I . I . 1 . I
o
o
o
•
o
o
o
o
o
•
o
o
in
o o
o o
o o
o
o
U)
o
o
o
o
m
DISTANCE (FtfGT)
Figure 131. Calculated airborne north-south profile of vortical gradient at 250 ft for Well Number 12.
-------
VELU12 CALC N-S PROFILE. 250 FT.
oo
' I ' I ' I '
o
o
CO
o
o
N.
O
O
o
o
10
o
o
o
o
ro
o
o
(M
o o
o o
— (M
o
o
o
o
V
o
o
to
o
o
U)
o
o
o
o
CO
DISTANCE (FEET)
Figure 132. Calculated airborne north-south profile of horizontal gradient at 250 ft for Well Number 12.
-------
10
TEST WELL CALC N-S PROFILE, 150 FT.
55196.7
in
<
3:
2:
<
o
55190.8
tj 55185.8
UJ
a:
o
UJ
z
(J
55180.8
55175.7
55171.6
' I '
' I ' I T/lS.' I ' I ' I ' ! ' I ' I ' I '-J
I.I.I
o
o
in
o
o
U)
o
o
K
O
o
oo
DISTANCE (FEET)
Figure 133. Calculated airborne total field at 150 ft for two identical casings separated 200 ft.
-------
TEST WELL CAI.C N-S PROFILE. 150 FT.
3:
CD
Z
a
ui
oc
UJ
H
55193.5
55192.1
55187.7 -
55183.4 -
55179.0 -
55174.7 -
55171.7
DISTANCE (FEET)
Figure 134. Calculated airborne total field at 150 ft for two identical casings separated 300 ft.
-------
TEST WELL CALC N-S PROFILE. 200 FT
LU
% 55173.3
z:
O
o
00
I
o
o
o
o
o
o
in
i
o
o
O
o
o
o
CM
I
O
O
O O
O O
— (M
O
O
O
O
O
O
in
o o
o o
vo rs
o
o
CO
DISTANCE (FEET)
Figure 135. Calculated airborne total field at 200 ft for two identical casings separated 300 ft.
-------
TEST WELL CALC N-S PROFILE. 200 FT.
•vj
ro
55183.6
55182.6
55180.3
z 55178.1
3
UJ
cc
u
55175.9
55173.6
55172.4
o
o
CD
I
' I ' I ' T ' I ' I
I r I 1 I ' I ' I ' I ' I '
I i i . I i I . I . i . i . i . i . i . i .
O
o
K
O
o
o
o
IT;
I
O
O
O
o
K)
I
O O
O O
M —
I I
o
•
o
O O
O O
— CM
O
O
o
o
o
o
in
o
o
o
o
o
o
00
DISTANCE (FEET)
Figure 136. Calculated airborne total field at 200 ft for two identical casings separated 400 ft.
-------
wat 02 sp N-S
-15
-40
'%-60-40-20 0 20 40 60 60 100
X(fO
HELL &2 SP y-
y.
£
v^»
a.
en
-15
20 020406380 03
X(ft)
160189200
Figure 137. Self-potential profiles over Well Number 2.
173
-------
HELL 13 SP N-S
10
-15
-40
-65
-400-358-300-250-203-150-100 -53 0 50 168 152 220 250 3S3
X(ft)
. m.L 13 SP tf-E
w
s
Si
C I . . . . t - . . . I . . . . f . . Tf ' • • • • ' • • • • { • 1 1 - ' • • - - ' • 1 | • ' • • • • t • ,.!....!. .A. I....I.
3400 -350 -303 -253 -200 -153 -101 -59 0 50 160 153 200 253 380
350 4,30
35d 400
X(fl)
Figure 138. Self-potential profiles over Well Number 3.
174
-------
#6 s? N-S
10
-15
8?
t ... I ... 8 ... t ...>... t ... I ... I
-83-60-40-20 0. 20 40 60 83 103
X(fl>
6 SP y-E
10
S
Q_
to
-40
u~T00-80-60-40-20^0" 20 40 80 E3 100
X(fU
Figure 139. Self-potential profiles over Well Number 6.
175
-------
raj. *7 SP N-S
-65
!2£2-18§-16§-14$-l20-100-88-60-40-20 0 20 40 63
X(fl)
¥ELL §7 SP tf-E
VX
163 2G3
eiVB-Vaa-iB^ea '4a -ia 4a "B' " aa" 40" ea" eii 'iea i^a iia ie^'iea 200
Figure 140. Self-poteiitial profiles over Well Number 7.
176
-------
N-S
10
§ -'5
-40
~6403-60-60-40-20 0 20 40 60 80 100
XCfO
^-E
10
S "5
t ... t ... t ... I ... I ... 8 ...»...»
-80-60-40-20 0 20 40 60 80 169
X(ft)
Figure 141. Self-potential profiles over Well Number 10.
177
-------
H&L #11 N-S
10
§ ->5
-40
-80-60-40-22 0 20
X(fO
IELL #11 SP W-
-60-40-2S 0 2S 4060 80 100
X(fO
Figure 142. Self-potential profiles over Well Number 11.
178
-------
VELUM SP N-S
o_
co
a
O-
10
-15
-40
~8-^ 00-80 -60 -40 -20 0 20 40 60 80 100
XCft)
VELUP14 SP V-E
10
-15
-40
~64 00-80-60-40-20 0 20 40 60 80 100
- X (ft)
Figure 143. Self-potential profiles over Well Number 14.
179
-------
Q.
in
0.
co
WELU15N SP N-S
s
'6400-80-60-40-20 0 20 4(f"6QJ"80 100
X (ft)
VELL015N SP W-E
w
10
-15
-40
"6400-80-60-40-20 0 20 ' 40' 60' 80 '"100
X(ft)
Figure 144. Self-potential profiles over Well Number 15 N
(not centered on well).
180
-------
Q-
to
WELU15S SP N-S
10
-15
-40
"6~^00-80-60-40-20 0 20 40 60 80 ICO
X(ft)
i
v_/>
Q-
to
WELU15S SP W-E
w
10
-15
-40
_pcr I i . . I . . . < . . . i . . . I i i i t i i » 1 i t r 1 i i < 1 i i i I i ( „ .
-100-BO-60-40-20 0 20 40 60 80 100
X(ft)
Figure 145. Self-potential profiles over Well Number 15 S
(not centered on well).
181
-------
•VELU16 SP N-S
Q-
LO
\^s
Cl-
10
-15
-40
'-^00-80-60-40-20 0 20 40 60 80 100
X(ft)
WEUJ16 SP W-E
10
-15
-40
64 00-80-60-40-20 0 20 40 60 80 100
X(ft)
Figure 146. Self-potential profiles over Well Number 16.
182
-------
Q_
to
Q_
CO
WELU17 SP N-3
s
10
-15
-40
"6-^00-80-60-40-20 0 20 40 60 80 100
XCft)
VELU17 SP H-E
w
10
S -15
-40
~-^00-8C-60-40-20 0 20 40 60 80 100
X(rt)
Figure 147. Self-potential profiles over Well Number 17.
183
-------
CO
WELL 12 DO! N-S
95
70
45
• •
60WT00
X(fl)
'-"«)--'--''-f'ft'--;i--t--t*--fg-" '
8 213 40 60 W lWl2M40 160 i832B3
PARALLEL TO LIME •
PERPENDICULAR TO LIME •
YELL *2 EM31 tf-E
95
70
45
* «
• • B *
*V .'«
?-2MW"l6WlVd Y&Y0f):fo'-&"40'-20* "0"" "^" Vd" 6^" erf '{mils {40"i6fl'i80"203
X(fl)
Figure 148. Electromagnetic profiles over Well Number 2, using the EM-31 system.
-------
N-S
co
at
60
53
• o
• * .
• •
•
99
• . t
7B
62
5S
40
BELL S3 eei H-E
,w
E
* « •
. t .
PARALLEL TO LINE
PERPENDICULAR TO LINE °
^Bante^fe' :49 -^a"^1^^'^" &" aTJca
xcm
Figure 149. Electromagnetic profiles over Well Number 3, using the EM-31 system.
-------
«ELL ra tffiRIZ-COPLAKER N/S UhE - 1 S/21/82 COIL SPACING - 423
IN-PHASE - SOLID LIKE AND (•> CUT-PHASE - DAS2D U^ AND <*)
3555 h*
-2 a
DISTANCE (
Figure 150. Electromagnetic N-S profile over Well Number 3, using Slingra*.
186
-------
VELL « VEmCAL-CDPUNER M/S LINS - 1 S/21/S2 COIL FACING - 4S3
IH-PHAS - SOLID Uh£ AND <•> OUT-PHASS - tt^S-ED LINE AND C*>
N
-18
355S hz
222
139 1
tsa ^
119
73
S3
-IS
= 3 7B
g- ..,- 1~ \—«L '1 V — *—- ~- ...- t— " i " M
-2 e 2
DISTANCE < « l& f% 5
Figure 151. Electromagnetic N-S profile over Hell Number 3, using SUngram.
187
-------
APPENDIX I.
BRIEF SYNOPSIS CF THE PROGRAM "CASING"
The program "CASING", written in Fortran 77, has two modes of operation:
1) the forv.vsrd mode, and 2) the inverse mode. In the forward mode the program
calculates the magnetic field components Bx, By, Bz, H and F, using equations
(1) and (3) and the spatial derivatives of these components (except H), using
equations, (2) and (4), due to a linear distribution of magnetic monopole
pairs.
In the inverse mode, the program initializes the distribution of mo~opoles
within a specified region of interest, and, together with the subroutine
"NLSOL" (an adaptive nonlinear least squares solver by Anderson, 1962), deter-
mines ihe final distribution of monopole pairs from a magnetic field data set
that specifies the observations, their coordinates, and the component type.
0-.
The program was designed to be highly interactive so that on initial use
one is assured of correct data entry (on subsequent runs, data can be read from
a file that was saved on the initial run). Host other options available in the
program, such as saving of data files, generation of randomly perturbed data
sets or randomly perturbed parameters, are interactively specified by the user.
Both the forward and the inverse versions of the program rely exclusively
on a large set of interdependent statement functions that specify the magnetic
field components (or derivatives) of interest. These appear in the subroutine
"CASINGFI" before the fi"St executable statement, as required by Fortran. The
functions have been coded in elementary subunits (e.g., specifying the distance
between two arbitrary ^oints) which are combined to yield the fields due to
pole pairs. Furth<_. summation over all pole pairs yields the final field
values et a point in space.
PLOTTING CAPABILITIES
The forward problem subroutine "CASINGFI" will enter an interactive plot-
ting section after the requested fields or derivatives have been generated.
The type of function, the direction of plotting, and the exact location of the
line of plotting in 3 dimensions are specified by the user. The data to be
plotted are printed, and, if requested, a one-dimensional profile of a magnetic
field component is generated. The actual plotting is done by the plot package
resident on the VAX -11/780 system at the USGS, Golden, Colorado. Both termi-
nal output graphics for rapid viewing and hard copy graphics produced on a
Hewlett-Packard plotter can be obtained. Any number of graphs can be generated
a
188
-------
sequentially and the program will exit the plotting loop only at the direction
of the user.
PORTABILITY OF THE PROGRAM
Except for the plotting section, this program can be implemented on any
system supporting Fortran IV plus for Fortran 77. With some minor modification
the program could also be adapted to run on smaller systems. There are no
machine dependent constants in the code.
FURTHER SCIENTIFIC POTENTIAL
The program "CASING" can be used to generate or analyze geomagr.etic data
of the type currently of interest to investigations that rely on magnetic field
data. It is especially well suited to simulation studies where data inversion
techniques are needed. 3y a sequence of simulations where 1) field data are
acquired, 2) these data are randomly perturbed, and 3) the inverse mode is used
to attempt to recover the original parameters, one can determine the limits and
accuracy of inverting certain types of data sets.
Because of the strong reliance on statement functions, functions currently
not in the program can be easily embedded. Thus, dipole (quadrupole, etc.) or
even continuous distributions could be incorporated without difficulty.
Consequently, demagnetization effects could be studied.
189
-------
LISTING OF PROGRAM "CASING"
A listing of program "CASING" is given on the following pages.
190
-------
r CA3I .'OS
? >
C PfOGrt*' «P.ifTC'. «i Lurilr'r A. .•••Jfl, J'JLY,1952
c
C
C THE PhOUR»H. MAS 1>J .'Ul'to OK 05AVE: CD *FUh
C «i:a C2J *I.AIr!£.
C
C I* THE 'I^VERac* *.C.TE
C THE SUbROUTI*i CASI:-Gri ObTAIhS THE V»PAS£TERS CF A WlST«IcUTJCN
C OF POLES A.VU CASlxvO rKC^ iAC..t.IXC DATA.
C
C
CO««ON/Blr;iT/IO.su(100).IALT
COn^OM/LZKEA
CO^MC'.VRU-iO/
1 .PEP-CENKJJ
•"COhNON/UiIT/IUrtlT
CHARACTER»«0 rH.lSRU^
CHAR»CTEfi*Su FIL£»>An£
INTEGER SLE.«
Ir.TCGER'4 ISEfD
, EXTERNAL CASI'.GFJ .PCODE.SUSZ.SUhENO
' DATA l£NTKY,IoM?.ISEEJ/u.«,24421/
C —
C
C READ IN THt Tl'PE OF Ron Thl? IS: SPECIFi EITnER FORWArtO OR
C INVERSE ON THE FIP5T DATA CARD STAf.TIr.? I- THE r'XPST COLU.-i.<
C
• PITE(6,»i* t"»TEa FILL*.A«-.t
1 CF T«E CASI-.G FAKAVtlc.8 IfiPUT FILE. (PRESS
2 IF INPUTI:»G FRU.I THE TEK.-.Jrt»L. J '
IUMT=IU~IT»1
CALL A5SI(.r:(IbMT.FILc:<^.v-e.SLc:»trILEN«xe))
END1F
^RITEC6.») * fl'TEK ThE FILE^A^L
t iMfchE THE IJPUT PAKArtETtKS ARE TO *E RECOHDEO.*
2 ,'IF YOU 00 fiOT »15h TO BtCORO THE If ARAME1EPS PRESS *
IF(£Ltrl(FlLE.TA».£}.CT.l)T->E:.
117
CALL A£Sir.-;(io"ir,FII.LI.A-.ii.Si,'.i.
S Au i»V£SSE/FOF-iA!»D PhQbLE«?'
Reproduced from
best available cony. \*j
191
-------
INTEGER
CHARACTtS«lJ •'A.-.tS *•
DATA .\A«t;S/"FlELD3 ?','?*S.«f.ErEP£ ?'/
WRITECo.*)' CJ YOU «AHT kA:;f)0.»i.Y PiRTURoED VALUtS fOH THE
) ' iF i.0. Ph£SS <*ETUR*>; OTnERilSE,
REALMS, t
hRlIC(6.») ' 0 = fiC ; 1 s YtS
REAOCS,*)IPANOO.y
JFClRAf:OCM.E(j.O)RETUi •JC->fUL£S,.\CASIr.'CS)
, 3)
COUIVALE.
-------
INTECcS
CHAKACTEk*20
CKARACTtR«lJ -IA--ICS *•
DATA fcAsts/'FiFL&s ?','?»s«r.j;fZBS ?'/
W«1TEC6,»)' 00 YOU KiuT fe»:.t)0.«Lr PtSTURcED VALUtS FOH THE '.
) ' iF ~0. PRESS ; OTHER-USE, EKTiK FILENP'-E
REAOCO, 1 )FILL^»>^E
IFCSLf.f.
' 0 = NC ; 1 s VtS *
A«OOM
IFdRACOCM.ECl.ORETURr.1
FORMATCA)
WRITEC6,')' ENTER A.'iT 5 DISIT ISTCCcK FOx THE SEED
1 OF Tnt P.ASOO.X NU-.etR CEStRATCR; CURKENT StEO IS *,ISEED
RCAO(S.*}ISEE3
WRITEC6.»)' B)f *«AT *4AXIl*U:< DECIMAL FRACTION CO YOU «A\T.
I THE DATA TO at PERTURBED? (E.G., .2=JO% , ETC.)'
READ(5,«)PEKCE:.TC1)
IF{IAS<.EO.UTKE>J
CALL ASSIGlidUNIT.FILErJAHc.SLEhCFILElAME))
ELSEIF(IASK.E0.2}VHEN
W".TTE(6.*)' fcY kKAT «*XI»«.Urt DECIMAL FRACTION 00 IfCU -ANT
/hi EARTH"S FIELD TO BE FtH/L'RBcD?'
ENOIF
' RETOR.V
END _
C
c
SU6ROuTI;«C CASIf>CFICYOt)S,XIf,,ePARA.'«3...FCALC.Iri,IDt:tO
C
c
C DEFINE THE PARAMETERS OF THE PPOSLt.M
C
C
PARAMETER (:.C*SISGS=10 ,N
PARAKE~ERCCO'<*'=1.£»8)
pARAytTEH(nx=«*i.fa=*i,^z=«i)
PAf
-------
2
3
c
c
c
CO«/ON/NA=«ES/IFX.IFY.IFZ,IFS.Ir-F,JFD/l>X,IFi>Xt>y.IFDXl>Z.IFDYDX,
I IFOYDY,IFOYDZ,IFUZDX,IFUZOr,IFb20Z,IFDFOX,IFDFuV.XFOFDZ
OIHE..SIO.J MA^ESO(NCUf-.PS)
EOUIVALE.JCECuAhfSO.lFX)
COhMON/FjeLOSO/FIEi,DSOX,!.Y,.«Z.r;CC!YDX','DYDY'.»OYOZ*.
2
DATA tPLOT/1/
DATA *. U04P.Vl.E-7/
DATA XV'.NCNF'O./
DATA IZ. TEP/1/
DATA ZSRJ/U./
DATA FIE .OS/i.Xt.C-;a*0./
C
' C»«»»»««««*«»»HE BCCI'.M-VC OF ARIIh^.ETIC ST*TE?hYKX,Y.Z,X2.Y
194
-------
BZ(x,Y,z.xi,xt,;
1 OZ1(X,Y,Z.X1 ,ll.Zn-bZl(X.Y,2.;:2,Y2.Z2))
OXD/.KX.Y.Z.X1,Y1 .Zl)=-3.«*Xl(X.Xl)»*I/klU,Y,Z,Ai.Xl.Zl)«»5»
1 l./til(X,Y,Z,X!.Xl,Zl)*«3
UXDYKX,Y,Z.«l.M,*.i:<>-J.»fiAlCX,Xl)«AYl(Y,yi)/
1 RKX.Y.Z.Xl.f J,U)*«S
OXOZKX, t ,l,i\ ,Yl,Z.)«-J.»HXl(X,JU)»fi2l(Z.Zl)/
1 Rt(X,/,Z,Xl ,Y1,Z!)«»5
OYDXHX,Y.Z,/.J.Yl,Z».s-J.«F.U(Y,Yl)»KXl(X.XJ)/
1 RKX.Y.Z.Xl ,Y!.£i:**S
OYOY1(X,Y,Z,X1.Y1.Z1)=-3.*15Y1(Y,Y1)*«:/H1(X.Y,;
1 l./Rl(X.,Y,Z,Xl,fl,Zl)**3
OYOZKX.Y.Z.X1 .tl,Zl)=-3.*KYUY,Yn*RZl(Z,Zl)/
-*-
OZDXHX.Y.Z.Xl,]
1 R1(X,Y.Z,X1,Y1,Z1)»"5
DZDYl(X.Y,Z.Xl,Yl,Zl)=-3.« R3
1 RI(X.Y,Z.X1,YI.Z1)«»5
DZDZKX, Y.Z,Xl.Yl,Zi)=-3.»t>ZlU,Zl)«»2/P.lYtZ.Xl,Yl.Zl)-DX:)YUX,Y,Z,X2,Y2,Z2))
DXOZ(X.YrZ.Xl.Yl,Zt,X2.Y2,Z2,I,J}sCHU(I,J)«
DYDXCX.lf.Z.Xl ,Y1,Z1 ,Xi,r2,Z^.I,
1 (DYDX1CX.Y.7..X1, n,Zl)-uYOXHX,Y,Z,X2,Y2.Z2))
DYDY(X.Y,Z,Xl,Yl,Zl.X2,Y2.Z2,I,J)sC.*.U(I.J)«
t (OYOYl(X.Y,2,Xl,k'l ,Zl)-LiJOYUX,V,Z,X2.Y2,Z2))
OYOZ(X(Y,Z,T.;,Y1 ,Zi,X2,Y2,Z2,I,J)sCnU(I.J)*
.1 (DYDZUX,Y,Z.X1,Y1 ,21 J-DVCZHX,Y,i.X^,Y2.Z2)0
D20XCX. f .Z.Xl.n.Zl ,x2,Y2,^?,I,J) = C:-iU('I.J)*
1 (DZDX: (i, Y.2.X1 . Yl,Zl)-iZDXltX, If , Z , X2 , *2 , i.2 ) )
OZDKCX.Y.Z.Xl ,V1,Z1 ,X2,Y2.Zi.I,J)=C-.UCI,J)»
•1 (DZDYUX.Y.Z.X1 ,Y1 ,21)-J20tl(X.-<.2.X2.Y2,Z2))
D2D2(X.Y,Z,X1,Y1 ,Z1 ,X2,Y:,2i,I,
c
£•*»••*«*«*«*«* tNO OF *FITHMATIC STATEMENT rUNCTIO«S«»»»««««»«»«»»"
C
'c
C OCriNC A FE«* RELEVANT COKST»'-TS
C
•PXS4. •*?*•<(!. )
OECTOPAD=PI/160.
C
C
C«*i*«**********«**T!lC dtCJ.i«'il:»IhS OF POLtS IK EACH CASING.
C
• RITEtb.'J* *HAf IS TrtE TOTAL NOr'BES OF CASIr.^S 1.4 fHIS P'-OrLE''?'
• RITt(e.«J'E.-.TcS l^E NU-si.*' oF POLE FAIRS In tACh CASIni:'
Reproduced from
best available copy.
-------
c
C CHECK TO StS IF Tnt ALLGTEt ?U"»EK GF CASI/.GS i.'.'D THE -fU^BL'S CF
C POLES IN EAC* CASI.-tC HAVf «-OT cEi... tCXC£E&tD.
C
IF(KCASl.«Cl.GT.-tCA5I'«v;S)34C<> 't.CASiNG3*
DO 70 ICASI:.-;=1 , '.CASING!
70 IF(i«POLElUC.'.SI..G).CT..iPOLe:3)ST&P •'.DOLES'
C
c
£ BEAD IK THE oaiE:;/AriD\: or EACH CASING (i;< otcuEES):
C BETACICASI.JGJs T«£ A'-GLE SET-tcl. The. HORIZONTAL AuC IHE
C LI'.E OF THE CASING.
C PKIf ICASI.-iGjs Jh:£ Ar-CLt itf-it* TrE HOSIZQ.JTAL PRCJtCTIOn
C CF Tht CASING A.iLi TKE USUAL X-AXIS IK 3-0. IT
C IS ALSO THE USUAL AZIXUThAL A;.GLt 1 1. 5PKSRICAL
C ' CCORDlftA-rtS.
c
WRITEC^.'J'Et.TER T«E OKiEi«7ATIOs (BETA, PHI) OF EACrt CASING:
DO 6 ICASI'.r, = l ,.\CASIr.Gl
NRITEC6.')' F'Jh CA5J.I.3 '.ICASIuG
IF(iRU:.-l.:lE.U)»kITt(IftU:n,«) &£TACICASIf.G),PMI(ICA6IfiC)
6 CONTINUE
•C
C COHVERI 0«IEf.TATIOV P>«F ALTERS TO FADlAnS.
.. C '
DO 7 IC«SI!,r7 = l
7
C
C READ I»< THS POLt STRENGTH S OF F.ACh FCLt A-'iD Th£ LENGTH OF EACH
C POLE. (TKE i) AT A FCrt A »E« CASLN? ShOuLD SIAP.T Oil A f.£* U&fA CAKD.)
C-
DO 1 ICASI(.G»1.NCASJNG1
NPst,PDLEHICA3I:;G)
«(RITt{().«)' TntFE APE '.tip. ' POLE PAIRS IN CASING ',ICASi.-G
WRIIECb. »)'EM^=< the POLE 'STfcEf-'GIh/PCLE SEPAPATIGU
t OF tACrf*
READ(InU.V,») C POL cSCIFOLi.ICiSING), LENGTH C I POL£,ICASI'JG),
t IPOUEel ,.'.P)
If (IRUK1.4E.O)
1 baiTE(It>.or.l,») (PGLCS(IPULE,XCASIr.C).Lb>.?th(IPOL£,ICASIMGJ
2 IPOLE=i...P)
1 CONTi::U£
C
C MULTIPLY PDLt STRC^CIHS 61 50.-E nELEVAhf CONSTANTS.
C
DO It ICASI'.C=U.»CASJ(.G1
DO 11 IPCLEsl.sP
CHy(IPUI.t;.ICASIrsG)=CONV«POLcS(IPOLE,ICASI
-------
RtAD(I«ljt. ,OXO. XF.INTX.ro. If F. INIY.ZO.ZF, Ir'VZ
IF(IRU..l.:«E.O);*aMF:(IKU'.l.*)XU,AF,iMX.YO,Y-.l«n.Z0.2F.IiNTZ
c
c CHECK ro SEE IF THE ALLOIKO oi.ttxsio'ts HAVE NOT *££« EXCEEDED
c
C
ir{INTXl.GT.NX.OR.IfcTYl.GT./-Y.OR.IMZl.CT.I . Yl (1 > ,Z1 (1 ) Of A POLE IN EACH CASING.
C THEN READ IN THE DISTANCE ALONG THE CASING OF THE OTHER POLES;
C STORE :HIS lafGKMAflCN IN XI (IPOLE, ICASINC) . «UTE THAI ONLY On£
C MEMBER CF EACH PULE PAIR IS READ IK Hf.Rt. ALSO NOTE THAT THE
C DATA FOR A N£« CASING SHOULD START ON A NE« DATA CARD.
C
00 12 ICAS1NG=1 .NCASIKC1
NPcMPOLElCICASIUG)
nRITE(6,*)' ENTER THE POSITION IX,Y,Z) OF A POLE IN CASING',
1 ICASING
REACCIRUN,*} XHl.lCA5I"G),iri(l,ICAr>ING),i:iCl.ICAS; KS)
1 «RITECIHUM,») XlCl.ICASJNC},- lt
00 12 IPOUE=2,NP
Yl(IPOLE,ICASING)=Yl(l.ICASIf1 (JPCLE,1CAS1SC)»
£2(If(JLt:,ICASI.NC}8Zl(lPOLE.ICASi.vC)»
L2(LEiGTt<(IPOi.t,ICASI
-------
14 COuTINac
C
c
C BEAD IN TrIE Ci>4Pw;<£M5 CF Tr!£ EArUfc'S MAGHETIC FIELD:
C
C
16 «RITe{6,»)'tHTiR TKE C3s?0:.E*TS X,t,Z OF The GEOMAGNETIC FIELD'
READ ( IKU.« . « J XEA5 TH . YEA* r K. Zc'AF.Th
C
r£ARlM=56rirCn£AP.Tr.»»2»ZEARIr:«»2)
C
i(RITE(6.»)'HO« fAWY FIELO CO.-.POxENTS ARE VOtf IMERESTED K«?'
IF('tCO.".Pl.«E.O)Tht;i
WKlTE(6,«) 'HHAT- f IELO CC-XFOf-E^TS APE IfGO INTERESTED l\t
1 (X.y,Z,H.r). EVi'cR EACH CCMPOt.EM OAME AnO PRESS
2 AFTEfl EACh.'
00 437 ICC.-.P = 1.^CO.'.P1
437 READ(IRUS,433)CCXP(ICOMO
433 FOft«ATCA)
IF{iaUM.\E.O)THEW
00 435 ICO*P=l,rtCOr-.Pl
«35 rf<»ITEtIRUxi,434)CO:'.PCICOr.P)
434 FORKAT(A)
ENOIF
ENDIF
WRIT?:(6,«)'Hu.i MAr.Y FIELD DERIVATIVES ARE YUU IKTERcSTED IS?'
..
•«RITc(o,«)'.nICn FttLD !JERI/ATrVES ARE Vi'J If.rfSESTEO I.'.?
.Dr-DZ,i)XD*.OXOY,UXCI.C»lfOX,01fDY,CtOi,OZO/,r)ZOi. CZDZ)
DO 438 IDCRlVsIDCRIVl,IDt:RIV2
438 REAO(InU.';,-i33)CChp(I£<£P.IV)
IFCIRUril.NE.OTHEN
00 436 ID£RIV2lD£KIVl,ig£RIV2
436
ENOIF
IS THE FtO) VALUE TO BE SUBTPACTEJ FROi F'
C
C INITIALIZE Trie PARAI-cTEF ARRAY 3PAKAV.S(I?KKA.1) hCSE
C USING THc JATA JUST rttiO IN.
C
DO 2i>
CO 2G
198
Reproduced (rom r »-^
best available copy, y; ^
-------
C )«6cTAUCASI'.G}
BO{l)=o?AHAHSCl)
Z«sl*i
BPAfcAXSCIJsC.IUdPl.'LC.XCa.SIf.'S)
BPkrtAMSCI
1 = 1*1
ELSE
I*I»1
BP»KAMS(I)=CrU(IPOLE,ICASING)
20
ILASTel
1*1*1
1*1*1
BOCI)«oPARA«!iCI)
00 303 160=1,10-3
RANDOM*?. *(.5-S A:. (ISEEl*J)
303 BO(IBO)=BO(lBU)»{
00 304 I30=Iu-2,IO
304 dO(ieO)=30(IoO)»(l«»PtHCEfI(2)»RANDO«)
. RMDIF -
C
C
C
£ ••Oav«««*»**t«f »««»«»«»E..U OF DATA INPUI»»»» »»»«»*•«••»• «»t» • c »•
C
c
C PRINT OUT Trf£ I .POT DATA:
199
-------
• i:CASI:.Gl
80 FOKr-.ATC l.lU.-iotR OF CASII.CSS '13,/J
00 60 ICA3i«GsI^CASI»:'1X,2CK9.3,1X),IJ' INTERNALS'//)
C
C PRINT OUT THE CEOKAGNE1IC FIELD COMPONENTS
C
WRITCC6,d2/XtARTH.lfEARTH,ZEARTH,HEARIH.rEASTH
82 FURMA7C* THE COr.PO'<£MS (X,3f,Z,H,F) OF Tht CEOMACNEfIC FItLr ARE
l^lXf/, 5CE12.4.1X)//)
C PRINT OUT THE COXPOilEKTS ^ECjESfEtf
C
WRITE(6.»)' THE FCLLOitlNO CC'IPONENTS HAVE SEEN RCOUESfEO:'
C END OF Pfil.iTlHG OF INPUT DATA
C
irCTHISRUN.EO. 'IH VERSE
C
DO 63
63 NAME5
C
C SET UP THE FINITE DIFFERENCE GKIO
C
C
XF(lNTX..-JE,0)TrtEfi
OX»(XF-XO)/IfiTX
ELSE
DX = 0.
CNDIF
OYc(tF-TO)/lNTlf
ELSE
CNDIF
OZ«(ZF-Z01/l:.TZ
ELSE
tNOiF
C
00 2!
21 XCIX)sXu*(lA-l)*DX
oo 22
Reproduced from
best available copy.
200
-------
22
DO 23 12=1 .1..TZ1
23 ZdZ)=ZO+dZ-i)»uZ
c
C PROCEED TO CALCULATE THt HACKtTlC FIELD COMPOHEUTS Ai.i/ tHil* OE-
C RIVATIVES FCM IMc SPEClf ItO niS?t(IfaUTIO:i OF POLES Ar.u CA5I -C5.
C
C SET UP THE I.'.JECtS FCA THE HECUESTcD
C
DO 73 IC = 1 .NCO.-.FSt
DO 73
73
C
C
DO 33 IF=1 ,*CUMPS1
DC 33 ICASlNC=l ,fJC»SI(-Cl
DO 33 IPOLE-1, ?
DO 31 IX«1 ,IiiTXl
DO 31 Ir=l,I«7Tl
DO 31 IZ=I,:NTZI
IF(CO«P(IF).£0.'X*)lMCt<
riEi osdx.n ,iz,ir)=ri£UuS(ix,it,iz.iF}»
2 Zl d?Cl,E,ICASlt.C;,X2dPOLE.IC*5IM;),r2dPGLC,ICASI*C),
3 22 (I POLE, I CAS I NO, IPOLt. JCASINC)
ELSEIF(COMP( IF).tC,.'t')THrK
riELDSdX,Iir.lZ,IF)sfI£LOSdX;iY,IZ,ir)»
CASI JG).
Z2(IPOLt;,ICASIr.C),
FIELOSdX,l!f.IZ.IF)eFIEuDSdX.iy.IZ.lF)*
t aZ(XdX).Y(I-/).ZdZ),XldPOLE,ICASI*'C>,yniPOLE,lCASf.C).
2 Zld?OLt:,2CiSI-.C)..T2dpr.l.C.lCASI.>!C
3 Z2dPOLE,ICASI»C),IPCLE.lCASInC)
ELSEIF(CO".P(IF).EO.'CXnx*)?M£M
2
3 ZZdPOLE, ICASING) , IPOLE.ICASINC)
ELSEIF(CO".P(IF).£0.'DXDr*)THEM
FIELDSCIX.IY.i:, JF)=FltLDS(IX,ir,IZ.lF)»
1 DXDY(XdX) . T(ir).2dJ),XldPCLE, JCASIi.O.Yt dPCLt.ICASIN'G).
2 ZldPOI.t . IC»SIVG),X2 d POLE, ICAS INC) ,Yidr1OLt1.IC*.SI'v).
3 Z2dPOLC.JCA$rt&},lPCLE,ICASISC>
riELDS(IX,IY,iZ.IF)cFIi:L3SdX.lY.IZ,ir)>
t DXOZ(XdX) .KIT) ,ZdZ),/ldPOLE,ICA51IIC),Yl dP(
-------
i D*D^(x(ix},y({Y),z(iz),xi t ipoLE, jCASi*C),t i
2 ZlUPOte,lCASK.G).X2(IPUt,E.IC*SiN<;
3 Z2(lPOLi,lCASI-.G) ,IPCLc,ICASING>
E«.StIF(CO>X')7nt.l
cI£LiJS(IX,IY. IZ.IF)=Firi,USUX,IY.IZ.IF)»
» DZDXlXUX),Ym).ZCIZ),XlCIPOLE,ICASl;JG),YlU?C.LE,ICASI!«G),
2 ZlUPGL£.ICASI'vC/.X2UP01.E.2C*SI«G>,Y2UPDLE.J»:A5I«u),
1 DZOYCX(rX),YCIY>,Z(IZ),XlCIPOLE,ICA5lNC),Yi(IPQl.f:.rCASI,lG),
2 ZHIPOLE,ICAS2NG),X2CIPOL£,ICASIMG),Y2(IfOLE,ICASIKC),
3 Z2 (I POLE, 1C A3 1 :/G ), I POLE, I CAS IMG)
ELSEIF(CO.«P(IF).EO.'F'JtHej.
FItLOS(IX,r/.12,IF)=
2
3
2 flEtDSdX.IY.IZ.IFif j«fttt.--S(IX,Ii, IZ,IFOYOXJ»
3 F
I Reproduced from
| best available copy
202 ~
-------
4 F1£LDS(IX,IV,IZ.IFF>
ELSEirtCO.-.FtlFJ.tO.'OFOIfjThtfl
FXELOS(IX,IY,IZ,lF)c
I tFIELD5{IX.lY.I*,IFX)»FItLDSCIX,It,IZ.lFiJXDY)»
• 1 FIELDS ( IX, 1Y.IZ.IFY) 'FIELDS (IX. If , IZ.IFDYDY)*
3 f IELOSCIX.IY.IZ.IFZ)«FI£LDSCIX,IY,IZ.IFDZDY)>/
4 FIELOSClX.IY.lZ.IFF)
ELSEIF(C04?UF).EC.'OFOZ-)THE«
riELOSUX.IY.IZ.IF) = -
1 (FIELOS(IX,IY,IZ,irX)»FIELOS»
3 FI£LCSUX,lr.lZ,IFZ)eFIECOSCIX,I]r,IZ,IFDZOZ})/
4 FIKLOSUX.IY.IZ.lFf)
ENDIF
41 CONTINUE
DO 801 lF=l,nCO"PSl
801 KRITEdJitCCRD.oCOMCC FIELDSC IX , I Y, IZ, IF } ,
\ XCIX).YCIY).Z(IZ>,CC*PUF),
2 IXftl.l.aXl),IY=l,I:MYl),IZ=l,lSTZll
ENOIF
IFCIRANDOM.-rf£.0)THEN
DO 310 Ir'sl,rtCO*PSl
DO 310 IX = 1,
00 310 IY = l.
DO 310 IZ = l.Jf.TZl
310
DO 901 IFsl...CO«PSl,
901 -RITECIRA IDO^,600)C(( FITLDSC IX . IY, IZ. IF ) ,
»' XCIXJ.tCIYj.ZdZj.CO-HCIKJ,
2 ix=i ,I:.TXI 1,11 = 1, iMri).iz=i,iMZU
ENOIF
SCO FGRVAT«C16.tf,lX,A5}
C
C
£**<•«***«»**«*« START CF PLOTTING SECTICrl »•»»«•*•»«» • DO YOU «ISH TO PLOT A FUNCTIOn?
1 ANY OTHER NO-HuitlC KEY a Hfi*
IRUN=5
50 READCIRU,l,«)OCDi
IF(COON.£3.1)TriEN
C
c SET tip IHE PLOTTING DATA
C
HRITEC6.W)' STARTING -PLOT NUBBER : '.IPLOT
W«ITe:(b.»)'-HICH CO-PONENI 00 YOU »A!«r TO PLOT?'
PEAOCIRJfl.4 33)KO«P
i.Rift(6,«)'».'LOT,I «f* 1,1
2
203
-------
WRITEC6,') ' 00 YOU »A«T FO PLOI THESE VALUtS?
1 1 = 1TE:S, A.'«V uTrtEK ;;ij:jF.RIC KEt=iiO*
READCIRU.-.,»)GOOr;
ZF'CCOOtJ. it.nrritN
IPLUT=IPLOT-1
GOTO 7.1
ENDIF
C
C SETUP THE PLOTTII/C SIr:UtiTIO:J
C
ISLC1)=1
WaiTEC6,*)'E.JTER ThE PLOTTING CEVICE KUM6EH:'
WRITE(6,*)'Ei.rER TITLE OF P'.OT:'
READ (IRO.V.«)?TIILE
WRITEC6.«)'E«TER TITLE OF X-AXIS*
READ (IRUN.*)XriTLE
WRITE(6.«)'C-.TER TiTLE OF t-AXIS*
P.E^D CIRUN.«)lfTITLE
CALL PLTS£T(IPLOTR,XBOARO,VBOARD,ISL)
KQPTS=4
XP(*)=X30ARD
XPC3)=2.
YP(3)=2.
XP(2)=0.
YPC2)=0.
XP(l)sXP(4)-X»>(3)-l.
YP(l)=/P(4}-y?(3)-.5
.ZCOMsQ
ZPNsO
IF(IPLOIR.tO.l) CALL TEKSETU?
CALL SCAi£(DX?.OfP.XP,YP.»OFTS,lER)
CALL LIVE(XTZ(l,ISIf<),?i-C
-------
62
C
c
C END OF CASISGSF
IFCTHISPUN.EO.'FOR^ARD'lRETUaH
ENUIF
C
C ***********«********BEGI'JNIhG OF INVERSE PROGRAM*********************
C
1=0
00 500 ICASIKG=l,NCASIfcCl
00 500 IPOLE=l,rt?OLEl(ICASIIIG)
IFCIPOLE.EO.UTHEN
IPARAM1=7
ELSE
IPARAMV=3
ENOIF
DO 500 IPARArfsi.IPARAnl
500 CONTINUE
DO 600 ICASlNGsi.NCASINGl
PHICICASIHG)=PC2,1.ICASING>
Yl(l.ICASING)=P(5,l,ICASI«G)
Z1(1,ICASING)=PC6.1 .ICASING)
.. LENGTH (1,ICASI«G)=P( 7,1 , ICASING)
1 B£TACICASII»G),PHI(ICASING)}
T2(l.ICASIXG}=yi(l,ICASIMG)-fL¥(LeNGTH(l,ICASING),
1 BETA(ICASING).PHKICASING))
Z2(l,ICASIfJG)=Zl(l.ICASI.\G)+L2(LE».CTH(l,ICASIIJG),
1 BETA(ICASING))
00 700 IPULE=2,NPCLP1 (JCASING)
CMUC I POLE, ICASIr.G) = PU,IPOLE. .^CASING)
Xl(IPOLE,ICASi;JG)=P(2,IPCLE,ICASIHS)
21CIPOLE,ICASING)=Z1C1,ICASING)+
I LZ(X1(IPOLE,ICASING),BETACICASING))
TltIPDLE,ICASING)=»Hl,ICASING) +
I Ly(XKIPOLE,ICA5If.G),BETA(ICASrNG),PHI(ICA?ING))
Xl(IC1OLE,ICASIHG)=Xl(l,ICASlKG)t-
1 t.X(Xl(IPOLE,ICASINC),e£TACICASINC),PHI(ICASIf-G))
LENGTH (IPOLE,ICASIHG)=P( 3, IPQLE.ICASING)
X2CIPOLE,ICASIfiG)=Xl(lPULE,ICASING)»
1 LX(LENCTH(IPOL£,ICASING).9ETACCA5ING>, •'HKICASING))
y2CIPOLE,ICASIhG)=Vl(IPOLE,ICASIf'G)»
I LY(LEHGTH(IPOLE,ICASING), BETA (ICASING), PHI (ICASING))
Z2CPOLE,ICASISG)=Z1UPOLE,ICASING)»
1 v7;LEN
700 CONTINUE
600 CONTINUE
tEAP,tH=6P*f
-------
IFdYPtd.O.t).' ' )TtFE(IN)=T»PE(Ir;-lJ
00 18 XC=l,KC*Sl!«Gl
DO 18 IPsl ,.VP';L£1 CIO
IFdVPcd.O.EO.'X '.OR.TYPEdNKtO.'F ')tH£N
XCASINGO » XCiSINGO »
2 Xl( IP.IC) ,Y1(IP.IC),Z1(IP.IC).
3 X2( IP, 1C), if 2 UP. 1C), 22 UP, 1C). IP, 1C)
ENOIF
IF(TyPt(l:O.£0.*Y
*CASI:;GO
2 XldP.IO.YldF.IC) ,21 dP.IC),
3 X2CP,JC),V2UP,IC),2ilIP,IC),It',XC)
ENOIF
IFdtPtCI-J.f'i.'Z '.OR.TYPtdNKtO.'F 'JTKS.-
ZCASZNGO s ZCASINGO +
1 S Z U I M C I . , 1 > , X I f : C 1 1; , 2 ) , X I H ( I N , 3 ) ,
2 XldP,IC).»-ldP,IC),ZltIP,IC),
3 X2 dP. 1C). i 2 (IP, 1C), Z2 (IP, 1C). IP, 1C)
ENDIF »
16 CONTINUE
IFdfPEd'O.EO.'F *)THEN
8(SQf:T(XCASiriCO»»2»YC»SIf:COc»2f2CASI'iCO«»Z))-rCORfi
*)THEfi
FCALC=ZCASI.GO
StirdyPtdlJ.
i'CALCsfCAalf.GO
c
c
C END OF INVERSE RO','?X*e
'C
C
END
C
C
c
SUBROUTINE PLOT1
2 IPLOT. I.-.rxi.I-.Tn.i.sTZl,f
-------
c •
C VIPD THt C9':PO.Nc.»T 10 ££ fLOITEil
C
00 S ICsl.-iCO.'.PSl
WRITE C 6, «)*•.;.
313
314
PEtUR.i
E'liKY PCOOECP.X,DPAPA.-i.».F,I.<.iP.IE)
R£ rUR;:
EXTRY SUJZCYCr.S.XIi;DEP.«»PAP«?'.S.W,i.OU««.:)OaS,TITLE,10iJT)
RET'JflM
207
-------
END
suoroutlne ttr.setuc
•- wrlte(»,'Untf«,s)-) cr>ar(27)//*2'.//efier(27)//' 12J*//
chariJ7)//'l'//cr.«rlli)//chaTl27)//'"*.'/
end
SUBROUTI it vrioo
«rite(«,'(lx. a,*)*) cn«r(27>//'l'//chartl2K/
char (27 )//'•» *//cn«r( ^7 )//cnar(12)//en«rCi7)//*0'//
ch*r(27)//*"*//cn»ri27)//*.2'//
enar (27)//*2*//cr«r (27)//*l2J*//charC27)//'CH*
..
INTEGER FU<«CTIOri SLE*i(SISINC) *^C:,/
CH»RACTER*l») STRl::G • ^-:." '••
00 10
IF(StRI:iC(I:J). .'.£.' *>liith
sLEnsi :: ..-
REIUPW ' ---
1C CONTINUE
c
RETURN
I Reproduced from
besl available copy, t. * J
208
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APPENDIX II
TIME AND COST ESTIMATES FOR MAGNETIC SURVEYS
The time and costs of magnetic surveys designed to locate wells are
difficult to estimate. Contractors have not had experience in making surveys
with the required specification, and actual costs would be highly dependent on
the location, size, and peculiarities of the specific area. The following
estimates can be used as a guide to relative costs and rates of production,
but the actual numbers would be used with great caution In planniny potential
work.
For small areas, where access is good, it would be more cost effective to
use ground surveys than airborne surveys. Using a memory magnetometer, in
which readings can be stored for later retrieval, and assuming a station spac-
ing of 25 feet (7.6 m) one person can measure about four stations/minute or
cover about 6,000 feet (1,820 m) per hour in sparsely vegetated, flat terrain.
Additional time would be required to take more than one reading at a station
or to make :ntasurements at additional stations when anomalies are found. By
use of a digitally recording base station and a desk top computer and plotter,
data could be processed and plotted at the local field office or at the crews'
living accommodations. Thus, problems could be identified and anomalies eval-
uated while the crew was in the field area.
If surveying could be done adequately by use of a magnetic compass for
direction and a "hip chain" (which leaves a cotton thread behind) for distance,
with occasional use of more accurate instruments to establish reference points,
two persons could survey and make magnetic measurements in about the same
amount of time as required for one person to make only measurements. If this
method were not sufficiently accurate or could not be used in the area of
interest for other reasons, surveying and marking station locations would
likely require considerably more time than the actual magnetic measurements.
The cost for a two-person crew Including salaries, living expenses, vehi-
cle, equipment rental, supplies, and overhead, but not including mobilization
to the field site, would be on the order of at least $10,000/4 weeks (1983
costs). By working a reasonable amount of overtime this crew might curvey,
process, and plot a maximum of 160-line miles in 4 weeks. If a line spacing of
50 feet (15.2 m) v/ere used, this would cover an area of 1.52 square miles (3.94
km2). This represents a cost of $6,600/square mile (2.59 km^) covered and
$62.50/line-mile (38.84/1ine-km). This is less than one-half the line-mile
costs given by Senti (1982) for mineral exploration, but much mineral explora-
tion is done in heavily vegetated terrain. Rates of production would be less
and costs greater if the crew had to spend time in obtaining landowner's
authorization for access to the land or if the crew interpreted the results and
203
-------
did additional detailed work to "pin-point" the location of suspected casings
or investigate questionable anomalies.
For areas larger than a few square miles, airborne surveys are likely to
be considerably less expensive than ground surveys. Although the costs per
line mile'may be roughly comparable for ground surveys and specialized airborne
surveys, the line spacing can be much greater for airborne surveys. Airborne
surveys are not practical for very small areas due to the high costs of mobil-
ization.
Costs for routine aeronagnetic surveys using small fixed-wing aircraft are
on the order of $8-14/1 ine-;;vile ($5-9/line-km), including data processing
provided: 1) several thousand line miles are flown in one block, 2) the lines
are at least 10-20 miles (10-32 km) long, and 3) Doppler ra 'ir and photographic
methods are used for flight path recovery. The costs for similar work done
with rotary-wing aircraft are about $25-30/1ine-mile ($16-19/line-km). Costs
per line mile are much greater if th- lines are short and the areas small end
if a microwave navigation system is required.
Following are the rough costs, based largely on informal discussion with a
particular contractor, for surveying using a rotary-wing aircraft and a micro-
wave i.nav'i gat ion system:
Insjyjllation and removal of equipment from aircraft..... $ 10,500
*»
Helicopter standby time during installation and mobilization
to area including up to 14 hours of flight time $ 7,000
Surveying, placement, and maintainence of transponders $ 3,000
Foul- days in field, equipment and crew at $2,000/day .....$ 8,000
Ten hours flight time at $500/hour for helicopter and pilot $ 5,000
Rent of microwave navigation system, one month minimum at
$5,000/month $ 5,000
Suppl ies and computer $ 1,500
Total $ 40,000
Line miles flown $ 400
Cost per line mile $ 100
Area flown (£00 ft spacing) 30.5 sq. mi.
Cost per sq. mi $ 1,320
Using the same mobilization costs and assuming that four weeks were spent
in the field to do a large project, the costs for the same system would be
roughly:
Total cost including 56 hours of production flying $125,000
210
-------
Line miles flown 2,000
Cost per line mile * 62.50
Area flown 151.52 sq. mi.
Cost per sq. mi $ 825
Similar costs were mentioned by other contractors; some items were less
and some more. In general, aeromagnetic contractors do not have dedicated
helicopters or microwave navigation systems; these are rented as required for
special projects.
The costs for gradiometer measurements using a fixed-wing aircraft would
likely be somewhat less than for total field measurements using a rotary-wing
aircraft. On the other hand, gradient measurements from a rotary-wing aircraft
would cost considerably more than total field measurements. Although gradient
measurements have been made; from rotary-uing aircraft, it appears that no
contractor is currently using this configuration.
/
The above estimates include tite cost of initial data processing and plot-
ting data in profile form. There v:ould be additional costs to contour, filter,
or interpret the data. Also, of course, in most cases ground checking of seme
anomalies would be required to complete evaluation of an area.
211
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