U.S. patent application number 09/854036 was filed with the patent office on 2003-10-30 for skin depth compensation in underground boring applications.
Invention is credited to Brune, Guenter W., Mercer, John E., Ng, Shiu S..
Application Number | 20030201126 09/854036 |
Document ID | / |
Family ID | 23260426 |
Filed Date | 2003-10-30 |
United States Patent
Application |
20030201126 |
Kind Code |
A1 |
Brune, Guenter W. ; et
al. |
October 30, 2003 |
Skin depth compensation in underground boring applications
Abstract
Arrangements, specific apparatus and associated methods for skin
depth compensation in underground boring applications are
described. Compensation for skin depth error is accomplished by
measuring a locating signal transmitted from a boring tool such
that measurements of the locating signal include skin depth error
introduced as a result of the electrical conductivity
characteristic of the earth. Thereafter, the measurements are used
in a way which determines a skin depth corrected position of the
boring tool. In one aspect, a multi-frequency approach is provided
which utilizes measured intensities of the locating field at two or
more frequencies to extrapolate a zero frequency value of
intensity. The zero frequency value of intensity is then used in
position determination. The multi-frequency approach does not
require knowledge of earth properties or ground surface geometry
since components of the measured magnetic field intensities of the
locating field measured at nonzero frequencies contain property and
geometry effects and pass them on to extrapolated zero frequency
values. Skin depth compensation in a number of locating scenarios
using a single frequency locating signal is introduced.
Inventors: |
Brune, Guenter W.;
(Bellevue, WA) ; Mercer, John E.; (Kent, WA)
; Ng, Shiu S.; (Kirkland, WA) |
Correspondence
Address: |
BOULDER PATENT SERVICE INC
1021 GAPTER ROAD
BOULDER
CO
803032924
|
Family ID: |
23260426 |
Appl. No.: |
09/854036 |
Filed: |
May 14, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09854036 |
May 14, 2001 |
|
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09323722 |
Jun 1, 1999 |
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6285190 |
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Current U.S.
Class: |
175/45 ;
175/61 |
Current CPC
Class: |
G01V 3/081 20130101;
E21B 47/02 20130101; E21B 47/0232 20200501 |
Class at
Publication: |
175/45 ;
175/61 |
International
Class: |
E21B 047/02 |
Claims
What is claimed is:
1. In an overall method of operating a system in which a boring
tool is moved through the ground in a region which includes an
electrical conductivity characteristic, said system including an
above ground arrangement for tracking the position of and/or
guiding the boring tool as the boring tool moves through the
ground, said system being configured for transmitting a locating
signal between the boring tool and said arrangement in said region,
the improvement comprising the steps of: compensating for skin
depth error by measuring said locating signal such that
measurements of the locating signal include skin depth error
introduced as a result of said electrical conductivity
characteristic and, thereafter, using said measurements in a way
which determines a skin depth corrected position of the boring
tool.
2. The improvement of claim 1 wherein said measurements are
produced by (i) transmitting the locating signal from the boring
tool to said arrangement at a preselected number of different
frequencies such that each frequency penetrates said region with a
different skin depth, and (ii) measuring the intensity of the
locating signal at each frequency to provide a number of intensity
measurements corresponding to the preselected number of said
different frequencies, and wherein the skin depth corrected
position of the boring tool is determined by using said intensity
measurements in combination.
3. The improvement of claim 2 wherein four preselected frequencies
are used.
4. The improvement of claim 3 wherein the preselected frequencies
are in the range of 2 to 40 kHz.
5. The improvement of claim 2 wherein said intensity measurements
are combined to extrapolate a zero frequency magnetic intensity for
a particular set of said intensity measurements and, thereafter,
the zero frequency magnetic intensity is used to determine the
position of the boring tool relative to said arrangement.
6. The improvement of claim 2 wherein determining the position of
the boring tool using said intensity measurements includes the
steps of (i) developing a set of magnetic intensity equations such
that one equation corresponds to each frequency for use with one of
the intensity measurements, said equations including a number of
coefficients in frequency equal to the number of intensity
measurements such that one of the coefficients is a constant which
represents a steady state electromagnetic value of the locating
signal, (ii) solving for said coefficients including the constant
coefficient and (iii) using said constant coefficient as an
electromagnetic reading at zero frequency to determine the position
of the boring tool relative to said arrangement at zero frequency
such the effect of skin depth is substantially reduced.
7. The improvement of claim 6 wherein four of said frequencies are
used and wherein said magnetic intensity equations are in the form:
S.sub.1=S.sub.0+af.sub.1.sup.05+bf.sub.1+cf.sub.1.sup.15
S.sub.2=S.sub.0+af.sub.2.sup.05+bf.sub.2+cf.sub.2.sup.15
S.sub.3=S.sub.0+af.sub.3.sup.05+bf.sub.3+cf.sub.3.sup.15
S.sub.4=S.sub.0+af.sub.4.sup.05+bf.sub.4+cf.sub.4.sup.15 where
S.sub.0 is said constant coefficient, a, b, and c are the remaining
coefficients and S.sub.1-S.sub.4 are the intensity measurements
corresponding to preselected frequencies f.sub.1-f.sub.4.
8. The improvement of claim 1 wherein certain ones of said
measurements are used to determine a value for skin depth to be
used during drilling, these certain measurements being obtained in
a calibration procedure by transmitting the locating signal from
the boring tool to said arrangement prior to drilling.
9. The improvement of claim 8 wherein said calibration procedure is
performed with the boring tool above ground.
10. The improvement of claim 8 wherein said locating signal is
transmitted at one fixed frequency.
11. The improvement of claim 8 wherein said arrangement includes a
portable walkover detector for use in locating said boring tool by
(i) using the walkover detector to generate electromagnetic data
which identifies an overhead position on the surface of the ground
that is directly above said boring tool in a way which is not
subject to skin depth error, (ii) measuring the overhead signal
strength of the locating signal transmitted from the boring tool
and (iii) using the overhead signal strength in conjunction with
the determined value of the skin depth to determine the depth of
the boring tool below the identified overhead position on the
surface of the ground such that the depth of the boring tool is
established based at least in part on said skin depth.
12. The improvement of claim 11 wherein said depth of the boring
tool along with the signal strength of the locating signal are
established by successive approximation using the expression: 18 D
= ( m B x G ( D ) ) 1 3 where D is the depth of the boring tool, m
is the signal strength of said locating signal, B.sub.x is the
signal strength of the locating signal as measured by the walkover
detector at said overhead position, .delta. is skin depth, and G is
a function representing deviation of magnetic measurements in a
conductive region.
13. The improvement of claim 12 wherein magnetic measurements in a
non-conductive region are consistent with a cubic law and wherein
the function G represents deviation of magnetic measurements from
the cubic law in a conductive region in terms of D/.delta..
14. The improvement of claim 12 wherein the expression
0<=D/.delta.<3 is satisfied.
15. The improvement of claim 8 wherein the boring tool moves
through the ground along an intended path while transmitting the
locating signal and moves in an orientation which includes pitch,
said boring tool including pitch sensing means and said locating
signal exhibiting a field defined forward point at the surface of
the ground with the boring tool at a particular point along the
intended path, said field defined forward point being vertically
above an inground forward point on said intended path through which
said boring tool is likely to pass and wherein said arrangement
includes a portable walkover detector, the boring tool being
located by (i) using the walkover detector to generate
electromagnetic data which identifies said forward point, (ii)
measuring the signal strength of the locating signal at said
forward point, as transmitted from the boring tool at said
particular point and (iii) using the measured signal strength of
the locating signal at said forward point in conjunction with said
determined value of the skin depth and a sensed pitch value,
determining the depth of the boring tool at said particular point
and a forward distance on said intended path from the particular
point at which the boring tool is located to said forward inground
point based at least in part on said skin depth such that the
location of the boring tool is established along said intended
path.
16. The improvement of claim 15 wherein the depth of the boring
tool at said particular point and said forward distance are
determined by solving the group of equations including: 19 B = B (
, , r ) B = B ( , , r ) tan = B B D = r sin ( + ) B y = B 2 + B 2
tan = r 2 = 2 + 2 where the locating signal is symmetric with
respect to a dipole axis and where D is the depth of the boring
tool, r is the distance between the forward point and the boring
tool, .xi. is a projected distance of r onto the dipole axis of the
boring tool, .eta., is a projected distance of r onto an axis which
is perpendicular to the dipole axis, .lambda. is an angle between r
and the dipole axis, B.sub.86 is a component of locating signal
intensity parallel to the dipole axis, B.sub..eta.is a radial
component of locating signal intensity parallel to the normal of
the dipole axis, .gamma. is measured pitch of the boring tool, B is
the overall intensity of the locating signal and .delta. is the
measured skin depth.
17. In an overall process in which a boring tool is moved through
the ground within a region along an intended path while
transmitting a locating signal, said region including an electrical
conductivity characteristic and said locating signal exhibiting a
field defined forward point which field defined forward point is
vertically above an inground forward point on said intended path
through which said boring tool is likely to pass with the boring
tool initially located at a particular point on the intended path,
said system including an above ground arrangement for tracking the
position of and/or guiding the boring tool as it moves through the
ground using a locating signal that is transmitted from the boring
tool to said arrangement such that the electrical conductivity of
said region results in a skin depth which modifies penetration of
the locating signal into said region and, consequently, which
produces skin depth error when magnetic readings of the locating
signal are used to determine the location of the boring tool
relative to said arrangement under an assumption that said region
is electrically non-conductive, a method of determining the depth
of said boring tool at said particular point, said method
comprising the steps of: a) measuring the skin depth in said region
in a predetermined way; b) identifying said field defined forward
point on or above the surface of the ground and identifying an
overhead point on or above the surface of the ground and directly
above the boring tool at said particular point; c) measuring a
forward distance defined at the surface of the ground between the
overhead point and the forward point; and d) using the forward
distance, said skin depth and certain characteristics of said
locating signal at said forward point, determining the depth of
said boring tool at said particular point.
18. The method of claim 17 wherein said locating signal includes a
vertical and a horizontal component and wherein the locating signal
includes the characteristic of its horizontal component being equal
to zero at said forward point.
19. In an overall process in which a boring tool is moved through
the ground within a region along an intended path while
transmitting a locating signal, said region including an electrical
conductivity characteristic and said locating signal exhibiting a
field defined forward point which field defined forward point is
vertically above an inground forward point on said intended path
through which said boring tool is likely to pass with the boring
tool initially located at a particular point on the intended path,
said system including an above ground arrangement for tracking the
position of and/or guiding the boring tool as it moves through the
ground using a locating signal that is transmitted from the boring
tool to said arrangement such that the electrical conductivity of
said region results in a skin depth which modifies penetration of
the locating signal into said region and, consequently, which
produces skin depth error when magnetic readings of the locating
signal are used to determine the location of the boring tool
relative to said arrangement under an assumption that said region
is electrically non-conductive, a method of determining the depth
of the boring tool from any forward point along the intended path
of the boring tool, said method comprising the steps of: a)
configuring the intended path in said region such that said forward
point is at a higher elevation on the surface of the ground than
said particular point; b) establishing the actual depth of the
boring tool at said particular point; c) measuring a vertical
elevation difference between the particular point and the forward
point; d) sensing the locating signal at said forward point while
the boring tool is at said particular point to determine an
uncorrected depth of the boring tool which is subject to skin depth
error; e) using the measured vertical elevation difference, the
actual depth of the boring tool at said particular point and the
uncorrected depth of the boring tool measured from the forward
point, determining a forward point skin depth correction factor; f)
after having advanced the boring tool to a subsequent particular
point on said intended path associated with a subsequent forward
point, determining a corrected depth of the boring tool i)
measuring the locating signal at said subsequent forward point
using said arrangement to produce electromagnetic data, ii)
determining the uncorrected depth of the boring tool at said
subsequent particular point using the electromagnetic data such
that the uncorrected depth at the subsequent particular point is
subject to skin depth error, and iii) multiplying the uncorrected
depth at the subsequent particular point by said forward skin depth
correction factor to determine depth of the boring tool at the
subsequent particular point corrected for skin depth.
20. The method of claim 19 wherein said skin depth correction
factor is given by 20 D OH + z G D FLP where D.sub.OH.delta. is the
actual depth of the boring tool at said particular point,
.DELTA.z.sub.G is the elevation difference between the particular
point and the forward point and D.sub.FP is the uncorrected depth
of the boring tool measured at said forward point.
21. A method of determining skin depth in a region of earth by
using a dipole transmitter configured for transmitting a signal
which exhibits a dipole field and a receiver configured for
receiving said signal along at least one receiving axis, said
method comprising the steps of: a) positioning said dipole
transmitter on the surface of the ground in said region; b)
transmitting the dipole signal from the dipole transmitter to said
receiver in a predetermined way to produce electromagnetic data;
and c) using the electromagnetic data to determine the skin depth
within region.
22. The method of claim 21 wherein said dipole field includes a
center axis and defines an orthogonal plane perpendicular to said
center axis which bisects said dipole field, said step of
positioning the dipole transmitter on the surface of the ground
including the steps of orienting the dipole transmitter such that
said center axis extends generally along the surface of the ground
with an orthogonal axis in said orthogonal plane also extending
generally along the surface of the ground and wherein the step of
transmitting said dipole signal from the dipole transmitter to the
dipole receiver includes the steps of (i) positioning the receiver
on said orthogonal axis at a first offset distance from said center
axis with said receiving axis substantially parallel to said center
axis and measuring a first value of said dipole signal along said
receiving axis, (ii) positioning the receiver on said orthogonal
axis at a second offset distance from said center axis with said
receiving axis substantially parallel to said center axis and
measuring a second value of said dipole signal along said receiving
axis, and (iii) using the first and second values of said dipole
signal as said electromagnetic data.
23. The method of claim 22 wherein the skin depth is determined
using the expression:
(g.sub.1x.sub.2.sup.3-g.sub.2x.sub.1.sup.3)d.epsilon..sup.3+(-
g.sub.1x.sub.2.sup.2-g.sub.2x.sub.1.sup.2)c.epsilon..sup.2+(g.sub.1x.sub.2-
-g.sub.2x.sub.1)b.epsilon.+g.sub.1-g.sub.2=0 where .delta. is skin
depth, .gamma. is equal to 1/.delta., B.sub.y is the first value of
said dipole field measured at said first offset distance from the
center axis and B.sub.y2 is the second value of said dipole field
measured at said second offset distance from the center axis where
the first and second offset distances are denoted as x.sub.1 and
x.sub.2, respectively, and g.sub.1=B.sub.y1x.sub.1.sup.3,
g.sub.2=B.sub.y2x.sub.2.sup.3.
24. In a system in which a boring tool is moved through the ground
in a region which includes an electrical conductivity
characteristic, said system including an above ground arrangement
for tracking the position of and/or guiding the boring tool as it
moves through the ground using a locating signal that is
transmitted between the boring tool and said above ground
arrangement such that the electrical conductivity of said region
results in a skin depth which modifies penetration of the locating
signal into said region and, consequently, which produces skin
depth error when magnetic readings of the locating signal are used
to determine the location of the boring tool relative to said above
ground arrangement under an assumption that said region is
electrically non-conductive, the improvement comprising: a
compensation arrangement forming part of said boring tool and/or
part of said above ground arrangement for compensating for skin
depth error based on measurements of said locating signal such that
a skin depth corrected position of the boring tool is
established.
25. The improvement of claim 24 wherein said compensation
arrangement includes a calibration arrangement which is configured
for determining the skin depth in said region using said locating
signal in a predetermined way and said compensation arrangement
further includes a processing arrangement which is configured for
using the skin depth during a drilling operation to determine said
skin depth corrected position of the boring tool.
26. The improvement of claim 25 wherein said compensation
arrangement forms part of the above ground arrangement.
27. The improvement of claim 25 wherein said locating signal is
transmitted at one frequency.
28. The improvement of claim 27 wherein said boring tool includes a
dipole transmitter configured for transmitting said locating signal
such that the locating signal is in the form of a dipole field
having a center axis and defining an orthogonal plane perpendicular
to said center axis which bisects said dipole field and wherein the
above ground arrangement is a portable detector which houses said
compensation arrangement and which includes said calibration
arrangement and further includes a receiving axis along which said
locating signal is detected, said calibration arrangement being
configured for determining the skin depth using at least two
measurements of said locating field which are obtained by
positioning the dipole transmitter on the surface of the ground
such that said center axis extends generally along the surface of
the ground with an orthogonal axis in said orthogonal plane also
extending generally along the surface of the ground and wherein the
locating signal from the dipole transmitter is measured at first
and second offset distances from said center axis to obtain said
two measurements, each measurement being obtained with the portable
detector placed on said orthogonal axis at said first and second
offset distances, respectively, having the receiving axis of the
portable detector oriented parallel to said center axis.
29. The improvement of claim 24 wherein said compensation
arrangement includes means forming part of said boring tool and
part of said above ground arrangement for transmitting said
locating signal through said region using at least two different
frequencies for any particular location of the boring tool within
said region and for receiving the locating signal at said different
frequencies to generate measurements of the locating field at said
different frequencies for use in determining said skin depth
corrected position of the boring tool at any particular location
within said region.
30. The improvement of claim 29 wherein the effect of skin depth is
determined by extrapolating a zero frequency magnetic intensity for
a particular set of said intensity measurements and, thereafter,
the zero frequency magnetic intensity is used to determine the
particular location of the boring tool relative to said
arrangement.
31. The improvement of claim 30 wherein said compensation
arrangement includes processing means forming part of said above
ground arrangement configured for using a set of magnetic intensity
equations in which each equation corresponds to one frequency for
use with one of the intensity measurements, said equations
including a number of coefficients equal in number to the number of
intensity measurements such that one of the coefficients is a
constant which represents a steady state electromagnetic value of
the locating signal, said processing means being configured for
solving for said coefficients including the constant coefficient
and, thereafter, for using said constant coefficient as an
electromagnetic reading to determine the particular location of the
boring tool relative to said arrangement at zero frequency such the
effect of skin depth is reduced.
32. The improvement of claim 31 wherein four of said frequencies
are used and wherein said magnetic intensity equations are in the
form: S.sub.1=S.sub.0+af.sub.1.sup.05+bf.sub.1+cf.sub.1.sup.15
S.sub.2=S.sub.0+af.sub.2.sup.05+bf.sub.2+cf.sub.2.sup.15
S.sub.3=S.sub.0+af.sub.3.sup.05+bf.sub.3+cf.sub.3.sup.15
S.sub.4=S.sub.0+af.sub.4.sup.05+bf.sub.4+cf.sub.4.sup.15 where
S.sub.0 o is said constant coefficient, a, b, and c are the
remaining coefficients and S.sub.1-S.sub.4 are the intensity
measurements corresponding to the plurality of frequencies
f.sub.1-f.sub.4.
33. The improvement of claim 29 wherein said boring tool includes
transmitter means forming part of said compensation arrangement
configured for transmitting said locating signal at said
frequencies and wherein said above ground arrangement includes
receiver means forming part of said compensation arrangement for
receiving the locating signal at said frequencies.
34. The improvement of claim 29 wherein transmitter means transmits
said frequencies in an alternating manner such that one frequency
at a time is transmitted.
35. The improvement of claim 34 wherein said frequencies alternate
at a rate which effectively causes all of the frequencies to be
transmitted from any one location of the boring tool irrespective
of movement of the boring tool caused by a drilling operation.
36. The improvement of claim 34 wherein said frequencies alternate
at a frequency at or above approximately 10 Hz.
37. The improvement of claim 24 wherein said above ground
arrangement includes a portable walkover detector configured for
receiving said locating signal and said locating signal is
transmitted from said boring tool.
38. The improvement of claim 37 wherein said compensation
arrangement includes means forming part of said boring tool and
part of said portable walkover detector for transmitting said
locating signal through said region using at least two frequencies
for any particular location of the boring tool within said region
and for receiving the locating signal at said frequencies to
generate measurements of the locating field at said frequencies for
use in determining said skin depth corrected position of the boring
tool at any particular location within said region.
39. The improvement of claim 24 wherein said locating signal is
transmitted from said boring tool and wherein said above ground
arrangement includes at least two detectors, each of which is
configured for receiving said locating signal at a fixed location
within said region to produce said measurements of the locating
signal.
40. The improvement of claim 39 wherein said compensation
arrangement includes means forming part of said boring tool for
transmitting said locating signal using at least two different
frequencies and means forming part of said above ground detectors
for receiving said frequencies for any particular location of the
boring tool within said region for use in generating measurements
of the locating field at said frequencies to determine said skin
depth corrected position of the boring tool.
41. A drilling apparatus for performing underground boring in a
region having an electrical conductivity which results in a skin
depth that modifies penetration of electromagnetic signals into
said region, said apparatus comprising: a) a boring tool which is
configured for moving through the ground including means for
emitting a locating signal using at least two frequencies each of
which is subject to said skin depth; and b) an above ground
arrangement configured for receiving said locating signal at said
frequencies as the boring tool moves underground, the received
frequencies being used in establishing a corrected position of the
boring tool in a way which compensates for said skin depth.
42. The apparatus of claim 41 wherein the effect of said skin depth
is compensated for by configuring said above ground arrangement to
extrapolate a zero frequency electromagnetic intensity for a
particular set of said intensity measurements produced at
substantially one particular location of the boring tool and,
thereafter, using the zero frequency electromagnetic intensity to
determine the particular location of the boring tool corrected for
said skin depth.
43. The apparatus of claim 42 wherein said above ground arrangement
includes processing means for using a series of magnetic intensity
equations in which each equation corresponds to one of said
frequencies for use with one of the intensity measurements, said
equations including a number of coefficients equal in number to the
number of intensity measurements such that one of the coefficients
is a constant which represents a steady state electromagnetic
status of the locating signal, said processing means being
configured for extrapolation by solving for said coefficients
including the constant coefficient and, thereafter, using said
constant coefficient as an electromagnetic reading to determine the
particular location of the boring tool relative to said arrangement
at zero frequency.
44. The improvement of claim 43 wherein four of said frequencies
are used and wherein said magnetic intensity equations are in the
form: S.sub.1=S.sub.0+af.sub.1.sup.05+bf.sub.1+cf.sub.1.sup.15
S.sub.2=S.sub.0+af.sub.2.sup.05+bf.sub.2+cf.sub.2.sup.15
S.sub.3=S.sub.0+af.sub.3.sup.05+bf.sub.3+cf.sub.3.sup.15
S.sub.4=S.sub.0+af.sub.4.sup.05+bf.sub.4+cf.sub.4.sup.15where
S.sub.0 is said constant coefficient, a, b, and c are the remaining
coefficients and S.sub.1-S.sub.4 are the intensity measurements
corresponding to the plurality of frequencies f.sub.1-f.sub.4.
45. The apparatus of claim 41 wherein said locating signal is
transmitted from the boring tool and said above ground arrangement
includes a portable walkover detector configured for receiving said
locating signal at said predetermined frequencies.
46. The apparatus of claim 41 wherein said locating signal is
transmitted from said boring tool and wherein said above ground
arrangement includes at least two detectors, each of which is
configured for receiving said locating signal at said frequencies
in a fixed location within said region.
47. The apparatus of claim 41 wherein four of said predetermined
frequencies are used.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention is related generally to the field of
locating and/or guiding an underground boring tool using a locating
signal which is transmitted through the ground and, more
particularly, to a method and associated apparatus for locating
and/or guiding the boring tool in a way which compensates for skin
effect that potentially introduces error in locating and/or guiding
the boring tool as a result of conductivity of the earth through
which the locating signal passes.
[0002] Referring to FIG. 1, boring tools are typically guided or
located by transmitting a dipole field from a dipole transmitter
which is positioned within the drill head of the boring tool. The
locating/dipole field is an oscillating signal that is generally
emitted from a dipole antenna oriented along the rotational axis of
the drill head. FIG. 1 illustrates a coordinate system including x,
y and z axes with a dipole transmitter D at its origin. For a point
p, at a radius r from the origin, the dipole equations are given
as: 1 B x = 3 x 2 - r 2 r 5 ( 1 ) B y = 3 xy r 5 ( 2 ) B z = 3 xz r
5 , and ( 3 ) r 2 = x 2 + y 2 + z 2 ( 4 )
[0003] Where B.sub.x, B.sub.y and B.sub.z represent orthogonal
components of the dipole field at point p. The dipole equations are
recited herein for the benefit of the reader since these equations
form a fundamental basis for the use of a dipole field in locating
applications. One such locating system is described, for example,
in U.S. Pat. No. 5,337,002 which is commonly assigned with the
present application. Traditionally, boring tool systems have not
used compensation for conductivity of the soil even though this
conductivity introduces a phenomenon commonly referred to as skin
effect. While skin effect can result in significant locating
errors, applicants submit that prior art systems have not provided
such compensation, at least in part, since it is perceived in the
art that compensation for skin effect is an extremely complex
proposition.
[0004] What prior art system designers have generally done is to
altogether ignore skin effect. This is tantamount to an assumption
of a non-conducting earth. Accordingly, the electromagnetic field
emitted by the magnetic dipole of a transmitter into a
non-conducting medium (such as air) is described mathematically by
the well known cubic law of a magnetic dipole (see FIG. 1).
Unfortunately, however, as a direct result of skin depth, drilling
in the earth can produce significant deviations from the cubic law
when a typical oscillating magnetic dipole field is used. The
latter term describes a magnetic dipole having a signal strength
that varies sinusoidally with time.
[0005] The present invention provides a highly advantageous and
heretofore unseen method and associated apparatus which provide
compensation for skin effect in underground boring tool
applications.
SUMMARY OF THE INVENTION
[0006] As will be described in more detail hereinafter, there are
disclosed herein arrangements, apparatus and associated methods for
skin depth compensation in underground boring applications.
Accordingly, in an overall method of operating a system in which a
boring tool is moved through the ground in a region which includes
an electrical conductivity characteristic and where the system
includes an above ground arrangement for tracking the position of
and/or guiding the boring tool as the boring tool moves through the
ground and in which the system is configured for transmitting a
locating signal between the boring tool and the arrangement in the
region, the improvement comprises compensating for skin depth error
by measuring the locating signal such that measurements of the
locating signal include skin depth error introduced as a result of
the electrical conductivity characteristic and, thereafter, using
the measurements in a way which determines a skin depth corrected
position of the boring tool.
[0007] In one aspect of the invention a multi-frequency approach is
provided which utilizes measured intensities of the locating field
at two or more frequencies to extrapolate a zero frequency value of
locating signal intensity. The zero frequency value of intensity is
then used in position determination. The multi-frequency approach
may be used in conjunction with walk-over type locators or with one
or more above ground receivers designed for receiving the locating
signal at fixed position(s). In one feature, the multi-frequency
approach of the present invention does not require knowledge of
earth properties or ground surface geometry. The components of the
measured magnetic field intensities of the locating field measured
at their selected frequencies contain property and geometry effects
and pass them on to extrapolated zero frequency values.
[0008] In another aspect of the invention, certain intensity
measurements of the locating signal are used to determine a value
for skin depth to be used during subsequent drilling, these certain
measurements being obtained in a calibration procedure by
transmitting the locating signal from the boring tool on the
surface of the ground to the above ground arrangement prior to
drilling.
[0009] In still another aspect of the invention, a determined value
of skin depth is used in one locating scenario with a walkover
detector in which the walkover detector is used to establish an
overhead position directly above the boring tool using a locating
signal transmitted at a single frequency. The measured overhead
signal strength of the locating signal transmitted from the boring
tool is then used in conjunction with the determined value of the
skin depth to determine the depth of the boring tool below the
overhead position on the surface of the ground such that the depth
of the boring tool is established based at least in part on the
skin depth.
[0010] In another locating scenario, with the locating signal
transmitted at a single frequency, the boring tool moves through
the ground along an intended path while transmitting the locating
signal and moves in an orientation which includes pitch. The boring
tool includes pitch sensing means and the locating signal exhibits
a field defined forward point at the surface of the ground with the
boring tool at a particular point along the intended path. The
field defined forward point being vertically above an inground
forward point on the intended path through which the boring tool is
likely to pass. The boring tool is located by using a walkover
detector to receive electromagnetic data which identifies the
forward point. Signal strength of the locating signal is then
measured at the forward point, as transmitted from the boring tool
at the particular point, and the measured signal strength of the
locating signal is used at the forward point in conjunction with
the determined value of the skin depth and a sensed pitch value to
determine the depth of the boring tool referenced to the particular
point and to determine a forward distance on the intended path from
the particular point at which the boring tool is located to the
in-ground forward point.
[0011] Alternatively, the field defined forward point may be
located on or immediately above the surface of the ground and an
overhead point may be identified on or immediately above the
surface of the ground directly above the boring tool at the
particular point. The forward distance is measured between the
overhead point and the forward point as, defined at the surface of
the ground. Using the forward distance, the determined value of
skin depth and certain characteristics of the locating signal at
the forward point, a skin depth corrected depth of the boring tool
at the particular point is determined.
[0012] In another alternative, the intended path of the boring tool
in the region is configured such that the forward point is at a
higher elevation on the surface of the ground than the particular
point. The actual depth of the boring tool is then established at
the particular point and a vertical elevation difference is
measured between the particular point and the forward point.
Thereafter, the locating signal is sensed at the forward point
while the boring tool is at the particular point to determine an
uncorrected depth of the boring tool which is subject to skin depth
error. Using the measured vertical elevation difference, the actual
depth of the boring tool at the particular point and the
uncorrected depth of the boring tool measured from the forward
point, a forward point skin depth correction factor is determined.
During subsequent drilling operations the forward point skin depth
correction factor is used in determining skin depth corrected depth
with the boring tool at subsequent particular points.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The present invention may be understood by reference to the
following detailed description taken in conjunction with the
drawings briefly described below.
[0014] FIG. 1 is a diagrammatic illustration of a coordinate system
for purposes of describing the well know magnetic dipole
equations.
[0015] FIG. 2 is a diagrammatic elevational view of a horizontal
drilling operation being performed in a region of ground using a
portable walkover detector, shown here to illustrate the effects of
skin depth on locating the boring tool.
[0016] FIG. 3 is a diagrammatic elevational view of another
horizontal drilling operation being performed in a region of ground
using a portable walkover detector, shown here to illustrate the
effects of skin depth on locating the boring tool with the walkover
detector at a forward locate point.
[0017] FIG. 4 is diagrammatic elevational view of still another
horizontal drilling operation being performed in a region of ground
using a locating/tracking system including fixed position above
ground locating field detectors, shown here to illustrate the
effects of skin depth on locating the boring tool in a system using
such fixed position above ground locating field detectors.
[0018] FIG. 5 is a plot of transverse and radial absorption
parameters against the ratio of range to skin depth, shown here to
illustrate the nature of these absorption parameters with
increasing range to skin depth ratios.
[0019] FIG. 6 is a plot of absorption parameters versus the ratio
of range to skin depth for rich agricultural earth extending to
infinity in all directions, shown here to illustrate selected
points on the absorption parameters for use in validating the
multi-frequency approach of the present invention.
[0020] FIG. 7 is a block diagram illustrating a multi-frequency
transmitter manufactured in accordance with the present invention
and suitable for use in a boring tool.
[0021] FIG. 8 is a block diagram illustrating a multi-frequency
receiver manufactured in accordance with the present invention and
suitable for use in a portable walkover detector or fixed position
detector.
[0022] FIG. 9 is a perspective view of the surface of the ground on
which a calibration procedure is being performed for determination
of skin depth in accordance with the present invention using a
portable walkover detector.
[0023] FIG. 10 is a plot illustrating a two point calibration
function F.
[0024] FIG. 11 is a diagrammatic elevational view of an overhead
position determination setup, illustrating the determination of a
skin depth corrected depth of the boring tool.
[0025] FIG. 12 is a plot representing the deviation from the cubic
law obtained from a curve fit of Wait's theoretical results valid
for a semi-infinite conductive region and zero transmitter pitch in
the range 0<D/.delta.<3.
[0026] FIG. 13 is a diagrammatic elevational view of a forward
locate position determination setup, shown here to illustrate
determination of a skin depth corrected depth of the boring tool
from the forward locate point.
[0027] FIG. 14 is a diagrammatic elevational view of a surface
offset distance position determination shown here to illustrate a
variation in which an above ground measurement between the forward
locate point and an overhead point directly above the boring tool
is used in determining the skin depth corrected depth of the boring
tool.
[0028] FIG. 15 is a diagrammatic elevational view of an above
ground elevation offset distance position determination setup,
shown here to illustrate still another variation in which a forward
locate point skin depth correction factor is developed for use in
subsequent drilling operations.
[0029] FIG. 16 is a diagrammatic elevational view of a dual point
common elevation position determination setup, shown here to
illustrate the use of two identifiable points having a
substantially common elevation.
DETAILED DESCRIPTION OF THE INVENTION
[0030] Attention is immediately directed to FIG. 2 which
illustrates a boring system 10 operating in a region 12. It is
noted that like reference numbers are used to refer to like
components wherever possible throughout the various figures. The
surface of the ground is indicated by the reference number 14.
System 10 includes a boring tool 16 that is positioned on the end
of a drill string 18 which is only partially shown. Boring tool 16
includes a dipole transmitter 20 having an antenna 22 that
transmits a dipole locating field 24. The latter is received using
a walkover portable locator/detector 30. Specific details regarding
the implementation of system 10, as well as details regarding the
implementation of other types of systems in accordance with the
present invention will be given at appropriate points hereinafter.
For the moment, discussions will be limited to more general details
regarding skin effect as related to the operation of system 10 in
order to facilitate the reader's understanding.
[0031] Still referring to FIG. 2, locating field 24, emitted by
antenna 22 into a non-conducting medium (not shown) such as air is
described mathematically by the cubic law, as mentioned above.
However, drilling takes place in the earth such as, for example, in
region 12 which is assumed to possess electrical conductivity
characteristics. These characteristics result in significant
deviations from the cubic law when locating field 24 varies
sinusoidally in time at a frequency f. With conductivity of region
12 denoted as .sigma., the penetration distance of locating field
24 as well as the shape of the magnetic field lines which make up
the field depend on the frequency and conductivity parameters.
Penetration distance is often called skin depth and is defined as:
2 = 1 f ( 5 )
[0032] where .mu. denotes the permeability of the earth and .delta.
is the skin depth. Thus, skin depth decreases if conductivity,
.sigma., permeability, .mu., or frequency, f, increase. Conversely,
skin depth becomes infinite at zero frequency or conductivity, in
which case the magnetic field is again described by the magnetic
dipole relationship. The significance of the zero frequency
characteristics will become apparent at an appropriate point below.
Increasing conductivity and/or frequency serve to weaken the
magnetic flux intensity recorded by locator 30 above ground. If
skin effect is not accounted for, the boring tool can appear to be
at a position farther from the detector than in actuality. In the
present example, where measurements are being taken with a
walk-over locator directly over the drill head (OH), the
transmitter can appear deeper, at position A, where the boring tool
is shown in phantom.
[0033] Referring now to FIG. 3, system 10 is shown once again with
locator 30 at a different position. Specifically, the locator is
shown at what is referred to as a forward negative locate point
(FNLP) or, more simply, forward locate point (FLP) (see, for
example, above referenced U.S. Pat. No. 5,337,002). An "X" is
indicative of the configuration of the receiving antenna within
locator 30. At the FLP, the flux lines of the locating field are
characteristically vertically oriented. In the absence of skin
depth compensation, when the locator is at the forward locate
point, dipole transmitter 22 can appear deeper and shifted farther
away from the locator at position B where the boring tool is shown
in phantom.
[0034] U.S. patent application Ser. No. 08/835,834, filing date
Apr. 16, 1997, entitled Systems, Arrangements and Associated
Methods for Tracking and/or Guiding an Underground Boring Tool is
commonly assigned with the present application and is incorporated
herein by reference. One example of a highly advantageous
locating/guidance system conforming with the subject application is
shown in FIG. 4 and is generally indicated by the reference number
40. System 40 uses one or more above ground detectors 42
positionable at fixed locations within region 12 for reception of
locating signal 24. With regard to the present application, skin
depth produces an effect in system 40 which is similar to that
described with reference to FIG. 3. That is, boring tool 16 appears
(shown in phantom) to be at position C at a deeper depth and
shifted away from detectors 42.
[0035] In some prior art systems, an above ground calibration
procedure (not shown) is performed in an attempt to measure the
signal strength of the dipole transmitter to be used in the boring
tool with no consideration of the influence of skin effect. For
example, the dipole transmitter and the locator are placed on the
surface of the ground at a known separation and orientation. In
this regard, it is recognized herein that skin depth has an effect
on signal strength when such a calibration procedure is performed.
Moreover, the skin effect in this above ground procedure varies
from the skin effect encountered when the boring tool is beneath
the surface, which further complicates provisions for skin depth
compensation. The accuracy of skin depth obtained from an above
ground calibration depends to a great extent on the homogeneity of
the soil. Skin depth will be accurate if the conductivity of the
soil near ground surface, where the calibration has been performed,
is similar to that of the soil above the transmitter. Specifically,
in the calibration procedure for ranges up to about three times
skin depth, skin effect causes an increase in recorded strength of
the transverse component of flux intensity and hence the distance
between transmitter and receiver appears smaller while an opposite
trend can be observed for the radial component of the flux
intensity.
[0036] Having generally described the influence of skin depth,
attention is now directed to details concerning provisions for
effective compensation. The discussion immediately above,
concerning an above ground calibration procedure, evidences that
each component of the magnetic flux intensity is affected
differently by earth conductivity and dipole frequency. An exact
solution, available for the components of magnetic flux intensity
of a magnetic dipole immersed in homogenous earth (i.e., having a
uniform conductivity) of infinite extent is given in U.S. Pat. No.
4,710,708, issued to Rorden et al. Rorden, however, relies on the
solution only to show that skin effect can be ignored when the
range of interest is significantly less than the skin depth.
Accordingly, Rorden uses a locating frequency that is low enough
(generally 1-100 Hz) to produce a sufficiently high skin depth in
equation 5 above to accomplish this objective. The present
invention, however, considers the use of such low frequencies as
unacceptable because common signal detection hardware and sensors
such as coil loops are more sensitive at higher frequencies.
Additionally, state of the art systems such as, for example,
systems 10 and 40 described above contemplate the use of the
locating signal as a carrier for the purpose of transmitting data
to above ground locations wherein the data are encoded upon the
locating signal. Carrier frequencies in the range of 1-100 Hz limit
data transmission capabilities optimistically to rates in the range
of only 0.5 to 50 Hz according to the Nyquist criteria.
[0037] Referring to FIG. 5, transverse and radial absorption
parameters are shown plotted against the ratio of range, r, to skin
depth, .delta., based on the Rorden expressions for these values.
Exponential decay is shown for comparison. It is of interest here
to note that Rorden fails to provide a plot such as that of FIG. 5
and, even though Rorden lists the equations, he fails to observe
that the transverse and radial components are each affected in a
different way as r/.delta. increases. Both components, however,
approach exponential decay asymptotically for large values of
r/.delta.. At the same time, it is important to understand that the
usefulness of the Rorden teachings is inherently limited, in a
practical sense, because the presence of a ground surface is not
modeled. As will be seen, the present invention resolves the
difficulties in using locating signals having frequencies
sufficiently high for providing ease of detection and adequate data
transfer rates using the locating signal as a carrier while
providing effective and highly advantageous compensation for skin
effect, even though the locating frequencies used are high enough
to encounter levels of skin effect that should not be ignored.
[0038] In one implementation of the present invention, which is
applicable to essentially any underground boring system including
systems 10 and 40 described above, the recognition must be
emphasized that the locating field is governed by the cubic law of
a magnetic dipole if the signal frequency goes to zero, because the
skin depth goes to infinity regardless of the conductivity of the
earth. At first blush, this recognition may seem of little
importance to one of ordinary skill in the art since, as a
practical matter, static magnetic fields (i.e., at zero frequency)
are useless in the present application. That is, only a time
varying field is readily measurable with sensitive detectors such
as coils. However, the present invention overcomes the seeming
uselessness of attempting a solution at zero frequency by providing
a highly advantageous multi-frequency approach which allows the
formulation of a zero frequency solution. Moreover, the
multi-frequency approach taken by the present invention may readily
be implemented using existing technologies, as will be seen
immediately hereinafter.
[0039] The multi-frequency approach of the method of the present
invention requires transmission and reception of the locating field
using at least two different frequencies. While specific
implementations to be described rely on the use of four different
frequencies, it is to be understood that any number of frequencies
of two or more may be employed. To some extent, it is considered
that accuracy may be enhanced, however, when more than two
frequencies are used. Details regarding frequency selection will be
provided at an appropriate point below. In the four frequency
implementation under discussion, measurement of the locating field
is made at one or more above ground locations using either one or
more detectors configured for use at fixed locations and/or using a
portable walkover locator. Receivers in either a portable walkover
locator or in fixed position above ground detectors may be
configured in essentially the same manner, in accordance with these
teachings. During operation of any system utilizing the
multi-frequency approach of the present invention, measurements are
made at the above ground locations corresponding to each of the
selected frequencies. Thereafter, these measurements are utilized
in a highly advantageous way which serves to extrapolate a zero
frequency measurement. For example, it may be assumed for any
particular above ground location that the component of the magnetic
field intensity of the locating signal measured at the i-th
frequency f.sub.1 depends on skin depth according to: 3 S I = S 0 F
( D I ) ( 6 )
[0040] where S.sub.0 is a constant which corresponds to the
intensity of the locating field at zero frequency, .delta..sub.i is
the skin depth at each of the selected frequencies, D is the depth
or some characteristic length scale of the boring tool and F is a
function to be determined. Thus, the objective is to establish the
value of S.sub.0 based on the values S.sub.1. To that end, for each
of the selected frequencies, an interpolation polynomial or any
other suitable mathematical function including an exact solution,
if obtainable, may be used to provide a curve fit to the measured
data for each of the frequencies. As an example, a cubic polynomial
can be used to approximate the function, F, at the four required
frequencies. Introducing the definition of skin depth, the magnetic
field intensities can be written as:
S.sub.1=S.sub.0+af.sub.1.sup.05+bf.sub.1+cf.sub.1.sup.15 (7)
S.sub.2=S.sub.0+af.sub.2.sup.05+bf.sub.2+cf.sub.2.sup.15 (8)
S.sub.3=S.sub.0+af.sub.3.sup.05+bf.sub.3+cf.sub.3.sup.15 (9)
S.sub.4=S.sub.0+af.sub.4.sup.05+bf.sub.4+cf.sub.4.sup.15 (10)
[0041] Equations 7-10 are a set of linear equations for the unknown
coefficients So, a, b and c that can be solved employing standard
solution methods. It should be noted that this approach is very
efficient numerically, requiring a small matrix to be inverted with
coefficients depending on the chosen frequencies. Once a value for
S.sub.0 is obtained, the position of the boring tool can be
determined using the well known cubic equations 1-4 above.
Remarkably, there is no need to determine the skin depth values
.delta..sub.1 . Since the selected frequencies are chosen prior to
initiation of drilling, the inversion of this matrix need only be
performed once. Other formulations of signal strength at each
frequency, S.sub.1, may be used. For example, one possible
formulation may be based on the exact solution of Rorden in which
exponential decay is observed for large values of r/.delta., the
equations may be expressed in the form: 4 S I = S 0 - r I G ( r I )
( 11 ) S I = - cf i 0 5 ( S 0 + a f i 0 5 + b f i ) ( 12 )
[0042] where G is a function to be determined and all other values
are described above. It should be noted that this approximation
also requires measurements at four frequencies but the four
resulting equations for unknown coefficients S.sub.0, a, b, c are
nonlinear. Hence, the solution method is somewhat less efficient
than one based on polynomial approximations, but remains applicable
over a wider range of skin depth. Once again, there is no need to
determine the values .delta..sub.1 .
[0043] Referring to FIG. 6, an important feature of the multiple
frequency approach of the method of the present invention resides
in the fact that it does not require knowledge of earth properties
or ground surface geometry. The components of the magnetic field
measured at nonzero frequencies contain property and geometry
effects and pass them on to extrapolated zero frequency values.
FIG. 6 demonstrates the validity of this approach for a simplified
case, rich agricultural earth (i.e., meaning higher conductivity
soil) extending to infinity in all directions. In this example, any
variations of earth conductivity and the effect of ground surface
and air on the magnetic field are neglected. The transverse and
radial absorption parameters, representing the deviation of the
magnetic field from the cubic law of magnetic dipoles, are plotted
vertically against the ratio of range to skin depth as dashed lines
indicated by the reference numbers 50 and 52, respectively. Points
50a-d and 52a-d have been selected on each absorption parameter
curve corresponding to transmitter frequencies of 2, 8, 14 and 20
kHz, respectively. As seen, extrapolation of the curve using the
polynomial formulation of equations 7-10 provides magnetic field
data that are within 2% of known exact values for the absorption
parameters at zero frequency (i.e., the known value of 1.0 for both
of the absorption parameters at zero frequency). In the method of
the present invention, the extrapolation is performed for magnetic
intensity, however, the present example serves to illustrate the
validity of this approach even though the absorption parameters
were extrapolated since magnetic intensity is the product of the
cubic law and absorption parameter. Even though the discussion
dealt with distributed conductivity of soil, the multiple frequency
approach will work for other field distortions due to conductivity
including but not limited to buried electrical conductors, pipes,
plates and rebar.
[0044] With regard to selection of frequencies at which the
locating signal is to be transmitted, it is noted that an unlimited
number of different frequency combinations may be employed. Since
an extrapolation to zero frequency is being performed, however, it
is considered that the frequencies should be as low as possible
while still providing for adequate detection and transmission of
data, using the locating signal as a carrier. For example,
frequencies in the range of 2-40 kHz are considered as
acceptable.
[0045] Referring now to FIG. 7, having described the
multi-frequency approach of the method of the present invention,
descriptions will now be provided of components appropriate for use
in systems which utilize the approach. FIG. 7 illustrates a
multi-frequency transmitter manufactured in accordance with the
present invention and generally indicated by the reference number
100. Transmitter 100 includes a sensor/conditioning section 102 and
a carrier generation/antenna drive section 104. Transmitter 100 is
generally configured for use in a boring tool, in certain
instances, the transmitter may be used in above ground applications
such as, for example, in a calibration and/or system test unit (not
shown).
[0046] Still referring to FIG. 7, sensor/conditioning section 102
includes a suitable group of sensors in this instance comprising,
for example, a three-axis gyro 106, a three-axis magnetometer 108,
a three-axis accelerometer 110, a roll/pitch sensor 112, a
temperature sensor 114 and a battery sensing section 116. Physical
parameters at the outputs of magnetometer 108, accelerometer 110
and roll/pitch sensor 112, as well as the transmitter battery
conditions using battery sensing section 116 and temperature using
temperature sensor 114, are provided to a multiplexer 118 which
then transfers all of these signals in multiplexed form to an
analog to digital converter 120. The latter digitizes and converts
the multiplexed signals into digital format, for example, at either
an 8-bit or 12-bit resolution, depending on accuracy requirements.
Thereafter, a microprocessor 122 processes all of the parameters
provided from the analog to digital converter and converts the
parameters into information relating to the in-ground transmitter
coordinates or relating to down-hole conditions. For example,
during this parameter processing, the microprocessor may perform
linearization and temperature compensation on the output of
roll/pitch sensor 112 in order to calculate an absolute pitch
position of the boring tool. The pitch output may further be
compensated based on the determination of a particular roll
position. Linearization and compensation coefficients are generated
during factory calibration and stored in a calibration constant
section 124 which comprises a non-volatile memory area within
transmitter 100. It is noted that programming of microprocessor 122
is considered to be within the ability of one having ordinary skill
in the art in view of this overall disclosure.
[0047] Once the calculations are complete relating to all of the
signals from sensors in sensor/conditioning section 102, the
results are transmitted to one or more above ground locations. To
that end, carrier generation/antenna drive section 104 includes an
oscillator 126 which provides a clock signal to microprocessor 122
and to a divide by N counter 128. The latter receives a frequency
select input from microprocessor 122 on an f select line 130 such
that the divide by N counter may selectively generate any one of a
wide range of carrier frequencies. The carrier frequency may be
selected by microprocessor 122 under software control in a number
of different ways. In one configuration, frequency selection can be
performed at the beginning of the drilling operation, for example,
after monitoring of background noise levels at various frequencies
such that noisy frequencies may be avoided. Such noisy frequencies
may be attributed, for instance, to traffic loops, invisible dog
fences, cable TV, and power lines in a particular region. In
another configuration, the transmitter may change frequencies on
the fly, after the drilling has started. On the fly frequency
change can be initiated either by the microprocessor using a
pre-determined algorithm, or by the request of the drilling
operator, for example, using a signal transmitted by telemetry from
the surface to the boring tool or transmitted through the drill
string using an isolated electrical conductor or based on
possibilities such as, for example, boring tool roll orientation
sequence and roll rate. Particularly advantageous arrangements for
automatically forming an isolated electrically conductive path
between the drill rig and an in-ground device such as a boring tool
to provide power and signal paths are disclosed in co-pending U.S.
patent application Ser. No. ______, filing date ______(attorney
docket no. DCI-P018), which is incorporated herein by
reference.
[0048] The selected carrier frequency is then passed to a
modulation section 132 which is configured for modulating data from
sensor/conditioning section 102 onto the selected carrier
frequency. Modulation section 132 receives the data on a data line
134 from microprocessor 122 and also receives a modulation
selection signal on a mod select line 136 connected with the
microprocessor. The modulation selection signal may select, for
example, phase modulation or amplitude modulation, or combinations
of both. The modulation scheme may be programmed either before or
during the drill, much in the same manner as in the case of the
carrier frequency, described above.
[0049] With continuing reference to FIG. 7, data modulation section
132 passes a modulated carrier signal to a driver section 140. The
driver section receives a power selection input on a power select
line 142 from microprocessor 122. In this way, the output of
transmitter 100 may be tailored to drilling conditions, for
example, to conserve battery power in a shallow drill run or to
increase transmitter output at longer ranges and/or drilling depths
or even to stop transmission altogether during idle periods of a
drilling operation. Control of the power as well as other functions
can be achieved using procedures such as have been described for
frequency control. The transmitter can send encoded data (as is
done for roll, pitch and other parameters) to allow the receiver to
adjust its calibration for the new signal strength. This will allow
the operator to continue monitoring depth or range without the need
to recalibrate while drilling. An antenna drive signal is produced
on an antenna line 144 which is coupled to an antenna 146 which
generally comprises a dipole antenna for emanation of locating
signal 24.
[0050] In accordance with the multi-frequency approach of the
present invention, described above, transmitter 100 may alternately
transmit one of four selected carrier frequencies from the boring
tool. The carrier frequencies may alternate at any suitable rate
such as, for example, 10 Hz and may be selected in accordance with
considerations described previously. It should be appreciated that
transmitter 100 is configured for flexibility in carrying out the
method of the present invention. That is, fewer or more than four
carrier frequencies may readily be transmitted either individually
or simultaneously.
[0051] Turning now to FIG. 8, a multi-frequency receiver
manufactured in accordance with the present invention is generally
indicated by the reference number 150. Locating signal 60 is
received by an antenna arrangement 152 which may include three
orthogonally arranged x, y and z antennas indicted by reference
numbers 154, 156 and 158, respectively. The locating signal
received by each antenna is first amplified by respective very low
noise pre-amplifiers 160a-c prior to processing. This
pre-amplification maintains the received signal-to-noise ratio
while making any noise introduced by subsequent circuitry
relatively negligible. The amplified antenna signals (not shown)
are then fed to mixers 162a-c to be translated down to a lower
intermediate frequency (IF). In this manner, any locating signal
frequency within a suitable design range such as, for example, 2-40
kHz can be received through appropriate adjustment of the
frequencies of the mixers such that outputs of the mixers fall
within a selected IF band.
[0052] Still referring to FIG. 8, the mixers are followed
immediately by narrow-band, band-pass filters 164a-c which
essentially pass only the locating signals at the translated IF
frequency. The IF frequency can be either the sum or the difference
of the carrier frequency and the mixer frequency. The filtered x, y
and z signals are further amplified by programmable-gain amplifiers
(PGA's) 166a-c before being received by an analog-to-digital
converter 168. PGA's 166 provide over 96 dB of dynamic range and
are each directly controlled by a digital signal processor (DSP)
170. One suitable DSP is the ADSP2185L, a sixteen bit fixed point
DSP manufactured by Analog Devices, Inc. Analog-to-digital
converter (ADC) 168 digitizes the received signals, at a rate
controlled by a direct digital synthesizer (DDS) 172 which is, in
turn controlled by DSP 170. The DSP and DDS receive an oscillator
signal from an oscillator 174. Using the oscillator signal and
based on control from the DSP, the DDS generates a local oscillator
frequency (LO) for mixers 162. The ADC digitizes the received
signals at the rate determined by the DDS and converts the signals
to a binary number two's complement format. The conversion rate is
either four times the IF frequency, if a quadrature sampling scheme
is used, or may be significantly less than the IF frequency, if an
under-sampling scheme is chosen. The resolution of the ADC may be
12-bit to 16-bit. All axes are simultaneously sampled in order to
maintain relative phase.
[0053] Continuing to describe receiver 150, digital signal
processor DSP 170, controls all operations of the receiver
including mixing frequency, PGA gain, and a selected signal
processing algorithm. In the case of a quadrature sampling scheme,
the DSP samples the received signals at four times their IF
(translated) frequency and then multiples the received signals it
by a separate Sine and Cosine sequence to obtain in-phase and
quadrature-phase components. This process converts the received
signal from its IF frequency down to a base-band frequency that
contains modulated data, if present, while, at the same time,
breaks down the signal into its in-phase (I) and quadrature-phase
(Q) components. The I and Q components are each passed through a
simple low-pass filter (not shown) to remove everything but the
modulated data. The filtered outputs are then used to obtain the
original data as well as further processing to recover signal
magnitude and sign information. Additionally, the outputs are also
used, along with a modified phase-lock-loop technique known as
Costas loop, for controlling the DDS frequency (which controls the
mixer frequency and ADC sample rate) and the PGA gain settings. The
exact algorithm varies depending on the modulation scheme used but
may be developed by one having ordinary skill in the art in view of
this overall disclosure.
[0054] If under sampling (not shown) is used, the DSP would sample
the received signals at a rate much lower than the IF frequency.
The digitized data is then processed using a matched filter to
obtain data, magnitude, and sign information as well as for PGA
gain control. Irrespective of sampling, the DSP implementation is
considered to be highly advantageous, resulting in a very flexible
and adaptive multi-frequency receiver. Many modifications (not
shown) are possible in view of this disclosure for purposes of
performance improvement. For example, mixers 162 can be eliminated
by replacing narrow-band band-pass filters 164 with broadband
band-pass filters and using ADC 168 to perform quadrature sampling
and direct-to-base-band conversion (digital mixing) in a single
operation. In order to receive the locating signal at different
frequencies, DSP 170 may either sample the data at different rates
or sample everything at a single, fixed rate and then perform rate
conversion in software using decimation and interpolation
techniques (known as digital re-sampling). As mentioned previously,
it should be appreciated that receiver 150 may readily be
incorporated into either a portable walkover locator or into
detectors designed for use at fixed positions with a drilling
region.
[0055] Having described a highly advantageous multi-frequency
approach for use in skin depth compensation, skin depth
compensation techniques using a single frequency locating signal
will now be described with regard to a number of different
exemplary scenarios. It is to be understood that existing systems
using portable locators may readily be adapted in conformity with
these teachings or, alternatively, new systems using either a
portable locator and/or one or more locating field detectors
designed for positioning at fixed locations within a drilling
region are also readily adaptable in view of these teachings.
[0056] Referring now to FIG. 9, the techniques disclosed herein for
use with single frequency locating signal transmission initially
rely on a determination of the skin depth in the drilling region.
As mentioned previously, some prior art systems utilize an above
ground calibration procedure in an attempt to relate the signal
strength of a dipole transmitter to distance without skin depth
compensation. The present invention introduces a technique for
performing an above ground calibration procedure which not only
provides dipole signal strength, but also yields a value for skin
depth in the drilling region which may be used in subsequent
position determination techniques accounting for skin depth. FIG. 9
illustrates a calibration procedure being performed using a
portable walkover detector 260 in a region 262. The calibration
procedure is performed on the surface of the ground which is
assumed to be planar for purposes of simplicity, having x and y
coordinate axes defined as shown. A dipole transmitter 264 is
diagrammatically illustrated and is oriented along the y axis while
being centered upon the x axis. Preferably, the transmitter should
be the transmitter which is to be used during subsequent drilling
operations in a drilling configuration such as housed in the drill
head (not shown) placed on the surface of the ground.
Alternatively, the transmitter itself may be positioned on the
ground, but it must be remembered that measurements are likely to
be affected by any housing later positioned around the
transmitter.
[0057] Still referring to FIG. 9, the calibration procedure is
performed with the walkover locator at two offset positions along
the x axis indicated by the reference numbers 266a, corresponding
to an offset distance of x1, and 266b, corresponding to an offset
distance of x2. Transmitter 264 transmits locating signal 24 at a
single frequency. It is to be understood that the calibration
procedure may just as readily be performed using a detector which
is intended for location at a fixed position within the drilling
region following the calibration procedure. In this regard,
irrespective of the specific form of the detector instrument to be
used in the calibration procedure, the instrument should be
positioned such that its locating field sensor arrangement is on
the x axis. In the instance of a walkover locator having an antenna
configuration as described, for example, in above referenced U.S.
Pat. No. 5,337,002, which is commonly assigned with the present
application, the plane of the antenna arrangement should be aligned
parallel to the y axis of the transmitter. In the instance of a
locating field detector including three orthogonal receiving axes,
such as described in above incorporated U.S. application Ser. No.
08/835,834, the detector arrangement is somewhat arbitrary since
signals measured along the three axes can be transformed
mathematically into any desired directions.
[0058] Using the configuration shown in FIG. 9, the calibration
procedure is performed by measuring the components of the magnetic
flux intensity B.sub.y1, and B.sub.y2 at positions x.sub.1 and
x.sub.2, respectively. Geophysical theory provides an equation for
the calculation of dipole strength and skin depth that has the
general form:
B.sub.y=B.sub.y(x,y,m,.delta.) (13)
[0059] where B.sub.y is a measured intensity, x and y are the
coordinates of the locator/detector, m is the signal strength of
the dipole transmitter and .delta. is the skin depth. At this time,
a preferred method is based on the theory of Wait et al (Journal of
Geophysical Research, Vol. 58, No. 2) which is valid for zero
transmitter pitch, level ground surface and homogeneous soil
conditions, as are present in FIG. 7. Wait solves Maxwell's
equations with boundary conditions at the ground surface correctly
satisfied. Since the calibration procedure provides two values of
magnetic flux intensity and the distances x.sub.1 and x.sub.2, two
nonlinear equations for calculating m and .delta. are obtained:
B.sub.y1=B.sub.y(x.sub.1,),m,.delta.) (14)
B.sub.y2=B.sub.y(x.sub.2,0,m,.delta.) (15)
[0060] The deviation of B.sub.y from the cubic law is approximated
in the range 0<=x/.delta.<3 by: 5 B y = m x 3 F ( x ) , and (
16 ) F ( x ) = 1 + b x + c ( x ) 2 + d ( x ) 3 ( 17 )
[0061] where the function F is shown in FIG. 10. The unknown
coefficients b, c and d can be obtained from this graph using
standard numerical techniques.
[0062] Using equations 16 and 17, the following equations can be
obtained which can be solved for m and .delta.: 6 B y1 = m x 1 3 [
1 + b x 1 + c ( x 1 ) 2 + d ( x 1 ) 3 ] ( 18 ) B y2 = m x 2 3 [ 1 +
b x 2 + c ( x 2 ) 2 + d ( x 2 ) 3 ] ( 19 )
[0063] The solution is obtained in 2 steps. First, the following
variables are defined after introduction in equations 18 and 19: 7
g 1 = B y1 x 1 3 ( 20 ) g 2 = B y2 x 2 3 ( 21 ) = 1 ( 22 )
[0064] Subtracting equation 19 from equation 18 provides equation
23 for .epsilon..
(g.sub.1x.sub.2.sup.3-g.sub.2x.sub.1.sup.3)d.epsilon..sup.3+(g.sub.1x.sub.-
2.sup.2-g.sub.2x.sub.1.sup.2)c.epsilon..sup.2+(g.sub.1x.sub.2-g.sub.2x.sub-
.1)b.epsilon.+g.sub.1-g.sub.2=0 (23)
[0065] Equation 23 can be solved employing a standard method such
as Newton's to yield .delta.. Thereafter, dipole strength, m,
follows directly from: 8 m = B y1 x 1 3 1 + b x 1 + c ( x 1 ) 2 + d
( x 1 ) 3 ( 24 )
[0066] Thus, dipole signal strength, m, and skin depth, .delta.,
are established for use in subsequent position determinations.
[0067] Turning now to FIG. 11, in a first scenario, an overhead
position determination setup (hereinafter OH setup) is generally
referred to by the reference number 270 with a detector (not shown)
at a position 272 located directly overhead (hereinafter OH setup)
of transmitter 264 transmitting locating signal 24. At this
location, the flux lines of the magnetic locating field are
characteristically horizontal substantially over the transmitter.
The detector measures the horizontal component of the magnetic flux
intensity B.sub.x. With m and .delta. known from the foregoing
above ground calibration transmitter depth and with a measured
value of intensity, B.sub.xD, from the detector, D, is determined
from a single equation written symbolically as: 9 B xD = B x ( m ,
D , D ) ( 25 )
[0068] The exact form of equation 25 can either be obtained from
geophysical theory or from dimensional analysis. Applying the
latter (e. g., P. W. Bridgman, Dimensional Analysis, 1931) six
variables are identified governing the physics of OH setup depth
measurement. The variables include B.sub.x, .mu., .sigma., f, D and
m which have been defined previously. Furthermore, four fundamental
units including length, time, volt, and ampere characterize the
problem. Hence according to the .pi.-theorem of dimensional
analysis six minus four or two non-dimensional groups describe the
OH setup measurements mathematically. The two non-dimensional
groups include 10 B x D 3 m ( 26 )
.mu..sigma.fD.sup.2 (27)
[0069] The second group given by equation 27 can be simplified to
D/.delta. using the definition of skin depth from equation 5. Hence
B.sub.x must be of the following general form:
[0070] Here, the function G represents the deviation from the cubic
law obtained from a curve fit of Wait's theoretical results valid
for a semi-infinite conductive and zero transmitter pitch in the
range 0.ltoreq.D/.delta.<3 medium, shown in FIG. 12. Since this
equation is nonlinear for depth D, an iterative procedure must be
formulated. As one example: 11 B x = m D 3 G ( D ) ( 28 ) D = ( m B
x G ( D ) ) 1 3 ( 29 )
[0071] Function iteration/successive approximation is performed
beginning with an initial guess for D, e. g. the value
corresponding to infinite skin depth. In successive approximations,
the procedure inserts the last available value for D on the right
hand side of this equation thereby calculating a new, more accurate
value. This process is repeated until changes between successive
values of D are reduced to a specified tolerance.
[0072] The analysis outlined immediately above provides the correct
functional relation between variables governing OH setup depth
measurement which can be written as: 12 G ( D ) = i = 1 N c i ( D )
d i ( 30 )
[0073] The unknown coefficients c.sub.1 and d.sub.i must be
obtained from another source, for example, Wait's theory or a
physical experiment conducted in different soil conditions and at
various depths. Another method for obtaining these coefficients
relies entirely on numerical modeling solving Maxwell's equations
and pertinent boundary conditions. Computer codes are commercially
available to aid in this task such as, for example, software by
Infolytica Corporation in Montreal, Canada.
[0074] Attention is now directed to FIG. 13 which illustrates a
second scenario representing a Forward Locate Point position
determination setup generally indicated by the reference numeral
290. It should be mentioned that even though the present
discussions are made with reference to the forward locate point,
these concepts are equally applicable to the rear locate point. In
this instance, detector 30 measures the magnitude of the magnetic
flux intensity B (not shown) as a result of locating signal 24
transmitted from transmitter 264 within drill head 274. In
addition, transmitter pitch .gamma. is measured. In order to
calculate transmitter depth from these measured quantities the
following equations must be solved: 13 B = B ( , , r ) ( 31 ) B = B
( , , r ) ( 32 ) tan = B B ( 33 ) D = r sin ( + ) ( 34 ) B y = B 2
+ B 2 ( 35 ) tan = ( 36 ) r 2 = 2 + 2 ( 37 )
[0075] The definitions of the geometric variables D, r, .xi.,
.eta., .lambda. are given in FIG. 13. It is noted that transmitter
depth is the distance from the ground surface to the transmitter.
Since the locator antennas measure signals above ground, the
distance between the antennas and ground must be subtracted from
the computed depth. These variables and the two components of the
magnetic field intensity B.sub.86 and B.sub.72 make up a total of 7
unknowns that can be obtained from the listed seven equations using
standard numerical methods. An example of a convenient solution
method is to rewrite the equations in terms of polar coordinates r,
.lambda. using
.xi.=r cos .lambda. (38)
.eta.=r sin .lambda. (39)
[0076] This transformation eliminates two equations. The remaining
equations then read: 14 B = B ( r , , r ) = 3 cos 2 - 1 r 3 H 1 ( r
) ( 40 ) B = B ( r , , r ) = 3 sin cos r 3 H 2 ( r ) ( 41 ) tan = B
B ( 42 ) B y = B 2 + B 2 ( 43 ) D = r sin ( + ) ( 44 )
[0077] Note that the equations for the components of magnetic field
intensity express the cubic law of a magnetic dipole multiplied by
a function H.sub.1, or H.sub.2 that accounts for the effect of skin
depth. The latter is known from an above ground calibration, as
described above. Details of these functions can be derived
employing either geophysical theory or dimensional analysis.
Further, note that equation 44 for transmitter depth is uncoupled
from the other equations allowing independent solution for the
position coordinates r and .lambda. of the FLP based on the
following nonlinear equations: 15 B ( r , , r ) tan - B ( r , , r )
= 0 ( 45 ) B y 2 - B 2 ( r , , r ) - B 2 ( r , , r ) = 0 ( 46 )
[0078] where the variables have been defined above. These equations
can be solved employing any of the standard solution methods for
sets of nonlinear equations such as, for example, Newton's and
function iteration.
[0079] Turning now to FIG. 14, in a third scenario, a surface
offset distance position determination setup is generally indicated
by the reference number 320. This setup technique uses the FLP and
OH points indicated by the reference numbers 322 and 324,
respectively. In this regard, it is noted that the locations of
these points are affected as a result of skin depth. At forward
locate point 322, the horizontal component, B.sub.x, of the
magnetic flux intensity vanishes. This fact can be used to derive a
formula for transmitter depth D as a function of a horizontal
distance, .DELTA.x.sub.G, at the surface of the ground between OH
point 324 and FLP 322. In applications where skin effect can be
neglected, a simple equation for depth, D, can be derived from the
cubic law for a dipole field:
D={square root}{square root over (2)}.DELTA.x.sub.G (47)
[0080] In order to account for skin effect relying on B.sub.x=0, a
different form of the equation is used which is written in symbolic
notation as: 16 B x ( r , x G , D ) = 0 ( 48 )
[0081] Here, skin depth .delta. is obtained from an above ground
two-point calibration as described earlier and .DELTA.x.sub.G can
be measured easily using available standard distance measurement
methods. Details of this equation can also be derived from
geophysical theory, e. g., the aforementioned work published by
Wait. In general, an explicit formula for depth cannot be derived
from this equation since it will most likely be nonlinear in D,
therefore, the expression must be solved numerically employing a
suitable standard solution method such as Newton's or function
iteration.
[0082] Attention is now directed to FIG. 15 which illustrates a
fourth, above ground elevation offset distance position
determination setup generally indicated by the reference number
360. This setup technique is useful in conjunction with an OH
measurement of drill head depth, D.sub.OH.delta., which accounts
for skin depth such as, for example, described above in the OH
position determination setup associated with FIG. 11. The elevation
offset technique requires a measurement of elevation change,
.DELTA.z.sub.G, between an OH point 362 and a FLP 364 with
transmitter 264 at one position 366. Generally, this measurement
will be performed once early in a drilling operation. With the
drill head at position 366, FLP-depth, D.sub.FLP.delta., (wherein
.delta. indicates compensation for skin depth) can be calculated
from the over head depth, D.sub.OH.delta., and the measured
elevation change using:
D.sub.FLP.delta.=D.sub.OH.delta.+.DELTA.z.sub.G (49)
[0083] Still referring to FIG. 15, the present technique is
especially useful for a walk-over locator that is able to
accurately measure over-the-head depth accounting for skin effect,
but is not configured for skin depth compensation from the FLP.
Since depth measured with such a locator at a forward locate point
does not include skin effect, the ratio D.sub.FLP.delta./D.sub.FLP
obtained at transmitter position 366 can be employed to correct
subsequent FLP depth measurements using the formula: 17 D FLP h = (
D OH + z G D FLP ) 1 D FLP k ( 50 )
[0084] Here, the subscripts l and k denote the first and k-th
locating positions respectively. It should be noted that this
correction is linear and hence can only be expected to give
accurate results for small depth variations and homogeneous soil
properties.
[0085] Referring to FIG. 16, a dual point common elevation position
determination setup is generally indicated by the reference number
380. Accordingly, magnetic measurements are made at any two
identifiable points having a common elevation. These measurements
are combined to obtain transmitter depth in the presence of skin
effects. It is assumed that ground elevation changes only
moderately between these two points so that the same locator
elevation can be maintained by simply raising or lowering the
locator/detector unit relative to the surface of the ground. This
approach does not require an above ground calibration since skin
depth is determined from magnetic field data together with
transmitter depth. Two such identifiable points are the OH and the
FLP points, as indicated. At the OH location there is only a
horizontal magnetic flux B.sub.x and at the forward locate point
there is only a vertical flux component B.sub.y. Even though
transmitter 264 is shown in a level orientation in this figure, its
pitch is not required to be zero. The governing equations have
already been described above for techniques relying on separate OH
and FLP measurements. Specifically, equations including (28) and
(31) to (37) may be used for the solution of transmitter depth D,
skin depth .delta. and the variables r,.xi.,.eta.,.lambda.,B.sub.86
, B.sub..eta., defined above. An example of a practical solution
method can be derived by modifying the approach given previously
for solving the set of equations (31) to (37). There the method
requires the simultaneous solution of the two nonlinear equations
(42) and (43) for the geometric parameters .lambda. and r. Here D,
.delta.,.lambda. and r are obtained by solving the 4 nonlinear
equations (28), (44), (45) and (46) simultaneously employing any
standard numerical solution methods such as Newton's and function
iteration.
[0086] In that skin depth compensation arrangements and associated
methods disclosed herein may be provided in a variety of different
configurations and modified in an unlimited number of different
ways, it should be understood that the present invention may be
embodied in many other specific forms without departing from the
spirit of scope of the invention. Therefore, the present examples
and methods are to be considered as illustrative and not
restrictive, and the invention is not to be limited to the details
given herein, but may be modified within the scope of the appended
claims.
* * * * *