U.S. patent application number 11/081958 was filed with the patent office on 2006-09-21 for calibration of xx, yy and zz induction tool measurements.
This patent application is currently assigned to Baker Hughes Incorporated. Invention is credited to Gulamabbas Merchant, Vladimir S. Mogilatov, Luis M. Pelegri.
Application Number | 20060208737 11/081958 |
Document ID | / |
Family ID | 37009644 |
Filed Date | 2006-09-21 |
United States Patent
Application |
20060208737 |
Kind Code |
A1 |
Merchant; Gulamabbas ; et
al. |
September 21, 2006 |
Calibration of xx, yy and zz induction tool measurements
Abstract
Measurements made with a multicomponent logging system oriented
in a horizontal position above the surface of the earth must
satisfy certain relationships. These relationships are used to
establish calibration errors in the system.
Inventors: |
Merchant; Gulamabbas;
(Houston, TX) ; Pelegri; Luis M.; (Humble, TX)
; Mogilatov; Vladimir S.; (Novosibirsk, RU) |
Correspondence
Address: |
MADAN, MOSSMAN & SRIRAM, P.C.
2603 AUGUSTA
SUITE 700
HOUSTON
TX
77057
US
|
Assignee: |
Baker Hughes Incorporated
|
Family ID: |
37009644 |
Appl. No.: |
11/081958 |
Filed: |
March 16, 2005 |
Current U.S.
Class: |
324/330 ;
324/339; 324/343 |
Current CPC
Class: |
G01V 13/00 20130101;
G01V 3/28 20130101 |
Class at
Publication: |
324/330 ;
324/339; 324/343 |
International
Class: |
G01V 3/16 20060101
G01V003/16; G01V 3/10 20060101 G01V003/10; G01V 3/18 20060101
G01V003/18 |
Claims
1. A method of using a system having at least one transmitter and a
plurality of receivers for making multicomponent induction
measurements, the method comprising: (a) positioning the system
above the surface of the earth; (b) orienting the system so that an
axis of the at least one transmitter is substantially parallel to
the surface and substantially collinear with an axis of at least
one of the plurality of receivers; (c) obtaining multicomponent
measurements at at least one frequency and at least one rotational
angle of the system; and (d) determining from the multicomponent
measurements an indication of a calibration error in at least one
of the multicomponent measurements.
2. The method of claim 1 wherein: (i) the system is adapted for use
in a wellbore in the earth formation; and (ii) the at least one
transmitter comprises three transmitters orthogonal to each
other.
3. The method of claim 2 wherein the three transmitters are not at
substantially the same position (non co-located).
4. The method of claim 1 wherein the system is adapted for aerial
use.
5. The method of claim 2 wherein the multicomponent measurements
comprise xx, yy, and zz measurements, and wherein determining the
indication of the calibration error comprises using a relation of
the form: H.sub.xx=H.sub.yy+H.sub.xx where H.sub.xx, H.sub.yy and
H.sub.zz are magnetic field measurements in the xx, yy, and zz
directions.
6. The method of claim 3 wherein: (i) the multicomponent
measurements comprise xy, and zz measurements; (ii) the at least
one rotation angle comprises an angle .phi.; and (iii) determining
the indication of the calibration error comprises using a relation
of the form: .sigma..sub.xy=.sigma..sub.zz sin 2.phi. where the
.sigma.'s are apparent conductivity values at the angle .phi..
7. The method of claim 5 wherein the at least one rotation angle
comprises angles of 0.degree. and 90.degree.;
8. A system for making multicomponent induction measurements, the
system comprising: (a) at least one transmitter and a plurality of
receivers that make multicomponent measurements at at least one
frequency and at least one rotational angle; (b) a processor which
determines from the multicomponent measurements made at a
substantially horizontal configuration of the system an indication
of a calibration error in at least one of the multicomponent
measurements.
9. The system of claim 8 wherein the at least one transmitter
comprises three transmitters orthogonal to each other, the three
transmitters disposed on a logging tool conveyed into a borehole in
the earth formation.
10. The system of claim 9 wherein the three transmitters are not at
substantially the same position (non co-located).
11. The system of claim 8 further comprising one of (i) a fixed
wing aircraft, and, (ii) a helicopter, which maintains the at least
one transmitter and the plurality of receivers in the substantially
horizontal configuration.
12. The system of claim 9 wherein the multicomponent measurements
comprise xx, yy, and zz measurements, and wherein the processor
determines the indication of the calibration error comprises using
a relation of the form: H.sub.xx=H.sub.yy+H.sub.zz where H.sub.xx,
H.sub.yy and H.sub.zz are magnetic field measurements in the xx,
yy, and zz directions.
13. The system of claim 10 wherein: (i) the multicomponent
measurements comprise xy, and zz measurements; (ii) the at least
one rotation angle comprises an angle .phi.; and (iii) the
processor determines the indication of the calibration error
comprises using a relation of the form:
.sigma..sub.xy=.sigma..sub.zz sin 2.phi. where the .sigma.'s are
apparent conductivity values at the angle .phi..
14. The system of claim 12 wherein the at least one rotation angle
comprises angles of 0.degree. and 90.degree.;
15. The system of claim 9 wherein the processor is at one of (i) a
downhole location, (ii) a surface location, and, (iii) a remote
location.
16. A machine readable medium for use with a system having at least
one transmitter and a plurality of receivers for making
multicomponent induction measurements, the medium comprising
instructions for: (a) positioning the system above the surface of
the earth; (b) orienting the system so that an axis of the at least
one transmitter is substantially parallel to the surface and
substantially collinear with an axis of at least one of the
plurality of receivers; (c) obtaining multicomponent measurements
at at least one frequency and at least one rotational angle of the
system; and (d) determining from the multicomponent measurements an
indication of a calibration error in at least one of the
multicomponent measurements.
17. The medium of claim 16 wherein: (i) the system is adapted for
use in a wellbore in the earth formation; and (ii) the at least one
transmitter comprises three transmitters orthogonal to each
other.
18. The medium of claim 17 wherein the three transmitters are not
at substantially the same position (non co-located).
19. The medium of claim 16 wherein the system is adapted for aerial
use.
20. The medium of claim 17 wherein the multicomponent measurements
comprise xx, yy, and zz measurements, and wherein the instructions
further comprise a relation of the form: H.sub.xx=H.sub.yy+H.sub.zz
where H.sub.xx, H.sub.yy, and H.sub.zz are magnetic field
measurements in the xx, yy, and zz directions.
21. The medium of claim 18 wherein: (i) the multicomponent
measurements comprise xy, and zz measurements; (ii) the at least
one rotation angle comprises an angle .phi.; and wherein the
instructions further comprise a relation of the form:
.sigma..sub.xy=.sigma..sub.zz sin 2.phi. where the .sigma.'s are
apparent conductivity values at the angle .phi..
22. The medium of claim 16 wherein the medium is selected from the
group consisting of (i) a ROM, (ii) an EPROM, (iii) an EAROM, (iv)
a Flash Memory, and, (v) an optical disk.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The invention is related generally to the field of
transverse electromagnetic induction measurements wherein the
multicomponent measurements are made with antennas that may be
transversely inclined to one another. The method is applicable for
both well logging operations and for airborne electromagnetic
measurements.
[0003] 2. Description of the Related Art
[0004] Electromagnetic induction resistivity well logging
instruments are well known in the art. Electromagnetic induction
resistivity well logging instruments are used to determine the
electrical conductivity, and its converse, resistivity, of earth
formations penetrated by a borehole. Formation conductivity has
been determined based on results of measuring the magnetic field of
eddy currents that the instrument induces in the formation
adjoining the borehole. The electrical conductivity is used for,
among other reasons, inferring the fluid content of the earth
formations. Typically, lower conductivity (higher resistivity) is
associated with hydrocarbon-bearing earth formations. The physical
principles of electromagnetic induction well logging are well
described, for example, in, J. H. Moran and K. S. Kunz, Basic
Theory of Induction Logging and Application to Study of Two-Coil
Sondes, Geophysics, vol. 27, No. 6, part 1, pp. 829-858, Society of
Exploration Geophysicists, December 1962. Many improvements and
modifications to electromagnetic induction resistivity instruments
described in the Moran and Kunz reference, supra, have been
devised, some of which are described, for example, in U.S. Pat. No.
4,837,517 issued to Barber, in U.S. Pat. No. 5,157,605 issued to
Chandler et al and in U.S. Pat. No. 5,600,246 issued to Fanini et
al.
[0005] The conventional geophysical induction resistivity well
logging tool is a probe suitable for lowering into the borehole and
it comprises a sensor section containing a transmitter and receiver
and other, primarily electrical, equipment for measuring data to
infer the physical parameters that characterize the formation. The
sensor section, or mandrel, comprises induction transmitters and
receivers positioned along the instrument axis, arranged in the
order according to particular instrument or tool specifications and
oriented parallel with the borehole axis. The electrical equipment
generates an electrical voltage to be further applied to a
transmitter induction coil, conditions signals coming from receiver
induction coils, processes the acquired information, stores or by
means of telemetry sending the data to the earth surface through a
wire line cable used to lower the tool into the borehole.
[0006] Conventional induction well logging techniques employ coils
wound on an insulating mandrel. One or more transmitter coils are
energized by an alternating current. The oscillating magnetic field
produced by this arrangement results in the induction of currents
in the formations which are nearly proportional to the conductivity
of the formations. These currents, in turn, contribute to the
voltage induced in one or more receiver coils. By selecting only
the voltage component which is in phase with the transmitter
current, a signal is obtained that is approximately proportional to
the formation conductivity. In conventional induction logging
apparatus, the basic transmitter coil and receiver coil has axes
which are aligned with the longitudinal axis of the well logging
device. (For simplicity of explanation, it will be assumed that the
borehole axis is aligned with the axis of the logging device, and
that these are both in the vertical direction. Also single coils
will subsequently be referred to without regard for focusing coils
or the like.) This arrangement tends to induce secondary current
loops in the formations that are concentric with the vertically
oriented transmitting and receiving coils. The resultant
conductivity measurements are indicative of the horizontal
conductivity (or resistivity) of the surrounding formations. There
are, however, various formations encountered in well logging which
have a conductivity that is anisotropic. Anisotropy results from
the manner in which formation beds were deposited by nature. For
example, "uniaxial anisotropy" is characterized by a difference
between the horizontal conductivity, in a plane parallel to the
bedding plane, and the vertical conductivity, in a direction
perpendicular to the bedding plane. When there is no bedding dip,
horizontal resistivity can be considered to be in the plane
perpendicular to the bore hole, and the vertical resistivity in the
direction parallel to the bore hole. Conventional induction logging
devices, which tend to be sensitive only to the horizontal
conductivity of the formations, do not provide a measure of
vertical conductivity or of anisotropy. Techniques have been
developed to determine formation anisotropy.
[0007] Thus, in a vertical borehole, in a clastic sedimentary
sequence, a conventional induction logging tool with transmitters
and receivers (induction coils) oriented only along the borehole
axis responds to the average horizontal conductivity that combines
the conductivity of both sands and shales. These average readings
are usually dominated by the relatively higher conductivity of the
shale layers and exhibit reduced sensitivity to the lower
conductivity sand layers where hydrocarbon reserves are produced.
To address this problem, loggers have turned to using transverse
induction logging tools having magnetic transmitters and receivers
(induction coils) oriented transversely with respect to the tool
longitudinal axis. Such instruments for transverse induction well
logging has been described in PCT Patent publication WO 98/00733 of
Beard et al. and U.S. Pat. No. 5,452,761 to Beard et al.; U.S. Pat.
No. 5,999,883 to Gupta et al.; and U.S. Pat. No. 5,781,436 to
Forgang et al.
[0008] One difficulty in interpreting the data acquired by a
transversal induction logging tool is associated with vulnerability
of its response to borehole conditions. Among these conditions is
the presence of a conductive well fluid as well as wellbore fluid
invasion effects. A known method for reducing these unwanted
impacts on the transversal induction logging tool response was
disclosed in L. A. Tabarovsky and M. I. Epov, Geometric and
Frequency Focusing in Exploration of Anisotropic Seams, Nauka, USSR
Academy of Science, Siberian Division, Novosibirsk, pp. 67-129
(1972) and L. A. Tabarovsky and M. I. Epov, Radial Characteristics
Of Induction Focusing Probes With Transverse Detectors In An
Anisotropic Medium, Soviet Geology And Geophysics, 20 (1979), pp.
81-90.
[0009] There are a few hardware margins and software limitations
that impact a conventional transversal induction logging tool
performance and result in errors appearing in the acquired data.
The general hardware problem is typically associated with an
unavoidable electrical field that is irradiated by the tool
induction transmitter simultaneously with the desirable magnetic
field, and it happens in agreement with Maxwell's equations for the
time varying field. The transmitter electrical field interacts with
remaining modules of the induction logging tool and with the
formation; however, this interaction does not produce any useful
information. Indeed, due to the always-existing possibility for
this field to be coupled directly into the receiver part of the
sensor section through parasitic displacement currents, it
introduces the noise. When this coupling occurs, the electrical
field develops undesirable electrical potentials at the input of
the receiver signal conditioning, primarily across the induction
coil receiver, and this voltage becomes an additive noise component
to the signal of interest introducing a systematic error to the
measurements.
[0010] Reduction of noise is of paramount importance, and a
hardware solution to the problem is taught in U.S. Pat. No.
6,586,939 to Fanini et al, having the same assignee as the present
invention and the contents of which are fully incorporated herein
by reference. Proper correction is necessary in order to obtain
meaningful interpretations of multicomponent induction logging
data.
[0011] Multicomponent EM measurements are also now being used in
airborne applications. As discussed in Smith et al., time-domain
airborne electromagnetic (AEM) systems historically measure the
inline horizontal (x) component. New versions of the
electromagnetic systems are designed to collect two additional
components [the vertical (z) component and the lateral horizontal
(y) component] to provide greater diagnostic information. An
example of such a system is shown in FIG. 3. This is illustrative
of the GEOTEM.RTM. of Fugro Airborne Surveys Corp. Shown therein is
a fixed wing aircraft 201 carrying a transmitter loop antenna 207
and a towed three component sensor 203 above the earth 205. Other
configurations using helicopter borne sensors also exist. As
discussed in Smith, measurements may be made with the transmitter
in different source orientations.
[0012] In areas where the geology is near horizontal, the
z-component response provides greater signal-to-noise, particularly
at late delay times. This allows the conductivity to be determined
to greater depth. In a layered environment, the symmetry implies
that they component will be zero; hence a nonzero y component will
indicate a lateral inhomogeneity. The extent of contamination of
the y component by the x and z components can be used to ascertain
the strike direction and the lateral offset of the target,
respectively. Having the z and y component data increases the total
response when the profile line has not traversed the target. This
increases the possibility of detecting a target located between
adjacent flight lines or beyond a survey boundary.
[0013] Hardware solutions of the type discussed by Fanini et al.
are not practical for airborne systems where the transmitter and
receiver are spatially separated. Even for transverse induction
logging instruments such as the 3DEX.TM. of Baker Hughes
Incorporated, it would be desirable to have an independent
assessment of the calibration of the different components of
multicomponent measurements. The present invention addresses this
need.
SUMMARY OF THE INVENTION
[0014] One embodiment of the present invention is method of using a
system having at least one transmitter and one or more receivers
for making multicomponent induction measurements. The system is
positioned above the surface of the earth and oriented so that an
axis of the at least one transmitter is substantially parallel to
the surface and substantially collinear with an axis of at least
one of the receivers. Multicomponent measurements are obtained at
one or more frequencies and one or more rotational angles of the
system. Multifrequency focusing of the multicomponent measurements
may be done. The multicomponent measurements are analyzed to get a
calibration error in at least one of the multicomponent
measurements.
[0015] In one embodiment of the invention, the multicomponent
measurements are made by a system is adapted for use in a wellbore
in an earth formation that includes three orthogonal transmitters.
The three transmitters may not be at the same spatial position. In
an alternate embodiment of the invention, the multicomponent
measurements are made by a system is adapted for airborne use. The
multicomponent measurements may be selected from xx, xy, yy, and zz
measurements.
[0016] Another embodiment of the invention is a system for making
multicomponent induction measurements. The system includes one or
more transmitters and one or more receivers for making
multicomponent measurements at one or more frequencies at one or
more rotational angles. The system also includes a processor which
determines from multicomponent measurements made at a substantially
horizontal configuration of the system an indication of a
calibration error in at least one of the multicomponent
measurements. The system may include three orthogonal transmitters
that may not be co-located on a logging tool. In another embodiment
of the invention, the transmitters and receivers may be conveyed on
a fixed wing aircraft or a helicopter. The multicomponent
measurements may be selected from xx, xy, yy, and zz measurements.
The processor may be at a downhole location, a surface location, or
a remote location.
[0017] Another embodiment of the invention is machine readable
medium for use with a system having one or more transmitters and
one or more receivers for making multicomponent induction
measurements. The medium includes instructions for positioning the
system above the surface of the earth, instructions for orienting
the system so that an axis of a transmitter is substantially
parallel to the surface and substantially collinear with an axis f
at least one of the plurality of receivers; instructions for
obtaining multicomponent measurements at at least one frequency and
at least one rotational angle of the system; and instructions for
determining from the multicomponent measurements an indication of a
calibration error in at least one of the multicomponent
measurements. The instructions may cover a system used in a
wellbore or an airborne system. The machine readable medium may
include ROMs, EPROMs, EAROMs, Flash Memories and Optical disks.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The invention is best understood by reference to the
accompanying figures wherein like numbers refer to like components
and in which:
[0019] FIG. 1 (Prior Art) shows an induction instrument disposed in
a wellbore penetrating earth formations;
[0020] FIG. 2 (Prior Art) shows the arrangement of transmitter and
receiver coils in the multicomponent induction logging tool
marketed under the name 3DEX.TM.;
[0021] FIG. 3 (prior art) illustrates equipment used for
multicomponent airborne electromagnetic measurements;
[0022] FIG. 4 shows a logging tool oriented horizontally above the
earth as needed for calibration according to the method of the
present invention; and
[0023] FIG. 5 is a flow chart of the method of the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0024] Referring now to FIG. 1, an electromagnetic induction well
logging instrument 10 is shown disposed in a wellbore 2 drilled
through earth formations. The earth formations are shown generally
at 4. The instrument 10 can be lowered into and withdrawn from the
wellbore 2 by means of an armored electrical cable 6 or similar
conveyance known in the art. The instrument 10 can be assembled
from three subsections: an auxiliary electronics unit 14 disposed
at one end of the instrument 10; a coil mandrel unit 8 attached to
the auxiliary electronics unit 14; and a receiver/signal
processing/telemetry electronics unit 12 attached to the other end
of the coil mandrel unit 8, this unit 12 typically being attached
to the cable 6.
[0025] The coil mandrel unit 8 includes induction transmitter and
receiver coils, as will be further explained, for inducing
electromagnetic fields in the earth formations 4 and for receiving
voltage signals induced by eddy currents flowing in the earth
formations 4 as a result of the electromagnetic fields induced
therein.
[0026] The auxiliary electronics unit 14 can include a signal
generator and power amplifiers (not shown) to cause alternating
currents of selected frequencies to flow through transmitter coils
in the coil mandrel unit 8.
[0027] The receiver/signal processing/telemetry electronics unit 12
can include receiver circuits (not shown) for detecting voltages
induced in receiver coils in the coil mandrel unit 8, and circuits
for processing these received voltages (not shown) into signals
representative of the conductivities of various layers, shown as 4A
through 4F of the earth formations 4. As a matter of convenience
the receiver/signal processing/telemetry electronics unit 12 can
include signal telemetry to transmit the conductivity-related
signals to the earth's surface along the cable 6 for further
processing, or alternatively can store the conductivity related
signals in an appropriate recording device (not shown) for
processing after the instrument 10 is withdrawn from the wellbore
2.
[0028] Referring to FIG. 2, the configuration of transmitter and
receiver coils in a preferred embodiment of the 3DExplorer.TM.
induction logging instrument of Baker Hughes is shown. Three
orthogonal transmitters 101, 103 and 105 that are referred to as
the T.sub.x, T.sub.z, and T.sub.y transmitters are shown (the
z-axis is the longitudinal axis of the tool). Corresponding to the
transmitters 101, 103 and 105 are associated receivers 107, 109 and
111, referred to as the R.sub.x, R.sub.z, and R.sub.y receivers,
for measuring the corresponding magnetic fields. In one mode of
operation of the tool, the H.sub.xx, H.sub.yy, H.sub.zz, H.sub.xy,
and H.sub.xz components are measured, though other components may
also be used.
[0029] The method of the present invention is based upon measuring
the different components of the induced magnetic field with the
logging tool in a horizontal position over the surface of the
earth. For the airborne EM system, this is requires some
modification of the apparatus shown in FIG. 3. The body of the
three-component sensor 203 would be provided with aerofoils that
produce sufficient lift so that the receivers are at the same
elevation as the transmitters. For a logging tool, this
configuration is illustrated in FIG. 4 where the tool 225 is
positioned horizontally in air over the earth. The surface of the
earth is denoted by 251 and boundaries of layers of the earth are
indicated by 253, 255 etc. Also indicated are a three-component
transmitter 261 and a three component receiver 263 with x, y and z
coils as indicated. The air has, for all practical purposes, a
conductivity .sigma.=0, while the earth layers have conductivity
.sigma..noteq.0.
[0030] When the x-axis is vertical, certain relationships exist
between the different components of a triaxial tool. The tool is
placed horizontal in air above the earth at a height of h.sub.s.
The earth is considered to be horizontally layered. The
conductivity of each layer can be arbitrary and there may be
anisotropy present. The figure shows only one tri-axial transmitter
array and one tri-axial receiver array. In a tool like 3DEX, there
are two transmitter arrays at different spacing from the receiver
and with moments such that the signal in air far from any objects
or earth is zero. In the case considered here, the distance h.sub.s
is small enough so that there is influence of the earth. The
orientation of the array is such that the X-coils face towards the
earth, the Y-coils and Z-coils are horizontal as shown in the
figure.
[0031] Let the transmitter magnetic moments for the X, Y and Z
transmitters be M.sub.x, M.sub.y and M.sub.z respectively.
Initially, let .sigma..sub.AIR=.sigma..sub.0.noteq.0. Then, the
magnetic field in the receivers X, Y and Z due to transmitter X, Y
and Z respectively are H.sub.xx, H.sub.yy and H.sub.zz. The
response can be obtained as a solution to Maxwell's Equations.
Assuming all the magnetic moments are equal to unity, the results
can be expressed as the integrals: H xx = .intg. 0 .infin. .times.
.zeta. 3 .beta. .times. ( e - .beta. .times. z - z s + R 0 .times.
e - .beta. .function. ( z 0 - z + h s ) ) .times. J 0 .function. (
.zeta. .times. .times. x ) .times. d .zeta. ( 1 ) ##EQU1## where
R.sub.0 is the reflection coefficient for the interface between air
and layered earth; Z is the variable of integration; .beta. = 2 - k
0 2 ; ##EQU2## k o = .omega. .times. .times. .mu. o .times. .sigma.
0 ; ##EQU2.2## .sigma..sub.0=Conductivity of the layer in which the
tool is located. For Air .sigma..sub.0=0; .mu..sub.0=Magnetic
Permeability of the layer in which the tool is located; .omega.=2
.pi.f; f=transmitter frequency; z=Z location of receiver; z.sub.s=Z
location of transmitter; h.sub.s=distance of receiver above layer
boundary; z.sub.0=Z location of the layer boundary; J.sub.0=Bessel
function of the first kind of order zero; J.sub.1=Bessel function
of the first kind of order one;
[0032] Using .sigma..sub.0=0, k.sub.0=0, and .beta.=.xi. we can
simplify H.sub.xx to H xx = .intg. 0 .infin. .times. .xi. 2
.function. ( e - .xi. .times. z - z s + R 0 .times. e - .times.
.xi. .function. ( z 0 - z + h s ) ) .times. J 0 .function. ( .zeta.
.times. .times. x ) .times. d .zeta. . ( 2 ) ##EQU3## Similarly H
zz = .intg. 0 .infin. .times. .zeta. 2 .function. ( - e - .xi.
.times. z - z s + R 0 .times. e - .xi. .function. ( z 0 - z + h s )
) .times. ( J 0 - J 1 .xi. 2 ) .times. d .zeta. ( 3 ) H yy = .intg.
0 .infin. .times. ( - e - .xi. .times. z - z s + R 0 .times. e -
.xi. .function. ( z 0 - z + h s ) ) .times. J 1 .times. d .zeta. .
( 4 ) ##EQU4## Hence H zz + H yy = .intg. 0 .infin. .times. .zeta.
2 .function. ( - e - .xi. .times. z - z s + R 0 .times. e - .xi.
.function. ( z 0 - z + h s ) ) .times. J 0 .times. d .zeta. . ( 5 )
##EQU5## Taking the difference of above sum with the expression for
H.sub.xx we get H .times. xx - ( H .times. zz + H .times. yy ) = 2
.times. .intg. 0 .infin. .times. .xi. 2 .times. e - .xi. .times. z
- z s .times. J 0 .function. ( .zeta. .times. .times. x ) .times. d
.zeta. = 2 R 3 .times. ( 2 - 3 .times. x 2 R 2 ) . ( 6 ) ##EQU6##
where x is the spacing between transmitter and receiver, R = x 2 +
( z - z s ) 2 . ##EQU7## For a horizontal tool, x=L, and z=z.sub.s.
Hence H xx - ( H zz + H yy ) = - 2 L 3 . ( 7 ) ##EQU8## As
mentioned before, in a tri-axial tool, the measurement is done
using a single transmitter with two receivers with their moments
such that the magnetic field is canceled in air far from earth.
Assuming the moments of the two receivers are M.sub.1 and M.sub.2
and the corresponding spacings are L.sub.1 and L.sub.2, the above
expression becomes: H xx - ( H zz = H yy ) = - 2 .times. ( M 1 L 1
3 - M 2 L 2 3 ) = 0. ( 8 ) ##EQU9##
[0033] The preceding expression is the result of the fact that the
measurements in air cancel. If we have the situation that the
measurements are made with a single receiver and two transmitters
with their moments canceling the receiver magnetic field in air
then by reciprocity, the above result is still valid. Hence,
H.sub.xx=H.sub.zz+H.sub.yy. (9) It should be noted that the above
result is valid for collocated or equally spaced coils. The array
is horizontal and the axis of the X coils is parallel to the normal
to the earth surface. In terms of apparent conductivities, the
above relation becomes:
.sigma..sub.xx=2.sigma..sub.zz+.sigma..sub.yy. (10) The factor of 2
is due to the different tool constants used to convert the
Z-component to conductivity as opposed the one used for X or Y
component.
[0034] Various consequences of the eqn. (9) can also be derived.
Consider the case when the tool is rotated around its axis. The
corresponding measurements can be expressed in terms of the primary
measurements at no rotation as follows:
H.sub.xx=cos.sup.2(.phi.)H.sub.xx+sin.sup.2(.phi.)H.sub.yy (11)
H.sub.yy=sin.sup.2(.phi.)H.sub.xx+cos.sup.2(.phi.)H.sub.yy (12)
H.sub.zz=H.sub.zz. (13) where .phi. is the angle of rotation of
X-axis around Z-axis. When we compute an expression similar to eq.
(8), we get: H ^ xx - ( H ^ zz + H ^ yy ) = cos 2 .function. (
.PHI. ) .times. ( H xx - H zz - H yy ) + .times. .times. sin 2
.function. ( .PHI. ) .times. ( H yy - H zz - H xx ) .times. .times.
= - 2 .times. sin 2 .function. ( .PHI. ) .times. H zz ( 14 )
##EQU10## The corresponding apparent conductive relation is:
{circumflex over (.sigma.)}.sub.xx-(2{circumflex over
(.sigma.)}.sub.zz+{circumflex over (.sigma.)}.sub.yy)=-4
sin.sup.2(.phi.).sigma..sub.zz (15). Similarly, for cross component
measurement: H ^ xy = 1 2 .times. sin .function. ( 2 .times. .PHI.
) .times. ( H yy - H xx ) = - 1 2 .times. sin .function. ( 2
.times. .PHI. ) .times. H zz ( 16 ) ##EQU11## and {circumflex over
(.sigma.)}.sub.xy=-sin(2.phi.).sigma..sub.zz. (17)
[0035] In reality, it is not practical to have the x-, y- and
z-coils for the transmitter (and the receiver) co-located, i.e., at
the same spatial position. For non-co-located coils, eqn. (17) is
also approximately correct for multifrequency focused signals.
Multifrequency focusing is discussed in U.S. Pat. No. 5,884,227 to
Rabinovich et al., having the same assignee as the present
invention and the contents of which are incorporated herein by
reference. The method includes extrapolating magnitudes of the
receiver signals at a plurality of frequencies to a response which
would be obtained at zero frequency. In one embodiment of the
invention, at least one of eqns. (10) and (17) is used as a
consistency check on the calibration achieved by the hardware such
as that disclosed in Fanini.
[0036] Additional relations exist that can be used for checking the
consistency of the different components of measurements. With the
tool in the orientation shown in FIG. 4, the measurements of the
magnetic field components may be denoted by: {tilde over
(H)}.sub.xx=H.sub.xx+.delta..sub.xx {tilde over
(H)}.sub.yy=H.sub.yy+.delta..sub.yy {tilde over
(H)}.sub.zz=H.sub.zz+.delta..sub.zz (18), where .delta..sub.xx,
.delta..sub.yy and .delta..sub.zz are the respective errors in the
measurements made of the corresponding components. From eqn. (4) it
follows that P 1 = H ~ zz + H ~ yy - H ~ xx = H zz + H yy - H xx +
.delta. zz + .delta. yy + .delta. xx = .delta. zz + .delta. yy -
.delta. xx . ( 19 ) ##EQU12##
[0037] Generally, it is easier to achieve calibration of the
z-coils. Calibration of the z-coils is discussed, for example, in
U.S. Pat. No. 5,293,128 to Zhou et al., having the same assignee as
the present invention and the contents of which are fully
incorporated herein by reference. If it is assumed that the zz
measurements are properly calibrated, then eqn. (19) gives an
indication of the relative error between the xx and yy
measurements. If the zz measurements are not assumed to be properly
calibrated, then it is possible to determine the calibration error
in the zz measurements.
[0038] Determination of the error in the zz measurements involves
rotating the tool shown in FIG. 3 by 90.degree. about the tool
axis, thus interchanging the x- and y-axis (with a sign reversal).
We can then evaluate P 2 = H ~ zz + H ~ xx - H ~ yy = H zz + H xx -
H yy + .delta. zz + .delta. xx + .delta. yy = .delta. zz + .delta.
xx - .delta. yy . ( 20 ) ##EQU13## From eqns. (19) and (20), it
follows that: P 1 + P 2 2 = .delta. zz . ( 21 ) ##EQU14## Thus, if
the quantity given by eqn. (21) is zero, then the zz component is
properly calibrated.
[0039] Turning now to FIG. 5, a flow chart illustrating the method
of the present invention is shown. The z-axis is of the tool (or
the transmitter on the aircraft) is oriented to horizontal 301.
Multicomponent measurements are made at one or more frequencies 303
at at least one rotational angle. As noted above, for co-located
transmitter (and receiver) coils, measurements at a single
frequency are sufficient. For non co-located coils, mutlifrequency
measurements may be made. As further noted above, at the very If
the coils are not co-located, then a multifrequency focusing (MFF)
is applied to the measurements 305. Next, calibration errors are
determined 307. As noted above, this is done using eqns. (1)-(7).
It is noted that even for an aeromagnetic system with only a single
transmitter coil, some calibration information can be obtained
using eqn. (3), so that the method of the invention can be
practiced with a system having a single transmitter and a plurality
of spaced-apart receivers.
[0040] The operation of the transmitter and receivers may be
controlled by one or more processors. For wireline applications,
the downhole processor and/or the surface processor may be used.
Part of the processing may be done at a remote location away from
the wellbore. Implicit in the control and processing of the data is
the use of a computer program implemented on a suitable machine
readable medium that enables the processor to perform the control
and processing. The machine readable medium may include ROMs,
EPROMs, EAROMs, Flash Memories and Optical disks.
[0041] While the foregoing disclosure is directed to the preferred
embodiments of the invention, various modifications will be
apparent to those skilled in the art. It is intended that all
variations within the scope of the appended claims be embraced by
the foregoing disclosure.
* * * * *