Abstract:
Various embodiments include apparatus and methods of operation with respect to well logging. Apparatus and methods can include a tool having an arrangement of spaced apart transmitter antennas and receiver antennas in transmitter receiver antenna pairs to make shallow measurements and deep measurements. The signals acquired from the shallow measurements and deep measurements can be processed to provide a look ahead signal in a drilling operation. The transmitter and receiver antennas can be oriented to cancel or substantially cancel out signals from layers between the transmitter antenna and the receiver antenna in response to the transmitter being operated downhole in a well. Additional apparatus systems and methods are disclosed.
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Notices, Deadlines & Correspondence
LOOK-AHEAD OF THE BIT APPLICATIONS
Technical Field
The present invention relates generally to systems having well logging
capability.
Background
In drilling wells for oil and gas exploration, understanding the structure
and properties of the geological formation surrounding a borehole provides
information to aid such exploration. However, the environment in which the
drilling tools operate is at significant distances below the surface and
measurements to manage operation of such equipment are made at these
locations. Logging is the process of making measurements via sensors located
downhole, which can provide valuable information regarding the formation
characteristics. Measurement techniques can utilize electromagnetic signals that
can make deep measurements, which are less affected by the borehole and the
effects of the zone invaded by the drilling, and shallow measurements, which are
near the tool providing the probe signals. Most conventional tools are located
above the drill motor on the drill string and make measurements from formations
that have already been penetrated by the drill bit. Further, the usefulness of such
measurements may be related to the precision or quality of the information
derived from such measurements.
Brief Description of the Drawings
Figure 1 shows a block diagram of an example apparatus having a tool to
make measurements ahead of a drill bit, according to various embodiments.
Figure 2 shows features of an example method for a look-ahead of the bit
applications in a drilling operation, in accordance with various embodiments.
Figures 3A and 3B illustrate a look-ahead signal calculation, in
accordance with various embodiments.
Figures 4A and 4B illustrate a layer signal cancellation effect, in
accordance with various embodiments.
Figures 5A and 5B show integrated geometrical factors for a tool, in
accordance with various embodiments.
Figure 6 shows tilt angle combinations that achieve layer signal
cancellation effect for different dip angles, where the strike angle of the dip is
aligned with dipoles, in accordance with various embodiments.
Figure 7 shows integrated geometrical factors for a highly conductive
medium, in accordance with various embodiments.
Figure 8 shows geometrical factors associated with two different
spacings, in accordance with various embodiments.
Figures 9A-9C show three examples of layer signal cancelling
configurations and associated sensitivity regions, in accordance with various
embodiments.
Figures 10A and 10B show examples of basic configurations of a deep
measurement and a shallow measurement, in accordance with various
embodiments.
Figure 1 shows a comparison of a time lapse differential measurement
versus a layer signal cancelling measurement, in accordance with various
embodiments.
Figure 12 shows an example data acquisition system, in accordance with
various embodiments.
Figure 13 shows features of an example method of calculation of lookahead
signal via shallow and deep inversion, in accordance with various
embodiments.
Figure 14 shows features of an example method of the look-ahead signal
calculation by using only shallow signals, in accordance with various
embodiments.
Figure 15 illustrates an example calculation of a look-ahead signal via
deconvolution, in accordance with various embodiments.
Figure 16 illustrates an example calculation of deep layer properties via
full inversion, in accordance with various embodiments.
Figure 17 illustrates an example calculation of deep layer properties via
simple inversion, in accordance with various embodiments.
Figure 18 illustrates an example of a calculation of deep layer properties
via inversion, in accordance with various embodiments.
Figure 1 illustrates an example of a geosteering decision chart, in
accordance with various embodiments.
Figure 20 shows geometric factors associated with two different spacings
between transmitter and receiver, in accordance with various embodiments.
Figure 1 illustrates a non-causal deconvolution filter, in accordance
with various embodiments.
Figure 22 illustrates a causal deconvolution filter, in accordance with
various embodiments.
Figures 23 and 24 each shows a synthetic log with a zero dip angle and
four layers in an inversion process, in accordance with various embodiments.
Figure 25 shows a synthetic log with four layers in a deconvolution
process, in accordance with various embodiments.
Figures 26 and 27 compare standard and layer signal cancelling
configurations for a case with a large number of layers with resistivity variation,
in accordance with various embodiments.
Figure 28A-C shows an example step response model and example
differential signal models, in accordance with various embodiments.
Figure 29 shows skin effect corrected signals for an example case, in
accordance with various embodiments.
Figure 30A-B shows inverted distance to boundary and conductivity
contrast for an example case, in accordance with various embodiments.
Figure 31 depicts a block diagram of features of an example system to
control activation of arrangements of antennas and process received signals for
look-ahead of the bit applications, according to various embodiments.
Figure 32 depicts an embodiment of a system at a drilling site, according
to various embodiments.
Detailed Description
The following detailed description refers to the accompanying drawings
that show, by way of illustration and not limitation, various embodiments in
which the invention may be practiced. These embodiments are described in
sufficient detail to enable those skilled in the art to practice these and other
embodiments. Other embodiments may be utilized, and structural, logical, and
electrical changes may be made to these embodiments. The various
embodiments are not necessarily mutually exclusive, as some embodiments can
be combined with one or more other embodiments to form new embodiments.
The following detailed description is, therefore, not to be taken in a limiting
sense.
Figure 1 shows a block diagram of an embodiment of an apparatus 100
having a tool 105 to make measurements ahead of a drill bit that can be used to
determine a look-ahead signal and to determine properties downhole in a well
102. Tool 105 can have an arrangement of transmitters and receivers 110-1,
110-2 . . . 110-(N-1), 110-N structured relative to a longitudinal axis 107 of tool
105. These transmitters and receivers can be operated to capture signals near
tool 105 in regions behind tool 105 and regions adjacent to the sides of tool 105.
These relatively short range signals can be referred to as shallow signals. These
transmitters and receivers also can be operated to capture signals in regions in
front of tool 105 and with tool 105 arranged on a drilling structure, the signals
captured from in front of tool 105 can include regions ahead of a drill bit. These
relatively long range signals, deeper than shallow signals, can be referred to as
deep signals. The arrangement of transmitters and receivers 110-1, 110-2 . . .
110-(N-1), 110-N can be operated by selecting transmitters - receivers pairs
defined by the spacing between the transmitter and the receiver in each
respective pair. Large spacings can be used to probe ahead of the drill bit and
acquire deep signals. Smaller spacings can be used to probe in the formation
regions around tool 105. A deep signal and a shallow signal may be correlated
to the transmitter - receiver spacing, which may in turn be set by the location of
the transmitters and receivers behind the drill bit. For example, a shallow
measurement may include contributions from regions about one inch to about 0
ft from the tool and a deep measurement may include contributions from regions
about 5 ft to about 200 ft from the tool. In making shallow and deep
measurements, the deep measurements include contributions from regions
farther from the tool than shallow measurements. For example, the deep
measurements can provide contributions from distances from the tool that are,
but not limit to, at least 25% larger than the distances that provide contributions
in the shallow measurements. The difference in contribution distances can be
less than or more than 25% larger.
An arrangement of transmitter antennas and receiver antennas can be
structured along longitudinal axis 107 of tool 105, which is essentially
perpendicular to the cross section of the tool corresponding to the cross section
of a collar in a drill string. The arrangement can include the transmitters and
receivers spaced apart from each other such that one of the transmitters or
receivers is located nearest the drill bit and a last of the transmitters or receivers
in the arrangement is the farthest from the drill bit. The one transmitter or
receiver nearest the drill bit can be located as close to the drill bit as possible.
The closer to the drill bit that the arrangement begins, the formation properties
farther away from the drill bit can be determined. The first antenna may be
placed on a collar behind the drilling motor. Alternatively, the first antenna may
be placed on the drilling motor rather than on a collar behind the drilling motor.
Transmitter-receiver pairs can be arranged, such as by orientation, on
tool 105 relative to longitudinal axis 107 of tool 105 by using a special
combination of transmitter tilt angle and receiver tilt angle such that signals from
the layers between the respective transmitter and receiver of the pair can be
cancelled out. The transmitter tilt angle may be the same as the receiver tilt
angle or different from the receiver tilt angle. For instance, the receiver may
have a zero tilt angle and the transmitter may have a non-zero tilt angle. This
arrangement of the transmitter and receiver on tool 105 can make tool 105
insensitive to properties of the region to the side of the tool. Processing of
signals acquired by the receiver of the pair in response to a probe signal
transmitted by the transmitter of the pair can be implemented to eliminate
around-the-tool effects and focus ahead of the bit. Structuring transmitters and
their corresponding receivers at a particular layer signal cancelling orientation
can be realized for a given dip angle. For transmitters and their corresponding
receivers structured at a particular layer signal cancelling orientation for a dip
angle of zero degrees, for example, operation at a different dip angle may result
in less than complete layer signal cancellation. However, there can be range of
dip angles different from the dip angle for which the transmitter and receiver are
structured for essentially complete cancellation of the signals from layers at
which the signal from the layers is substantially cancelled. Substantial
cancellation can include 90% cancellation relative to the optimum cancellation.
Transmitters and receivers 110-1, 110-2 . . . 110-(N-1), 110-N of tool 105 can be
of sufficient number to allow for transmitter-receivers pairs of different
orientation such that an optimum cancellation of a layer signal can be attained by
tool 105 for a number of different dip angles.
Look-ahead measurements to provide a look-ahead signal or determine
formation properties ahead of the drill bit can be made by tool 105 without using
transmitter-receiver pairs oriented such that operation of the transmitter-receiver
pairs do not provide layer signal cancellation. Data from one or more shallow
measurements can be subtracted from a deep measurement to provide a lookahead
measurement. The data from the look-ahead can be processed to provide
a look-ahead signal and to determine formation properties ahead of the drill bit.
Tool 105 can have a plurality of antennas arranged in pairs. A first
transmitter - receiver antenna pair can have a spacing between the transmitter
and the receiver of the first transmitter - receiver antenna pair in a range from
two feet to twenty feet to make a shallow measurement such that layer signals
are substantially cancelled out between the transmitter and the receiver of the
first transmitter - receiver antenna pair. A second transmitter - receiver antenna
pair can have a spacing between the transmitter and the receiver of the second
transmitter - receiver antenna pair in a range from twenty feet to a hundred feet
to make a deep measurement such that layer signals are substantially cancelled
out between the transmitter and the receiver of the second transmitter - receiver
antenna pair. The transmitter antenna of the first transmitter - receiver antenna
pair is arranged as the transmitter antenna of the second transmitter - receiver
antenna pair or the receiver antenna of the first transmitter - receiver antenna pair
is arranged as the receiver antenna of the second transmitter - receiver antenna
pair.
Apparatus 100 can include a control unit 120 to control activation of the
transmitters of tool 105 and reception of signals at the receivers of tools 105.
Control unit 105 can be structured to be operable to select antennas of a plurality
of antennas in one or more transmitter - receiver pairs arranged to perform one
or more deep measurements and one or more shallow measurements when the
apparatus is operated downhole in a well. Control unit 120 can be arranged to be
operable to select antennas of the plurality in one or more transmitter - receiver
pairs arranged to substantially cancel out layer signals between the transmitter
antenna and the receiver antenna of the respective transmitter - receiver pair
when the tool is operated downhole in a well. Control unit 120 can be arranged
to conduct, among other operations using a transmitter antenna and a
corresponding receiver antenna, an absolute deep measurement, a ratio deep
measurement with an additional receiver, or a compensated deep measurement
with an additional receiver and an additional transmitter such that layer signals
are substantially cancelled between transmitter and receiver antenna pairs in the
respective measurements. Control unit 120 can operate tool 105 having four
antennas arranged to make shallow measurements and deep measurements and
to substantially cancel out layer signals from operation of the four antennas.
Control unit 0 can operate tool 105 having less than four antennas arranged to
make shallow measurements and deep measurements and to substantially cancel
out layer signals from operation of the four antennas. Control unit 120 can be
operated in conjunction with data processing unit 126 to process signals received
from the receivers in tool 105.
Data processing unit 126 can be structured to be operable to process data
from one or more deep measurements and one or more shallow measurements to
generate a look-ahead signal substantially without or substantially without
contributions from regions adjacent sides of the tool. Data processing unit 126
can include instrumentalities to perform one or more techniques to process
signals from shallow measurements and signals from deep measurements to
generate a look-ahead signal. A look-ahead signal is defined as signal correlated
to the region ahead of the drill bit associated with a drilling operation. Data
processing unit 126 also can use the generated look-ahead signal to determine
formation properties ahead of the drill bit. The look-ahead signal and/or the
determined formation properties ahead of the drill bit can be used to make
geosteering decisions. Geosteering is an intentional control to adjust drilling
direction.
The techniques to determine the look-ahead signal and/or the formation
properties ahead of the drill bit can include various applications of inversion
operations, forward modeling, using synthetic logs, and filtering techniques.
Inversion operations can include a comparison of measurements to predictions of
a model such that a value or spatial variation of a physical property can be
determined. A conventional inversion operation can include determining a
variation of electrical conductivity in a formation from measurements of induced
electric and magnetic fields. Other techniques, such as a forward model, deal
with calculating expected observed values with respect to an assumed model. A
synthetic log is a modeled log based on modeled response of the tool in known
formation parameters. The synthetic log is created by numerically modeling the
interaction of the tool and the formation, usually involving simulation of each
depth of the log point by point.
Data processing unit 126 can be arranged to be operable to equalize data
from one or more shallow measurements in terms of geometrical factors to the
data from one or more deep measurements such that difference between data
from the one or more deep measurements and the equalized data from the one or
more shallow measurements provides the look-ahead signal. The equalization
can be realized via a deconvolution filter. Data processing unit 126 can be
arranged to be operable to perform an inversion based on signals from the one or
more shallow measurements and signals from the one or more deep
measurements and operable to subtract an anticipated deep signal, derived from
the inversion, from a measured deep measurement signal to generate the lookahead
signal. Data processing unit 126 can be arranged to be operable to
perform an inversion based on signals from the one or more shallow
measurements without input from the one or more deep measurements and
operable to subtract a signal resulting from the inversion being applied to a
forward modeling of a deep configuration to generate the look-ahead signal.
Data processing unit 126 can use data attained with transmitter-receiver antenna
pairs selected such that a layer signal between the transmitter antenna and the
receiver antenna of the respective transmitter-receiver pair is substantially
cancelled out in response to the transmitter antenna being operated. Data
processing unit 126 can use data attained from transmitter-receiver antenna pairs
that do not operate with signal cancellation from layers.
Transmitters and receivers 110-1, 110-2 . . . l lO-(N-l), 110-N of tool 105
can be arranged with collocated multiple antennas with different tilt angles.
Circuitry and processing devices executing instructions in control unit 120 and
data processing unit 126 can be operated to synthetically create tilt angles by
combining signals from the collocated multiple antennas with different tilt
angles. This scheme allows apparatus 100 to algorithmically optimize signal
cancellation for different formation dip angles. Circuitry and processing devices
executing instructions in control unit 120 and data processing unit 126 can be
operated to synthetically create tilt angles by combining signals from the
collocated multiple antennas to synthetically create the tilt angle to cancel
signals from layers between the collocated multiple antennas. The optimized
signal cancellation can be used to provide a look-ahead signal and evaluation
formation properties ahead of a drill bit.
Transmitters and receivers 110-1, 110-2 . . . HO-(N-l), 110-N oftool 105
can be arranged with a set of transmitters and receivers having selected tilt
angles such that signals from layers outside the region between the respective
transmitters and receivers of this set can be cancelled. This provides an opposite
cancellation to the layer signal cancellation between transmitter and
corresponding receiver previously discussed. This produces a shallow reading
that is focused around the tool and it can be used in the place of other shallow
measurements mentioned herein. A transmitter antenna and a receiver antenna
can be arranged along a longitudinal axis of tool 105 such that at least one of the
transmitter antenna or receiver antenna has a tilt angle with respect to the
longitudinal axis of the tool where the orientations of transmitter antenna and the
receiver antenna, with respect to the longitudinal axis and with respect to each
other, provide for signals from layers outside the region between the respective
transmitter and receiver to be operatively cancelled. Circuitry and processing
devices executing instructions in control unit 120 and data processing unit 126
can be operated to synthetically create tilt angles by combining signals from the
collocated multiple antennas to cancel signals from layers outside the region
between the collocated multiple antennas. In applications where signals
associated with tilt angles of transmitter and receiver are synthetically generated
from collocated antennas with different tilt angles, the same transmitter and
receiver pair can be used for both focusing ahead and focusing around tool 105.
Control unit 1 0 and/or data processing unit 126 can be located at the
surface of well 102 operably in communication with tool 105 via a
communication mechanism. Such a communication mechanism can be realized
as a communication vehicle that is standard for well operations. Control unit
120 and/or data processing unit 126 can be distributed along the mechanism by
which tool 105 is placed downhole in well 102. Control unit 120 and/or data
processing unit 126 can be integrated with tool 105 such that control unit 120
and/or data processing unit 126 are operable downhole in well 102. Control unit
120 and/or data processing unit 126 can be distributed along tool 105. Such
embodiments can provide stable and deep evaluation of formations that have not
yet been penetrated by the drill bit during a drilling operation, prevention of
dangerous situations such as blow-outs, and enhanced recovery of hydrocarbons
by providing a geosteering mechanism.
Apparatus 100 can be structured for an implementation in the borehole of
a well as a measurements-while-drilling (MWD) system such as a loggingwhile-
drilling (LWD) system. Tool 105 can be located at the drill bit of the
drilling operation. Alternatively, apparatus 100 may be configured in a wireline
configuration.
Figure 2 shows features of an example embodiment of a method for a
look-ahead of the bit application in a drilling operation. At 210, activation of a
tool disposed downhole is controlled, where the tool has an arrangement of
spaced apart transmitter antennas and receiver antennas operable in selected
transmitter-receiver pairs. Controlling activation of the tool can include
selecting operation of transmitter-receiver antenna pairs such that layer signals
between the transmitter antenna and the receiver antenna of the respective
transmitter-receiver pair are substantially cancelled out in response to the
transmitter antenna transmitting a probe signal. Transmitter-receiver antenna
pairs can be operated in which signals from layers between the transmitter
antenna and the receiver antenna of the respective transmitter-receiver pair are
not cancelled with respect to a probe signal from the transmitter.
At 220, a deep signal from a deep measurement using a transmitterreceiver
pair is acquired and one or more shallow signals from one or more
shallow measurements using one or more other transmitter-receiver pairs are
acquired. In situations where there is not a cancellation of layer signals from
operating the transmitter, multiple shallow measurements can be made.
At 230, the one or more shallow signals are processed, generating a
modeled signal relative to regions adjacent sides and back of the tool. At 240, a
look-ahead signal substantially without contributions from the regions adjacent
the tool is formed by processing the deep signal with respect to the modeled
signal.
Processing the one or more shallow signals and forming the look-ahead
signal can include equalizing the one or more shallow signals in terms of
geometrical factors to the deep signal such that difference between the deep
signal and the equalized one or more shallow signals provides the look-ahead
signal. Equalizing the one or more shallow measurements can include
generating a shallow to deep translation filter via a deconvolution of shallow
geometric factors and deep geometric factors. Processing the one or more
shallow signals can include performing an inversion based on the one or more
shallow signals and the deep signal such that the modeled signal is derived as an
anticipated deep signal from the inversion. Subsequently, forming the lookahead
signal can include subtracting the modeled signal from the deep signal to
generate the look-ahead signal. Processing the one or more shallow signals can
include performing an inversion based on the one or more shallow signals
without input from the deep signal and applying a signal resulting from the
inversion to a forward modeling of a deep configuration to provide the modeled
signal. Subsequently, forming the look-ahead signal can include subtracting the
modeled signal from the deep signal to generate the look-ahead signal.
In various embodiments, an inversion can be conducted using the lookahead
signal and parameters of layers around the tool to generate resistivities and
positions of deep layers ahead of a drill bit corresponding to the tool. The lookahead
signal can be analyzed downhole during a drilling operation and a
geosteering decision can be made downhole based of the analysis. Alternatively,
the geosteering decision can be made at the surface from reviewing the analysis
or conducting the analysis at the surface. The surface activities can be
conducted via a user interface operable with a display that provides the analysis
or portions of the analysis to an operator. Resistivities and positions of deep
layers can be generated as the drill bit moves ahead. The drilling operation can
be stopped based on a determination that resistivity changes as the drill bit
moves ahead exceeds a threshold for resistivity change. Exceeding the threshold
may be indicative of dangerous pressure changes ahead of the drill bit.
Generally, all commercially available electromagnetic tools are most
sensitive to the formation properties that are in the section between the
transmitter and the receiver positions. However, in some applications, it may be
desirable to have more sensitivity above or below this section. For example,
such sensitivity may be desirable for geosteering. For geosteering,
measurements can be made in the vicinity of the drill bit while drilling to guide
the well trajectory effectively towards productive zones or to stop drilling before
dangerous zones are penetrated. Although several attempts have been made to
design tools that are sensitive to formation properties ahead of the bit, in almost
all cases, these tools remain more sensitive to formation properties to the side of
the tool. As a result, measurements are complicated by formation profile
variations around the tool.
In various embodiments, a process can be implemented to eliminate
around-the-tool effects and focus ahead of the bit. This process can be achieved
by using a special combination of transmitter tilt angle and receiver tilt angle to
cancel out signals from layers that are between transmitter and receiver and
make the tool insensitive to properties of the region to the side of the tool. See,
for example, Figures 4A and 4B. The resulting sensitive areas are shown in the
left box of Figure 3A, where Figure 3A illustrates a look-ahead measurement
from layer signal-cancelling tilt angles. As a second procedure, a separate
shallower measurement can be equalized in terms of geometrical factor to the
former measurement via a deconvolution filter, and then subtracted from the
former measurement. See, for example, the middle and right boxes of Figure
3A. However, it is noted that the process shown in Figure 3A can provide
significant value to evaluating a drilling operation if shallow measurements are
not subtracted. Alternatively, the process can use the subtraction with arbitrary
tilt angles without layer signal cancellation as shown in Figure 3B, which
illustrates a look-ahead measurement from arbitrary tilt angles.
It has been disclosed previously that for a special transmitter and receiver
tilt angle combination of a tool, it is possible to cancel out the direct signal from
the transmitter to the receiver of the tool. In a different approach in an example
embodiment, the signals that are due to formation layers in between the
transmitter and receiver are cancelled out. It should be noted that, although this
special tilt angle combination does not produce sensitivity reduction when
individual points in the three-dimensional space are concerned, it produces
sensitivity elimination on planar boundaries with given dip and strike due to
layer signal cancellation effects over the surfaces as illustrated in Figures 4A and
4B. Figure 4A illustrates example layer signal cancellation effects with a
boundary in between transmitter and receiver. Figure 4B illustrates example
layer signal cancellation effects with a boundary outside transmitter-receiver
section. As a result, an embodiment of an example process can be restricted to
planar surfaces with known dip and strike angles. It has been observed from
studies that even if the surfaces are not perfectly planar, or dip and strike are not
precisely known, processes discussed herein can still achieve good cancellation.
Figures 5A and 5B show integrated geometrical factors for a tool. These
factors are for a single transmitter, single receiver tool operating at a frequency
of f=500 Hz with a spacing of di=24 feet in a high resistivity region. Figure 5A
shows the integrated (in radial direction) geometrical factors obtained by
creating a synthetic log of a very thin low-contrast layer at zero dip angle. Curve
561 is for a transmitter tilt angle of 0° and receiver tilt angle of 45°. Curve 562 is
for a transmitter tilt angle of 45° and receiver tilt angle of 45°. Curve 563 is for a
transmitter tilt angle of 50° and receiver tilt angle of 50°. Curve 564 is for a
transmitter tilt angle of 55° and receiver tilt angle of 55°. It can be seen from
Figure 5A that, at the transmitter and receiver angle of 55°, the geometrical
factor diminishes at all positions between the transmitter and the receiver. It
should be noted that, although transmitter and receiver tilt is chosen equal in
these cases, layer signal cancelling may be achieved with different transmitter
and receiver tilt angles. Figure 5B shows a similar plot but for 30° formation
boundary dip angle. Curve 571 is for a transmitter tilt angle of 0° and receiver
tilt angle of 45°. Curve 572 is for a transmitter tilt angle of 45° and receiver tilt
angle of 45°. Curve 573 is for a transmitter tilt angle of 50° and receiver tilt
angle of 50°. Curve 574 is for a transmitter tilt angle of 55° and receiver tilt
angle of 55°. In this case, layer signal cancellation can still be achieved, but at a
different angle of approximately 45° as shown in curve 572. Even at the nonoptimum
tilt angle of 55°, a relatively good cancellation is achieved. As a result,
a 45 or 5° tilt angle tool is expected to perform well in the dip angle range of 0-
30° for the frequency and spacing used. This methodology can be used to design
tools that are optimum for different dip angle ranges. It is also important to note
that similar optimization process can be used to achieve the opposite
cancellation: signal from outside the region between the transmitter and
receivers can be cancelled by adjusting the transmitter and receiver tilt angles
accordingly. This produces a shallow reading that is focused around the tool and
it can be used in the place of any shallow measurement that is mentioned herein.
One way to obtain such configuration is to start with the configuration in Curve
561, and decrease the transmitter and receiver tilt angles until sensitivity
between the transmitter and the receiver is substantially larger than the signal
outside on that region. In the case where signals associated with tilt angles of
transmitter and receiver are synthetically generated from collocated antennas
with different tilt angles, same transmitter and receiver pair can be used for both
focusing ahead and focusing around.
Figure 6 shows tilt angle combinations that achieve layer signal
cancellation effect for different dip angles, where strike angle of the dip is
aligned with dipoles. The transmitter antenna-receiver antenna spacing is 24 ft
with operation at 500 Hz in a high resistivity region. Curve 681 is for a dip
angle of 30°. Curve 682 is for a dip angle of 15°. Curve 683 is for a dip angle of
30°. Curve 684 is for a dip angle of 45°. Curve 686 is for a dip angle of 60°.
Curve 681 is for a dip angle of 75°. It can be seen from Figure 6 that the
cancellation method works up to approximately 60 degrees for a wide range of
angle combinations for the configuration used. Multiple transmitters or receivers
can be combined to achieve cancellation effect in a wider range. A cross-dipole
or tri-axial tool can be used to synthesize dipole vectors at tilt angles that
optimally cancel layer signals.
Figure 7 shows integrated geometrical factors for a highly conductive
medium. These factors are for a tool with a single transmitter, single receiver
tool operating at a frequency of f=500 Hz with a spacing of feet at dip
angle of q< =3 ° jn a region having a resistance of R=l ohm. Curve 771 is for a
transmitter tilt angle of 0° and receiver tilt angle of 45°. Curve 772 is for a
transmitter tilt angle of 44.5° and receiver tilt angle of 44.5°. Curve 773 is for a
transmitter tilt angle of 42.5° and receiver tilt angle of 42.5°. Curve 774 is for a
transmitter tilt angle of 40.5° and receiver tilt angle of 40.5°. Although very
good cancellation can be achieved for any dipping angle for high resistivity
background, a reduction in cancellation performance is observed in highly
conductive medium as shown in Figure 7. Here, the optimum performance is
achieved at 42.5° as shown in curve 773. Operation at lower frequencies allows
successful cancellation at higher conductivity values.
Figure 8 shows geometrical factors associated with two different
spacings. Figure 8 also shows subtraction of geometrical factors associated with
the two different spacings. These factors are for a tool operating at a frequency
of f=500 Hz in a high resistivity region at a dip angle of q =0° with a spacing of
di=24 feet, having signal shown in curve 891, and a spacing of di=20 feet,
having signal shown in curve 892. The geometrical factors for the 24 ft spacing
are subtracted from the geometrical factors for the 20 ft spacing, indicated in
curve 893. It can be seen from Figure 8 that, by using the subtraction,
geometrical factor can be minimized around the back of the tool and focused
towards the front. Signals discussed herein are presented in terms of mili-mhos.
Such signals can be obtained by multiplying the voltages by associated tool
coefficients using well-known procedures.
Figures 9A-9C show three embodiments of layer signal cancelling
configurations and associated sensitivity regions. Figure 9A relates an absolute
measurement to a ratio measurement of Figure 9B and to a compensated
measurement of Figure 9C. The ratio measurement in Figure 9B may eliminate
the need for calibration of the transmitter, since any multiplicative effect on
transmitter signal is cancelled out. Tilt angle for both first and second receivers
can be adjusted differently for cancellation. Simultaneous cancellation can be
achieved at both receivers. The compensated measurement in Figure 9C can
further eliminate a requirement for calibration on both the transmitters and
receivers, and can also remove the multiplicative temperature variations on the
receivers. Simultaneous cancellation can be achieved at both receivers for both
transmitters, especially when distance between antennas in front of the tool and
back of the tool is kept small. In various embodiments, one of the antennas can
be placed as close as possible to the bit to increase depth of detection ahead of
the bit.
Figures 10A and 10B show examples of configurations of a deep
measurement and a shallow measurement. In general, a total of four antennas
can be used: a transmitter and a receiver for shallow measurements and a
transmitter and a receiver for deep measurements. However, as shown in Figure
10A, a common transmitter or receiver can be used to reduce the number of
antenna elements. A deep measurement has a sensitivity that extends farther
than a shallow measurement and receives signals earlier than the shallow
measurement, as drilling commences. A deep measurement typically has longer
transmitter-receiver spacing when compared to a shallow measurement;
however, this is not absolutely required. Lower operating frequencies can
provide for larger distances of investigation than higher frequencies for the same
transmitter-receiver antenna pair. Typical transmitter/receiver spacing for deep
measurement is 20-100 feet, while the transmitter/receiver spacing for shallow
measurement is 2 feet to 20 feet. Shallow spacing can be large enough to allow
compensation for sensitivity to borehole and invasion effects. To ensure
optimum focusing, shallow measurement should be made as close as possible to
the drill bit. Deep sensitivity increases with increasing transmitter and receiver
tilt angles, however this also amplifies borehole and mandrel effects. At least
one of transmitter or receiver can be tilted to produce azimuthal sensitivity.
Azimuthal sensitivity is important for a geosteering application, since it allows
for determination of a distinction between signals coming from different
directions. Typical frequency ranges for shallow and deep measurements
include 500 Hz - 10 MHz and 50 Hz - 100 KHz, respectively. Multiple
frequencies can be used for differentiating different deep layer distances. Figure
10B indicates that an existing tool configuration, such as a commercially
available tool, can be used for shallow or deep measurements. Such a tool can
be realized by an azimuthal deep resistivity (ADR) sensor.
An ADR sensor having tilted antennas in an azimuthal array can
acquire measurements in a number of discrete directions, called bins or bin
directions, allowing for a number of different depths of investigation to
determine distance and direction to multiple bed boundaries. For example, an
ADR can be arranged with transmitters and receivers to use 32 discrete
directions and 14 different depths of investigation. However, ADR
arrangements can use more or less than 32 discrete directions and/or more or less
than 14 different depths of investigation. An ADR sensor can add a dimension
to measurements by using tilted receiver antennas and acquiring data from all
possible transmitter-to-receiver spacings a number of times (corresponding to the
number of bins) per tool revolution. Tilt of the receivers confers directional
sensitivity to the array of ADR sensors. Deeper readings provided by the ADR
can improve reaction time, allowing for increased drilling speed. An ADR
sensor can provide fully compensated petrophysical-quality resistivity
measurements and deep reading geosteering measurements combined in one tool
to minimize bottom hole assembly (BHA) length. The azimuthal readings
provide for derivation of anisotropy resistivity values, R (horizontal) and Rv
(vertical), and dip.
Figure 11 shows a comparison of a time lapse differential measurement
versus a layer signal cancelling measurement. The layer signal cancelling
measurement in this example is made with transmitter tilt angle and receiver tilt
angle at 55° operating at 500 Hz in a high resistivity region, where its signal is
represented by curve 1142. The time lapse differential measurement in this
example is made with transmitter tilt angle at 0° and receiver tilt angle at 45°,
where the differential signal is represented by curve 1141. The time lapse
differential measurement can be calculated by subtracting the signal received at
one tool position from another tool position 0.2 inches away. It can be seen from
Figure 11 that layer signal cancelling measurement can focus much deeper due
to second order decay with respect to depth, when compared to third order decay
of the differential time-lapse measurement.
Figure 12 shows a block diagram of an embodiment of an apparatus
1200, such as a data acquisition system, having a tool 1205 with transmitting
antennas 1210-T-l . . . 1210-T-N and receiving antennas 1210-R-l . . . 1210-RM,
operable in a borehole in which tool 1205 is placed. Transmitting antennas
1210-T-l . . . 1210-T-N and receiving antennas 1210-R-l . . . 1210-R-M can be
configured along tool 1005 such that each has a tilt angle with respect to
longitudinal axis 1207 of tool 1005. Transmitter antennas or receiver antennas
may have a tilt angle of zero degrees. At least one combination of a transmitting
antenna and a receiving antenna can be arranged with tilt angles such that the
transmitting antenna and the receiving antenna of the combination are arranged
to cancel out signals from layers that are between the transmitting antenna and
the receiving antenna of the combination and make tool 1205 insensitive to
properties of the region to the side of tool 1205, when tool 1205 is operatively
disposed downhole in a well. The tilt angles of the transmitting antenna and the
receiving antenna of the combination can be different. At least one combination
of a transmitting antenna and a receiving antenna can be arranged with tilt angles
such that the transmitting antenna and the receiving antenna of the combination
are arranged to cancel out signals from layers outside the region between the
transmitting antenna and the receiving antenna of the combination, when tool
1205 is operatively disposed downhole in a well. The tilt angles of the
transmitting antenna and the receiving antenna of the combination can be
different. Transmitting antennas 1 0-T- . . . 1 10-T-N and receiving
antennas 1210-R-l . . . 1210-R-M may include collocation of antennas with
different tilt angles in which one or more tilt angles are synthetically created and
signal cancellation is realized synthetically. The synthetic cancellation can be
for signals from layers between the collocated antennas or from signals from
layers outside the region between the collocated multiple antennas.
Apparatus 1200 can include a system control center 1220, transmitters
1212-1 . . . 1210-N, receivers 1214-1 . . . 1214-M, a data acquisition unit 1222,
a data buffer 1224, a data processing unit 1226, and a communication unit 1228
in addition to tool 1205 with transmitting antennas 1210-T-l . . . 12 10-T-N and
receiving antennas 1210-R-l . . . 1210-R-M. System control center 1220 can
include a central processing unit (CPU), analog electronics, digital electronics, or
various combinations thereof to manage operation of other units of apparatus
1200. System control center 1220 can generate a signal and feed the signal to
transmitters 1212-1 . . . 1212-N. The signal can be generated within a frequency
in range 100 Hz to 10 MHz. Other frequency ranges may be used. Transmitters
1212-1 . . . 1212-N can direct currents to transmitting antennas 1210-T-l . . .
1210-T-N, which emit electromagnetic waves into the formation. Although tool
1205 is operable to cancel out signals from layers that are between the
transmitting antenna and the receiving antenna of a selected combination and
make tool 1205 insensitive to properties of the region to the side of tool 1205,
multiple transmitting antennas can be used to gather additional data to improve
sensing of formation parameters. For example, transmitting antennas at different
distances to the receiving antennas may produce images with different depth and
resolution. As another example, antennas with different tilt angles or
orientations may be used to produce sensitivity to anisotropic formation
parameters.
One of more of N transmitting antennas can be driven by the signal
provided by system control center 1220. The signal may consist of a sine wave
at the desired frequency for frequency domain applications. In a time domain
application, the signal can be a pulse with a certain shape and frequency
spectrum. The transmitters can be simultaneously or sequentially activated and
they can be kept on for a time long enough to allow transients to die off and
noise effects to diminish via stacking. The received signals can be transformed
into a domain where incident portion of the signal can be separated from the
reflected portion. One particular example for such transformation is Hilbert
transform. The signals at the receivers are provided to system control center
1220, which can be stored at the data buffer 1224 before finally being
communicated to the surface. System control center 1220 can also control or
interfere with the geosteering operation essentially autonomously without
consulting to the surface, so that decisions can be made with minimal delay.
Electromagnetic wave signals that are received at receiving antennas
1210-R-l . . . 1210-R-M can be directed to corresponding receivers 1214-1 . . .
1214-M and system control center 1220. Operation of apparatus 1200 can
include multiple frequencies being transmitted and received at the same time for
better time utilization. In such an operation, a sinusoidal waveform, a square
waveform, or other time-based waveforms may be used to excite multiple
frequencies simultaneously at each transmitting antenna 1210-T-l . . . 1210-T-M
or individual frequencies at transmitter antennas 1210-T-l . . . 1210-T-M.
Received signals corresponding to the multiple frequencies can be separated by
filters at the receiving end in data acquisition unit 1222. For each transmitting
antenna 1210-T-l . . . 1210-T-M, received signals at all receivers 1214-1 . . .
1214-M can be recorded. Data buffer 1224 can be used to store received signal
for processing.
Data processing unit 1226 can be used to perform inversion or other
processing on the data. The processing and the inversion can be continued in
accordance with processing features similar to or identical to embodiments
taught herein. Inversion operations can include a comparison of measurements
to predictions of a model such that a value or spatial variation of a physical
property can be determined. A conventional inversion operation can include
determining a variation of electrical conductivity in a formation from
measurements of induced electric and magnetic fields. Other techniques, such as
a forward model, deal with calculating expected observed values with respect to
an assumed model. In various embodiments, an inversion process, conducted
with respect to apparatus 1200, may be performed downhole or in an analysis
unit, such as a computer, at surface 1204 after the data is transferred to surface
1204. Communication unit 1228 can communicate the data or results to surface
1204 for observation and/or determination of subsequent action to be taken in a
drilling operation related to the measurements taken with apparatus 1200. The
data or results may also be communicated to other tools downhole and used to
improve various aspects of locating and extracting hydrocarbons.
With the shallow and deep data obtained, it is possible to do brute-force
inversion on a full set of received measurements. However, instead enhanced
processing may be attained with a procedure to divide the whole operation into
two parts: calculation of a look-ahead signal and calculation of formation layer
properties from the look-ahead signal. This two part approach allows
interpretations directly from the look-ahead signal, even if solution for deep
layer horizontal resistivity Rh, vertical resistivity Rv and position is not unique.
Figure 13 shows features of an example embodiment of a method of calculation
of look-ahead signal via shallow and deep inversion. This calculation can take
advantage of full inversion using both a shallow signal 1311 and a deep signal
1312. Shallow signal 131 1 and deep signal 1312 can be provided for numerical
inversion 1331 . Numerical inversion 1331 can use a number of different
conventional techniques including, but not limited to, pattern matching and
iterative methods. A library 1332 and forward model 1333 can assist numerical
inversion 1331. Inverted borehole parameters from borehole correction 1334
can be fed back to numerical inversion 1331 to obtain better estimates. Output
from numerical inversion 1331 can include layer resistivities (¾, R ), layer
positions (z), dip angle (Q), strike angle ( ), borehole radius (¾), borehole
resistivity (¾), eccentricity (decc), and eccentricity azimuth ( ecc) These
parameters can be feedback to borehole correction 1334 to update borehole
correction 1334. These factors can also be fed forward to provide data for layers
around or behind the tool 1335 for further processing. Deep layer resistivities
(¾, Rv), deep layer positions (z) output from numerical inversion 1331 are not
provided for determination of the look-ahead signal, the data kept for further
processing with measured deep signal 1312 relates to layers around or behind the
tool. Data for layers around or behind the tool 1335 can be provided for forward
modeling 1336 to provide a deep configuration correlated to the layers around or
behind the tool. Output from forward modeling 1336 provides a modeled signal
that is an anticipated deep signal from the layers around the tool, which can be
directed to subtraction node 1337. A look-ahead signal can be obtained by
subtracting an anticipated deep signal from the layers around the tool from the
measured deep signal.
Figure 14 shows features of an example embodiment of a method of the
look-ahead signal calculation by using only a shallow signal 141 1. In this case,
inverted layers are all near the tool since shallow measurement is mostly
sensitive near the tool. Shallow signal 1411 can be provided for numerical
inversion 1431. Numerical inversion 1431 can use a number of different
conventional techniques including, but not limited to, pattern matching and
iterative methods. A library 1432 and forward model 1433 can assist numerical
inversion 1431. Inverted borehole parameters from borehole correction 1434
can be fed back to numerical inversion 1431 to obtain better estimates. Output
from numerical inversion 1431 can include layer resistivities (Rh, Rv), layer
positions (z), dip angle Q), strike angle (f), borehole radius (¾), borehole
resistivity (Rb), eccentricity (decc), and eccentricity azimuth ( ecc)- These
parameters can be feedback to borehole correction 1434 to update borehole
correction 1434. These factors can also be fed to forward modeling 1436 with
the deep configuration to yield a signal that only includes layers near the tool.
Output from forward modeling 1436 provides a modeled signal that only
includes layers near the tool, which can be directed to subtraction node 1437. As
a result, when the modeled signal is subtracted from the measured deep signal
1412, the look-ahead signal can be obtained.
Figure 15 illustrates an example embodiment of a calculation of lookahead
signal via deconvolution. Such a look-ahead signal calculation can be
performed in a manner that does not involve an inversion. In this case, forward
modeling 54 can be performed to obtain shallow geometrical factors 542 as a
function of depth, associated with deep configurations. Forward modeling 1543
can be performed to obtain deep geometrical factors 1544 as a function of depth,
associated with shallow configurations. The formation dip may be provided to
forward modeling 154 1 and forward modeling 1543 . One way to obtain the
geometric factor is to perform a synthetic log of a formation that consists of a
background resistivity and a very thin layer at depth 0. Background resistivity is
assumed to be sufficiently larger compared to inverse of the frequency, in which
case, no significant skin effect is observed. The method illustrated in Figure 15
is also expected to work when there are some skin effects, but such method uses
custom geometric factors to be calculated with the specific resistivity. However,
resulting look-ahead signal may be contaminated by shallow signal due to nonlinearity
induced by the skin effect.
After geometrical factors are computed, a filter is calculated by
deconvolving a shallow geometric factor from a deep geometric factor 1545. In
geosteering applications, there is no access to future signal values, so filter can
be converted to causal 1551, for example, by enforcing zero values on the future
side of the filter and adding a sum of removed values to the last available filter
coefficient. In situations where dipole orientations of the transmitter and
receiver are not optimal (for example, if they do not provide good layer signal
cancellation), the transmitter and receiver can be rotated to any angle provided
that cross-dipole measurements can be made to optimize dipole orientation 1552
for deep signal 1512 and to optimize dipole orientation 1554 for shallow signal
151 1. In situations where transmitting or receiving antennas are rotating, the
resulting different antenna dipole orientations can be combined for similar
optimization.
Filter application 1556 to shallow signal equalizes its resolution and
centering to the deep measurement providing a translated shallow signal 1157.
This allows effective subtraction of the shallow signal from the deep signal, at
subtraction node 1537, without creating effects due to resolution difference. A
skin depth and borehole correction procedure 1555 for shallow signal 151 1 and a
skin depth and borehole correction procedure 1553 for deep signal 1512 can also
be applied before subtraction and filtering to remove, and hence equalize, skin
depth and borehole effects. The above methodology is free of inversion and it
can work even in situations where inversion is not supposed to work very well.
The methodology can be processed very quickly to be applied while geosteering,
since the biggest computational part is the filter application.
Figure 16 illustrates an example embodiment of a calculation of deep
layer properties via full inversion. Even though look-ahead signal alone can be
useful in applications, it may be desired to calculate resistivity and position of
the layers ahead of the bit. This can be performed by an inversion algorithm that
takes into account all known information such as around the tool layer
parameters, as shown in Figure 16. A look-ahead signal can be provided for
inversion 163 1 along with near tool parameters such as layer resistivities (¾,
Rv), layer positions (z), dip angle (0), strike angle ( ), borehole radius (r ),
borehole resistivity (¾,), eccentricity (de Cc) and eccentricity azimuth ( > ) -
library 1632 and forward model 1633 can assist inversion 1631. Inversion 1631
can include using one or more techniques, such as but not limited to, analytical
formulas, pattern matching, and iterative methods to output deep layer
resistivities (Rj,, Rv) and deep layer positions (z).
Figure 1 illustrates an example embodiment of a calculation of deep
layer properties via simple inversion. In cases where only the dip angle (0) and
the strike angle ( < >) are known, the resistivity change and layer position can be
obtained by inversion as shown in Figure 17. A look-ahead signal can be
provided for inversion 1 3 1 along with dip angle (0) and strike angle (f ) . A
library 1732 and forward model 1733 can assist inversion 1731. Inversion 1731
can include using one or more techniques, such as but not limited to, analytical
formulas, pattern matching, and iterative methods to output deep layer
resistivities (¾, Rv) and deep layer positions (z). Since the geometrical factor is
inversely proportional to square of the distance to layer boundary, analytical
formulas can be utilized for inversion. Since large resistivity changes may
indicate large pressure changes, results from this calculation may be used in
stopping the drilling for safety before approaching dangerous zones.
Figure 18 illustrates an example embodiment of a calculation of deep
layer properties via inversion. The calculation method shown in Figure 18 can
be used to invert distance and resistivity of layers. The calculation may begin
with dip angle (Q) and strike angle ( ) provided for forward modeling 1833. If
skin depth is sufficiently small or it can be sufficiently compensated, there is an
approximately linear relationship between the conductivity at each layer and the
signal that it generates at the receivers. As a result, given the signal due to a
small perturbation on the conductivity distribution, what the signal contribution
would be for a layer with any conductivity can be predicted. For that purpose, at
183 1 from forward modeling 1833, a step response, (d , can be generated by
synthetically logging a two layer formation, where only a very small contrast of
Ds exists in between layer conductivities. At 1832, based on the linearity
property, the total signal at a «'th measurement at depth z in a case with a single
layer perturbation can be written as
"(z) = , k rm l + " lr l lU" d) , (1)
where con trast is the conductivity difference between the layer that the tool is in
and the layer that is ahead of the tool, and ba round is the conductivity due to the
layer that the tool is current in. At 1834, in order to remove the effect of
unknown background, a differential signal can be calculated
DSM"( o lm ,,d) = o l (u"(d)-U"(d - Dz)) (2)
At 1835, effect of conductivity contrast can be removed by considering a ratio of
differential signals from the n'th and 'th measurements as follows
RDS d DSM " (3)
DSM d)
A look-ahead signal, s (z), at a «'th measurement at depth z can be provided, at
1836, to calculate differential signal DS (z) = ( (z) - s (z- Dz)). At 1837, a
ratio of a differential signal can be calculated using the result from 1836 as
RDS m(z) = DS (z)/ DSm(z). At 1838, as shown in Figure 16, a differential
signal obtained from the measurements can be inverted for distance, d""'(z), and
conductivity, "con r ( ) of the layers ahead of the tool by using the
relationships in equations 1-3. Distance d"m{z) can be found such that RDS m(z)
= RDSM m(d). Conductivity "conlrast (z) can be found such that DS (z) =
DSM ( OT ra d""'(z)). Each estimation with different n and m produce results
with different depth of detection and the optimum measurements can be visually
or algorithmically picked, at 1839. Deep layer resistivities (¾, Rv) and deep
layer positions (z) can be output from this inversion process. When the tool is
far from the boundary, only deep measurement is expected to produce good
results. As the tool gets closer to the boundary, measurements with lower depth
of detection can be valid. The processing disclosed in Figure 18 requires the
layer boundary to be in range of at least two different measurements. Although
deep measurements can see deeper, shallow measurements can be more accurate
since they are less affected by boundaries of multiple layers.
In various embodiments, the processing schemes taught herein can be
repeated and new measurements can be added as the tool drills/moves. Figure
1 illustrates an example embodiment of a geosteering decision chart. A lookahead
signal along with deep layer resistivities (Rh, Rv) and deep layer positions
(z) can be provided for visual and/or algorithmic inspection 151 from which a
geosteering decision can be made. Geosteering decisions can be made by a
person who is observing the results of the processing of the measurements at the
surface. Alternatively, geosteering decisions can be made downhole by an
automated system. An automated system can respond much more quickly, due
to inherent lags associated with downhole telemetry to provide data to the
surface. The look-ahead signal is proportional to the strength of the resistivity
contrast and distance of the change. As a result, the look-ahead signal can give
useful indication about the nature of the approaching layers. Since deep layers
that are far with large contrast create very similar signal with near layers with
small resistivity contrast, it may be difficult in some cases to find unique results
for resistivity and distance. In such cases, the look-ahead signal itself can be
used for making a decision. Another alternative is to use a-priori knowledge
about layer resistivities or distances to remove the non-uniqueness problem.
Existing efforts in the literature have focused on increasing sensitivity
ahead of the tool, but reduction of sensitivity around the tool has not been
addressed. As a result, existing tools receive a mix of signals from around and
ahead of the tool, which is either very difficult or not possible to separate. In
various embodiments, special antenna tilt angles to achieve layer signal
cancellation effect on the layers between the transmitters and receivers can be
utilized. This essentially completely eliminates the sensitivity to those layers.
Furthermore, an alternative method that utilizes deconvolution and inversion of
multiple spacing data to reduce sensitivity to layers that are near the tool can be
used. The resulting method can provide look-ahead capability in practical
scenarios with multiple layers of varying resistivities, as opposed to the methods
that suffer significant difficulties and complications.
Figure 20 shows geometric factors associated with two different spacings
between transmitter and receiver. In this example, a 4 ft. spacing is used for a
shallow measurement operating at 15 kHz with an antenna tilted at 45° and an
antenna tilted at 0° having signal shown in curve 2096. A 24 ft. spacing is used
for a deep measurement operating at 500 Hz with an antenna tilted at 45° and an
antenna tilted at 0° having signal shown in curve 2097. The tool offset is defined
as the true vertical position of the tool along the z-axis, where z-axis is pointing
upward. It can be seen from Figure 20 that the deep measurement is more
sensitive to deep positions (z>0). The sensitivity is maximum and constant
when the layer boundary is between the transmitter and the receiver (-4