Apparatus and method for determining the resistivity of earth formations

An apparatus for determining the resistivity of formations surrounding an earth borehole. An elongated electrically conductive body is movable through the borehole. A first transmitter establishes a first current in the body from a first transmitter position on the body, the first current traveling in a path that includes the body and the formations. An electrode is mounted on the body and has a surface that is electrically isolated from the surface of the body. A first electrical signal, resulting from the first current, is measured at the electrode. A second transmitter establishes a second current in the body from a second transmitter position on the body that is spaced from the first transmitter position, the second current traveling in a path that includes the body and the formations. A second electrical signal, resulting from the second current, is measured at the electrode. A current monitor measures the axial current passing a monitor position on the body to obtain a monitor current value. An indication of formation resistivity is derived as a function of the first electrical signal, the second electrical signal, and the monitor current value.

FIELD OF THE INVENTION 
This invention relates to the field of well logging and, more particularly, 
to well logging apparatus for determining earth formation resistivity. The 
invention has general application to the well logging art, but the 
invention is particularly useful for logging-while-drilling (also called 
measurement-while-drilling). 
BACKGROUND OF THE INVENTION 
Resistivity logging, which measures the electrical resistivity of 
formations surrounding an earth borehole, is a commonly used technique of 
formation evaluation. For example, porous formations having high 
resistivity generally indicate the presence of hydrocarbons, while porous 
formations having low resistivity are generally water saturated. In 
so-called "wireline" well logging, wherein measurements are taken in a 
well bore (with the drill string removed) by lowering a logging device in 
the well bore on a wireline cable and taking measurements with the device 
as the cable is withdrawn, there are several techniques of resistivity 
logging which use elements such as electrodes or coils. Various 
arrangements of electrodes, on the logging device and at the earth's 
surface, have been utilized to measure electrical currents and/or 
potentials from which formation resistivity can be derived. For example, 
button electrodes have been employed on a pad which is urged against the 
borehole wall. These electrodes have been used to obtain azimuthal 
resistivity measurements, and focusing techniques have been employed to 
obtain resistivity measurements that have substantial lateral extent into 
the formations and provide relatively high vertical resolution resistivity 
information. 
Various techniques for measuring resistivity while drilling have also been 
utilized or proposed. Techniques employed in wireline logging may or may 
not be adaptable for use in logging-while-drilling equipment. The borehole 
presents a difficult environment, even for wireline logging, but the 
environment near the well bottom during drilling is particularly hostile 
to measuring equipment. For logging-while-drilling applications, the 
measuring devices are housed in heavy steel drill collars, the mechanical 
integrity of which cannot be compromised. Measurement approaches which 
require a substantial surface area of electrically insulating material on 
the surface of a drill collar housing are considered impractical, since 
the insulating material will likely be damaged or destroyed. This is 
particularly true for measuring structures that would attempt to attain 
intimate contact with the newly drilled borehole wall as the drill string 
continues its rotation and penetration, with the attendant abrasion and 
other stresses. 
One resistivity measuring approach is to utilize a plurality of toroidal 
coil antennas, spaced apart, that are mounted in insulating media around a 
drill collar or recessed regions thereof. A transmitting antenna of this 
nature radiates electromagnetic energy having a dominant transverse 
magnetic component, and can use the electrically conductive body of the 
drill collar to good advantage, as described next. 
In U.S. Pat. No. 3,408,561 there is disclosed a logging-while-drilling 
system wherein a receiving toroidal coil is mounted in a recess on a drill 
collar near the drill bit and a transmitting toroidal coil is mounted on 
the drill collar above the receiver coil. The drill collar serves as part 
of a one-turn "secondary winding" for the toroidal antennas, the remainder 
of such "secondary winding" including a current return path through the 
mud and formations. The voltage induced in the receiver toroidal coil 
provides an indication of the resistivity of formations around the drill 
bit. U.S. Pat. No. 3,305,771 utilizes a similar principal, but employs a 
pair of spaced-apart transmitting toroidal coils and a pair of 
spaced-apart receiving toroidal coils between the transmitting toroidal 
coils. 
As generally described in the prior art, a transmitter toroidal coil 
mounted on a drill collar induces current in the drill collar which can be 
envisioned as leaving the drill collar, entering the formations below the 
transmitter coil, and returning to the drill string above the transmitter 
coil. Since the drill collar below the transmitter coil is substantially 
an equipotential surface, a portion of the current measured by a lower 
receiver toroidal coil mounted near the drill bit tends to be laterally 
focused. This can provide a "lateral" resistivity measurement of 
formations adjacent the drill collar. Also, a portion of current leaving 
the drill stem below the receiver coil provides a "bit resistivity" 
measurement; that is, a measurement of the resistivity of the formations 
instantaneously being cut by the bit. [See, for example, the 
above-identified U.S. Pat. Nos. 3,408,561 and U.S. Pat. No. 3,305,771, and 
publications entitled "A New Resistivity Tool For Measurement While 
Drilling", SPWLA Twenty-Sixth Annual Logging Symposium (1985) and 
"Determining The Invasion Near The Bit With The MWD Toroid Sonde", SPWLA 
Twenty-Seventh Annual Logging Symposiuan (1986).]Thus, the prior art 
indicates that a measurement-while-drilling logging device using toroidal 
coil transmitting and receiving antennas can be employed to obtain lateral 
resistivity measurements and/or bit resistivity measurements. 
Reference can also be made to the following which relate to 
measurement-while-drilling using electrodes and other transducers: U.S. 
Pat. No. 4,786,874, U.S. Pat. No. 5,017,778, and U.S. Pat. No. 5,130,950. 
Resistivity measurements obtained using transmitting and receiving toroidal 
coils on a conductive metal body are useful, particularly in 
logging-while-drilling applications, but it is desirable to obtain 
measurements which can provide further information concerning the downhole 
formations; for example, lateral resistivity information having improved 
vertical resolution, azimuthal resistivity information, and multiple 
depths of investigation for such resistivity information. 
In copending U.S. Pat. No. 5,235,285; assigned to the same assignee as the 
present application, there is disclosed an apparatus utilizing a toroidal 
coil antenna mounted, in an insulating medium, on a drill collar to induce 
a current which travels in a path that includes the drill collar and earth 
formations around the drill collar. [See also U.S. Pat. No. 5,200,705 
assigned to the same assignee as the present application.] As was 
generally known in the art, one or more toroidal coil receiving antennas 
can be mounted, in an insulating medium, on the drill collar to obtain the 
types of measurements described above. The apparatus of the referenced 
copending Application expands on the toroid-to-toroid type of measurement 
to obtain further useful information about the downhole formations. In one 
form thereof at least one electrode is provided on the drill collar and is 
utilized to detect currents transmitted by the transmitter toroidal coil 
which return via the formations to the electrode(s) laterally; that is, 
approximately normal to the axis of the drill collar. The electrodes 
preferably have a relatively small vertical extent, and the measurements 
taken with these electrodes are useful in obtaining formation resistivity 
with relatively high vertical resolution, as well as relatively high depth 
of investigation for the resolution provided. The electrodes can also 
provide azimuthal resistivity information. Thus, resistivity logging 
measurements are obtained that can supplement or replace resistivity 
measurements obtained with toroidal coil receiving antenna(s). The 
electrode(s) can be mounted in a drill collar or on a stabilizer blade 
attached to or integral with the drill collar. In embodiments thereof, 
button-type electrodes are utilized, as well as ring-type electrodes. The 
one or more receiving ring electrode or button electrode can be 
electrically isolated from the main metal body of the drill collar, using 
rubber or other insulating material, and the electrical potential kept at 
the same value as the surrounding metal. The current leaving the electrode 
can be measured, and the measurement ideally would determine the 
resistivity of formations in the region immediately surrounding the 
electrode. However, under certain conditions the measurement may not be 
accurately representative of the resistivity of the region immediately 
surrounding the electrode, and it is among the objects of the invention to 
provide improvement in accuracy of logging devices under such conditions. 
SUMMARY OF THE INVENTION 
Applicant recognizes that the measurement at an electrode in the described 
type of system is, at least to some degree, determined by the total 
current distribution into the overall body of the apparatus which, in the 
described system, is the drill collar and the conductive drill string 
coupled therewith. The total current distribution, in turn, depends to 
some extent on the formation resistivity along the entire length of the 
drill string. A problem arises when the current measured at the previously 
described electrode(s) is affected to a substantial degree by formations a 
meaningful distance from the region of the electrode, and such formations 
have resistivities that are different than the resistivity of the 
formations in the region of the electrode(s). For example, a problem 
occurs in the logging-while-drilling apparatus when the measuring 
electrode(s) is traversing a resistive bed and the drill bit cuts into a 
more conductive bed. When this happens the current being emitted from the 
electrode decreases, falsely indicating a more resistive formation in the 
region of the electrode. [This occurs when the electrode is below the 
transmitter, as in the embodiment illustrated in the above-referenced U.S. 
Pat. No. 5,235,285. Conversely, if the electrode is above the transmitter, 
the current being emitted from the electrode increases, falsely indicating 
a more conductive formation in the region of the electrode.] The present 
invention greatly reduces this and other problems. 
In accordance with an embodiment of the invention, an apparatus is 
disclosed for determining the resistivity of formations surrounding an 
earth borehole. [In the present application, any references to the 
determination or use of resistivity are intended to generically mean 
conductivity as well, and vice versa. These quantities are reciprocals, 
and mention of one or the other herein is for convenience of description, 
and not intended in a limiting sense.] An elongated electrically 
conductive body is movable through the borehole. A first transmitter means 
is provided for establishing a first current in the body from a first 
transmitter position on the body, said first current traveling in a path 
that includes the body and the formations. An electrode is mounted on the 
body and has a surface that is electrically isolated from the surface of 
the body. [Throughout the present application, "mounted on" and "mounted 
in" are both intended to generically include "mounted on or in".] Means 
are provided for measuring at the electrode a first electrical signal 
resulting from the first current. A second transmitter means is provided 
for establishing a second current in the body from a second transmitter 
position on the body that is spaced from the first transmitter position, 
the second current traveling in a path that includes the body and the 
formations. Means are provided for measuring at the electrode a second 
electrical signal resulting from the second current. Current monitor means 
are provided for measuring the axial current passing a monitor position on 
the body to obtain a monitor current value. Means are then provided for 
deriving an indication of formation resistivity as a function of the first 
electrical signal, the second electrical signal, and the monitor current 
value. 
In one embodiment of the invention, the current monitor means comprises 
means for obtaining a first monitor current value when the first 
transmitter means is operative, and means for obtaining a second monitor 
current value when the second transmitter means is operative, the deriving 
means being operative to derive said indication of formation resistivity 
as a function of the first electrical signal, the second electrical 
signal, said first monitor current value, and said second monitor current 
value. In a form of this embodiment, a further current monitor means is 
provided at a further monitor position for measuring the axial current 
passing a further monitor position on the body to obtain a further monitor 
current value, and the deriving means is operative to derive the 
indication of formation resistivity as a function of the further monitor 
current value. 
As described further in detail hereinbelow, the present invention operates 
to effectively reduce or eliminate the deleterious effects that 
resistivity bedding contrasts in the general vicinity of the tool can have 
on the intended measurement of the resistivity of formations surrounding 
the measuring electrode, 
Further features and advantages of the invention will become more readily 
apparent from the following detailed description when taken in conjunction 
with the accompanying drawings.

DETAILED DESCRIPTION 
Referring to FIG. 1, there is illustrated a measuring-while-drilling 
apparatus as described in the above-referenced U.S. Pat. No. 5,235,285, 
and in which an embodiment of an improvement of the invention can be 
employed. [As used herein, and unless otherwise specified, 
measurement-while-drilling (also called measuring-while-drilling or 
logging-while-drilling) is intended to include the taking of measurements 
in an earth borehole, with the drill bit and at least some of the drill 
string in the borehole, during drilling, pausing, and/or tripping.] A 
platform and derrick 10 are positioned over a borehole 11 that is formed 
in the earth by rotary drilling. A drill string 12 is suspended within the 
borehole and includes a drill bit 15 at its lower end. The drill string 12 
and the drill bit 15 attached thereto are rotated by a rotating table 16 
(energized by means not shown) which engages a kelly 17 at the upper end 
of the drill string. The drill string is suspended from a hook 18 attached 
to a travelling block (not shown). The kelly is connected to the hook 
through a rotary swivel 19 which permits rotation of the drill string 
relative to the hook. Alternatively, the drill string 12 and drill bit 15 
may be rotated from the surface by a "top drive" type of drilling rig. 
Drilling fluid or mud 26 is contained in a pit 27 in the earth. A pump 29 
pumps the drilling fluid into the drill string via a port in the swivel 19 
to flow downward (arrow 9) through the center of drill string 12. The 
drilling fluid exits the drill string via ports in the drill bit 15 and 
then circulates upward in the region between the outside of the drill 
string and the periphery of the borehole, commonly referred to as the 
annulus, as indicated by the flow arrows 32. The drilling fluid thereby 
lubricates the bit and carries formation cuttings to the surface of the 
earth. The drilling fluid is returned to the pit 27 for recirculation. An 
optional directional drilling assembly (not shown) with a mud motor having 
a bent housing or an offset sub could also be employed. 
Mounted within the drill string 12, preferably near the drill bit 15, is a 
bottom hole assembly, generally referred to by reference numeral 100, 
which includes capabilities for measuring, processing, and storing 
information, and communicating with the earth's surface. [As used herein, 
near the drill bit means within several drill collar lengths from the 
drill bit.] The assembly 100 includes a measuring and local communications 
apparatus 200 which is described further hereinbelow. In the example of 
the illustrated bottom hole arrangement, a drill collar 130 and a 
stabilizer collar 140 are shown successively above the apparatus 200. The 
collar 130 may be, for example, a pony collar or a collar housing 
measuring apparatus which performs measurement functions other than those 
described herein. The need for or desirability of a stabilizer collar such 
as 140 will depend on drilling parameters. Located above stabilizer collar 
140 is a surface/local communications subassembly 150. The subassembly 
150, described in further detail in the above-referenced U.S. Pat. No. 
5,235,285, includes a toroidal antenna 1250 used for local communication 
with the apparatus 200, and a known type of acoustic communication system 
that communicates with a similar system at the earth's surface via signals 
carried in the drilling fluid or mud. The surface communication system in 
subassembly 150 includes an acoustic transmitter which generates an 
acoustic signal in the drilling fluid that is typically representative of 
measured downhole parameters. One suitable type of acoustic transmitter 
employs a device known as a "mud siren" which includes a slotted stator 
and a slotted rotor that rotates and repeatedly interrupts the flow of 
drilling fluid to establish a desired acoustic wave signal in the drilling 
fluid. The driving electronics in subassembly 150 may include a suitable 
modulator, such as a phase shift keying (PSK) modulator, which 
conventionally produces driving signals for application to the mud 
transmitter. These driving signals can be used to apply appropriate 
modulation to the mud siren. The generated acoustic mud wave travels 
upward in the fluid through the center of the drill string at the speed of 
sound in the fluid. The acoustic wave is received at the surface of the 
earth by transducers represented by reference numeral 31. The transducers, 
which are, for example, piezoelectric transducers, convert the received 
acoustic signals to electronic signals. The output of the transducers 31 
is coupled to the uphole receiving subsystem 90 which is operative to 
demodulate the transmitted signals, which can then be coupled to processor 
85 and recorder 45. An uphole transmitting subsystem 95 is also provided, 
and can control interruption of the operation of pump 29 in a manner which 
is detectable by the transducers in the subassembly 150 (represented at 
99), so that there is two way communication between the subassembly 150 
and the uphole equipment. In existing systems, downward communication is 
provided by cycling the pump(s) 29 on and off in a predetermined pattern, 
and sensing this condition downhole. This or other technique of 
uphole-to-downhole communication can be utilized in conjunction with the 
features disclosed herein. The subsystem 150 may also conventionally 
include acquisition and processor electronics comprising a microprocessor 
system (with associated memory, clock and timing circuitry, and interface 
circuitry) capable of storing data from a measuring apparatus, processlng 
the data and storing the results, and coupling any desired portion of the 
information it contains to the transmitter control and driving electronics 
for transmission to the surface. A battery may provide downhole power for 
this subassembly. As known in the art, a downhole generator (not shown) 
such as a so-called "mud turbine" powered by the drilling fluid, can also 
be utilized to provide power, for immediate use or battery recharging, 
during drilling. It will be understood that alternative acoustic or other 
techniques can be employed for communication with the surface of the 
earth. 
As seen in FIG. 2, the subsystem 200 includes a section of tubular drill 
collar 202 having mounted thereon a transmitting antenna 205, a receiving 
antenna 207, and receiving electrodes 226, 227, 228 and 235. In the 
illustrated subsystem the transmitting antenna 205 comprises a toroidal 
antenna (see also FIG. 3) having coil turns wound on a ferromagnetic 
toroidal core that is axially coincident with the axis of the drill collar 
202. The core may have a circular or rectangular cross-section, although 
other shapes can be used. The purpose of this toroidal transmitter is to 
induce a voltage along the drill collar. The drill collar and the 
formations correspond to a one turn secondary winding. If the transmitter 
is excited with a drive voltage V.sub.T and the transmitter toroid has 
N.sub.T turns, then the voltage induced along the drill collar will be 
V.sub.T /N.sub.T. That is, the voltage difference between the drill collar 
above the transmitter and the drill collar below the transmitter will be 
V.sub.T /N.sub.T. The resultant current travels in a path that includes 
the drill string and the formations (as well as the borehole fluid which 
is assumed to have substantial conductivity). The receiving electrodes 
226, 227 and 228 are button electrodes mounted in a stabilizer 220, and 
electrode 235 is a ring electrode. The receiving antenna 207 is another 
toroidal coil antenna. The toroidal receiver measures the axial current 
flowing through the drill collar. If the receiver toroid contains N.sub.R 
turns and the current in the drill collar is I, then the current flowing 
through the receiver winding into a short circuit will be I/N.sub.R. 
Referring now also to FIG. 3 as well as FIG. 2, there are illustrated 
further details of the structure of the measurement and communication 
subsystem 200 that is housed in the drill collar 202. An annular chassis 
290, which contains most of the electronics, fits within the drill collar 
202. In this configuration, the drilling mud path is through the center of 
the chassis, as illustrated by arrows 299 (FIG. 2). The chassis 290 has a 
number of slots, such as for containment of batteries (at position 291, 
see FIG. 2) and circuit boards 292. In this configuration, the circuit 
boards are in the form of elongated thin strips, and can accordingly be 
planar. Other circuit board configurations or circuit packaging can be 
utilized. The transmitting toroidal antenna 205 [which can also be 
utilized in a communications mode as a receiver] is supported in a 
suitable insulating medium, such as "VITON" rubber 206. The assembled 
coil, in the insulating mediuan, is mounted on the collar 202 in a 
subassembly which includes a protective tapered metal ring 209, that is 
secured to the collar surface by bolts (not shown). The antenna wiring, 
and other wiring, is coupled to the annular circuit assembly via bulkhead 
feed-throughs, as represented at 261 (for wiring to antenna 205), 266, 
267, 268 (for wiring to electrodes 226, 227 and 228, respectively), and 
263 (for wiring to electrode 235 and antenna 207). The receiving toroidal 
coil antenna 207 is constructed in generally the same way, although with 
more coil turns in the described configuration, in insulating medium 211, 
and with protective ring 213. The receiving ring electrode 235 is also 
mounted in an insulating medium such as a fiberglass-epoxy composite 236, 
and is held in a subassembly that includes tapered ring 237, which can be 
integrated with the protective ring for the receiving antenna 207. 
The three button electrodes 226, 227 and 228 are provided in stabilizer 
blade 220 which may have, for example, a typical straight or curved 
configuration. [The electrodes can alternatively be mounted in the drill 
collar itself.] Two of four (or three) straight stabilizer blades 219 and 
220 are visible in FIGS. 2 and 3. The stabilizer blades are formed of 
steel, integral with a steel cylindrical sleeve that slides onto the drill 
collar 202 and abuts a shoulder 203 formed on the drill collar. The 
stabilizer is secured to collar 202 with lock nuts 221. The blades can be 
undersized to prevent wear of the electrodes. The button electrode faces 
have generally round (in this case, circular) peripheries which will be 
generally adjacent the borehole wall. The button faces can have generally 
cylindrical curvatures to conform to the stabilizer surface or can have 
flat faces with surfaces that are slightly recessed from the stabilizer 
surface shape. These electrodes span only a small fraction of the total 
circumferential locus of the borehole and provide azimuthal resistivity 
measurements. Also, these electrodes have a vertical extent that is a 
small fraction of the vertical dimension of the stabilizer on which they 
are mounted, and provide relatively high vertical resolution resistivity 
measurements. In the described configuration, the surfaces of electrodes 
226, 227 and 228 have diameters of about 1 inch (about 2.5 cm.), which is 
large enough to provide sufficient signal, and small enough to provide the 
desired vertical and azimuthal measurement resolution. The electrode 
periphery, which can also be oval, is preferably contained within a 
circular region that is less than about 1.5 inches (about 3.8 cm.) in 
diameter. In the described configuration, the top portion of each 
electrode is surrounded by an insulating medium, such as "VITON" rubber, 
which isolates the electrode surface from the surface of the stabilizer 
blade 220. A fiberglass epoxy composite can be used around the base of the 
electrode. The electrodes 226, 227 and 228 (see also FIG. 4) provide a 
return path from the formations to the collar 202 (of course, when the AC 
potential reverses the current path will also reverse), and the current is 
measured to determine lateral resistivity of the region of the formation 
generally opposing the electrode. The electrodes 227 and 228 are 
respectively further from the transmitter than the electrode 226, and will 
be expected to provide resistivity measurements that tend to be 
respectively deeper than the measurement obtained from electrode 226. The 
electrodes are mounted in apertures in the stabilizer 220 that align with 
apertures in the drill collar 202 to facilitate coupling of the electrodes 
to circuitry in the annular chassis 290. 
In one electrode configuration, the electrode body is directly mounted, in 
the manner of a "stud", in the stabilizer body. As seen in FIG. 5 (and 
also in FIG. 3), the metal button electrode (226, for example) is mounted 
in an insulating medium 251, such as "VITON" rubber, and its neck portion 
engages threading 252 in collar 202. A small toroidal coil 253 is seated 
in an insulating mediuan 255, which can also be "VITON" rubber, in a 
circular recess in the collar surface. The toroidal coil 253 is used to 
sense current flow in the electrode 226. The leads from coil 253 pass 
through a bulkhead feed-through (see FIG. 3) to circuitry shown in FIG. 5. 
In particular, one conductor from the current sensing toroidal coil 253 is 
coupled to the inverting input of an operational amplifier 256. The other 
conductor from toroidal coil 253, and the non-inverting input of 
operational amplifier 256, are coupled to ground reference potential; e.g. 
the body of drill collar 202. A feedback resistor R.sub.1 is provided 
between the output and the inverting input of operational amplifier 256. 
The circuit equivalent is illustrated in FIG. 6 which shows the button 
electrode stud as a single turn through the core of toroidal coil 253, the 
number of turns in the coil being N. The gain of operational amplifier 256 
is very high, and V.sub.A, the voltage difference between the inverting 
and non-inverting input terminals is very small, virtually zero. The input 
impedance of the operational amplifier is very high, and essentially no 
current flows into either input terminal. Thus, if the current flow in the 
electrode 226 is I.sub.B, and the current flow in the toroidal coil 
"secondary" is I.sub.B /N, the current I.sub.B /N flows through the 
feedback resistor R.sub.1, making the amplifier output voltage R.sub.1 
I.sub.B /N. 
Referring to FIG. 7, there is shown a diagram of a further configuration of 
a button electrode. The electrode body (e.g. 226') is supported on an 
insulating mounting frame 271 formed of a material such as epoxy 
fiberglass composite, and is sealed with "VITON" rubber insulating 
material 273. The electrode is coupled, via a bulkhead feed-through, to 
one end of the primary coil of a transformer 275, the other end of which 
is coupled to ground reference potential (e.g., the collar body). The 
secondary winding of transformer 275 is coupled to the inputs of an 
operational amplifier 256' which operates in a manner similar to the 
operational amplifier 256 of FIGS. 5 and 6. A feedback resistor R.sub.2 is 
coupled between the output of the operational amplifier 256' and its 
inverting input, and the output is designated V.sub.B. Derivation of the 
output voltage as a function of the electrode current I.sub.B is similar 
to that of the circuit of FIG. 6, except that in this case the turns 
ratio, secondary to primary, is n.sub.2 /n.sub.1, and the expression for 
the output voltage is V.sub.B =R.sub.2 I.sub.B n.sub.1 /n.sub.2. An 
advantage of this electrode arrangement and circuit is that n.sub.1 can be 
increased to increase the output voltage sensitivity to the current being 
measured. 
FIG. 8 illustrates a form of the ring electrode 235 utilized in the FIG. 2 
configuration. The ring electrode, which can be welded into a single 
piece, is seated on fiberglass-epoxy insulator 236, and is sealed with 
viton rubber 239. A conductor 238 that can be brazed or welded to the ring 
electrode 235, is coupled, via a feed-through, to circuitry similar to 
that of FIG. 7, with a transformer 275, an operational amplifier 256, a 
feedback resistor R.sub.2, and an output V.sub.B. The current sensing 
operation of this circuit is substantially the same as that of the FIG. 7 
circuit. 
As described in the above-referenced U.S. Pat. No. 5,235,285, the apparent 
resistivity of the formation is inversely proportional to the current I 
measured at the electrode. If the voltage at the electrode relative to the 
voltage of the drill collar surface above the toroidal coil transmitter 
coil 205 is V, the apparent resistivity is R.sub.app =kV/I, where k is a 
constant that can be determined empirically or by modeling. If desired, a 
correction can be applied to compensate for electromagnetic skin effect. 
FIG. 9 shows a general representation of the known type of 786,137. current 
pattern that results from energizing the transmitter toroidal coil in a 
well being drilled with mud having substantial conductivity, as 
illustrated for example in the above-referenced U.S. Pat. No. 5,235,285. 
The pattern will, of course, depend on the formations' bed pattern and 
conductivities, the example in FIG. 9 being for the simplified case of 
uniform conductivity. 
FIG. 10 shows a block diagram of an embodiment of downhole circuitry in 
subassembly 200 for implementing measurements and/or for transmitting 
information to the surface/local communications subassembly 150, as 
described in the above-referenced U.S. patent application Ser. No. 
786,137. The button electrodes 226, 227 and 228 and ring electrode 235 are 
each coupled, via the previously described sensing and amplification 
circuits (e.g. FIGS. 5-8, now referred to by reference numerals 1011-1014, 
respectively), to a multiplexer 1020. The output of the receiver toroidal 
coil 207 is also coupled, via a sensing and amplification circuit 1015, to 
the multiplexer 1020. The multiplexer 1020 is under control of a computer 
or processor 1025, as represented by the line 1020A. The processor 1025 
may be, for example, a suitable digital microprocessor, and includes 
memory 1026, as well as typical clock, timing, and input/output 
capabilities (not separately represented). The processor can be programmed 
in accordance with a routine illustrated in FIG. 11. The output of 
multiplexer 1020 ie coupled, via a bandpass filter 1030, to a programmable 
gain amplifier 1033, the gain of which can be controlled by the processor 
1025 via line 1033A. The output of amplifier 1033 is coupled to a 
rectifier 1035, a low-pass filter 1036, and then to an analog-to-digital 
converter 1037, the output of which is coupled to the processor 1025 via a 
buffer 1039 that is controlled by the processor. [This and other buffers 
can be part of the processor memory and control capability, as is known in 
the art.] The bandpass filter 1030 passes a band of frequencies around the 
center frequency transmitted by the transmitter toroidal coil 205. The 
processor 1025 controls the multiplexer 1020 to select the different 
receiver outputs in sequence. The gain of programmable amplifier 1033 can 
be selected in accordance with the receiver being interrogated during a 
particular multiplexer time interval and/or in accordance with the 
received signal level to implement processing within a desired range. The 
amplified signal is then rectified, filtered, and converted to digital 
form for reading by the processor 1025. 
As described in the above-referenced U.S. Pat. No. 5,235,285, the 
transmitter of subassembly 200 can operate in two different modes. In a 
first mode, the transmitter toroidal coil 205 transmits measurement 
signals, and the signals received at the electrodes and the receiver 
toroidal coil are processed to obtain formation measurement information. 
In a second mode of operation, the transmitter toroidal coil 205 is 
utilized for communication with the transmitter/receiver in the 
surface/local communications subassembly 150 (FIG. 1). 
A sinewave generator 1051, which may be under control of processor 1025 
(line 1051A) is provided and has a frequency, for example, of the order of 
100 Hz to 1 M Hz, with the low kilohertz range being generally preferred. 
In one operating embodiment, the frequency was 1500 Hz. The generated 
sinewave is coupled to a modulator 1053 which operates, when the system is 
transmitting in a communications mode, to modulate the sinewave in 
accordance with an information signal from the processor 1025. The 
processor signal is coupled to modulator 1053 via buffer 1055 and 
digital-to-analog converter 1057. In the illustrated embodiment the 
modulator 1053 is a phase modulator. The output of modulator 1053 is 
coupled to a power amplifier 1060, which is under control of processor 
1025 (line 1060A). The output of power amplifier 1060 is coupled, via 
electronic switch 1065, to the transmitter toroidal coil antenna 205. Also 
coupled to the toroidal coil antenna 205, via another branch of electronic 
switch 1065, is a demodulator 1070 which, in the present embodiment is a 
phase demodulator. The output of demodulator 1070 is, in turn, coupled to 
analog-to-digital converter 1072 which is coupled to the processor 1025 
via buffer 1074. The processor controls electronic switch 1065, depending 
on whether the toroidal coil antenna 205 is to be in its usual 
transmitting mode, or, occasionally, in a receiving mode to receive 
control information from the surface/local communications subassembly 150. 
Referring to FIG. 11, there is shown a flow diagram of a routine for 
programming the processor 1025 as first described in the above-referenced 
U.S. Pat. No. 5,235,285. In the example of the routine set forth, 
functions are performed or controlled in a repetitive sequential fashion, 
but the program may alternatively be set up with a routine that handles 
the indicated tasks on a prioritized basis, or with a combination of 
sequential and prioritized functions. Also, the processor may be 
multi-ported or multiple processors may be used. The routine has two basic 
modes; a "measurement" mode wherein the toroidal coil antenna 205 is 
transmitting for the purpose of obtaining measurement signals at the 
receiving electrodes 226-228 and 235 and the receiving toroidal coil 
antenna 207, and a "local communications" mode wherein the toroidal coil 
antenna 205 is utilized to transmit and/or receive modulated information 
signals to and/or from a toroidal coil antenna located in the 
surface/local communications subassembly 150 (FIG. 1), for ultimate 
communication with equipment at the earth's surface via mud pulse 
telemetry equipment which is part of the subassembly 150. The block 1115 
represents the initializing of the system to the measurement mode. Inquiry 
is then made (diamond 1118) as to which mode is active. Initially, as just 
set, the measurement mode will be active, and the block 1120 will be 
entered, this block representing the enabling of the sinewave generator 
1051 and the power amplifier 1060 (FIG. 10). The electronic switch 1065 is 
then set to the measurement/send position (block 1122) [i.e., with the 
toroidal coil antenna 205 coupled to the power amplifier 1060], and the 
multiplexer 1020 is set to pass information from the first receiver (block 
1125), for example the closest button electrode 226. The data is then read 
(block 1128) and the resistivity, as measured by the electrode from which 
the data has passed, is computed [for example in accordance with the 
relationships set forth above in conjunction with FIGS. 5-8] and stored 
(block 1130), and can be sent to output buffer 1055 (block 1132). Inquiry 
is then made (diamond 1140) as to whether the last receiver has been 
interrogated. If not, the multiplexer 1020 is set to pass the output of 
the next receiver (for example, the button electrode 227), as represented 
by the block 1143. The block 1128 is then re-entered, and the loop 1145 
continues until data has been obtained and processed from all receivers. 
When this is the case, the operating mode is switched (block 1150), and 
inquiry is made as to which mode is active. Assuming that the local 
communications mode is now active, the block 1160 is entered, this block 
representing the transmission of the latest frame of data to the main 
communications subassembly. In particular, data from the processor 1025 
(or from the optional buffer 1055) is coupled to the modulator 1053 to 
modulate the sinewave output of generator 1051 for transmission by antenna 
205. At the end of a frame of data, a "ready to receive" signal can be 
transmitted (block 1165). The sinewave generator and power amplifier are 
then disabled (block 1168), and the electronic switch 1065 is set to the 
"receive" position. [i.e., with the toroidal coil antenna 205 coupled to 
the demodulator 1070] (block 1170). A frame of information can then be 
received via buffer 1074, as represented by the block 1175. During this 
time, as represented by the arrows 1176 and 1177, other processor 
computations can be performed, as desired. The block 1150 can then be 
re-entered to switch the operating mode, and the cycle continues, as 
described. The information received from the surface/local communications 
subassembly can be utilized in any desired manner. For description of the 
surface/local communications subassembly, reference can be made to the 
above-referenced U.S. Pat. No. 5,235,285. 
In general, the resistivity obtained from the electrodes in the previously 
described manner is an accurate indication of the resistivity of 
formations in the region immediately surrounding the electrode, but under 
certain conditions this may not be the case. As noted above, Applicant 
recognizes that the measurement at an electrode in the described type of 
system is, at least to some degree, determined by the total current 
distribution into the overall body of the apparatus which, in the 
described system, is the drill collar and the conductive drill string 
coupled therewith. The total current distribution, in turn, depends to 
some extent on the formation resistivity along the entire length of the 
drill string. A problem arises when the current measured at the indicated 
electrode(s) is affected to a substantial degree by formations a 
meaningful distance from the region of the electrode, and such formations 
have resistivities that are different than the resistivity of the 
formations in the region of the electrode(s). For example, a problem 
occurs in the logging-while-drilling apparatus when the measuring 
electrode(s) is traversing a resistive bed and the drill bit cuts into a 
more conductive bed. When this happens the current being emitted from the 
electrode decreases, falsely indicating a more resistive formation in the 
region of the electrode. As described further below, other conditions can 
give rise to errors in resistivity indications. 
Consider the arrangement of FIG. 12, which has a toroidal transmitter T1 
and a ring electrode R on a conductive body 1202 which is like the drill 
collar 202 in a logging-while-drilling setup of the general type shown in 
FIGS. 1-3. A further toroidal transmitter T2, also called a lower 
transmitter, is located near the drill bit. For this example, the lower 
transmitter T2 is about 24 inches from the end of the bit 15, the upper 
transmitter T1 is about 84 inches from the end of the bit, and the ring 
electrode is equidistant from the transmitters, i.e., about 54 inches from 
the end of the bit. The logging device is assumed to be in a formation of 
resistivity 2000 ohm-m having a bed of resistivity 20 ohm-m and a 
specified thickness Simulated resistivity logs for five such bed 
thicknesses [8, 4, 2, 1 and 0.5 feet] are shown left-to-right in FIG. 13. 
[This and other simulated logs hereof are computed without consideration 
of borehole effect, which will be small if the transmitter-to-electrode 
spacing is larger compared to the standoff between the electrode and the 
borehole wall.] The simulated resistivity logs, as a function of the depth 
of ring R, are computed for transmission by the upper transmitter T1 
(solid line) and by the lower transmitter T2 (dotted line). [As above, 
resistivity is inversely proportional to the measured ring current.] For 
operation with the upper transmitter, relatively large horn-shaped 
artifacts labelled A1 through A5 can be observed to occur when the logging 
tool enters the bed; that is, in this case, when the bit first cuts into 
the bed. The length of this artifact is approximately equal to the 
distance from the ring to the bit. There is also an artifact on the lower 
side of the bed for the thin beds, labelled B1 through B3. This artifact 
has a length approximately equal to the transmitter-ring spacing minus the 
bed thickness and so is absent for thick beds greater in extent than the 
transmitter receiver distance. The simulated ring resistivity computed 
when the lower transmitter is active (dotted line) has initial artifacts 
which roughly oppose A1 through A5, and other serious distortions. 
Consider next the arrangement of FIG. 14, which is like that of FIG. 12, 
but also has a receiver (or monitor) toroid M0 at about the position of 
the ring electrode R to monitor the axial current flowing up or down 
through the conductive body at the position of the ring R. The axial 
current which is induced by T1 is linear with respect to the voltage 
induced on the drill collar and inverse to the resistivity of the earth 
formation surrounding the tool. The axial current which is induced by T2 
is linear with respect to the voltage induced on the drill collar by T2 
and inverse to the resistivity of the earth formation surrounding the 
tool. Assume that the excitation voltage of the upper transmitter is fixed 
while the excitation voltage of the lower transmitter is adjustable. The 
net axial current which flows along the drill collar at any point is the 
linear superposition of the induced current from T1 and T2. Assume that 
the voltage of T2 can be adjusted so that the net axial current flowing 
through the monitor toroid M0 is zero. This will require that the current 
induced by T2 be approximately opposite in phase to the current induced by 
T1, so that when the upper transmitter is driving current down the tool, 
the lower transmitter is driving the current up, and vice versa. All of 
the current leaving the tool between the lower transmitter and the monitor 
returns to the tool below the lower transmitter while all of the current 
leaving the tool between the upper transmitter and the monitor returns to 
the tool above the upper transmitter. This has the effect of isolating the 
region of the tool above the monitor from the region of the tool below the 
monitor since no current flows between them, either on the collar or 
through the formation. As a result, the resistivity determined from the 
ring current more accurately represents the resistivity of formations 
surrounding the ring R. 
A similar result can be obtained by energizing the transmitters separately 
and computing a compensated ring current. In the arrangement of FIG. 14 
[or that of FIG. 15, which includes a lower receiving or monitoring toroid 
M2, to be subsequently considered], the upper position is designated 1, 
the lower position is designated 2, and the center position is designated 
0. The ring and toroid currents when the upper transmitter is operated at 
an arbitrary but fixed voltage are R.sub.1, M.sub.01, and M.sub.21 and the 
ring and toroid currents when the lower transmitter is operated at the 
same voltage are R.sub.2, M.sub.02, and M.sub.12. Consider a compensated 
current of the form: 
##EQU1## 
In equation (1a), the ratio M.sub.01 /M.sub.02 is the adjustment factor 
for the lower transmitter to achieve the condition of zero axial current 
at MO. The expression R.sub.1 +M.sub.01 /M.sub.02 R.sub.2 is the ring 
current for the condition of zero axial current. 
The two terms in equation (1a) add. This is due to the fact that operating 
the two transmitters in opposition in order to achieve a zero axial 
current at the monitor toroid causes an increase in the ring current. That 
is, when the upper transmitter drives a current down the mandrel, current 
flows out of the ring. Similarly when the lower transmitter drives current 
up the mandrel, it also causes current to flow out of the ring. The 
implication of this processing on the noise is that, since the terms add, 
the noise in the output is not amplified as would be the case if one took 
a small difference between two large numbers. 
FIG. 16 shows the response [resistivity, inversely proportional to 
compensated ring current] for the same beds as in FIG. 13. The artifact A1 
through A5 (of FIG. 13), which occurs as the tool enters the bed, is 
greatly reduced. The smaller artifact B1 through B3 on the downside of the 
thinner beds is almost unchanged. The shape of the log within the bed is 
improved, but could still stand improvement. 
FIGS. 13 and 16 illustrate performance when relatively conductive beds are 
encountered. FIGS. 17 and 18 illustrate performance in thin beds that are 
more resistive than the formations in which they are located. The contrast 
ratio is again 100 to 1 (2000 ohm-m beds in 20 ohm-m formations). FIG. 17 
shows that in this case the uncompensated log using the upper transmitter 
is reasonably good without compensation, and FIG. 18 shows the improvement 
using the indicated compensation of equation (1). 
To better understand the compensation approach, reference can be made to 
FIGS. 19, 20, and 21, which illustrate current path lines for a tool just 
above an 8 foot thick conductive bed. In FIG. 19 transmission is from the 
upper transmitter (at 84 inches on the depth scale) and the ring electrode 
is just above the bed boundary (the ring electrode being at 54 inches on 
the depth scale), the resistivity contrast ratio being 10 to 1. [A lower 
contrast ratio than before is used to facilitate visualization of the 
current line plots.] It is seen in FIG. 19 that the current lines emerge 
from the bed and curve upward into the more resistive shoulder. This 
distortion accounts for the horn-shaped artifacts such as A1 in FIG. 13. 
FIG. 20 shows the same situation, but with transmission from the lower 
transmitter, T2. FIG. 21 illustrates the compensated situation, with 
current from the two transmitters superposed. The current paths near the 
borehole at about the position of the ring are substantially parallel to 
the bed and are not distorted by the presence of the bed. The fact that 
the current paths are substantially independent of the presence of the bed 
below the ring electrode explains the improved response. 
The monitor toroid M0 should preferably be at substantially the same 
position as the ring electrode R to obtain excellent compensation. [An 
arrangement of ring, toroid, and protective covering ring, as first shown 
above in FIG. 3, will effectively put a ring and toroid receiver at 
substantially the same receiver position.] However, even if there is some 
distance between them, improvement will be realized from the indicated 
compensation. 
The condition of zero axial current at the monitor M0 fixes the ratio of 
the voltages generated by transmitter T1 and transmitter T2 or, 
equivalently, the ratio of factors to be applied to the respective ring 
currents R.sub.1 and R.sub.2. It does not set the overall level of the 
transmitter voltages. Choice of the prefactor as 1/M.sub.02 corresponds to 
a fixed voltage at T1 and a voltage at transmitter T2 of M.sub.01 
/M.sub.02. This can be seen from equation (1a). If instead of 1/M.sub.02 
one uses a prefactor of 1/M.sub.01, this corresponds to the lower 
transmitter producing a fixed voltage, while the upper transmitter 
produces a voltage M.sub.02 /M.sub.01 times as large. In this case, one is 
trying to electrically remove the effect of the upper portion of the tool. 
This produces an inferior log from what corresponds to a short 
asymmetrical tool with poor response. 
At present, the most preferred multiplying factor is 1/M.sub.21, where 
M.sub.21 is the current produced by the upper transmitter measured at the 
lower monitor toroid M2 (which is at substantially the same position as 
the lower toroidal transmitter T2--see FIG. 15). [By reciprocity, M.sub.21 
is equal to the current M.sub.12 that would be produced by the lower 
transmitter measured at an imaginary monitor M.sub.1 located at the 
position of the upper transmitter.] Logs produced using this compensation, 
that is, with the compensated ring current 
##EQU2## 
are shown in FIGS. 22 and 23. FIGS. 22 and 23 are for the tool arrangement 
previously described, with FIG. 22 having conductive beds and FIG. 23 
having resistive beds. In both cases, as in previous logs, the contrast 
ratio is 100 to 1. The logs match well to the bed patterns, with only 
small artifacts. 
There is another way to visualize the compensation represented by equation 
(2), in terms of both transmitters operating at adjustable levels. 
Transmitter T1 operates at a relative level of M.sub.02 /M.sub.21. This is 
the ratio of the current from the lower transmitter measured at the 
central monitor divided by the current measured at the upper transmitter. 
Thus, it is sensitive to the leakage of current between the upper 
transmitter and the ring. Similarly, the lower transmitter operates at a 
relative level M.sub.01 /M.sub.21 which is the ratio of currents from the 
upper transmitter measured at the central monitor divided by the current 
measured at the lower transmitter. This is sensitive to the leakage of 
current between the lower transmitter and the ring. Thus both transmitters 
are operated to compensate for leakage between that transmitter and the 
monitor. 
The foregoing assumes that the ratio M.sub.02 /M.sub.12 precisely 
compensates for the effect of "shielding" by a conductive bed between the 
upper transmitter and the ring electrode. The tacit assumption is that the 
conductive regions have the same effect on the leakage of current between 
the ring electrode and the upper transmitter from the lower transmitter as 
they do on the "shielding" of the ring from the upper transmitter. This is 
true to first order. 
A general expression can be set forth in which one term contains a factor 
times R.sub.1 and the second term contains a factor times R.sub.2. These 
factors are measures of leakage and are functions of the ratios of monitor 
currents as follows: 
##EQU3## 
where F.sub.1 and F.sub.2 are compensation functions, and the requirement 
of zero axial current can be relaxed. Further generalization can be 
achieved by adding additional transmitters and monitors and so making the 
functions F.sub.1 and F.sub.2 more general. 
It can be noted that leakage can be practically eliminated by covering the 
region between the transmitters and the electrode with an insulating 
material. When combined with the described compensation technique, this 
can provide an excellent resistivity log. A drawback is the fragility of 
the insulating material in a logging-while-drilling application. Also, the 
resultant measurement has more response close to the tool, and a far 
larger borehole effect. 
FIG. 24 illustrates an embodiment which is similar to that of FIG. 15, but 
wherein the toroidal monitor M2 at the lower transmitter position is 
replaced by the toroidal monitor M1 at the upper transmitter position. By 
reciprocity, M.sub.12 (signal at M1 with transmitter T2 energized) can be 
measured and will provide substantially the same value as M.sub.21, for 
use in equation (2). The principle of reciprocity would also permit the 
reversal of position of other transmitter/receiver combinations from which 
signals are obtained. For example, a further transmitter TO could be 
provided adjacent the ring electrode to be used in conjunction with a 
monitor toroidal antenna at the bottom position, and the monitor signal 
obtained from this transmitter/receiver would be equivalent, by 
reciprocity, to the previously indicated M.sub.01. 
FIG. 25 illustrates an embodiment like that of FIG. 15, but with a button 
electrode B (which may be of the type previously described) replacing the 
ring electrode R. As described above, azimuthal resistivity information 
can be obtained from the button electrode. Typically one or more button 
electrodes and/or one or more ring electrodes may be employed, in 
conjunction with one or more monitor toroids such as MO. A second button 
electrode, B', is shown in FIG. 25. The described type of compensation can 
improve the vertical response of multiple electrodes (which provide 
different depths of investigation) and make their vertical responses more 
similar. Different depths of investigation can also be obtained by 
providing additional transmitters and monitors which are spaced different 
distances from the electrodes. These can be operated either sequentially 
or at different frequencies. The longer transmitter/electrode spacings 
will generate responses that are relatively deep, while the shorter 
transmitter/electrode spacings will provide relatively shallow responses. 
The electronics for the foregoing embodiments can be of the type set forth 
in the block diagram of FIG. 10 having the further features shown in the 
block diagram of FIG. 26. In particular, the switch 1065 (FIG. 10) is 
under control of the processor 1025 (FIG. 10) and couples an energizing 
signal to either transmitter T1 or T2. [If desired, these transmitters can 
be operated simultaneously out of phase, as previously described.] The 
multiplexer 1020 (FIG. 10), which is also under control of processor 1025, 
in this case receives inputs from the ring R via amplifier 2611, from one 
or more further rings represented at R' via amplifier 2612, from the 
button B via amplifier 2613, from one or more further buttons represented 
at B' via amplifier 2614, from receiver (monitor) toroid M0 via amplifier 
2615, and from receiver (monitor) toroid M2 via amplifier 2616. 
FIG. 27 is a flow diagram of a routine for programming a processor, such as 
the processor 1025 of FIG. 10 (as modified by FIG. 26) to implement 
operation of the embodiment of FIG. 15 in accordance with a form of the 
invention. The block 2710 represents the enabling of transmission from 
transmitter T1, this being implemented by control of switch 1065. The 
blocks 2715, 2720 and 2725 respectively represent the measurement and 
storage of signal data received at receivers R, M0 and M2, the functions 
being initiated by controlling the multiplexer 1020 in sequence to obtain 
these measurements. In particular, the block 2715 represents the reading 
and storage of data from the ring electrode R to obtain R.sub.1, the block 
2720 represents the reading and storage of data from monitor toroid M0 to 
obtain M.sub.01, and the block 2725 represents the reading and storage of 
data from monitor toroid M2 to obtain M.sub.21. The transmitter T1 is then 
turned off and the transmitter T2 is enabled, as represented by the block 
2735. The blocks 2740 and 2745 respectively represent the measurement and 
storage of signal data received at receivers R and M0, these functions 
again being initiated by controlling the multiplexer 1020. In particular, 
the block 2740 represents the reading and storage of data from ring 
electrode R to obtain R.sub.2, and the block 2745 represents the reading 
and storage of data from monitor toroid M0 to obtain M.sub.02. The 
transmitter T2 is then turned off (block 2750) and the corrected ring 
current is computed (block 2755) from equation (2). The apparent 
resistivity can then be obtained from the ring current as previously 
described, in accordance with R.sub.app =kV/I. 
In the flow diagram of FIG. 27, currents are generated and measured by 
operating transmitters T1 and T2 alternately. A similar result can be 
achieved utilizing frequency multiplexing, where both transmitters are 
operated simultaneously, but at different frequencies. This generates a 
current in the tool which has components at two frequencies. The current 
at any of the sensors (monitor, ring, or button) which comes from either 
transmitter can be determined by separating the received signal by 
frequency, such as with bandpass filters. 
FIG. 28 illustrates a portion of the electronics that can be employed when 
the upper and lower transmitters are to be operated simultaneously and the 
monitor current is utilized to "balance" the resultant currents to contain 
a substantially zero axial current condition at the monitor toroid, such 
as the previously described monitor toroid MO. The AC source 2810 (which 
may, for example, be coupled to the transmitters through a switch, as in 
prior embodiments), is coupled to each of the transmitter toroidal 
antennas T1 and T2 via respective amplitude modulators 2820 and 2830. 
[Only one such amplitude modulator is strictly necessary, the general case 
being shown in this diagram.] The toroidal antennas are wired in phase 
opposition, so that they generate respective axial currents in the 
conductive body that travel in opposite directions. The amplitude 
modulators 2820 and 2830 are under control of processor 1025. The 
processor also receives a sample of the AC output via flip-flop 2850 which 
is switched to a different binary output state as the AC signal changes 
polarity, so that the processor knows the phase of the AC signal. In this 
case, the multiplexer 1020 is shown as receiving the output of the ring 
electrode R and the monitor toroidal antenna MO. In operation, when the 
current received at the monitor toroid M0 is above a predetermined 
threshold, amplitude control is sent to modulator 2820 and/or 2830 to 
reduce the current sensed by the monitor toroid in the manner of a 
conventional closed loop control. This embodiment is presently considered 
less preferred as it does not make use of the M.sub.21 (or M.sub.12) type 
of prefactor that is obtained by considering the effect of current from a 
transmitter independently. 
The principles of the invention are also applicable to logging in an earth 
borehole with the drill string removed. FIG. 29 illustrates a logging 
device 2940 for investigating subsurface formations 2931 traversed by a 
borehole 2932. The logging device is suspended in the borehole 2932 on an 
armored cable 2933, the length of which substantially determines the 
relative depth of the device 2940. The cable length is controlled by 
suitable means at the surface such as a drum and winch mechanism (not 
shown). Electronic signals indicative of the information obtained by the 
logging device can be conventionally transmitted through the cable 2933 to 
electronics 2985 and recorder 2995 located at the surface of the earth. 
Alternatively, some or all processing can be performed downhole. Depth 
information can be provided from a rotating wheel 2996 that is coupled to 
the cable 2933. 
The logging device 2940 includes elongated generally cylindrical sections 
2951, 2953, 2955 and 2957 which may be formed, for example, of conductive 
metal pipe. Electrically insulating isolators, 2961 and 2963 are located 
at the intersection of sections 2951 and 2953 and the intersection of 
sections 2955 and 2957, respectively. The isolators 2961 and 2963 may 
comprise, for example, threaded annular fiberglass pipe couplers. Located 
between the sections 2953 and 2955 is an electrode 2970, which is 
illustrated in the present embodiment as being a ring electrode, but could 
also be one or more button and/or ring electrodes. In the embodiment of 
FIG. 29, the ring 2970 is a conductive metal ring that is mounted between 
two more isolators 2973 and 2975. 
In the present embodiment, the electronics, shown adjacent the logging 
device for ease of illustration, are located in the central hollow portion 
of one or more of the pipe sections of the device, although it will be 
understood that the electronics could alternatively be located in an 
adjacent module coupled above or below the device 2940, such as by a 
further coupler that may be conductive or non-conductive, with wiring that 
passes through the hollow sections and the annular couplers, as necessary. 
Power and computer processor control can be provided, for example, from 
the uphole electronics via cable 2933, it being understood that some of 
these functions, including communications capability, can be provided 
downhole, as is well known in the art. In the embodiment of FIG. 29, AC 
energizing sources for transmitters T1 and T2 are shown at 2958 and 2959, 
respectively. [Although separate energizing sources are illustrated, it 
will be understood that a common transmitter energizing source could 
alternatively be utilized.] The AC frequency may be, for example, in the 
range 100 Hz to 1 MHz. Conductor pair 2941 is coupled across pipe sections 
2951 and 2953 and to one side of a switch 2942, the other side of which is 
coupled to either the transmitter T1 [switch position (a)] or to a low 
impedance winding of a current sense transformer 2943 [switch position 
(b)] which, in the illustrated embodiment, has a turns ratio 1:N.sub.1. 
The transformer secondary is coupled across the inverting and 
non-inverting inputs of an operational amplifier 2944, the non-inverting 
input of which is coupled to ground reference potential by resistor 
R.sub.1. A feedback resistor R.sub.2 is coupled between the output of 
operational amplifier 2944 and the inverting input thereof. The output of 
operational amplifier 2944 is designated V.sub.M1. 
A conductor pair 2945 is coupled across the pipe sections 2955 and 2957, 
and to one end of a switch 2946, the other end of which is coupled to 
either the transmitter T2 [switch position (b)] or to the short circuit 
2947 [switch position (a)]. The switches 2942 and 2946 are under common 
control. 
A further conductor pair 2981 couples pipe sections 2953 and 2955 via a low 
impedance winding of current sense transformer 2983 having an indicated 
turns ratio of N.sub.3 :1. The secondary winding of transformer 2983 is 
coupled across the inverting and non-inverting inputs of an operational 
amplifier 2984, the non-inverting input of which is coupled to ground 
reference potential by resistor R.sub.3. A feedback resistor R.sub.4 is 
coupled between the output of operational amplifier 2984 and the inverting 
input thereof. The output of operational amplifier 2984 is designated 
V.sub.M0. 
A further conductor pair 2991 couples the ring electrode 2970 to the pipe 
section 2955 (which is, in turn, effectively shorted to pipe section 2953 
by the low impedance winding of transformer 2983) via a low impedance 
winding of current sense transformer 2993 having an indicated turns ratio 
of N.sub.2 :1. The secondary winding of transformer 2993 is coupled across 
the inverting and non-inverting inputs of an operational amplifier 2994, 
the non-inverting input of which is coupled to ground reference potential 
by resistor R.sub.5. A feedback resistor R.sub.6 is coupled between the 
output of operational amplifier 2994 and the inverting input thereof. The 
output of operational amplifier 2994 is designated V.sub.R. 
Operation is similar to the previously described case for sequential 
energizing of the transmitters T1 and T2, and the obtainment of 
measurement signals at the ring electrode and the monitor positions. [In 
this case, the second monitor is at the same position as the upper 
transmitter, as in the analogous arrangement of M1 in FIG. 24.] The 
electronics control can be similar to that described in conjunction with 
FIGS. 10, 11, 26 and 27. In particular, with the switches 2942 and 2946 at 
position "a", the transmitter T1 is operative and pipe sections 2955 and 
2957 are shorted. Measurements are taken to obtain the voltages V.sub.R1 
and V.sub.M01. The ring current I.sub.R is obtained from 
EQU V.sub.R =(R.sub.5 +R.sub.6)I.sub.R /N.sub.2, (4) 
that is: 
EQU I.sub.R =V.sub.R N.sub.2 /(R.sub.5 +R.sub.6). (5) 
Similarly, the monitor current M.sub.0 is obtained from 
EQU V.sub.M0 =(R.sub.3 +R.sub.4)M.sub.0 /N.sub.3, (6) 
that is: 
EQU M.sub.0 =V.sub.M0 N.sub.3 /(R.sub.3 +R.sub.4). (7) 
Using the same convention as above, V.sub.R1 and V.sub.M01 are the voltages 
obtained with transmitter T1 enabled. Next, the switches 2942 and 2946 are 
put in position (b), the transmitter T2 is enabled, and the pipe sections 
2951 and 2953 are effectively shorted. Measurements are taken to obtain 
the voltages V.sub.M02 (from which the current M.sub.02 is obtained in 
accordance with equation (7) above) and V.sub.M12. The monitor current 
M.sub.1 is obtained from 
EQU V.sub.M1 =(R.sub.1 +R.sub.2)M.sub.1 /N.sub.1, (8) 
that is: 
EQU M.sub.1 =V.sub.M1 N.sub.1 /(R.sub.1 +R.sub.2). (9) 
Again, using the same convention ae above, VM.sub.02 and VM.sub.12 are the 
voltages obtained with transmitter T2 enabled. The compensated ring 
current, I.sub.RC, is 
EQU I.sub.RC =(M.sub.02 /M.sub.12)I.sub.R1 +(M.sub.01 /M.sub.12)I.sub.R2. (10) 
Apparent resistivity in the region surrounding the ring electrode is 
inversely proportional to the corrected ring current. 
The embodiment illustrated in FIG. 29 uses isolators in establishing 
electrical potential differences between conductive sections of the body 
of the logging device, and to electrically isolate the electrode 2970. 
Also, currents are measured with direct current flow occurring through a 
low impedance winding of a current sense transformer. It will be 
understood that, for example, the voltage gaps at isolators 2961 and/or 
2963, and their associated sources could alternatively be toroidal 
transmitters and their associated sources as in previous embodiments, and 
that currents can be measured using toroidal receivers. Also, the 
electrode may be, for example, a button or ring electrode of the type 
previously described. Similarly, it will be understood that the techniques 
illustrated in FIG. 29 could be employed, in whole or in part, in a 
measurement-while-drilling embodiment, but are presently considered less 
preferred for such application from at least the standpoint of 
construction ruggedness. 
The invention has been described with reference to particular preferred 
embodiments, but variations within the spirit and scope of the invention 
will occur to those skilled in the art. For example, it will be understood 
that while separate toroidal antennas are shown for transmitting and 
receiving from substantially the same position (there being certain 
practical advantages to having different antennas for use as transmitter 
and receiver), a single toroidal antenna can be shared for this purpose 
using suitable switching. Also, it will be understood that functions which 
are illustrated as being implemented using a processor control can 
alternatively be implemented using hard-wired analog and/or digital 
processing.