Logging method and apparatus for investigating geometrical characteristics of a borehole and for investigating formation resistivity
BACKGROUND OF THE INVENTION 
     The invention relates to a method and to apparatus for investigating geometrical characteristics of a borehole, and more particularly for detecting the distances between a logging sonde and the wall of a borehole in a plurality of directions around the sonde. The invention also relates to the application of such a technique to a logging method and apparatus for investigating the azimuthal resistivities of earth formations through which a borehole passes in order to correct said resistivity measurements. 
     Logging apparatuses are known that detect distances between a logging sonde and the wall of a borehole in a plurality of directions around the sonde. The purpose of such apparatuses is to measure a plurality of borehole diameters. An example of a mechanical implementation of such a multiple caliper tool is described in U.S. Pat. No. 4,251,921 (Fink). That apparatus comprises articulated arms adapted to come into contact with the wall of the borehole and a system for measuring the spread of the arms. That apparatus requires numerous moving mechanical parts that are liable to wear and that run the risk of jamming in difficult boreholes. 
     A different implementation of such a multiple caliper apparatus, based on acoustics, is described in U.S. Pat. No. 4,827,457 (Seeman et al.). That apparatus has the advantage of measuring a plurality of borehole diameters without contacting the borehole wall. It nevertheless requires a large number of acoustic sensors that are relatively expensive. 
     U.S. Pat. No. 4,087,740 (Suau) describes a logging apparatus having electrodes for determining the mean diameter of a borehole. In that apparatus, a first current is emitted which flows mainly into the formations, together with a second current that flows mainly in the borehole fluid. Two resistivity signals are derived in response to the first and second currents and the two resistivity signals are combined to deduce the mean diameter of the borehole. Such apparatus does not give information on the eccentring of the sonde in the borehole, nor does it give indication concerning the shape of the cross-section of the borehole. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to provide a logging technique to obtain information on the eccentring of a sonde in a borehole and/or on the shape of the cross-section of the borehole, while not making contact with the borehole wall. 
     Another object of the invention is to provide a logging technique for detecting a plurality of radial distances between a logging sonde and the wall of a borehole, by using electrodes. 
     Still another object of the invention is to provide a logging technique for measuring azimuthal resistivities of the formations through which a borehole passes and in which the measurements can be corrected to take account of the eccentring of the sonde and/or of the irregular shape of the cross-section of the borehole. 
     In a first aspect, the present invention provides a logging method for investigating geometrical characteristics of a borehole in which an elongate sonde body is suspended, wherein electrical currents ( Ic i ) are emitted between an array of azimuthal current electrodes (Aaz i ) circumferentially spaced apart on the body and an annular current electrode (A) disposed on the body, the annular electrode (A) being longitudinally spaced apart from the array of azimuthal electrodes (Aaz i ) in such a manner that the emitted currents flow mainly through the borehole fluid. Output signals (Rc i ) are generated that are a function of the resistivity of the zones through which the currents flow, thereby obtaining information relating to the distances between the body and the wall of the borehole in a plurality of directions around the sonde. 
     Preferably, the emission of the currents (Ic i ) is controlled in such a manner that they are equal to one another and of constant amplitude (Ic). The potential differences (ΔVc i ) caused by the emitted currents (Ic i ) between azimuthal monitor electrodes (Maz i ) associated with the azimuthal current electrodes (Aaz i ) and an annular electrode (M) associated with the current annular electrode (A) are detected, and output signals (Rc i ) are generated such that each is a function of the ratio (ΔVc i  /Ic) of the detected potential (ΔVc i ) divided by the current (Ic). 
     A logging apparatus for implementing this method comprises: an elongate sonde body adapted to be displaced along the borehole; an array of circumferentially spaced apart azimuthal current electrodes (Aaz i ) disposed on the body; an annular current electrode (A) longitudinally spaced from the array of azimuthal electrodes so that the currents emitted between the array of azimuthal current electrodes (Aaz i ) and the annular current electrode (A) flow mainly through the borehole fluid; means for emitting currents (Ic i ) between the azimuthal electrodes (Aaz i ) and the annular electrode (A); and means for generating output signals (Rc i ) that are a function of the resistivity of the borehole zones through which the currents flow, thereby providing information concerning the distances between the body and the wall of the borehole in a plurality of directions around the sonde. 
     Preferably, the device includes an annular monitor electrode (M) associated with the annular return electrode (A) and an azimuthal monitor electrode (Maz i ) associated with each azimuthal current electrode (Aaz i ). 
     In a second aspect, the invention provides a method of investigating the resistivity of formations through which a borehole passes, the method comprising the following steps: emitting first currents (Iaz i ) from an array of circumferentially spaced apart azimuthal current electrodes (Aaz i ) disposed on an elongate sonde body adapted to be moved along the borehole; generating first output signals (Raz i ) representative of the resistivity of the zones through which the first currents (Iaz i ) flow; emitting second currents (Ic i ) via the azimuthal current electrodes (Aaz i ), which second currents flow mainly through the fluid of the borehole; and generating second output signals (Rc i ) representative of the resistivity of the zones through which the second currents (Ic i ) flow, said second output signals being indicative of the distances between the body and the wall of the borehole in a plurality of directions around the sonde, for correcting the first output signals (Raz i ). 
     Preferably, the first currents (Iaz i ) are emitted at a first frequency and the second currents (Ic i ) are emitted at a second frequency different from the first. Auxiliary currents at the first frequency are emitted into the formations by annular current electrodes (A2) disposed on the body on either side of the array of azimuthal electrodes (Aaz i ) to focus the first currents (Iaz i ). The second currents (Ic i ) are emitted between the azimuthal,electrodes (Aaz i ) and the annular current electrodes (A2) with equal amplitudes. 
     Each of the second output signals (Rc i ) is a function of the ratio (ΔVc i  /Ic) of the potential difference (ΔVc i ) detected between a monitor azimuthal electrode (Maz i ) and annular monitor electrodes (M3 M4) divided by the amplitude (Ic) of the second currents (Ic i ). To correct the first output signals, signals are generated that are representative of correction coefficients (Cex i ) using the equations: 
     
         Cex.sub.i =12 Rc.sub.i ΣRc.sub.i. 
    
     An apparatus according to the second aspect of the invention comprises: an elongate sonde body adapted to be displaced along the borehole; an array of circumferentially spaced apart azimuthal current electrodes (Aaz i ) on the body; two annular guard electrodes (A2) disposed longitudinally on the body on either side of the array of azimuthal current electrodes (Aaz i ); means for emitting first currents (Iaz i ) via the azimuthal current electrodes (Aaz i ); and means for generating first output signals (Raz i ) representative of the resistivity of the formations in a plurality of directions around the sonde. The apparatus further includes means for emitting second currents (Ic i ) via the azimuthal current electrodes (Aaz i ), which second currents flow mainly through the borehole fluid; and means for generating second output signals (Rc i ) representative of the resistivity of the zone through which the second currents flow, to provide an indication of the distances between the body and the wall of the borehole in a plurality of directions around the sonde whereby the first output signals (Iaz i ) can be corrected. 
     The apparatus preferably includes monitor azimuthal electrodes (Maz i ) respectively associated with the current azimuthal electrodes (Aaz i ) and two monitor annular electrodes (M3, M4) respectively associated with the guard electrodes (A2). 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The characteristics and advantages of the invention appear more clearly from the following description given by way of non-limiting example and made with reference to the accompanying drawings, in which: 
     FIG. 1 shows a logging apparatus of the invention comprising a sonde fitted with electrodes for investigating the geometrical characteristics of a borehole; 
     FIG. 2 shows a preferred configuration of the electrodes carried by the logging sonde of FIG. 1; 
     FIG. 3 is a block diagram of electrical circuits preferably usable in the apparatus of FIG. 1; 
     FIG. 4 is a block diagram of a variant of the electrical circuits usable in the apparatus of FIG. 1; 
     FIG. 5 shows a logging sonde for investigating the resistivity of formations in accordance with a second aspect of the invention in which the detected geometrical properties of the borehole are used for correcting measurements; 
     FIG. 6 shows a configuration of the electrodes carried by the logging sonde of FIG. 5; and 
     FIG. 7 is a block diagram of the electrical circuits that are preferably used in the apparatus of FIG. 5. 
    
    
     DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
     With reference to FIG. 1, a logging apparatus for investigating a borehole 10 passing through the earth formations 11 comprises a sonde 12 suspended in the borehole at the end of a multiconductor cable 13. The cable 13 passes over a sheave 14 and is wound onto a winch 15 for moving the sonde 12 along the borehole. The winch 15 forms a part of a surface unit 16. 
     The sonde 12 comprises an elongate body 17 having a top section 20 comprising a sealed metal envelope containing electrical circuits, and a bottom section 21 suitable for being fitted with sensors (not shown) for investigating earth formations. Such sensors may be electrodes, induction coils, nuclear sensors, acoustical transducers, or other forms of sensor. In addition to such sensors, the bottom section 21 carries a set 22 of electrodes for detecting the geometrical characteristics of the borehole. Information on the shape and the size of the cross-section of the borehole and also on the eccentring of the sonde 12 within the borehole are of interest either per se for providing information about the state of the borehole, or else for correcting measurements performed on the formations. 
     With reference to FIG. 2 which shows the set of electrodes 22 disposed on the sonde 12 in greater detail, the bottom section 21 of the body carries an annular current electrode A, an annular monitor electrode M associated with the current electrode A, and an array of twelve, circumferentially spaced apart, azimuthal electrodes. The annular current electrode A may be disposed entirely to one side of the monitor electrode M as shown in the figure, or it may comprise a portion above the annular electrode M, and a portion below it. Each azimuthal electrode includes an azimuthal current electrode Aaz i  surrounding an azimuthal monitor electrode Maz i , where i is an index in the range 1 to 12. 
     The array of azimuthal electrodes is longitudinally spaced apart from the annular current electrode A so that the currents emitted between the azimuthal electrodes and the annular electrode A flow mainly through the borehole fluid. The width in the longitudinal direction of the gap between adjacent edges of the electrode A and of the electrodes Aaz i  is of the same order of magnitude as the radial distances to be detected between the sonde 12 and the wall of the borehole. In a preferred embodiment, this gap is made to be about 5 cm wide. 
     To provide measurements of the distances between the sonde and the wall of the borehole in a plurality of directions around the sonde, currents Ic i  are emitted between the azimuthal current electrodes Aaz i  and the annular current electrode A. Potential differences ΔVc i  appear between each of the azimuthal monitor electrodes Maz i  and the annular monitor electrode M. The apparent resistivity Rc i  of the zone through which each current Ic i  passes is given by the following equation: 
     
         Rc.sub.i =k1ΔVc.sub.i /Ic.sub.i 
    
     in which k1 is a constant coefficient that depends on the shape of the sonde 12. Each current Ic i  has a portion which flows into the formations and another portion which flows through the borehole fluid. It has been found that each apparent resistivity Rc i  is a function of the radial distance between the sonde and the borehole wall opposite the corresponding azimuthal electrode Aaz i . Therefore, to obtain information on said distances, signals are generated that are representative of the resistivities Rc i . 
     Information is thus obtained on the eccentring of the sonde in the borehole and on the possibly irregular shape of the section of the borehole without increasing the mechanical complexity of the apparatus. 
     FIG. 3 is a block diagram of electrical circuits for generating such signals and constituting a preferred embodiment of the invention. In this embodiment, the amplitudes of the currents Ic i  are maintained equal to a common value and the potential differences ΔVc i  are detected. 
     To the left of the figure, the above-described electrodes A, M, Maz i , and Aaz i  are shown diagrammatically, with a single electrode Maz i  and a single electrode Aaz i  being shown to simplify the description. An oscillator 30 provides an alternating voltage for controlling twelve current sources 33 i . The output from each of the current sources 33 i  is connected firstly to an azimuthal current electrode Aaz i  and secondly to an annular current electrode A for emitting an alternating current Ic i  between said electrodes. The twelve current sources 33 thus emit twelve equal currents Ic 1 . The common value Ic of the twelve equal currents Ic i  is detected at the outlet of the oscillator 30 by an amplifier 31 whose output is applied to a phase sensitive detector 32. 
     The potential difference ΔVc i  caused by each current Ic i  between each azimuthal monitor electrode Maz i  and the annular monitor electrode M is detected by an amplifier 34 i  whose output is applied to a phase sensitive detector 35 i . The phase references required by the phase sensitive detectors 32 and 35 i  come from the oscillator 30. The rectified values of Ic and of the potential differences ΔVc i  are applied to a calculation circuit 36 which generates signals Rc i  using the following equation: 
     
         Rc.sub.i =k1ΔVc.sub.i /Ic 
    
     The calculation circuit 36 may also generate twelve signals Cex i  representative of eccentricity coefficients in which the influence of variations in the resistivity of the borehole fluid is practically eliminated by using the following equation: 
     
         Cex.sub.i =12 Rc.sub.i /ΣRc.sub.i 
    
     these coefficients are a function of the relative distances between the sonde and the wall of the borehole in twelve directions around the sonde. 
     In the embodiment described, the calculation circuit is disposed in the surface equipment 16 while the other circuits are contained in the top section 20 of the sonde 12. The thirteen rectified signals Ic and ΔVc i  are thus sent from the sondes to the surface via the cable 13. Naturally, any other distribution of the circuits shown in FIG. 3 between the surface and the sonde could be envisaged. 
     FIG. 4 is a diagram of the electrical circuits for generating signals Rc i  in a different embodiment of the invention. In this variant, the amplitude of the potential differences ΔVc i  is kept equal to a common value and it is the respective currents Ic i  that are detected. 
     An oscillator 40 provides an alternating voltage to the primary winding of a transformer 41 having a first secondary winding connected between the annular monitor electrode M and one of the inputs of a differential amplifier 44 i . The other input of the differential amplifier 44 i  is connected to an azimuthal monitor electrode Maz i , and its output is applied to a current source 45 i . The outputs from the current sources 45 i  are connected firstly to corresponding azimuthal current electrodes Aaz i  and secondly to the annular current electrode A. In this way, the emission of the alternating currents Ic i  is controlled in such a manner that the potential differences ΔVc i  appearing between the annular monitor electrode M and each of the azimuthal monitor electrodes Maz i  is kept equal to a potential difference ΔVc of fixed amplitude. The common value ΔVc of the twelve equal potential differences ΔVc i  is detected by means of a second secondary winding of the transformer 41 connected to an amplifier 42 and then to a phase sensitive detector 43. 
     The current Ic i  emitted by each azimuthal current electrode Aaz i  is detected by a series resistance 46 i  of low value placed on an output of each current source 44 i . The terminals of each resistance 46 i  are connected to the inputs of an amplifier 47 i  whose output is applied to a phase sensitive detector 48 i . The phase references required by the phase sensitive detectors 43 and 48 i  are taken from the oscillator 40. A calculation circuit 49 generates signals Rc i  using the following equations: 
     
         Rc.sub.i =k1ΔVc/Ic.sub.i 
    
     In the variant of FIG. 4, as in the variant of FIG. 3, when the calculation circuit 49 is on the surface, thirteen signals need to be transmitted via the cable 13. In the absence of servo-control for keeping the amplitudes of the currents Ic i , or the amplitudes of the potential differences ΔVc i  constant, it is also possible to detect twelve currents Ic i  and twelve potential differences ΔVc i . Under such circumstances, twenty-four signals are transmitted to the surface via the cable 13. 
     In the embodiments described above, the potential differences are detected on monitor electrodes that are isolated from the current electrodes. It is also possible to connect the detection amplifiers 34 i  and 44 i  to the annular current electrode A and/or to the azimuthal current electrodes Aaz i . The measurements then suffer from errors due to the contact impedances of the electrodes and also to the resistances of the connection wires. However, solutions can be found for reducing such errors, e.g. by using electrodes that are selected for their low contact impedances. 
     FIG. 5 shows a logging sonde 50 for investigating the resistivity of formations in which measurements are corrected by detecting the geometrical properties of the borehole. The sonde 50 suspended from a cable 13 comprises an elongate body 51 having a top section 52 which contains the electrical circuits and a bottom section 53 which carries the electrodes. 
     The bottom section 53 carries a first set of annular electrodes Ao, M1-M&#39;1, M2-M&#39;2, A1-A&#39;1, and A2-A&#39;2 for implementing the known &#34;Double Laterolog&#34; technique in deep mode LLd and in shallow mode LLs using the technique described in U.S. Pat. No. 3,772,589 (Scholberg). The electrode A2 is made of two portions having an array of azimuthal electrodes 54 together with annular monitor electrodes M3 and M4 disposed therebetween as shown in greater detail in FIG. 6. The array of azimuthal electrodes is used for measuring azimuthal resistivities as described in French patent application No. 91 14702, filed Nov. 28, 1991. 
     With reference to FIG. 6 which shows the top portion of the bottom section 53, the body 51 forms two guard electrodes A2 which are respectively associated with two annular monitor electrodes M3 and M4 which are electrically interconnected. The annular monitor electrodes M3 and M4 are isolated relative to the electrodes A2 and they are situated, for example, inside respective ones of the electrodes A2. The electrode M4 could also be disposed beneath the top electrode A2 while the electrode M3 could be disposed above the bottom electrode A2. Between the two guard electrodes A2 there is disposed an array 54 of twelve azimuthal electrodes that are circumferentially spaced apart from one another. Each azimuthal electrode includes an azimuthal current electrode Aaz i  surrounding an azimuthal monitor electrode Maz i , where i is an index in the range 1 to 12. 
     To obtain resistivity measurements in a plurality of directions around the sonde, measurement currents Iaz i  are emitted into the formations at a first low frequency f1 by the azimuthal current electrodes Aaz i . These currents are focused by auxiliary currents emitted by the electrodes A2. A servo-control system formed by twelve servo-control loops controls the measurement currents Iaz i  so as substantially to cancel each potential difference ΔVc detected between the interconnected annular monitor electrodes M3 and M4 and each of the azimuthal monitor electrodes Maz i . In addition, the potential Vaz of the interconnected annular monitor electrodes M3 and M4 is detected, and output azimuthal signals Raz i  are generated each of which is a function of the ratio of the potential Vaz detected on the annular monitor electrodes divided by the current Iaz i  as emitted by a respective azimuthal electrode, in compliance with the following equation: 
     
         Raz.sub.i =k2 Vaz/Iaz.sub.i 
    
     where k2 is a coefficient that depends on the shape of the sonde. This technique is described in detail in the above-mentioned French patent application No. 91 14702. 
     Azimuthal resistivity measurements obtained in this way are sensitive to the eccentring of the sonde in the borehole. To obtain information on said eccentring for the purpose of correcting the measurements, the distances between the azimuthal electrodes and the wall of the borehole are also detected. 
     To do this, second currents Ic i  are also emitted into the borehole fluid between the azimuthal current electrodes Aaz i  and the annular monitor electrodes M3 and M4, but at a higher, second frequency f2. These currents Ic i  are maintained equal to one another so that it suffices merely to detect a single current Ic. In addition, the potential differences ΔVc i  that appear between each of the azimuthal monitor electrodes Maz i  and the interconnected annular monitor electrodes M3 and M4 are detected and second output signals Rc i  are generated, each of which is a function of the ratio of a respective detected potential difference ΔVc i  divided by the current Ic emitted by each azimuthal electrode in compliance with the following equation: 
     
         Ic.sub.i =k1ΔVc.sub.i /Ic 
    
     where k1 is a coefficient that depends on the shape of the sonde. 
     Information is thus obtained on the eccentring of the sonde in the borehole and on the possibly irregular shape of the section of the borehole at the exact depth where measurements are being performed. It is therefore of little importance whether or not the sonde is at an angle relative to the axis of the borehole. In addition, the mechanical complexity of the apparatus is not increased since the same electrodes are used both for azimuthal resistivity measurements and for measuring geometrical characteristics. 
     With reference to FIG. 7, a preferred embodiment of the electrical circuits used in the sonde of FIG. 5 is shown. To the bottom and to the right of FIG. 7 there can be seen diagrammatic representations of the electrodes A2, M3, and M4, together with a single electrode Maz i  and a single electrode Aaz i . Alternating current It at the frequency f1 of 35 Hz is sent from a source on the surface 60 to the downhole sonde via one or more of the conductors 61 in the cable 13. This total current It is detected downhole by means of a low value series resistance 62 whose terminals are connected to an amplifier 63 followed by a bandpass filter 64 centered on the frequency f1. The phase of the total current It is also detected by means of a phase detection circuit 65. By measuring the total current It downhole and by measuring its phase downhole, it is possible to eliminate the effects of any distortion that may occur due to transmission along the cable 13. A fraction of the total current is applied via a conductor 66 to the electrodes A2 which are electrically short circuited together as represented diagrammatically by a connection 67. The total current flows between the current electrodes and a remote electrode B situated on the surface. 
     A portion of the circuitry is used for making azimuthal measurements of the resistivity of the formations. The interconnected annular monitor electrodes M3 and M4 are connected to the input of a measurement amplifier 70 whose other input is connected to a reference electrode N which is constituted by the armor of the cable. The output of the amplifier 70 is applied to a bandpass filter 71 centered on the frequency 35 Hz and it provides an alternating-signal vaz representative of the potential difference between the reference electrode N and the electrodes M3 and M4. 
     Each azimuthal monitor electrode Maz i  is connected to a differential input of a preamplifier 72 i  having a wide frequency band and having its other input connected to the annular monitor electrodes M3 and M4. The output of each preamplifier 72 i  is connected to the input of a high gain amplification stage 73 i  which also has a filter function at 35 Hz, and which is in turn connected to a current source 74 i  formed by a voltage-to-current converter. The output current from the source 74 i  is applied between the guard electrode A2 and the azimuthal current electrode Aaz i  associated with the electrode Maz i  under consideration. The loop 72 i , 73 i , and 74 i  controls the emission of each current Iaz i  so as to cancel the potential difference between M3, M4 and the corresponding azimuthal monitor electrode Maz i . 
     The output signal of the amplification stage 73 i  is applied to a measurement amplifier 75 i  followed by a bandpass filter 76 i  centered on the frequency 35 Hz so as to provide an alternating signal Iaz i  representative of the measurement current emitted by the azimuthal electrode Aaz i . As represented by dashed lines in FIG. 4, the apparatus includes twelve identical channels. 
     The signals Vaz and It, and the twelve signals Iaz i  are applied to a multiplexer 77. A timing circuit 78 controls the timing at which the signals Vaz, It, Iaz i  are sampled. 
     Another portion of the circuits serves to detect the radial distances between the azimuthal electrodes and the wall of the borehole. A clock 80 provides pulses at a frequency f2 of 64 kHz to an analog switch 81 which produces a squarewave signal at the same frequency which is applied to a bandpass filter 82. The sinewave voltage of fixed amplitude Ic that appears at the output from the filter 82 is applied to the current sources 74 i  so as to emit sinewave currents Ic i  of fixed amplitude and of frequency f2 between each of the azimuthal electrodes Aaz i  and the electrodes A2. 
     The output signal from each of the preamplifiers 72 i  contains a component at the frequency f2 which is the potential drop ΔVc i  due to one of the currents Ic i  flowing mainly through the borehole fluid. The output of each preamplifier is connected to a multiplexer 83 which also receives the output signal Ic from the filter 82 and which is sampled under the control of a signal coming from the timing circuit 78. The output signal from the multiplexer 83 is applied to an amplifier 84 having a filter function centered on the frequency of 64 kHz so as to eliminate signals at a frequency other than f2. The output from the amplifier 84 is connected to a phase sensitive detector 85 having a phase reference at 64 kHz from the clock 80, with the phase sensitive detector 85 being followed by a low-pass filter 86. The multiplexed output signal from the filter 86 which is a sequence of DC signals corresponding to the common amplitude of the currents Ic i  and to the amplitudes of the potential differences ΔVc i , is applied to the multiplexer 77. 
     The output of the multiplexer 77 is applied to an analog-to-digital converter 90 including a variable gain input amplifier. The digital outputs from the converter 90 are applied to a digital processor circuit 91 constituted by a digital signal processor (DSP) programmed to perform a phase synchronized rectification function and a low-pass filter function on the digital signals It, Vaz, and Iaz i . The phase reference required by the rectification function comes from the phase detection circuit 65. The processor circuit 91 also provides a control signal to the variable gain amplifier of the analog-to-digital converter 90 so as to reduce the dynamic range of the input signals to the converter. 
     The multiplexed digital signals represent the amplitudes of the currents or voltages Vaz, It, Iaz i , Ic and ΔVc i  and they are applied to a telemetry circuit 92 suitable for modulating and transmitting said signals to the surface via the cable 13. These downhole signals are received and demodulated at the surface by a telemetry circuit 93 and they are then input into a computer 94 which may be a Microvax microcomputer as sold by Digital Equipment Corporation, for example. The computer 94 performs demultiplexing of the signals Vaz, It, Iaz i , Ic, and ΔVc i , and it calculates raw formation resistivity signals Raz i , together with signals Rc i  representative of the radial distances between the sonde and the wall of the borehole, and it then calculates corrected resistivity signals Raz(cor) i  using the following equations: 
     
         Raz.sub.i =k2 Vaz/Iaz.sub.i 
    
     
         Rc.sub.i =k1 ΔVc.sub.i /Ic 
    
     
         Cex.sub.i =12 Rc.sub.i /ΣRc.sub.i 
    
     
         Raz(cor).sub.i =Raz.sub.i /Cex.sub.i 
    
     in which k1 and k2 are predetermined constants that depend on the shape of the downhole sonde. 
     The various resistivity signals are recorded as a function of depth in a recorder device 95 which may include an optical recorder and a magnetic recorder. 
     It may be observed that in the above embodiment, the increase in the complexity of the device due to adding geometrical measurements thereto is minimized by maximum reuse of circuits that are already required for obtaining the resistivity signals Raz i . The sources 74 i  and the pre amplifiers 72 i  are used simultaneously for both types of measurement Raz i  and Rc i . Finally, numerous other circuits such as the multiplexer 77, the converter 90, and the telemetry circuits 92 and 93 are common to both types of measurement. 
     The embodiments described above may naturally be subjected to numerous variants or improvements While remaining within the ambit of the invention as defined in the following claims.