Apparatus for determining the resistivity of a subsurface earth formation at different lateral distances from a bore hole wall

Abstract

Apparatus for investigating subsurface earth formations traversed by a borehole comprising a system of electrodes consisting of a central electrode A 0 and four pairs of electrodes M 1 -M' 1 , M 2 -M' 2 , A 1 -A' 1 , A 2 -A' 2 respectively short-circuited and aligned symmetrically on both sides of the electrode A 0 . This apparatus comprises arrangements which, for a frequency ƒ 2 , establish a potential gradient between electrodes A 1 -A' 1 and A 2 -A' 2 . A source of alternating current of frequency ƒ 1 is connected between the electrodes A 1 -A' 1 and A 2 -A' 2 and a source of alternating current of frequency ƒ 2 between a surface electrode B and electrodes A 2 -A' 2 . The potential difference between electrodes M 1 -M 2 and M' 1 -M' 2 is maintained substantially at zero by circulating a current between electrodes A 1 -A' 1 and electrode A 0 . Such an apparatus allows simultaneous measurement in a borehole of the electrical resistivities of the subsurface earth formations extending over relatively small and relatively large lateral distances from the wall of the borehole.

I claim: 
     
       1. An apparatus for the electrical investigation of earth formations traversed by a borehole, comprising: a. an electrode system comprising a central electrode .Iadd.for emitting current having frequencies f 1  and f 2  into said formation .Iaddend.and four pairs of electrodes respectively shortcircuited and aligned symmetrically about said central electrode at increasing distances therefrom, the central electrode and the electrodes of the third and fourth pairs being called current electrodes, the electrodes of the first and second pairs being called voltage electrodes;   b. means for producing an alternating current at a first frequency, f 1 , coupled between the .[.electrodes of the fourth pair and at least one of the other current electrodes.]. .Iadd.third electrode pair and the fourth electrode pair to focus f 1  current emitting from said central electrode.Iaddend.;   c. means for producing an alternating current at a second frequency, f 2 , coupled between .[.one of the current electrodes and.]. an electrode at electrical infinity with respect to the electrode system.Iadd., and one of the third and fourth electrode pairs, said one of the third and fourth electrode pairs being further coupled through a low impedance at frequency f 2  with the other of said third and fourth electrode pairs to focus f 2  current emitting from said central electrode.Iaddend.;   d. means for maintaining the potential difference between the first and second pairs of electrodes at substantially zero, said means adapted to monitor the potential difference between the first and second pairs of electrodes and to emit current from the central current emitting electrode in response to the measured potential difference to reduce the potential difference to zero; and   e. means for measuring the electrical potential proximate to one of the first and second pairs of electrodes and the current emitted from the central electrode to produce therefrom signals representative of the electrical resistivity of the formation .[.located.]. at different lateral distances from the borehole.   
     
     
       2. The apparatus of claim 1 wherein said means for producing an alternating current at frequency f 1  is coupled between said third and fourth pairs of electrodes and said means for producing an alternating current at frequency f 2  is coupled between the fourth pair of current electrodes and the electrode at electrical infinity.Iadd., said third and fourth pairs of electrodes being coupled by a relatively high-impedance path at frequency f 1  and by a low-impedance path at frequency f 2  .Iaddend.. 
     
     
       3. The apparatus of claim 2 further comprising means .Iadd.coupled between the electrodes of the third and fourth pairs of electrodes .Iaddend.for maintaining at the frequency f 2  a potential gradient of predetermined value .[.between the electrodes of the third and fourth pairs of electrodes.]. .Iadd.therebetween.Iaddend.. 
     
     
       4. The apparatus of claim 3 wherein the potential gradient between the third and fourth pairs of electrodes at frequency f 2  is maintained at substantially zero volts. 
     
     
       5. The apparatus of claim 3 wherein the means for maintaining a predetermined potential gradient between the third and fourth pairs of electrodes comprises; a. a fifth pair of electrodes positioned one on each side of the central electrode between the third and fourth pairs of electrodes; and   b. means for measuring the potential gradient at frequency f 2  between the fourth and fifth pairs of electrodes and adapted to supply a current to the formation at the frequency f 2  in response to the potential difference between the fourth and fifth pairs of electrodes to maintain the potential difference between the fourth and fifth electrodes at the predetermined potential gradient.   
     
     
       6. An apparatus for investigating earth formations traversed by a borehole, comprising: a plurality of electrodes adapted for movement through a borehole, said electrodes comprising a central current .[.emitting.]. electrode, first and second pairs of potential monitoring electrodes positioned on opposite sides of the central electrode and first and second pairs of current electrodes positioned on opposite sides of the central current .[.emitting.]. electrode and further from the central electrode than the potential monitoring electrodes;   .Iadd.b. means for controllably supplying current having frequencies f 1  and f 2  from the central current electrode; .Iaddend.   .[.b..]. .Iadd.c. .Iaddend.means for producing a current at frequency f 1  coupled between the first and second pairs of current .[.emitting.]. electrodes .Iadd.to focus f 1  current emitting from the central current electrode.Iaddend.;   .[.c..]. .Iadd.d. .Iaddend.means for producing a current at frequency f 2  coupled between the second pair of current .[.emitting.]. electrodes and a point at electrical infinity from said plurality of electrodes .Iadd.to focus f 2  current emitting from the central current electrode.Iaddend.;   .[.d.]. .Iadd.e. .Iaddend.means .Iadd.coupled between the first and second pair of current electrodes .Iaddend.for maintaining the impedance .[.between the first and second pair of current emitting electrodes.]. .Iadd.therebetween .Iaddend.at frequency f 2  substantially equal to zero;   .[.e.]. .Iadd.f. .Iaddend.means for maintaining the potential difference between the first and second pairs of potential monitoring electrodes substantially at zero volts.Iadd., .Iaddend.said means adapted to monitor the potential difference between the first and second pairs of potential electrodes and to .[.supply.]. .Iadd.control the .Iaddend.current .Iadd.supplied .Iaddend.from the central current .[.emitting.]. electrode in response to the potential difference between the first and second pairs of potential electrodes to maintain the potential difference substantially equal to zero; and   .[.f.]. .Iadd.g. .Iaddend.means for measuring the potential proximate to the potential monitoring electrodes and the current emitted from the central electrode and to provide output signals representative of the resistivity at different lateral distances from the borehole wall.   
     
     
       7. The apparatus of claim 6 wherein the means for producing currents at frequencies f 1  and f 2  comprise: a. a current amplifier, the output of the amplifier being coupled between the first and second pairs of current electrodes and having an output impedance substantially equal to zero at the frequency f 2  ;   b. a source of alternating current of frequency f 1  coupled to the input of the current amplifier; and   c. a source of alternating current of frequency f 2  coupled betwen the second pair of current electrodes and a point at a substantial electrical distance from the plurality of electrodes.   
     
     
       8. The apparatus of claim 7 wherein the sources of alternating current of frequencies f 1  and f 2  each comprise a variable gain amplifier allowing an adjustment of the amplitude of the said currents. 
     
     
       9. The apparatus of claim 8 wherein said sources of alternating current of frequencies f 1  and f 2  are synchronized. 
     
     
       10. The apparatus of claim 6 wherein the means for maintaining the impedance of frequency f 2  between the first and second pairs of current electrodes substantially equal to zero, comprises: a. a third pair of electrodes positioned between said first and second pairs of current emitting electrodes; and   b. a current amplifier means having an input coupled between the second pair of current emitting electrodes and the third pair of electrodes and an output coupled between the first and second pairs of current emitting electrodes, the amplifier means being adapted to supply current at frequency f 2  to the formation in response to a potential difference at frequency f 2  measured between the second pair of current emitting electrodes and the third pair of electrodes to maintain the potential difference between the first and second pairs of current emitting electrodes at frequency f 2  substantially equal to zero.   
     
     
       11. The apparatus of claim 6 further comprising: a. means coupled to said current and voltage measuring means adapted to separate the measured currents and voltages into components at frequencies f 1  and f 2  and to provide signals representative of the current and voltage at frequencies f 1  and f 2  ;   b. means adapted to receive the current and voltage signals at frequency f 1  and to provide a first output signal representative of the resistivity of a first zone in the formation; and   c. means adapted to receive the current and voltage signals at frequency f 2  and to provide a second output signal representative of the resistivity of a second zone in the formation.   
     
     
       12. The apparatus of claim 11 further comprising means adapted to receive said first and second output signals for recording said first and second output signals as a function of depth. 
     
     
       13. The apparatus of claim 12 wherein one of the input terminals of the said voltage measuring means is connected to the electrodes of the second pair of electrodes. 
     
     
       14. The apparatus of claim 11 wherein the means adapted to separate the measured current and voltage signals comprise: a. two frequency modulators, the input of one coupled to the output of the voltage measuring means and the input of the other coupled to the output of the current measuring means and operating respectively at frequencies f 3  and f 4  ;   b. two filters coupled respectively to the outputs of the modulators, one filter adapted to pass the signals of frequency f 3  and the other filter adapted to pass the signals of frequency f 4  ; and   c. two demodulators coupled to the outputs of the filters adapted to demodulate the signals at frequencies f 3  and f 4 .   
     
     
       15. The apparatus of claim 11 further comprising means adapted to receive said current and voltage signals at frequency f 1  and to produce a first error signal representative of the difference between the product of the voltage multiplied by the current and voltage signals at frequency f 2  and to produce a second error signal representative of the difference between the product of the voltage multiplied by the current and a reference value, said first and second error signals being supplied respectively to the sources of alternating current of frequencies f 1  and f 2  to control the gain of the output of said sources so as to keep the product of the current and voltage constant. .Iadd. 
     
     
       16.  An apparatus according to claim 1, wherein said means for producing an alternating current at frequency f 1  is coupled between said third and fourth pairs of electrodes, said means for producing an alternating current at frequency f 2  is coupled between one of the third and fourth pairs of electrodes and the electrode at electrical infinity and said third and fourth pairs of electrodes are coupled with a relatively low impedance at f 2  and a relatively high impedance at f 1 . .Iaddend..Iadd.17. An apparatus according to claim 16, in which said third and fourth pairs of electrodes are coupled by frequency dependent circuit means. .Iaddend. .Iadd.18. An apparatus according to claim 17, in which said means for producing an alternating current at frequency f 1  includes an output coupled between said third and fourth pairs of electrodes, said output circuit comprising said frequency dependent circuit means and having a relatively high impedance at frequency f 1   
     
     
        and a relatively low impedance at frequency f 2 . .Iaddend. .Iadd.19. An apparatus according to claim 17, in which said frequency dependent circuit means also couples said means for producing an alternating current at said first frequency between said third and fourth pairs of electrodes. .Iaddend. .Iadd.20. An apparatus according to claim 6, in which said means for maintaining the impedance between the first and second pairs of current emitting electrodes at frequency f 2  substantially equal to zero comprises frequency dependent circuit means having substantially zero impedance at frequency f 2 . .Iaddend. .Iadd.21. An apparatus according to claim 20, in which said frequency dependent circuit means has substantial impedance at frequency f 1 . .Iaddend. .Iadd.22. An apparatus according to claim 20, in which said means for producing a current at frequency f 1  includes an output circuit coupled between said first and second pairs of current emitting electrodes, said output circuit comprising said frequency dependent circuit means and having a relatively high impedance at frequency f 1  and a relatively low impedance at frequency f 2 . .Iaddend.