CA2082046A1 - Apparatus and method for assessing the geophysical characteristics of a core sample - Google Patents

Abstract

Apparatus for assessing geophysical characteristics by measuring resistivity of a core sample comprises a first array (C1) of current electrodes, a second array (C2) of current electrodes, a constant current source and sink to pass constant current between the electrodes in the arrays (C1, C2), control means supplying substantially equal currents at each of the electrodes and second control means to ensure that the current received by the electrodes (C2) is substantially equally distributed between them. The illustrative apparatus further comprises a third array (P1-64) of potential electrodes adapted to be positioned at spaced intervals on a sample to be assessed. Computer records the results and controls operation of the illustrative apparatus.

Description

W091/17437 PCT/GB91!00721 2~8204~
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APPARATUS ~ND METHOD FOR ASSESSING THE GEOPHYSICAL
CHARACTERISTICS OF A CORE SAMPLE

This invention is concerned with improvements in or relating to an apparatus and method suitable for use in assessing geophysical characteristics of a core sample.

Resistivity measurement has become an established technique for mapping features under the earth's suxface and equi~ment is mass produced for this purpose, for uqe "in the fieldll where the geometry of the area does not impose any restriction, see for example our copending Patent Application No. 8924934.6.

Recent work has been carried out taking resistivity measurements of core samples extracted from boreholes.
The size and shape of the samples render the usual testing process time-consuming and unreliable.

Resistivity is measured in the ground by passing a fixed current between two electrodes and sensing the potential difference between two points: the voltage be~ween these points will be proportional to the resistivity of the ground between them. When voltage is measured it is, in effect giving a reading for ground between lines of equi-potential that pass through the two WO91~17437 PCT/GB91/00721 2~82~4~ 2 points: these lines of equi-potential should ideally be parallel planes and equally spaced over the region under examination (assuming a homogenous material).

When a core sample is removed from the ground it usually comes out in lengths of a metre or so, with a diameter of around 10 cm. This is then transported to a rock laboratory.

The moisture content of the samples has to be preserved, and so it is cut into lengths of about 20 -cm, covered in aluminium foil, dipped in wax and stored in a cold room.

The lengths of the samples are dictated by practical factors such as natural breaks during transit and the maximum size that can be easily handled and fit in a wax bath.

Using the known approach, the current distribution in the core sample becomes relevant. Practically, a length of core sample equal to the diameter of the core cannot be used at either end of the sample because the current flow in that region is not parallel (see Figure l); thus approximately 20 cm of every core sample is not useable and for samples less than 20 cm in length no useful information can be gathered.

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WO91/17437 PC~/GB91!00721 20~20~

The cost of drilling out core samples is hundreds of pounds per metre, and so it is desirable to make use of as much of each individual sample as possible. To do this the current would have to become parallel nearer to the ends.

The applicants have discovered that considerable improvement can be achieved using a multi-electrode current source. However it is not possible to use simple approaches, for example a disc electrode, or many electrodes connected to one terminal of a conventional current source since variations in contact resistance result in uneven and unpredictable current distribution.

One of the various objects of the present invention is to provide an improved apparatus suitable for use in assessing geophysical characteristics of a core sample.

Another of the various objects of the present invention is to provide an improved method of measuring geophysical characteristics of a core sample.

The invention provides in one of its various aspects apparatus suitable for use in assessing the geophysical characteristics of a core sample comprising a first array of first current electrodes, a second array of second current electrodes, a constant current circuit adapted, :

WO91/17437 PCT/~B91/00721 2082~

in use, to pass a constant current between the electrodes of said first and second arrays and co~prising first control means adapted to supply substantially equal current to each of said first electrodes and second control means adapted to ensure that the current received by the second array is substantially equally distributed between each of saî~i second electrodes, the apparatus further comprising a third array of third potential electrodes which, in use, are positioned at spaced positionS on a sample to be assessed and means for measuring the potential of the third electrodes.

The invention provides in another of its various aspects a method for assessing the geophysical characteristics of a core sample comprising positionlng a first array of first electrodes spaced from one another on a first region of the sample, positioning a second array of second electrodes spaced from one another on a second region of the sample generally at the opposite side of the sample to the first region, positioning a third array of third electrodes at known spaced positions on a third region of the sample, passing a constant elec~rical current through the sample from the first array to the second array, each of the first electrodes supplying substantially equal currents and each of the second electrodes receiving substantially equal currents, and determining th0 potential at each third electrode.

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WO91/17437 PC~/GB91/00721 2~2~4~

The use of standard equipment to measure resistivity is found to be quite time consuming which is undesirable not only for conventional reasons but also as it is detrimental to core samples which tand to dry out while not sealed. The potential measuring electxodes furthermore had to be placed in a sample, position recorded, and readings taken and recorded by hand. Data obtained was thus sparse in relation to time and effort involved.

Apparatus in accoxdance with the in~ention therefore utilises an array of potential measuring third electrodes and preferably comprises support mounting the potential measuring electrodes equally spaced one from the next;
individual electrodes are then preferably multiplexed to known voltage measuring circuits. Once the position of the support is recorded, the positions of the individual electrodes are at known positions.

Preferably apparatus in accordance with the invention further comprises computer means, for example a portable microcomputer, to read and store potential measurements and also to carry out any necessary control functions; the location of the electrode suppor~ can be entered using this arrangement ~ia the computer keyboard and the computer means can control the multiplex arrangement and store data recorded on a disc to be '' , ' ' ~ . '; ' ' . ' ' '' ' ' ', ' ' ' '' ~ . . , ' . ' ~'. ' ' "' , ' ' " ~
' WO91t17437 PCT/GB91/00721 2082~ 6 processed later. Preferably all electrode voltages are meacured relative to the same reference point, for example earth, so that data will be in the form of a potential field. Resistivity cannot be melasured using continuous D.C. in only one direction because of both polarisation and voltaic effects between the potential electrodes and the surface of the sample; switched direction D.C. is therefore preferably used, see Figure 3.

A typical potential wave form between first and second arrays Cl and C2 of current electrodes is shown in Figure 3b. The rise and fall shapes are due to electro-chemical effects. Similar processes cause a drifting D.C.
potential between Pl and P2 which is always present, Ref.
2. The use of switched D.C. means that the 'signal' voltage can be easily extracted from this back ground level.

Filter circuits to convert this type of signal into a form suitable for analog~le to digital conversion are already known.

In appara~us in accordance ~ith the invention the current source must operate such that the desired overall current passes between the curren~ electrodes and this current must be stable and constant. However it is not .. . . .
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WO9l/17437 PCT/CB91/00721 2~2~

essential that each individual electrode pass precisely the same current (although this is of course desira~le).
The size of the current is not important as such provided that it produces sufficiently large voltages to be measured but does not saturate the current source. There is room for error between nominal and actual current but once the actual value has been measured it must remain constant.

Various methods providing a substantially constant current at each individual slectrode may be used, for exampie individual constant currents sources and sinks for each individual electrode each having the necessary accuracy to provide the overall accuracy re~uired for the total current - however this is an extremely expensive option and unnecessary because only the total curren~
through the core sample must be carefully controlled. An alternative is current division (accepting minor variations in current from electrode to electrode) - the point at which measurements become possible on a core sample will hardl~ be affected by this provided total current flow is constant. Transistors might be usable but difficulty arising in selecting transistors with suffici~ntly good matching in ~he necessary current range.

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WO91/17437 PC~/GB91/00721 2~82~ 8 A preferred method provides a current source and sink of a simi.lar type provided for the overall current control, for each current alectrode. ~n adva.ntage of such a circuit is ~hat because each current elecl:rode has its own high gain operational amplifier with chain feedback, virtually any transistor (even ones of different types in some circumstances) might be used. A current sink on this principle is shown in Figure 4.

The. same reference voltage, Vref~, is fed to each electrode circuit, and if the Rf' resistors are 0.1%
tolerance which are reasonably cheap, the output currents must be very similar. If the op-amps are assumed to be ideal then by inspection, Rf'Io/N - Vref-Vref' where Vref-Vref~ is identical for each electrode. Thus the spread of Io/N will be the same magnitude as the spread of Rf'.

The use of individual feedback for each electrode also overcomes the early intercept voltage problem, which could be significant where the load has such vari~tion in contact resistance and electro-chemical effects.

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W091/17437 PCT/GB91/0~721 208204 b~

The total current is exactly the same as for one current source using a precision voltage reference and Rf resi~tor because as far as the overall circuit is concerned, all the electrode current sources together act just the same as one transistor.

The main advantage of this circuit is of course that one precision reference voltage and resistor, control the current through all electrodes and the splitting circuit uses cheap components, but still provides acceptable matching.

The circuit of Figure 4 is in fact a current sink, however, it can be transposed to act as a current source, working in the positive half of the voltage supply for the final multi-electrode sink-source circuit.

Obviously the sink and source would have to be as closely matched as possible, but perfect matching is very difficult.

In a preferred apparatus the current sink is made to match the current source by using feedback and error detection. To this end, the core sample is preferably provided with an earth electrode fitted to the current . . .
, ' WO91/17437 PCT~GB91/00721 ~0~20~

sink. Any error in matching produces a current to or from earth which is sensed and used to control the current sink (see Figure 5).

Ideally, in the steady state Ierror=O and so Ve=O.
The ou~put of Al has assumed a level such that (Vref'/Rf') x N = Is.

Assu~e now that the current sink starts to take too little current. The current source is still sending out its fixed current and so the excess flows to earth. The current has to flow through Re and if this is large, say lMQ, then a sizeable voltage across it is produced. The direction of this voltage sends the output of Al upwards.
This turns the current sink harder on, negating the initial drop in current and therefore reducing the error current to earth. -Similarly, if the circuit begins to sink too much current its drive is reduced by the action of the feedback.

Again, as with the current source, cheap components which provide quite acceptable matching can be used, while the total current is kept accurate by making Ierror approach zero.

2082~
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If Re is IMQ and a moderate performance op-amp is used where Vos =lOmV then Ierror = lOmV/lMQ = lOnA.

The major source of error is the input bias currents of the op-amp, say lOOnA.

The constan~ current through ~he load is likely to be over lmA, this produces an overall error due to current leakage of (llOnA/lmA) x 100~ = O.011%

Conveniently the support for the potential electrodes is arranged to contain 64 electrodes (although more may be used if desired); suitably these are arranged in a 4 x 16 grid. In the case of the large grid it is simpler to measure the voltage at each electrode with reference to a common point for example earth; voltage between any two electrodes can ~hen be calculated la*er using Kirchoff's laws. Only one multiplexor may therefore be required to send signals to the analogue signal processing circuit (see Figure 6 for example).

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20~2~'15 12 As the preferred apparatus requires alternating D.C.
current flow, a preferred apparatus comprises switching means. Any suitable switching means may be used to switch the current in direc~ions between the first and second array of current electrodes. Apparatus in accordance wi~h the invention is not liXely to require voltages exceeding + 30 volts and currents will normally be less than ~0 mA. Either relays or analogue switches can be used without difficulty: the switching frequency is likely to be a few hundred Hertz - slower switching will increase time taXen to carry out measurementc~
excessively. Analogue switches (which do not suffer from contact bounce) are preferred at this frequency and also because they can be switched directly.

A preferred apparatus also comprises circuits monitoring each electrode. It is possible for an individual first or second electrode to fall from the core sample or to make poor contact. Preferably current is monitored through each electrode, suitably by monitoriny the voltage across each Rf' resistor (see Figure 4); should any electrodes fail the same total current will still flow but remaining electrodes will carry a larger current. A suitable monitor circuit is shown in Figure 7 using a multiplexor: when any address i .
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W0~1/17437 PC~B91!00721 13 - 2~82046 is sent to t.he circuit it outputs the Rf' voltages for the appropriate electrodes of the same source onto separate output channels.

A preferred apparatus comprises digit:al lines for the D.C. switching, potential electrode multiplexing, current source monitor and the analogue signal multiplexing. All of the chips for the relevant functions are available with latching inputs controlled by a wR
line. This means that the number of digital lines required is that for the largest address (AO-A5 for 64-l multiplexor) plus decode lines for the various wR~s. The circuits which handle the analogue signal processing also require a few digital lines.

The preferred computer has a digital I/O card with 3 x 8 input/output blocks which can all be outputs, so there is no shortage of available lines.

There now follows a detailed description to be read with reference to the accompanying drawings of apparatus suitable for use in a assessing geophysical charac~eristics and a method of using the apparatus. It will be realised that this apparatus has been selected for description to illustrate the invention by way of example.

WO91/17437 PCT/GB91/0~721 2 0~2 ~ 4~ 14 In the accompanying drawings:-Figure l is a diagrammatic view showing the use ofsingle current electrodes to investigate a core sample;

Figure 2 is a diagrammatic view showing multiple electrodes; ~.`

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Figure 3 is a diagrammatic view showing various D.C.
switching wave forms;

Figure 4 is a circuit diagram showing a current sink;

Figure 5 is a circuit diagram of a self balancing current sink;

Figure 6 is a diagrammatic view of a multiplexor circuit for use in monitoring potential electrodes of apparatus ernbodying the invention;

Figure 7 is a diagrammatic view of a circuit for monitoring current electrodes;

Figure 8 is a block diagram of the circuitry of the illustrative apparatus;

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Figure 9 is a circuit diagram of a current sink of the illustrative apparatus;

Figure 10 is a circuit diagram of a current source of the illustrative apparatus;

Figure 11 is a diagrammatic view of a first experimental core test;

Figure 12 is a diagrammatic showing an alternative arrangement of electrodes;

Figure 13 is an oscillocope trace showing voltages between various electrodes in the use of the illustrative apparatus; and Figure 14 is a view showing a swtiching circuit of the illustrative apparatus.

The illustrative apparatus comprises a cur~ent source and sink, first and second arrays of first and second current electrodes, each comprising seven electrodes, a support for third potential electrodes namely a potential pad/ and other circuits as outlined above.

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2~820~ -The potential pad is cQnstructed from pcb test point probes se~ into a piece of vero board at 0.2'l spacing (i.e. every other hole) and potted up. The potential electrodes are connected in sets of eight via ribbon cable to the multiplexing board.

Alternatively, single ribbon cable with ~uro card type connector and purpose build pcb could be used. There are preferably seven electrodes in each of the first and second arrays, in each case six of the electrodes being arranged at the apices of a hexagon with the seventh at a central region of the hexagon. In use of the apparatus the first array of electrodes is posit.ioned in contact with one end face of the cylindrical core sample and the other array of electrodes at the opposite end face.

In the preferred current source and sink the reference voltage is provided by a lN827 6.2V temperature compensated zen~r diode. The break down voltage is extremely stable at lO ppm/C. The absolute accuracy is 5%. A lmA constant current FET J505, is used to minimise effects from variation in supply voltage and a 4.7nF
capacitor put across the zener diode to smooth out high frequency noise.

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WO91/17437 PCT/GB91/0072l 2082~4~

The op-amps providing overall control should be of fairly high quality with a low offset voltage and an 1~301 was chosen. The other op-amps can be of a lower standard as long as their bias currents do not become significant compared with the current controlled by them, or their offset voltages significant compared to the volt drop across the Rf' resistors. 741 op-amps were chosen due to their ready availability and cost.

The transistors used are VN46AF VMOS transistors which can handle up to 2A and 15W. It might be expected that if the sink circui~ uses N channel FETs then the source circuit, being as it were a reflection, would use P channel FETs. However, discrete P channel enhancement mode transistors are fairly scarce compared to N channel ones and to avoid any future complications, the source is modified to work with N channel devices. This is simply achieved by swapping connections to the + and - terminals of each op-amp controlling a source ~ransistor.

The choice of Rf and Rf~ depends on the current required. Initial tests were to be carried out passing current through a vessel of saturated sand, and 5-lO mA
is suitable for ~his medium, thus Rf = 6.2V/6.2mA = lKQ

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2082~4~ -If Rf' = Rf then each Rf~ drops .
Vrf' - Vrf/No electrodes.

For seven elec~rodes, Vrf' = 6.2/7 = 0.86 V.
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This voltage is very much greater than the offset voltage for 741 op-amps, and in itself would only give rise to a mall spread in current between electrodes.
Thus for seven electrodes it is convenient to put Rf' =
Rf. Of course Rf is O.Ol~ and Rf' is O.l~ tolerance for a final circuit, so they are only equa} in nominal magnitude.

All the other circuits comprise analogue switches and multiplexors.

The D.C. switching circuit (Figure l4) must be able to pass a fairly large current in terms of analogue i switches, which in general are used to feed voltage signals into high impedance loads.

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'. ' ~ ,~ : '',,, ' ,' ,': , :, , ' ., - , ' '~ : ' ' ' " ,,, W09~/17437 PCr/GB91/00721 2~2~6 i The ADG221KB is a suitable chip, it has a latching input, and contains 4 SPST switches. This means that one chip can be used to do the switchiny for one electrode pad. The chip can switch up to 30mA continuous D.C. at 44V, and is therefore within the demands.

The other multiplexors used are four 16-1 and three 8-1.

The criteria for choosing the chips was restricted by the voltage that they could work up to. The supply might ~e between + lOV to + 30V. The chips selec~ed are DG 526 DJ 16-1 multiplexor and the DG 528 CJ 8-l multiplexor.

In the current sink and source circuits it is important to ensure that the primary operational amplifier (LM301 in Figure 10) is sufficiently slow that correcting action of the other operational amplifiers (741 in Figures 9 and 10) is virtually instantaneous compared to the change in the primary operational amplifiers.

D.C. switching circuit of the illustra~ive apparatus was controlled using a TTL signal generator; the output square wave was passed through an invertor and both levels spread to control lines.

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W091J17437 PCT/GB9llO0721 2 ~2 ~L~ 20 Using the circui~ shown in Fiqures 9 and 10 overall current flow was set to about 6 mA using a lKQ ~f' resistors and ~f resistors. Results were as ~Eollows:-I(mA) I(mA) Cl 1 0.87~ C2 1 -0.880 2 0.872 2 -0.878 3 0.876 ;3 -0.877 4 0.878 4 -0.872 0.876 5 -0.876 6 0.873 6 -0.872 7 0.877 7 -0.876 __ 6.130 6.131 Spread from 0.880 to 0.872 = 0.917%
(Ignoring C21 the spread is 0.688%) Ierror = 32.9nA (32.9mV across l.OOMQ
Ierror is 0.00054% of C1 or C2 The tes~ was carried out using saturated sand as a load. Ierror was calculated by measuring the volt drop across a l~Q resistor placed in series with the electrode because the current i5 too small to measure directly on normal equipment.

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WO91/17437 PC~/GB91/00721 ~0820~

The measurements were taken with a 3~ d;git DVM.

The current distribution is within the ~olerance of the Rf~ resistors at under 1%. The sum of the Cl and C2 electrodes is same to within l part in 6000. The difference is most likely due to the inaccuracy of the last digit on DVMs. The error current which will in fact be the real difference between Cl and C2 gives rise to a missmatch of 5.4 ppm.

The matching between electrodes on the same side is quite acceptable, and the matching between Cl and C2 is very good indeed. To get similar matching using separate sources would require very well matched components indeed and would be very expensive. The l~ resistors used for this test cost 2p each.

In carrying out an illustrative method the firs~ and second arrays Cl, C2 of current electrodes were pushed into the ends of a cylindrical core sample in the hexagonal arrangement referred to abo~e and the potential electrode pad held in place. Electrode selection was achieved by using the multiplexor under the control of computer means which also operate~ the D.C. switching operation. Outputs from each potential electrode were recorded by the computer.

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W091/17437 PCT/GB91!0072]

20~34~ 22 A test on a core sample using a single position of the pad was carried out. Visual inspection of the site before hand showed a fine crack as in Figure 11.

The voltage field as measured directly shows the crack to some extent but since the voltage drops consistently along the core it is not obvious. The image can be enhanced by taking initial and final values of voltage along the core and using the straight line equation y = mx ~ c between these points. Thus deviations of the potential field from its ideal linear path are plotted in the Suppressed Gradient map.

However, it is the elec~ric field or potential gradient that is actually proportional to resistivity.

The component of electric field along the core can be obtained by taking the difference between successive readings. The resulting map clearly shows the small crack in an otherwise fairly uniform f.ield.

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,' '' ~' ' ~' ,' :: . -' WO91t17437 PCT/GB91/00721 2~820~6 ~ following test was carried out using multiple adjacent positionings of the electrode pad to cover a larger area (one of apparent uniformity). The same maps were produced for this test as the first.

The resulting plots show an overall backyround level with a feature running across near ~he middle. Th~s is probably hair line cracks which have occurred in transit or are due to drying out during testing.

One further test was carried out: the measurement was taken on the end of the core, see Figure 1~, and therefore measures horizontal rather than vertical resisti.vity. This test has the potential to show the orientation of the fabric of the core.

The various plots show the expected features and the visible crack in the first test is readily identifiable.

The horizontal test shows roughly parallel lines of potential as would be expected from a uniform current.
This makes interpretation a lot easier and could not be achieved with a two electrode current source whatever the length of the core.

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, W09ltl7437 PCT/GB91!00721 2~82~ 24 The cost and complexity of the system has been kept to a minimum without compromising its accuracy or stability, largely due to the use of current division and matching in the current sink-source by means of op-amp circuits employing feedback. The resulting current sink-source can, in principle, be extended to have any number of outputs which, while maintaining individual matching and balance overall, still use a single voltage and resistance raference.

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Claims (21)

1. Apparatus suitable for use in assessing the geophysical characteristics of a core sample comprising a first array of first current electrodes, a second array of second current electrodes, a constant current circuit adapted, in use, to pass a constant current between the electrodes of said first and second arrays and comprising first control means adapted to supply substantially equal current to each of said first electrodes and second control means adapted to ensure that the current received by the second array is substantially equally distributed between each of said second electrodes, the apparatus further comprising a third array of third electrodes which, in use, are positioned at spaced positions on a sample to be assessed and means for measuring the potential of the third electrodes.

2. Apparatus according to Claim 1 wherein one of the third electrodes is a reference electrode in relation to which the potential of each other third electrode is determined.

3. Apparatus according to either one of Claims 1 and 2 comprising computer means by which the potential field in a sample under investigation can be mapped.

4. Apparatus according to any one of the preceding claims comprising support means mounting the third electrodes equally spaced one from the next.

5. Apparatus according to Claim 4 wherein the support means is complementary to the surface of a core sample to which the third electrodes are to be applied.

6. Apparatus according to any one of the preceding claims wherein the third electrodes comprise PCB test point probes.

7. Apparatus according to any one of the preceding claims comprising computer means connected to the third electrodes and comprising a multiplexing arrangement, the construction and arrangement being such that the potential of each third electrode is measured sequentially and stored by the computer means.

8. Apparatus according to any one of the preceding claims comprising means to periodically change the polarity of the first and second array of electrodes whereby to periodically change the direction of direct current flow through the sample.

9. Apparatus according to any one of the preceding claims comprising a constant current source and a constant current sink adapted to be connected to either the first or second array of electrodes, both the source and sink comprising a plurality of constant current circuits each adapted to be connected to an associated one of the electrodes.

10. Apparatus according to Claim 9 wherein each constant current circuit comprises a transistor, an operational amplifier having its first input connected to a first common line carrying a reference voltage and its second input connected to a first terminal of the transistor and its output connected to a control terminal of the transistor, the second terminal of the transistor being connected to the associated electrode, each circuit further comprising a resistor connected between the first terminal and a second line common to all of the circuits, each of the resistors being of substantially the same resistance.

11. Apparatus according to Claim 10 wherein the second common line is connected to the second input of a primary operational amplifier the first input of the primary amplifier being connected to a first input line providing a constant primary reference voltage and the output of the primary amplifier connected with the first common line, the second common line also being connected through a stable resistor to a second input line, the primary reference voltage being applied between the first and second input lines whereby a constant current flows in the use of the apparatus through said stable resistor.

12. Apparatus according to either Claim 10 or Claim 11 wherein each of the stable resistors, the resistors of the constant current circuit, the operational amplifiers and the, transistors respectively are substantially identical in both current source and current sink.

13. Apparatus according to Claim 12 wherein the current sink comprises a line adapted to be connected between the sample and a first input terminal of a further operational amplifier, a resistor between the first and second input terminals, and the output connected to the first common line for said constant current circuits to provide said reference voltage thereon, said second input terminal of the further operational amplifier being earthed.

14. Apparatus according to any one of Claims 9 to 13 comprising switch means adapted to connect the first array to the source and the second array to the sink and vice versa.

15. Apparatus according to any one of the preceding claims comprising means for monitoring the current flow in each electrode and signalling if any fault is detected.

16. Apparatus suitable for use in assessing geophysical properties of core samples constructed arranged and adapted to operate substantially as hereinbefore described with reference to the accompanying drawings.

17. A method for assessing the geophysical characteristics of a core sample comprising positioning a first array of first electrodes spaced from one another on a first region of the sample, positioning a second array of second electrodes spaced from one another on a second region of the sample generally at the opposite side of the sample to the first region, positioning a third array of third electrodes at known spaced positions on a third region of the sample, passing a constant electrical current through the sample from the first array to the second array, each of the first electrodes supplying substantially equal currents and each of the second electrodes receiving substantially equal currents, and determining the potential at each third electrodes.

18. A method according to Claim 17 using apparatus according to any one of Claims 1 to 16.

19. A method according to either one of Claims 17 and 18 wherein the core sample is cylindrical and the first and second arrays are respectively put into electrical contact with opposite ends of the core, respectively.

20. A method according to Claim 19 wherein each array comprises seven electrodes, six positioned substantially at apices of a hexagon with the seventh at a central region.

21. A method according to Claim 19 wherein the first and second arrays of electrodes are positioned on diametrically opposite regions of the sample and the third array of electrodes is positioned at one end of the sample.