MiniRes manual, 30 July 2006
One of the most disconcerting events that occurs while taking resistivity measurements is to obtain negative resistance readings. Negative resistance readings should ALWAYS be examined with suspicion. A negative resistance reading should cause every bell and whistle to go off. It is possible, although extremely unlikely, that negative resistance readings can represent the true electrical response of a particular location. But that situation can ONLY arise under extreme conditions of 3 dimensionality and associated high contrast in subsurface resistivity distribution. It is unlikely that an operator will EVER measure a true negative resistance subsurface.
The vast majority of negative resistance measurements
are associated with two causes, instrument
is the cause of the negative resistance readings are:
1)
2)
There are several tests and behaviors that determine
whether the
a)
b) . Good field procedure
mandates that each electrode's contact resistance be minimized as much as
practical.with
water
c)
In general, the reciprocity theorem states that a perfect constant current generator applied to any two nodes (the transmitter ports) of any complicated linear circuit network (example: the earth and the electrodes and cable connections to it) may produce a voltage at any other two nodes (anywhere in the network - the receiver ports). The complex ratio of the receiver voltage to the transmitter current is the complex impedance of that network and those two ports. The reciprocity theorem states that if the positions of the constant current generator and the voltage receiver are swapped then the new complex ratio (impedance) of this new reciprocal configuration will be identical to the original. This theorem holds for the complex case, both RESISTIVITY and IP readings should be identical under normal or reciprocal configurations.
The reason that the reciprocity test is so effective is because it tests the validity of the assumption of the "perfect" constant current generator and the "perfect" receiver. When the transmitter electrodes are swapped for the receiver electrodes the transmitter and receiver are presented with, typically, different loading characteristics. If the transmitter is not capable of outputting an exactly equal amount of current with the new loading characteristics then the measured value in the reciprocal mode will be different. Likewise, if the receiver presents a different amount of "loading" in the reciprocal mode then the measured value will be different.
The reciprocity test senses several types of instrument and field procedure problems.
1) Instability of the transmitter's constant current generator under varying load conditions 2) Too low of an input impedance on the receiver's input 3) Too high (or low) of electrode contact resistance for the transmitter to maintain a constant current output 4) Too high of a receiver electrode resistance - causing the receiver's input impedance to load the reading - causing the measured reading to be lower than it should be 5) The infamous "cable reel" problem will exhibit its nature during the reciprocity test, especially if the configuration of the receiver reels is quite different from the configuration of the transmitter reels 6) The nested-bridge error condition (see below) may show up also, depending on the specific values in the individuals legs of each of the two nested bridges
1) Inability of the transmitter current generator to maintain a proper constant current 2) Too low of an input impedance on the receiver 3) Electrical leakage internal to the instrument 4) Nested-Bridge error condition described below
Model assumptions:
1) faceplate is the voltage reference, by definition zero volts
2) the leakage resistance of each receiver and transmitter terminal to the faceplate is 1 Gigaohm (1000 Megohms). This 1 Gigaohm value is reasonable and realistic, however, it is NOT realistic that all four leakage resistances be equal, but we assume so for the benefit of analysis of this model. The leakage can realistically be much better or worse than this value depending on the temperature, humidity, cleanliness of the binding posts' insulators and the type of material used for the binding post insulator.
3a) the contact resistance between the transmitter's C+ electrode and ground is 100 ohms
3b) the contact resistance between the transmitter's C- electrode and ground is 20 Kohms
4) the contact resistance between the receiver's P+ electrode and ground is 100 ohms
4a) the contact resistance between the receiver's P- electrode and ground is 10 Kohms
5) the earth's resistivity for this model is zero - it is a perfect conductor
6) the transmitter's constant current generator is outputting exactly 10 milliamps = 0.01 amps
7) assume that the receiver's input impedance is infinite, not loading the receiver's signal
8) The transmitter's 0.01A constant current generator will develop about 200 volts across the transmitter's output terminals (20 Kohms/.01Amp = 200 volts)
9) The 100 ohm and 20 Kohm transmitter electrode contact resistances will act as a voltage divider resulting in about +100 volts (with respect to the faceplate) between the faceplate and ground
10) The receiver's P- electrode contact resistance of 10 Kohm and its leakage resistance to the faceplate of 1 Gigaohm acts as a voltage divider resulting in a voltage of +99.999 volts at the P- terminal with respect to the faceplate
11) The receiver's P+ electrode contact resistance of 100 ohms and its leakage resistance to the faceplate of 1 Gigaohm acts as a voltage divider resulting in a voltage of about +100 volts at the P+ terminal with respect to the faceplate
12) The differential voltage between the P+ and P- terminals is +100-99.999 volts = +1 millivolt.
13) This +1 millivolt error voltage will create a error resistance reading of +0.1 ohms (+0.001volt/0.01A = +0.1 ohms)
14) If the transmitter and receiver electrode contact resistances are swapped then the same exercise can be carried out and the results would show a NEGATIVE error of -0.1 ohms
So, it is clear that this simple model can produce a negative resistance component of -0.1 ohms. This error would, normally, add itself to the "true" resistance reading. So, for example, if the "true" resistance reading of a particular array configuration was +0.045 ohms then the actual reading with the error would be +0.045 - 0.1 = -0.055 ohms and the operator, likely, would be perplexed by this NEGATIVE reading.
It is instructive to redraw the above electrical model in the form of two electrical bridges, with one inside of the other. This can be referred to as a NESTED BRIDGE electrical model. This makes it more clear that this complex response of the resistivity meter to leakages and contact resistances is a "balancing act" with characteristics of the common "bridge" circuit, but complicated by being "nested". This simple model explains several befuddling and mysterious aspects of resisitivity measurements:
A) The +1 millivolt error voltage described above can be reduced by DECREASING the value of either or both of the larger receiver or transmitter contact resistances
B) More, seemingly mysterious, is the fact that the + 1 millivolt error voltage can also be decreased by INCREASING either or both of the 100 ohm receiver or transmitter contact resistances, thus bringing the bridges more into balance
C) Also, it should be clear that the binding-post-to-faceplate leakage resistances can also be manipulated to increase or decrease the error voltage
D) It should be clear that this error voltage of +1 millivolt is of little consequence (a small percentage of the total "true" voltage) if the earth's resisitivity is very high and/or the Wenner Array "a" spacing is small. In other words, if the true earth resistance measurement is 15.000 ohms then this +1 millivolt error will only represent a 0.7% error.
E) That implies that this error becomes a greater problem as the earth's resistivity decreases and/or the Wenner Array "a" spacing increases. The problem may always be there, but it will become a greater percentage of the total as the "true" resistance measurement becomes smaller
F) Note that it is possible that varying ANY one of the leakage resistances or contact resistance may drastically change the error voltage. For example, if ONLY the transmitter contact resistances had been matched in the above model so that they were both 10 Kohms or both 100 ohms then the faceplate to ground voltage would be 0 volts and the imbalance of the receiver's contact resistances would be immaterial, there would be NO error voltage. Likewise, a balance of the receiver's electrode contact resistances would cause a high COMMON mode voltage but a zero DIFFERENTIAL voltage and there, again, would be NO error voltage.
G) On the other hand, it should be clear than an imbalance in any one of the legs of the nested bridge can be compensated by a counteracting imbalance in another leg of the nested bridge - another one of the befuddling mysteries explained with this simple model.
H) One of the key unusual characteristics of this "mysterious" situation is the fact that the error voltage is proportional to the VOLTAGE at the transmitter's binding post, and, typically, that voltage is very unstable and noisy. The reason for the noise and instability of the transmitter's output voltage is because, although the output current is precisely regulated, noise free and stable, the transmitter's two electrode contact resistances can change quite drastically with time, and as those contact resistances change, the transmitter's output voltage changes, and, therefore, the error voltage changes proportionately also. This is in distinct contrast to what is EXPECTED of a resistivity meter - that the response of the instrument is proportional to the CURRENT output of the transmitter - NOT the voltage output.
WIth this general understanding of this error phenomenon the question arises, how is it recognized and how is it ameliorated? The ideal situation is to have extremely LARGE leakage resistances from the binding posts to the faceplate - the higher the better. In the limiting condition of infinite leakage resistances from the binding posts to the faceplate this model indicates that the error voltage will disappear. Likewise, the ideal situation is to have extremely LOW electrode contact resistances. Again, in the limiting condition of zero resistance for each electrode contact resistance, the model indicates that the error voltage will disappear.
In practice these behaviors suggest that the binding posts' insulators should always be clean and free from moisture and that each electrode's contact resistance should be minimized. It also shows that a standard Wenner Array will have smaller percentage errors than a Schlumberger Array under identical conditions of contact resistances and leakage resistances - in this respect the Wenner Array is clearly superior.
A few ways to recognize this condition in the field is to reduce the electrode resistance (by pushing each electrode deeper into the ground) and look for a significant variation in the meter reading after adjusting each electrode. The NESTED BRIDGE model indicates that the meter reading may either increase or decrease by pushing any one electrode deeper in the ground - it depends on the particular imbalance that exists within the nested bridge.
Another way to test for the nested-bridge error condition is to add a resistance into one or more legs of the bridge and see if it unbalances or balances the bridge and, therefore, changes the resistance reading. This is NOT proof-positive of the nested-bridge error condition because other problems can create variations in readings when resistances are put in series with the electrodes.
Although this model is simplistic it is, nonetheless, true that EVERY resistivity meter and EVERY array setup will ALWAYS experience an error (however slight) from this situation. However, that error can be made negligible by:
1) Minimizing all electrode contact resistances
2) Maximizing all leakage resistances
3) Designing the resistivity array to measure a larger proportion of the voltage drop created by the transmitter current (hence, a Wenner Array will suffer less than a Schlumberger Array)
4) In the extremely unlikely event that it is too difficult to reduce all of the contact resistances sufficiently, then an attempt may be made to balance one or another of the legs of the bridges by INCREASING the contact resistances by pulling it out so that it is not so deeply in the ground.
The model presented above was simple, it only showed the zero resistance ground and the faceplate. In reality, every piece of conductor on the printed circuit board acts as a small "faceplate" and there is leakage between electronic components in the receiver and transmitter that make the model much more complicated. Significant design effort was expended on the MiniRes in order to minimize those leakage currents. The lowest leakage optical couplers were chosen for communication between the transmitter and receiver and the DC-DC converter was specifically chosen for its low leakage specifications. The printed circuit board itself has slots designed in to maximize the path length of leakage currents from the transmitter to the receiver greatly increasing the value of the leakage resistance between the transmitter and receiver |

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