1036 



EXPLORATION GEOPHYSICS 



boundaries will still be rounded and indefinite, and the apparent resistivity measured 

 will be dependent on the distance of the device from the formation boundaries.* 



The Limestone Sonde. — For the purpose of obtaining clearer and simpler logs in 

 hard formations, the limestone or hard formation sonde was devised according to the 

 scheme indicated in Figure 641. Four current electrodes, A and A', B and B', connected 

 as shown in the figure by means of insulated wires of negligible resistance, are arranged 

 so the AB =z A'B', and a measuring electrode M is placed in the middle of the device. 



The system being symmetrical, depths are 



Generator 



measured from the middle electrode M. 

 The arrangement behaves as a sym- 

 metrical combination of two three- 

 electrode sondes, which can be either two 

 normal or two lateral sondes, depending 

 on the relative lengths of AA' and BB'. 

 In practice an arrangement is used in 

 which AM = A'M = 20" and AB = 

 A'B' ■= 4" and which therefore corre- 

 sponds to a lateral combination. 



If, as in the upper part of Figure 

 642, this device is located opposite a 

 thick, highly-resistive layer, the flow of 

 current is confined entirely to the space 

 in the hole between electrodes A and B 

 and between electrodes A' and B'. In 

 this case no current flows from B or B', 

 up or down the hole away from the de- 

 vice. It follows from Ohm's law that B 

 and B' are at the same potential as any 

 point at a great distance from the device, 

 which is zero potential. Similarly, M is 

 at the same potential as A and A', since 

 no current flows in the space between A 

 and A'. 



The potential of electrode M is 

 therefore equal to the potential differ- 

 ence between electrodes A and B {or A' 

 and B'), and this is in turn equal to the 

 potential drop in the mud due to the flow 

 of current between A and B (or A' and 

 B'). As long as all the electrodes of the 

 device are opposite the hard, more resis- 

 tant formation, this potential difference 

 is dependent only on the hole size and the mud resistivity : if these are constant along 

 the hard formation, a constant apparent resistivity is recorded. 



If, on the other hand, as indicated in the lower part of the figure, the device is 

 located just above a conductive streak, the presence of the streak has the same effect 

 as a low resistance connecting adjacent portions of the device to points at zero potential. 

 Part of the current now flows in the paths indicated by the arrows, and the potential of 

 electrode M is correspondingly decreased. The presence of the conductive streak is thus 

 indicated by a relatively sharp, symmetrical depression on the apparent resistivity curve. 



* An interesting special case is the instance when the hole has been drilled into a resistive 

 formation, such as a salt bed, but has not completely penetrated it. In this case practically all the 

 current flows up the hole from the current electrode, and nearly none in a downward direction. A 

 lateral with A above M and N would give a practically zero reading in the formation, whereas a 

 normal with M and N above A would give a high reading corresponding to the potential drop in the 

 mud between electrodes M and A^. 



Fig. 641. — Electrode arrangement for logging 

 the more resistive or hard formations. 



