1028 EXPLORATION GEOPHYSICS 



however, that in an actual drill hole homogeneity is departed from in several 

 ways. Factors which affect the distortion of the equipotential surfaces 

 include: (1) the existence of the hole itself filled with drilling mud, and 

 (2) the inevitable non-homogeneities in the formations, as well as (3) the 

 existence in permeable formations, of a zone next to the hole which has 

 been invaded by the mud filtrate. 



In a heteregeneous medium, then, the exploring device measures a 

 quantity which will be called "apparent resistivity" pa and which is defined 

 for a normal sonde : 



E 



Pa = 47r AM • — 



and for a lateral sonde : 



AM 'AN A£ 



p' 



a = 47 



MN I 



where, as before, / is the current between electrodes A and B, E is the 

 potential of electrode M in the case of the normal sonde, and A£ is the 

 difference of potential between electrodes M and A^" in the case of the lateral 

 sonde. 



From these definitions, if the medium surrounding the device is homo- 

 geneous and of infinite extent, the value of the apparent resistivity will 

 be equal to the resistivity of the homogeneous medium. 



The apparent resistivity is an average value involving the resistivities 

 of all the different media surrounding the electrodes and depending on the 

 arrangement and spacing of the device. When sufficient information is 

 available regarding the conditions of the measurement, it is often possible 

 to use the measured values of apparent resistivity to arrive at the true 

 formation resistivity by means of resistivity departure curves, which will 

 be described later. 



Radius of Investigation. — The extent to which the various media 

 surrounding the electrodes affect the value of apparent resistivity is depend- 

 ent on the spacing of the electrodes, and is termed the "radius of investi- 

 gation." When a very short electrode spacing is used, the mud in the hole 

 may have a dominant effect on the value of resistivity obtained. As the 

 spacing is increased, the effect of the formations surrounding the mud 

 column becomes more important. For large spacings, the resistivity of the 

 surrounding formations becomes dominant. 



It is commonly assumed for simplicity, based on considerations of the 

 potential drops in the vicinity of the M electrode, that in near-homogeneous 

 media the radius of investigation of a normal device is equal to its AM 

 spacing. The radius of investigation of a lateral device is taken under the 

 same conditions as equal to its AO spacing. More precise ideas regarding 

 the radius of investigation of a device under various conditions may be 

 arrived at by the study of the resistivity departure curves. 



