Patent Publication Number: US-8115490-B2

Title: Concentric return and transmitter electrodes for imaging and standoff distances compensation

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This is a continuation application of U.S. patent application Ser. No. 12/178,590 filed Jul. 23, 2008, the entire disclosure of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention disclosed herein relates to imaging of subsurface materials and, in particular, to embodiments of electrodes useful for resistivity imaging. 
     2. Description of the Related Art 
     Drilling apparatus used for geophysical exploration often include sensors for collecting information about ambient subsurface materials. Sensors may include ones such as those used for resistivity imaging. However, certain problems arise in the use of sensors in a drill string. For example, conventional corrections are performed with calipers and other devices measuring the distance (mechanical, acoustic etc.). The main problem here is the different position of resistivity sensor and caliper, which makes the correction procedure doubtful if vibration occurs. 
     Therefore, what is needed is a design which offers accurate measurements of standoff at the same position as the resistivity measurements when performing measurement while drilling. 
     BRIEF SUMMARY OF THE INVENTION 
     Disclosed is a method of estimating a property of an earth formation penetrated by a borehole. The method includes: disposing into the borehole a sensor having a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement; injecting a first current of a first frequency into the formation by applying an alternating current voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode; injecting a second current of a second frequency into the formation by applying an alternating current voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode; measuring effective impedance for each of the currents; and estimating the property using the measurements of the effective impedance for each of the currents; wherein the estimating compensates for an influence of standoff distances of the sensor on the measurements. 
     Also disclosed is a system for estimating a property of an earth formation penetrated by a borehole, the system includes: a sensor configured to be disposed into the borehole, the sensor having a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement; and a processor coupled to the sensor, the processor being configured to execute instructions that implement a method, the method includes: injecting a first current, I 1 , of a first frequency, f 1 , into the formation by applying an alternating current (AC) voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode; injecting a second current, I 2 , of a second frequency, f 2 , into the formation by applying an alternating current (AC) voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode; measuring effective impedance, Z e , for each of the currents; estimating the property using the measurements of the effective impedance, Z e , for each of the currents; wherein the estimating compensates for an influence of standoff distances of the sensor on the measurements. 
     Further disclosed is a non-transitory computer readable medium comprising computer executable instructions for estimating a property of an earth formation penetrated by a borehole using a sensor disposed in the borehole and comprising a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement by implementing a method that includes: injecting a first current, I 1 , of a first frequency, f 1 , into the formation by applying an alternating current (AC) voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode; injecting a second current, I 2 , of a second frequency, f 2 , into the formation by applying an alternating current (AC) voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode; measuring effective impedance, Z e , for each of the currents; estimating the property using the measurements of the effective impedance, Z e , for each of the currents; wherein the estimating compensates for an influence of standoff distances of the sensor on the measurements. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIG. 1  depicts a sensor having a circumferential distribution of return electrodes along a drill; 
         FIG. 2  depicts effects of vibration and rotation of the drill on positioning of the sensor shown in  FIG. 1 ; 
         FIG. 3  depicts a sensor having an axial distribution of return electrodes along a drill; 
         FIG. 4  depicts aspects of an apparatus for conducting logging while drilling; 
         FIG. 5  depicts a sensor according to the teachings herein; 
         FIG. 6  is a graph depicting dependence of a geometric factor on standoff; 
         FIG. 7  is a graph depicting dependence of a reactive part of the impedance on standoff, where the curves are normalized to the largest return electrode; 
         FIG. 8  is a circuit diagram effectively depicting aspects of standoff dependence for the sensor; 
         FIG. 9  is a chart useful for estimating standoff as a function of real impedance; and 
         FIG. 10  is a flow chart providing an exemplary method for using the sensor of  FIG. 5 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Disclosed are techniques for using a sensor having a plurality of electrodes arranged in a concentric manner. The techniques provide for collection of data in challenging environments, such as downhole environments that include oil-based-mud. For a better appreciation of the teachings herein, and a context of the invention, consider the following aspects provided with regard to  FIGS. 1 and 2 . 
       FIG. 1  illustrates an arrangement of a sensor with four button electrodes (also referred to as “return electrodes  13 ”). The return electrodes  13  may be used for a variety of measurements, including those assessing a standoff distance, or simply “standoff  11 .” Standoff  11  as discussed herein is a distance from an outer surface of a drill  10  (or other such equipment) to a wall of a borehole  2 . As shown in  FIG. 2 , standoff  11  can vary as the borehole  2  typically does not include regular surfaces. 
     The return electrodes  5  depicted are in four related yet slightly different locations (shown as sensor electrodes “a,” “b,” “c,” and “d”). The use of such sensor electrodes provides for certain advantages when performing measurements and evaluating results. However, due to different positioning of each return electrode  13  on the drill  10 , each return electrode  13  measures a property of the borehole  2  at a different position. Therefore, assessment of standoff  11  with one return electrode  13  will not be based on the same information as used by another return electrode  13 . 
     Using such an arrangement of return electrodes  13 , it is not possible to uniformly apply the standoff correction. More specifically, measurement values have to be stored and an algorithm has to be applied. Usually, this takes place after one complete rotation. Further, and by way of example, due to vibration (frequency could be some Hz) the different electrodes have different distances by passing the same position. In this case, the correction applied for this position later would be wrong. This problem is more or less the same like for  FIG. 3 . 
     Another orientation, such as one shown in  FIG. 3 , where the buttons (i.e., return electrodes  13 ) may be positioned in vertical direction along the drill string  10 , is also problematic. In this embodiment, problems arise because the time delay depends on the rate of penetration and is therefore larger. Variation in standoff  11  arises due to vibration of the drill  10  and irregular shape of the borehole  2 , and is further complicated by a requirement to consider a rate of penetration. Because of vibration and longer time delay, it is not very likely that one sensor electrode will monitor the same location as another sensor electrode. Depending on distances between each of the sensor electrodes, the time delay may be long enough that the borehole shape may even slightly change. 
     Referring now to  FIG. 4 , there are shown aspects of an exemplary embodiment of an instrument  50  for conducting “logging-while-drilling” (LWD). The instrument  50  is included within a drill string  10  that includes a drill bit  4 . The drill string  10  provides for drilling of a borehole  2  into earth formations  1 . The drill bit  4  is attached to a drill collar  14 . The drill string  10  may include a plurality of couplings  15  for coupling various components into the drill string  10 . 
     Generally, the borehole  2  is filled with drilling mud. Drilling mud may be introduced for a variety of reasons, including provision of a pressure barrier. In some instances, it is advantageous to use oil-based-mud as the drilling mud. The instrument  50  disclosed herein is particularly useful in the presence of oil-based-mud (OBM). 
     As a matter of convention herein and for purposes of illustration only, the instrument  50  is shown as traveling along a Z-axis, while a cross section of the instrument  50  is realized along an X-axis and a Y-axis. 
     In some embodiments, a drive  5  is included and provides for rotating the drill string  10  and may include apparatus for providing depth control. Control of the drive  5  and the instrument  50  is achieved by operation of controls  6  and a processor  7  coupled to the drill string  10 . The controls  6  and the processor  7  may provide for further capabilities. For example, the controls  6  are used to power and operate sensors (such as antenna) of the instrument  50 , while the processor  7  receives and at least one of packages, transmits and analyzes data provided by the drill string  10  and/or components therein. In various embodiments of instruments for logging while drilling (LWD), the instrument  50  processes at least some of the data collected downhole. 
     Considering the instrument  50  now in greater detail, and also with reference to  FIG. 5 , in this embodiment, the instrument  50  includes a plurality of electrodes, and is referred to in the following discussion as a “sensor  50 .” For convention, the electrodes of the sensor  50  include at least one transmitter electrode  51  and a plurality of return electrodes  52 . Each of the electrodes is separated from the other electrodes by an insulator  57 . At least one sensor  50  may be disposed on an outer surface of the drill string  10  as deemed appropriate. 
     Generally, the sensor  50  includes a plurality of switches  53 . The switches  53  provide for controlling application of voltage to each of the electrodes. In short, each of the switches  53  may be toggled to provide for various arrangements of “firing” or energizing of each electrode. The voltage provided to each electrode may be of any frequency deemed appropriate, in any duration deemed appropriate, and in any combination as deemed appropriate. By controlling arrangement of the switches  53 , an apparent size of the return electrode  52  can be modified. Thus, not only is the size of the return electrode modified, but if a ring is switched to opposite polarity, also the size of the transmitter electrode is changed. 
     Generally, a power supply for the sensor  50  provides alternating current (AC) that is in a relatively high frequency, f, range (for example, of about 1 MHz to about 10 MHz). The sensor  50  may be operated at frequencies, f, above or below this range. For example, the sensor  50  may be operated in frequency ranges from about 100 kHz to 100 MHz. 
     In some embodiments, the return electrodes  52  are referred to as “sensor electrodes” and in other embodiments may be referred to as “button electrodes,” or simply as a “button.” In operation, the transmitter electrode  51  provides for one pole of an electric dipole, while the at least one return electrode  52  provides for the other pole. Accordingly, the sensor  50  makes use of a single electric dipole for electric imaging, generally at a high-frequency, f. Thus, it should be recognized that the terms “transmit” “return” and the various forms of these terms are merely illustrative of aspects of operation of the instrument  50 , particularly for embodiments using AC current, and are therefore not to be construed as limiting of the instrument  50 . 
     In some embodiments, achieving different button sizes at one location is accomplished by changing polarity of electrode rings for the return electrodes  52 . That is, the switches may be arranged so that inner electrode rings are dominating the outer rings or the other around. More specifically, only if the inner ring (c) has the same polarity as the button in the center (d), the polarity of the next outer ring (b) can be switched to the polarity of the inner electrodes, etc. In this way, one can guarantee that no alternating polarities are selectable. Of course, one should recognize that an apparent size of the transmitter electrode may be altered. For example, the outer return electrode (a) may be set to a polarity of the transmitter electrode  51 . Other combinations may be had. 
     Generally, the AC voltage source between the return electrode(s)  52  and transmitter electrode  51  is applied to provide sufficient conditions for injecting current, I, into the formation  1 . During the operation, the electrodes are generally maintained under an equivalent electrical potential. An output of the sensor  50  includes impedance measured between each return electrode  52  and the transmitter electrode  51 . Generally, the sensor  50  is mounted on an outer surface of the drill  10  and results in 360 degree coverage for imaging of the formation  1 . 
     Although it is considered that the sensor  50  is generally operated with supporting components as shown (i.e., the controls  6  and the processor  7 ), one skilled in the art will recognize that this is merely illustrative and not limiting. For example, in some embodiments, the sensor  50  may include at least one on-board processor  7 . 
     Turning now to the invention in greater detail, in one embodiment (see  FIG. 5 ), a series of the measurement return electrodes  52  (denoted as “a,” “b,” “c,” and “d”) are placed on a single circumferential pad attached to the drill  10 . The return electrodes  52  of different sizes are separated by isolative gaps, each gap including an insulator  57 . The source voltage of high frequency (generally of 1 MHz or above) is applied between the transmitter electrode(s)  51  and the return electrode(s)  52 . Generally, all of the return electrodes  52  are kept under the same electrical potential driven by the applied voltage, V. Generally, the measured value is the complex impedance, Z, through each return electrode  52 , or combination of return electrodes  52 . This arrangement provides capacitive coupling between the sensor  50  and the formation  1  and enables imaging of the formation  1  even in the conditions of a very resistive oil-based mud. 
     Using the sensor  50  as described above, users are effectively provided with a sensor of varying sizes. This provides users with an ability to, among other things, estimate a dimension of the standoff  11  (the dimension being useful for correcting data collected from the formation  1 ) and also to maintain a desired resolution during imaging (under conditions of variable standoff). 
     Equation (1) below provides a relationship where estimates of standoff  11  may be determined. That is, by performing measurements with return electrodes  52  of different sizes and by applying Eq. (1), standoff  11  may be estimated.
 
 G·Re ( Ż )= R   f   (1);
 
In Eq. (1), Re(Ż) represents a real part of measured impedance, R f , represents a resistivity of the formation, and G represents a geometric factor.
 
     It turns out that even in the presence of highly resistive drilling mud, the geometric factor, G, changes with the standoff  11 . The change becomes more pronounced for the more pronounced standoff and a smaller effective return electrode  52 . This effect is illustrated in  FIG. 6  where mathematical modeling results of the geometric factor, G, are presented. In this example, the results correspond to sizes of 16 millimeters (mm), 24 mm, 32 mm and 48 mm. The operating frequency in this example was 10 MHz, the distance from the center of the return electrode to the transmitter electrode was 96 mm. The resistivity, R f , (assuming a homogeneous formation) was 10 ohm-meters. As this figure shows, the geometric factor, G, of a large 48 mm return electrode  52  does not depend on the standoff  11 , if the standoff  11  is less than about 1.5875 centimeters (cm, or about 0.625 inches). For return electrodes  52  of 16 mm and 32 mm, the geometric factor, G, depends on the standoff  11  in the whole analyzed range of standoffs. If corrections are not made for this effect, the readings from small return electrodes  52  will produce an inaccurate image. Accordingly, using an imaginary part of the impedance for the corrections may address the inaccuracy. 
     As shown in  FIG. 7 , the normalized imaginary part of the impedance depends differently on the standoff. That is, there is a small difference between impedances where standoff is about 0.3175 cm (0.125 inches), while there is a significant difference between impedances at about 1.27 cm (about 0.5 in). To quantify behavior of the imaginary part of the impedance for the different size electrodes, the curves of  FIG. 7  may be divided by the curve corresponding to 48 mm size return electrode. The result of the division is presented in  FIG. 8  and represents a chart that is used for the standoff estimation. In order to perform the correction, a ratio between readings corresponding to an individual return electrode and the 48 mm return electrode  52  should be calculated. Then, for a given size of the return electrode (as shown in  FIG. 7 ) and calculated ratio (provided along the y-axis of  FIG. 7 ) the resulting graph enables finding of a standoff value (shown along the x-axis). As soon as the standoff  11  is known, the correction chart, such as the exemplary one provided in  FIG. 6 , may be used to find the geometric factor, G, corresponding to the given size of return electrode  52  and standoff  11 . 
     In this process, a selection of readings that maintain acceptable vertical resolution under the conditions of variable standoff may be made. In other words, under certain standoff conditions, readings from the small return electrodes  52  become non-recoverable. Even after being corrected for standoff, the readings cannot deliver an image of the formation  1 . Under such circumstances, readings corresponding to the return electrode  52  which is less affected by the standoff may be selected over readings from the smaller return electrodes  52 . These readings are generally capable of providing an image of the formation  1 . Modeling results demonstrate that an acceptable quality image is obtained when the size B return electrode  52  is at least three times bigger than the standoff. Using this criterion, readings that provide the best image for the given (estimated) standoff may be adaptively selected. Under conditions of a rugose borehole, this selection is similar to a low-pass filter, which filters out high frequency component from the data. This effect is illustrated in  FIG. 8 . 
     In  FIG. 8 , results of mathematical modeling are presented for different sizes of the return electrodes  52 . These results are provided for a homogeneous formation  1  and a rugose borehole. In this example, rugosity is simulated by changing the size of the borehole such that the standoff is periodically changing from 0.25 to 0.5 in. The width of the standoff varies from about 0.5 inches to about 4 inches. As shown in  FIG. 8 , the smaller the return electrodes, the bigger the effect of borehole irregularities on the readings. The opposite is true as well. That is, effectiveness of suppression of false readings is increased with bigger return electrodes  52 . 
     In the examples of  FIGS. 6 and 7 , the results were obtained under the assumption that resistivity of the oil-based mud, R obm , is about five or more orders of magnitude bigger than the resistivity of formation, R f . Although this assumption is generally valid for the vast majority of practical cases, there are some borehole fluids that are less resistive relatively to the formation. In this case, an additional step that includes correction for resistivity of the mud, R m , should be performed. This correction may be based a technique such as the one provided below. Correction for the finite resistivity of the mud should be performed at the first stage of the processing prior to the geometric factor correction. 
     As an example of correction for less resistive mud, consider the effective schematic circuit diagram presented in  FIG. 9 . The circuit provided may be equated to aspects of the electric function of the sensor  50 . This example shows that the measured effective impedance, Z e , depends on the internal impedance of the tool, Z T , the impedance due to the gap between the sensor and the formation, Z G , and the formation resistivity, R f . For simplicity, it is assumed that there is no gap between the return electrode  52  and the formation  1 . For applied voltage, U, and measured current, I, then the effective impedance, Z e , is estimated by Eq. (2): 
     
       
         
           
             
               
                 
                   
                     Z 
                     e 
                   
                   = 
                   
                     
                       
                         Z 
                         T 
                       
                       + 
                       
                         Z 
                         G 
                       
                       + 
                       
                         R 
                         f 
                       
                     
                     = 
                     
                       U 
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In case of a conductive formation (where resistivity of the formation R f ≦10 ohm-m) and oil-based mud, the contribution of the formation into the effective impedance, Z e , is small (R f &lt;&lt;&lt;Z T +Z G ) and it can be expected that a reduction of the sensitivity of the measured impedance to the resistivity of formation, R f . The gap impedance, Z G , which depends on the mud properties and the receiver standoff, becomes a major contributor into the effective impedance, Z e . Note that in Eq. (2), Z T  represents an impedance of the sensor  50 . To extract the information about formation resistivity, R f , multi-frequency measurements may be employed prior to data processing. Consider using two frequencies. First, assume that impedance measurements have been conducted using a first frequency, f 1  and a second frequency, f 2 . Each frequency (f 1 , f 2 ) permits estimation of correlating effective impedances Z e1  and Z e2 . This estimating may be performed according to Eq. (3): 
                       Z     e   ⁢           ⁢   1       =           ⅈω   1     ⁢   L     +     R   f     +     1       r     -   1       +       ⅈω   1     ⁢   C           =       A   1     +     ⅈ   ⁢           ⁢     B   1             ,     
     ⁢       Z     e   ⁢           ⁢   2       =           ⅈω   2     ⁢   L     +     R   f     +     1       r     -   1       +       ⅈω   2     ⁢   C           =       A   2     +     ⅈ   ⁢           ⁢     B   2                     (   3   )               
where A 1 , A 2  and B 1 , B 2  correspond to the real and imaginary parts of the impedances Z e1  and Z e2 , respectively. Eqs. (3) may be rearranged as provided in Eqs. (4), and Eqs. (5):
 
     
       
         
           
             
               
                 
                   
                     
                       
                         A 
                         1 
                       
                       - 
                       
                         A 
                         2 
                       
                     
                     = 
                     
                       
                         r 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             1 
                             
                               
                                 r 
                                 
                                   - 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       1 
                                     
                                     ⁢ 
                                     C 
                                   
                                   ) 
                                 
                                 2 
                               
                             
                           
                           - 
                           
                             1 
                             
                               
                                 r 
                                 
                                   - 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       2 
                                     
                                     ⁢ 
                                     C 
                                   
                                   ) 
                                 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           B 
                           1 
                         
                         
                           ω 
                           1 
                         
                       
                       - 
                       
                         
                           B 
                           2 
                         
                         
                           ω 
                           2 
                         
                       
                     
                     = 
                     
                       - 
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             
                               1 
                               
                                 
                                   r 
                                   
                                     - 
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         1 
                                       
                                       ⁢ 
                                       C 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             - 
                             
                               1 
                               
                                 
                                   r 
                                   
                                     - 
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         2 
                                       
                                       ⁢ 
                                       C 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           B 
                           1 
                         
                         
                           ω 
                           1 
                         
                       
                       - 
                       
                         
                           B 
                           2 
                         
                         
                           ω 
                           2 
                         
                       
                     
                     
                       
                         A 
                         1 
                       
                       - 
                       
                         A 
                         2 
                       
                     
                   
                   = 
                   
                     G 
                     = 
                     Cr 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Combining Eq. (5) with the first equation of Eqs. (4), resistivity of the gap, R g , may be found, as provided in Eq. (6): 
                     R   g     =       (       A   1     -     A   2       )     /     (       1     1   +       (       ω   1     ⁢   G     )     2         -     1     1   +       (       ω   2     ⁢   G     )     2           )               (   6   )               
Equation (5) allows estimation of capacitance C between the return electrode  52  and the formation  1 , while resistivity of formation, R f , may be derived from the Eq. (3), for example, by Eq. (7):
 
     
       
         
           
             
               
                 
                   
                     R 
                     f 
                   
                   = 
                   
                     
                       
                         A 
                         1 
                       
                       - 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   1 
                                 
                                 ⁢ 
                                 C 
                               
                               ) 
                             
                             2 
                           
                           ⁢ 
                           r 
                         
                         
                           
                             r 
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   1 
                                 
                                 ⁢ 
                                 C 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     = 
                     
                       
                         A 
                         2 
                       
                       - 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 C 
                               
                               ) 
                             
                             2 
                           
                           ⁢ 
                           r 
                         
                         
                           
                             r 
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 C 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Accordingly, and as depicted in  FIG. 10 , an exemplary and non-limiting method for estimating standoff  100  calls for selectively applying voltage to a plurality of concentric return electrodes and transmitter electrode  101 ; measuring the impedance  102 ; and estimating standoff using the measured impedance  103 . 
     In summary, a method for imaging borehole wall resistivity with 360 degree coverage in the presence of oil-based mud is described. A sensor for the imaging includes a circumferential pad mounted on a drill and containing a series of variable size buttons electrodes (i.e., return electrodes) separated by insulating gaps. That is, a size of the button electrode is determined by a number of ring electrodes having the same polarity. The voltage source between symmetrical transmitting electrodes and sensor buttons is applied to provide sufficient conditions for injecting current into the formation. An output of the sensor comprises a measurement of the complex impedance for each sensor electrode. The set of the buttons of different size provides enough flexibility to adjust imaging for the variable standoff conditions by correcting for the variable standoff and selecting readings the best suitable for the determined standoff. The 360 degree coverage is achieved via combination of the pad&#39;s shape, pad&#39;s azimuthal rotation, and a system to centralize the position of the imager in the well. 
     In support of the teachings herein, various analysis components may be used, including digital and/or an analog systems. The system may have components such as a processor, storage media, memory, input, output, communications link (wired, wireless, pulsed mud, optical or other), user interfaces, software programs, signal processors (digital or analog) and other such components (such as resistors, capacitors, inductors and others) to provide for operation and analyses of the apparatus and methods disclosed herein in any of several manners well-appreciated in the art. It is considered that these teachings may be, but need not be, implemented in conjunction with a set of computer executable instructions stored on a computer readable medium, including memory (ROMs, RAMs), optical (CD-ROMs), or magnetic (disks, hard drives), or any other type that when executed causes a computer to implement the method of the present invention. These instructions may provide for equipment operation, control, data collection and analysis and other functions deemed relevant by a system designer, owner, user or other such personnel, in addition to the functions described in this disclosure. 
     Further, various other components may be included and called upon for providing for aspects of the teachings herein. For example, a power supply (e.g., at least one of a generator, a remote supply and a battery), motive force (such as a translational force, propulsional force or a rotational force), magnet, electromagnet, sensor, electrode, transmitter, receiver, transceiver, antenna, controller, optical unit, electrical unit or electromechanical unit may be included in support of the various aspects discussed herein or in support of other functions beyond this disclosure. 
     One skilled in the art will recognize that the various components or technologies may provide certain necessary or beneficial functionality or features. Accordingly, these functions and features as may be needed in support of the appended claims and variations thereof, are recognized as being inherently included as a part of the teachings herein and a part of the invention disclosed. 
     While the invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications will be appreciated by those skilled in the art to adapt a particular instrument, situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.