Patent Publication Number: US-2016223702-A1

Title: Multi-component induction logging methods and systems having a trend-based data quality indicator

Description:
BACKGROUND 
     In the field of petroleum well drilling and logging, resistivity logging tools are frequently used to provide an indication of the electrical resistivity of rock formations surrounding an earth borehole. Such information regarding resistivity is useful in ascertaining the presence or absence of hydrocarbons. A typical resistivity logging tool includes a transmitter antenna and a pair of receiver antennas located at different distances from the transmitter antenna along the axis of the tool. The transmitter antenna is used to create electromagnetic fields in the surrounding formation. In turn, the electromagnetic fields in the formation induce an electrical voltage in each receiver antenna. Due to geometric spreading and absorption by the surrounding earth formation, the induced voltages in the two receiving antennas have different phases and amplitudes. Experiments have shown that the phase difference (Φ) and amplitude ratio (attenuation, A) of the induced voltages in the receiver antennas are indicative of the resistivity of the formation. The average depth of investigation (as defined by a radial distance from the tool axis) to which such a resistivity measurement pertains is a function of the frequency of the transmitter and the distance from the transmitter to the mid-point between the two receivers. Thus, one may achieve multiple radial depths of investigation of resistivity either by providing multiple transmitters at different distances from the receiver pair or by operating a single transmitter at multiple frequencies. 
     Many formations are electrically anisotropic, a property which is often attributable to extremely fine layering during the sedimentary build-up of the formation. Hence, in a formation coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities R x  and R y  in directions x and y, respectively, are the same, but resistivity R z  in the z direction is different from R x  and R y . Thus, the resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is known as the horizontal resistivity, R h , and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is known as the vertical resistivity, R v . 
     Compared to the conventional induction measurement, multi-component induction (MCI) logging is a 9-component measurement, and its non-diagonal components (denoted as XY, XZ, YX, YZ, ZX, and ZY) are more strongly affected by the tool location variations in the hole (e.g., due to tool eccentricity and tool azimuth angle) compared to the ZZ component and diagonal components (XX and YY), leading to a relatively greater degree of sensitivity to undesirable borehole effects. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Accordingly, there are disclosed in the drawings and the following description multi-component induction (MCI) logging systems and methods with a trend-based data quality indicator to alert the user to regions having inconsistent and potentially unreliable measurements. In the drawings: 
         FIG. 1  shows an illustrative logging while drilling (LWD) environment with dipping formation beds; 
         FIG. 2  shows an illustrative wireline logging environment with dipping formation beds; 
         FIG. 3  shows an illustrative antenna configuration for an MCI logging tool; 
         FIG. 4  shows illustrative antenna sub-arrays for an MCI logging tool; 
         FIG. 5  shows a block diagram of an illustrative logging system; 
         FIG. 6  shows an illustrative visual representation of log data with a quality index. 
         FIG. 7  shows an illustrative method for determining data quality indicators for MCI measurements; and 
         FIG. 8  shows an illustrative flowchart for iterative MCI logging using data quality indicators. 
     
    
    
     It should be understood, however, that the specific embodiments given in the drawings and detailed description thereto do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and modifications that are encompassed together with one or more of the given embodiments in the scope of the appended claims. 
     DETAILED DESCRIPTION 
     Disclosed herein are multi-component induction (MCI) logging systems and methods with one or more data quality indicators. The data quality indicators are qualitative and/or quantitative measures of MCI measurement consistency for different runs of an MCI logging tool in a borehole, for different frequencies of the MCI logging tool, and/or for different sub-arrays of the MCI logging tool. The data quality indicators may correspond to raw measurement data, to processed measurement data, and/or to inversion results such as a formation dip value, a horizontal resistivity value (R h ), and a vertical resistivity value (R v ). The data used to determine the data quality indicators may correspond to data collected after calibration and/or temperature correction. Such data quality indicators may be computed, stored, and displayed to an operator. Further, customer reports generated for MCI logging results may include such data quality indicators. Additionally or alternatively, such data quality indicators may be used in an iterative logging process, where logging runs are repeated with updated workflow parameters until resulting data quality indicators satisfy a cost function. 
       FIG. 1  shows a suitable context for describing the operation of the disclosed systems and methods. In the illustrated logging while drilling (LWD) environment, a drilling platform  102  is equipped with a derrick  104  that supports a hoist  106  for raising and lowering a drill string  108 . The hoist  106  suspends a top drive  110  that rotates the drill string  108  as it is lowered through the well head  112 . The drill string  108  can be extended by temporarily anchoring the drill string  108  at the well head  112  and using the hoist  106  to position and attach new drill pipe sections with threaded connectors  107 . 
     Connected to the lower end of the drill string  108  is a drill bit  114 . As bit  114  rotates, it creates a borehole  120  that passes through various formations  121 . A pump  116  circulates drilling fluid through a supply pipe  118  to top drive  110 , through the interior of drill string  108 , through orifices in drill bit  114 , back to the surface via the annulus around drill string  108 , and into a retention pit  124 . The drilling fluid transports cuttings from the borehole  120  into the pit  124  and aids in maintaining the integrity of the borehole  120 . 
     Drilling fluid, often referred to in the industry as “mud”, is often categorized as either water-based or oil-based, depending on the solvent. Oil-based muds are generally preferred for drilling through shale formations, as water-based muds have been known to damage such formations. 
     An MCI logging tool  126  is integrated into a bottom-hole assembly  129  near the bit  114 . The MCI logging tool  126  may take the form of a drill collar, i.e., a thick-walled tubular that provides weight and rigidity to aid the drilling process. As the bit extends the borehole  120  through the formations, the bottomhole assembly  129  collects multi-component induction measurements (using tool  126 ) as well as measurements of the tool orientation and position, borehole size, drilling fluid resistivity, and various other drilling conditions. 
     The orientation measurements collected by bottomhole assembly  129  may be obtained using an orientation indicator, which may include magnetometers, inclinometers, and/or accelerometers, though other sensor types such as gyroscopes may be used. Preferably, the orientation indicator includes a 3-axis fluxgate magnetometer and a 3-axis accelerometer. The combination of those two sensor systems enables the measurement of the rotational (“toolface”) angle, borehole inclination angle (“slope”), and compass direction (“azimuth”). In some embodiments, the toolface and borehole inclination angles are calculated from the accelerometer sensor output. The magnetometer sensor outputs are used to calculate the borehole azimuth. With the toolface, the borehole inclination, and the borehole azimuth information, multi-component induction logging tools disclosed herein can be used to steer the bit to the desirable bed. Formation dip and strike values can also between determined and used to steer the bit. 
     In wells employing acoustic telemetry for LWD, downhole sensors (including MCI logging tool  126 ) are coupled to a telemetry module  128  having an acoustic telemetry transmitter that transmits telemetry signals in the form of acoustic vibrations in the tubing wall of drill string  108 . An acoustic telemetry receiver array  130  may be coupled to tubing below the top drive  110  to receive transmitted telemetry signals. One or more repeater modules  132  may be optionally provided along the drill string to receive and retransmit the telemetry signals. Of course other telemetry techniques can be employed including mud pulse telemetry, electromagnetic telemetry, and wired drill pipe telemetry. Many telemetry techniques also offer the ability to transfer commands from the surface to the bottomhole assembly  129 , thereby enabling adjustment of the configuration and operating parameters of MCI logging tool  126 . In some embodiments, the telemetry module  128  also or alternatively stores measurements for later retrieval when the bottomhole assembly  129  returns to the surface. 
     At various times during the drilling process, the drill string  108  is removed from the borehole  120  as shown in  FIG. 2 . Once the drill string has been removed, logging operations can be conducted using a wireline logging tool  134 , i.e., a sensing instrument sonde suspended by a cable  142  having conductors for transporting power to the tool  134  and communications from the tool  134  to the surface. An MCI logging portion of the wireline logging tool  134  may have centralizing arms  136  that center the tool  134  within the borehole  120  as the tool  134  is pulled uphole. A logging facility  144  collects measurements from the wireline logging tool  134 , and includes computing facilities  145  for processing and storing the measurements gathered by the wireline logging tool  134 . 
       FIG. 3  shows an illustrative antenna configuration for MCI logging tool  126  or  134 . As shown, MCI logging tool  126  or  134  has a tilted transmit antenna  202  and two pairs of tilted receive antennas  204 ,  206  and  208 ,  210 , thereby providing four transmit-receive antenna pairings. As the MCI logging tool  126  or  134  moves along a borehole, it acquires attenuation and phase measurements of each receive antenna&#39;s response to transmit antenna  202 . In certain alternative embodiments, the MCI logging tool  126  or  134  measures in-phase and quadrature-phase components of the receive signals rather than measuring amplitude and phase. In either case, these measurements are collected and stored as a function of the MCI logging tool&#39;s position and orientation in the borehole. 
     The illustrated MCI logging tool  126  or  134  of  FIG. 3  has receive antennas  204  and  208  oriented parallel to the transmit antenna  202 , and receive antennas  206  and  210  oriented perpendicular to the transmit antenna  202 . In the illustrated example, each of the antennas share a common rotational orientation, with antennas  202 ,  204 ,  208  being tilted at −45° and antennas  206 ,  210  being tilted at +45° relative to the longitudinal tool axis. In a LWD embodiment (MCI logging tool  126 ), each of the coil antennas is mounted in a recess and protected by a non-conductive filler material and/or a shield having non-conducting apertures, and tool body is primarily composed of steel. In a wireline embodiment (MCI logging tool  136 ), the coil antennas may be mounted inside or outside a mandrel made of fiberglass or other materials. For both LWD and wireline embodiments, the relative MCI logging tool dimensions and antenna spacings are subject to variation depending on the desired tool properties. As an example, the distance between the receive coil pairs may be on the order of 0.25 m, while the spacing of the transmit coil to the midpoint between the receiver pairs may vary from about 0.4 m to over 10 m. 
       FIG. 4  shows illustrative antenna sub-arrays for MCI logging tool  126  or  134 . In  FIG. 4 , each antenna sub-array includes transmitter triad T x , T y , T z , which represent magnetic dipole antennas oriented parallel to the tool&#39;s x, y, and z axes respectively (denoted as x t , y t , z t ). Each sub-array also includes a main receiver triad, R x   m , R y   m , R z   m , and a bucking receiver triad R x   b , R y   b , R z   b , all of which represent magnetic dipole antennas oriented parallel to the tool&#39;s x, y, and z axes respectively. For a given sub-array, the main receiver triad is spaced at a distance L m  from the transmitter triad, and the bucking receiver triad is spaced at a distance L b  from the transmitter triad. Thus, the MCI logging  126  or  134  is represented in  FIG. 4  as N tri-axial sub-arrays (i.e., TR (1) , TR (2) , . . . , and TR (N) ), where each tri-axial sub-array includes a transmitter triad (T x , T y , and T z ), a main receiver triad (R x   m , R y   m , and R z   m ), and a bucking receiver triad (R x   b , R y   b , and R z   b ). In accordance with at least some embodiments, each antenna sub-array measures a nine-coupling voltage measurement at every log depth in the tool/measurement coordinate system (x t , y t , z t ). 
     The voltages measured on receivers of a sub-array can be converted into apparent conductivities. In at least some embodiments, the apparent conductivities are symbolically expressed in equation 1 as a 3×3 tensor or matrix for a multi-array tri-axial tool operated at multiple frequencies: 
     
       
         
           
             
               
                 
                   
                     
                       
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     where i=1, 2, . . . , N , j=1, 2, . . . , M , N is the total number of the tri-axial sub-arrays, and M is the total number of the operated frequencies. In equation 1,  σ a   (i, j)    is referred to as the MCI apparent conductivity tensor (R-signal or X-signal) in the tool coordinate system, σ IJ   (i, j)  are the measured-conductivity couplings of  σ a   (i, j)   , where I indicates the transmitter direction, and J indicates the receiver direction. For example, when I and J=x, σ IJ   (i, j)  is σ xx   (i, j) , when I and J=y, σ IJ   (i, j)  is σ yy   (i, j) , and when I and J=z, σ IJ   (i, j)  is σ zz   (i, j) , which are the traditional multi-array induction measurements. Including both R-signal and X-signal data yields 2*9*M*N measurements for every log point. As disclosed in greater detail for  FIG. 6 , a data quality indicator may be determined at least in part by comparing different conductivity measurements. 
     In at least some embodiments, resistivity information (e.g., R v , and R h ), formation dip information, distance information, and/or other information are plotted or mapped by visualization software (e.g., the visualization control module  320 ) that receives measurements from MCI logging tool  126  or  134 . Without limitation, the parameters that are displayed or represented by visualization software may include physical parameters such as tool orientation, formation resistivity values, R v , R h , formation dip, relative dip angles, strike angles, relative azimuth angles, bed dips, bed azimuths, drill path, distance to bed boundaries, water saturation, and formation porosity. In addition, trust values such as uncertainty estimates, inversion type information, and/or comparison information may be displayed or represented by visualization software. In addition, data quality indicators related to physical parameters may be displayed or represented. 
     By displaying or representing physical values, trust values, and/or data quality indicators, visualization software enables an operator to prepare a report. Alternatively, a report on measured physical parameters with data quality indicators may be generated automatically using software without input (or with limited input) from an operator. Further, an operator may select logging workflow adjustments for MCI logging tool  126  or  134  using visualized physical parameters and data quality indicators. In at least some embodiments, the logging process and workflow adjustments continue until the data quality indicators are greater than a threshold level and/or satisfy a cost function associated with the logging process. 
       FIG. 5  shows a block diagram of an illustrative logging system  300 . The logging system  100  includes an MCI logging tool  126  or  134  with MCI logging components  342  to collect MCI measurements. For example, the MCI logging components  342  may correspond to the antenna configuration of  FIG. 3  and/or the antenna sub-arrays described in  FIG. 4 . The MCI logging tool  126  or  134  also includes a controller  344  to direct various operations of the MCI logging tool  126  or  134 . The operations include setting or adjusting parameters for collecting raw data, processing the raw data, storing the raw and/or processed data, and transmitting the raw and/or processed data to the surface. A communication interface  346  of the MCI logging tool  126  or  134  enables MCI measurement data to be transferred to a surface communication interface  330 . The surface communication interface  330  provides the MCI measurement data to a surface computer  302  using known communication techniques (e.g., mud pulse, electromagnetic signaling, or a wired pipe arrangement). It should be understood that the MCI measurement data provided to the surface computer  302  from the MCI logging tool  126  or  134  may include raw measurement data, processed measurement data, inverted measurement data, visualization parameters, and/or data quality indicators. 
     As shown in  FIG. 5 , the surface computer  302  includes at least one processor  304  coupled to a display  305 , input device(s)  306 , and a storage medium  308 . The display  305  and input device(s)  306  function as a user interface that enables an operator (i.e., a drilling operator and/or logging operator) to view information, to input steering commands, to input logging workflow commands or values, and/or to interact with other software executed by processor  304 . 
     In at least some embodiments, the storage medium  308  stores data quality indicator software  310  with a consistency assessment module  314 , a visualization control module  320 , and a report generation module  322 . The storage medium  308  also includes a logging workflow manager  324 . Accordingly, in at least some embodiments, the input device(s)  306  (e.g., a touch screen, mouse, and/or keyboard) enables an operator to interact with the data quality indicator software  310 . Further, the input device(s)  306  may enable an operator to interact with a steering interface that assists the operator with steering decisions using visual representations of a formation. It should be understood that the operations of the data quality indicator software  310  apply to wireline logging systems as well as LWD systems. 
     In at least some embodiments, consistency assessment module  314  of the data quality indicator software  310  determines whether multi-run measurements collected by MCI logging tool  126  or  134  are stable or repeatable. Further, the consistency assessment module  314  determines whether single-run measurements collected by MCI logging tool  126  or  134  are consistent. To determine data quality indicators, the variation in single-run and/or multi-run measurements are compared. For example, a predetermined inequality pattern may be used to assess the quality of single-run measurements. Further, the degree of variation in single-run may be used to assess the quality single-run measurements. If available, the degree of variation in multi-run measurements may be used to assess the quality of multi-run measurements. In different embodiments, data quality indicators may be provided for raw measurement data, for processed measurement data, and/or for inversion results (e.g., a formation dip value, R h , and R v ). Some example comparisons and data quality indicators are provided below. 
     In at least some embodiments, calibrations and/or temperature corrections may be applied to the MCI logging tool  126  or  134  to improve measurement quality. However, some data quality issues (e.g., due to loose parts) cannot be overcome by calibration and temperature correction, but the degree of difference can still be tracked and corresponding data quality indicators may be generated. 
     Returning to the multi-array MCI tool notation of  FIG. 4 , the consistency assessment module  314  may perform various types of conductivity measurement analysis. Numerical simulations indicate analysis of combined MCI responses is appropriate. The basis for the combined response analysis is that even though all MCI responses are affected by tool position in a borehole (especially cross components σ IJ   (i, j) ), where I≠J), the effects of the tool position on some combined MCI responses may be reduced in the strike coordinate system. Accordingly, combined MCI responses may replace the raw data for the comparisons of different run measurements performed by the consistency assessment module  314 . 
     Further, numerical simulations indicate that for a given sub-array, MCI responses usually satisfy inequality equations for different frequencies (f (j) , j=1, 2, . . . , M): 
       σ IJ   (i, j+1) ≦σ IJ   (i, j) ≦σ IJ   (i, j−1)  or σ IJ   (i, j+1) ≧σ IJ   (i, j) ≧σ IJ   (i, j−1) ,   (2)
 
     where in a homogeneous full space or a thick-bed formation with or without a hole, the frequency values satisfy f (j+1) &gt;f (j) &gt;f (j−1) . Thus, the consistency assessment module  314  may determine whether MCI responses satisfy these inequality equations for different frequencies. 
     Further, numerical simulations indicate that for given frequencies (f (j) ), the MCI responses usually satisfy inequality equations for different sub-arrays (i=1, 2, . . . , N): 
       σ IJ   (i+1, j) ≦σ IJ   (i, j) ≦σ IJ   (i−1, j)  or σ IJ   (i+1, j) ≧σ IJ   (i, j) ≧σ IJ   (i−1, j) ,   (3)
 
     where in a full space or a thick-bed formation with or without a hole, the sub-array spacing values satisfy L (i−1) &gt;L (i) &gt;L (i+1) . Thus, the consistency assessment module  314  may determine whether MCI responses satisfy these inequality equations for different sub-arrays. 
     Accordingly, in at least some embodiments, the consistency assessment module  314  may utilize combined MCI responses, inequality equations for different frequencies, and/or inequality equations for different sub-arrays to determine data quality indicators. Further, the ratios for different frequencies and sub-arrays may be computed from inverted formation parameters and compared with predetermined thresholds. 
     Without limitation, a data quality indicator determined by the data quality indicator software  310  may be a binary value, where one state is “good quality” and other state is “bad quality”. Alternatively, a data quality indicator may have three or more levels. For example, a data quality indicator may be an integer with a value of 1 to 5, where 1 is “bad quality”, 2 is “fair quality”, 3 is “acceptable quality”, 4 is “good quality”, and 5 is “excellent quality”. Additional levels or fractional numbers may also be used as a data quality indicator value. 
     In at least some embodiments, the value of a data quality indicator may be lowest (e.g., 1 on a scale of 1 to 5) if an inequality pattern (equations 2 or 3) for MCI responses is not met. Further, the value of a data quality indicator may differ depending on measurement deviations. For example, if the inequality pattern is met, the following data quality indicator values may be selected: a 1 may be selected if the deviation is larger than 50%; a 2 may be selected if the deviation is between 20% and 50%, a 3 may be selected if the deviation is between 10% and 20%, a 4 may be selected if the deviation is between 5% and 10%, and a 5 may be selected if the deviation is smaller than 5%. 
     If available, multi-run data is analyzed to determine repeatability of MCI measurements. Additionally or alternatively, raw data is analyzed to determine logging environment issues and/or potential tool issues. Additionally or alternatively, processed data is analyzed to determine potential issues with processing as well as logging environment issues. In at least some embodiments, the decision regarding which data to analyze may depend on customer input regarding which frequency or frequencies to use. If a multi-frequency result is going to be delivered to the customer, then quality of the multi-frequency results can be analyzed to determine data quality indicators relevant to a customer request. Thus, determined data quality indicators may be relevant to a frequency or frequencies of interest to a customer, and/or to physical parameters of interest. 
     Returning to  FIG. 5 , the data quality indicator software  310  also comprises visualization control module  320 , which may display MCI measurement results or related data. For example, the visualization control module  320  may cause resistivity information (R v  and R h ), formation dip, strike angle, distance information, or other information to be plotted and displayed to an operator. Without limitation, the parameters that are displayed or represented by visualization control module  320  may include physical parameters such as tool orientation, formation resistivity values, vertical resistivity, horizontal resistivity, relative dip angles, relative azimuth angles, bed dips, bed azimuths, drill path, distance to bed boundaries, water saturation, and formation porosity. In addition, trust values such as uncertainty estimates, inversion type information, and/or comparison information may be displayed or represented by visualization control module  320 . In addition, data quality indicators related to physical parameters may be displayed or represented by visualization control module  320 . As an example, data quality values related to data quality ranges or indices may be used as data quality indicators. 
     The data quality indicator software  310  also comprises report generation module  322  to generate a MCI logging report with data quality indicators. In at least some embodiments, the report generated by report generation module  322  includes physical parameters values, trust values, and/or data quality indicators. The information in the report may be generated based on operator input, report generation rules, or both. As an example, an operator may view information presented by the visualization control module  320 , and may generate or update a report accordingly. Alternatively, report generation module  322  may generate a report without operator input or with limited operator input (e.g., an operator may edit a report that has already been generated). In some embodiments, a report is not generated until data quality criteria of MCI logging operations are met (as indicated by the data quality indicators). 
     As shown in  FIG. 5 , the storage medium  308  of surface computer  302  also includes a logging workflow manager  324  that enables logging control parameters, processing control parameters, inversion control parameters, visualization parameters, report generation, and/or data quality analysis to be adjusted for different logging runs. The adjustments made by the logging workflow manager  330  may be directed using operator input and/or established rules. Without limitation, the logging workflow manager  330  may enable adjustments to: the visualization of measurement data; filter types or filter coefficients; signal selection or signal weights; frequencies used; processing parameters; and/or other logging parameters (e.g., logging speed and power levels) based on automation rules. In at least some embodiments, the logging workflow manager  324  employs a cost function  326  to determine whether to perform additional measurement runs, where the cost function  326  relies on data quality indicators determined by the data quality indicator software  310 . Accordingly, logging workflow adjustments and additional runs by MCI logging tool  126  or  134  may continue until the cost function  332  is satisfied (e.g., if the data quality is above a threshold range, if the data quality is not improving, if the data quality has improved by more than a threshold percent compared to an initial quality threshold, and/or if the data quality has not improved by more than a threshold percent compared to an initial quality threshold), or until an operator selects to end logging operations. Further, the logging workflow manager  330  may provide a user interface that enables an operator to make adjustments to the automation rules, to the logging workflow of different runs and/or to the cost function  332 . 
     Although the data quality indicator software  310  and logging workflow manager  330  are described as software or modules stored by storage medium  308  and executed by processor  304 , it should be understood that at least some features of the data quality indicator software  310  and logging workflow manager  330  may be stored and executed by MCI logging tool  126  or  134 . 
       FIG. 6  shows an illustrative visual representation  360  of log data with a quality index. The visual representation  360  may be displayed, for example, on a computer monitor or in a report generated based on the MCI measurements described herein. As shown, the visual representation  360  charts a formation property log  362  as a function of depth. The formation property log  362  may correspond to raw data (e.g., conductivity measurements), processed data (e.g., combined MCI measurements), or inversion data (e.g., R v , R h , formation dip, formation strike) as described herein. The visual representation  360  also charts a quality log  364  as a function of depth. Thus, the example quality log  364  charts how data quality of the formation property log  362  varies as function of depth. The quality log  362  is determined, for example, by combining a plurality of data quality indicators for different depths. In at least some embodiments, a threshold indicator  366  is also displayed to indicate tool depths at which the quality of the formation property log  362  drops below a threshold level. Additional thresholds may be displayed to categorize data quality into finer groupings. 
     The visual representation  360  of  FIG. 6  is an example of displaying data quality indicators using position of a continuous line (the quality log  364  indicates higher data quality towards the right). In different embodiments, data quality indicators can be represented in other ways. For example, data quality indicators can be represented using a plurality of separate lines or symbols, where the position of the lines or symbols indicates quality. Further, data quality indicators can be represented as numerical values in a scale (e.g., 1 to 5, where 1 is lowest quality and 5 is highest quality), or as colors (e.g., red to green, where red in lowest quality and green is highest quality). In summary, the format of visual representation  360  is one of many possible ways to display measurement results and corresponding data quality indicators. Such data quality indicators may be included in a log report for review by an operator or customer. Additionally or alternatively, such data quality indicators may be utilized by an operator or automation rules to update logging control parameters. 
       FIG. 7  shows a method  400  for determining data quality indicators for MCI measurements. The method  400  may be performed by surface computer  302  and/or MCI logging tool  126  or  134 . As shown, the method  400  includes performing calibration and temperature correction for MCI logging tool  126  or  134  (block  402 ). At block  404 , MCI measurement data is received. The received MCI measurement data may correspond to MCI measurements associated with multiple runs, multiple frequencies, and/or multiple sub-arrays. At block  406 , raw data for different runs, for different frequencies, and/or for different sub-arrays are compared. For example, the comparison may determine whether measurements follow a predetermined inequality pattern (e.g., equations 2 or 3), the degree of difference between single-run measurements at different frequencies, the degree of different between single-run measurements for different sub-arrays, and/or the degree of difference between multi-run measurements. At block  408 , processed data for inverted parameters (e.g., formation dip, R v , and R h ) and borehole compensated (BHC) logs for different frequencies and/or for different sub-arrays are compared to determine the degree of different between processed results. At block  410 , data quality indicators for the MCI measurements are determined based on the comparisons of raw data and/or processed data as described herein. 
     In at least some embodiments, the method  400  may include various other steps. More specifically, step  406  and/or step  408  may include calculating the relative difference or standard deviation of measurements from different runs. Further, a determination regarding whether measurement distribution is within a threshold may be used to determine a data quality indicator. For cross components of multi-run measurements, the strike angle may be computed using MCI responses. Once the strike is known, MCI responses may be rotated to a zero-degree strike angle to obtain MCI data in the strike system. Further, combined MCI responses for different runs may be computed. Subsequently, the combined MCI responses are compared and the relative differences and standard deviations are determined. In at least some embodiments, a difference or deviation of up to 5% is acceptable. 
     As an example, the main-run measurements for different frequencies (e.g., 12, 36, 60, and 84 kHz for Xaminer™ MCI tool) and different sub-arrays may be compared. From the comparison of available multi-run measurements, a determination is made regarding whether there is a threshold agreement between all nine components (this shows the measurements are sufficiently precise). In order to reduce the effects of the so-called bias or systematic error and tool positions, other data comparisons are conducted (e.g., comparing combined signals, comparing measurements for different frequencies, and/or comparing measurements for different sub-arrays) to determine if data quality criteria are met and/or to determine data quality indicators as described herein. For example, if inequalities (e.g., σ IJ   (i+1, j) ≦σ IJ   (i, j) ≦σ IJ   (i−1, j)  or σ IJ   (i+1, j) ≧σ IJ   (i, j) ≧σ IJ   (i−1, j) ) are observed for different frequencies at a given run and sub-array, or for different sub-arrays of a given run and frequency, then at least some data quality criteria are considered to be met and the data quality indicators will so indicate. 
     In at least some embodiments, block  408  includes processing MCI data (e.g., radially one-dimensional (R1D) inversion and BHC) to obtain inverted parameters such as formation dip, R h  and R v . Further, the processed MCI data may be compared (e.g., comparing measurements for different frequencies and/or different sub-arrays) to determine relative differences and deviations for multiple measurements. 
     In at least some embodiments, step  408  includes computing the relative error or standard deviation (e.g., to quantitatively measure the consistency of inversion results) for different frequency measurements and/or different sub-array measurements. More specifically, the data quality of the raw measurements may be computed as: 
     
       
         
           
             
               
                 
                   
                     
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     where x j  represents the inverted parameter (e.g., x j  may be formation dip, R h , R v , the log transformation of R h (x j =log(R h )), or the log transformation of R v (x j =log(R v )) of the MCI measurement at the j-th frequency for the i-th sub-array). The value x j − x  is sometimes called the mean error or difference of x j . In equation 4, e r   (j)  is the relative difference between x j  and  x  and is sometimes expressed as a percentage (i.e., relative difference percentage=e r   (j) ×100). Further,  x  may be the arithmetic or weighted mean of the multi-frequency inverted results (x 1 , x 2 , . . . , x M ) expressed as, 
     
       
         
           
             
               
                 
                   
                     
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     Alternatively, the ratio of the standard deviation to the mean may be computed as, 
     
       
         
           
             
               
                 
                   
                     
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     where the ratio S′ is the coefficient of variation for a measurement, and is independent of measurement units. 
     In at least some embodiments, equation 4 may be used to evaluate the data differences for frequency inversions, and equations 6a and 6b are used to evaluate the data differences for multi-frequency inversion results. The relative difference or deviation describes the spread or dispersion of different frequency inversion results about the mean. For example, a small standard deviation indicates that all inverted results are clustered tightly around a mean value. Conversely, a large standard deviation indicates that the inverted values are scattered widely about the mean. In practice, differences are observed due to the measured errors and limitations of the processing methods. Thus, similar inverted results for different sub-arrays and frequencies indicate indirectly a higher data quality. 
     In at least some embodiments, step  410  may include determining data quality indicators in a variety of ways. For example, inequality patterns (e.g., equations 2 or 3) and measurement deviations may be used as previously discussed. In addition, values of e r   (j)  and S may be used, where smaller values of e r   (j)  and S indicate better data quality and can be used to select a data quality indicator accordingly. Further, data error for one or more components of different sub-arrays and frequencies may be compared with the values of e r   (j)  and S computed from the comparison of inversion parameters to determine a data quality indicator. 
     In at least some embodiments, the method  400  combines raw data comparisons and MCI data processing for the evaluation of measured data quality. Even if the multiple run measurements are not available, method  400  is able to determine a reasonable data quality indicator. In such case, the amount of logging time in the field may be reduced. In at least some embodiments, method  400  determines data quality indicators throughout the process of data acquisition, processing, and interpretation. 
       FIG. 8  shows an illustrative flowchart  500  for iterative MCI logging using data quality indicators. The method  500  may be performed by surface computer  302  and/or MCI logging tool  126  or  134 . As shown, the method  500  includes measuring raw data (σ xx , . . . , σ zz ) at block  502 , measuring processed MCI zz  data (R 10 , . . . , R 90 ) quality at block  504 , and measuring MCI data (e.g., R h , R v , dip, strike) at block  506 . At block  508 , the data measured at blocks  502 ,  504 , and  506  are compared with thresholds to determine one or more data quality indicators. For example, the thresholds may correspond to an inequality pattern (equations 2 or 3) or measurement deviation thresholds as described herein. It should be noted that not all of the data from blocks  502 ,  504 , and  506  need be utilized at block  508  (data from one of blocks  502 ,  504 ,  506  is sufficient). However, utilization of more data at block  508  can provide information for a wider range of stability and consistency issues. If a cost function is satisfied (determination block  510 ), a logging report is generated with data quality indicator information (block  512 ). If the cost function is not satisfied (determination block  512 ), a logging workflow is adjusted (block  514 ), and the method  500  returns to blocks  502 ,  504 , and  506 , and the steps of method  500  are repeated until the cost function is satisfied (determination block  510 ), or until an operator selects to end logging operations. In at least some embodiments, raw data, processor data, or inversion parameters can be displayed for analysis or reporting along with data quality indicators even if the cost function is not satisfied. In other words, step  512  may be performed after step  508  without regard to decision block  510 . 
     The method  500  illustrates that data quality indicators can be used in a feedback loop, where logging results are improved by adjusting workflow parameters such as visualization parameters, processing parameters, or other controllable parameters. In at least some embodiments, updating visualization parameters involves marking or removing data with low quality from logs. Such marking can be performed by placing arrows or text in low quality zones, or placing a curve that indicates the quality of the logs. It is also possible to adjust filters that are used in reduction of noise or horn effects. For example, filter cut-offs can be moved and the bands can be made wider or narrower depending on the requirements. Further, if too much horn effect or noise is found in the curves, filters can be adjusted to allow less of the signal out. Further, if a signal is very high in quality, filters can be adjusted to allow for more of the signal out. Filters can also be designed based on the quality parameters obtained for optimization. It is also possible to adjust the signal selection that is used in various stages of processing. For example, spacing that will be used in RID processing can be changed based on data quality indicators. In addition, the frequency that will be delivered can be chosen based on data quality indicators. In at least some embodiments, less weight can be given to signals with less quality, and vice-versa. It is also possible to switch an MCI logging tool to a different set of frequencies. As an example, if high frequencies are found to be more accurate, a frequency set centered around a high frequency can be used. It is also possible to adjust the listening time for each frequency based on data quality indicators. Finally, a fluid separator can be used in the borehole if the quality of curves are deemed too low due to water based mud effects that are outside tool operating range. 
     Numerous other modifications, equivalents, and alternatives, will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such modifications, equivalents, and alternatives where applicable.