Abstract:
Misalignment of the transmitter and receiver antennas of an induction logging tool is determined by positioning the logging tool with a conducting loop magnetically coupled to the transmitter antenna and/or the receiver antenna, and activating the transmitter at a plurality of rotational angles. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present application is a continuation-in-part of U.S. patent application Ser. No. 11/340,785 filed on 26 Jan. 2006. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention is related to the field of apparatus design in the field of oil exploration. In particular, the present invention describes a method for calibrating multicomponent logging devices used for detecting the presence of oil in boreholes penetrating a geological formation.  
         [0004]     2. Description of the Related Art  
         [0005]     Electromagnetic induction resistivity well logging instruments are well known in the art. Electromagnetic induction resistivity well logging instruments are used to determine the electrical conductivity, and its converse, resistivity, of earth formations penetrated by a borehole. Formation conductivity has been determined based on results of measuring the magnetic field of eddy currents that the instrument induces in the formation adjoining the borehole. The electrical conductivity is used for, among other reasons, inferring the fluid content of the earth formations.  
         [0006]     In general, when using a conventional induction logging tool with transmitters and receivers (induction coils) oriented only along the borehole axis, the hydrocarbon-bearing zones are difficult to detect when they occur in multi-layered or laminated reservoirs. These reservoirs usually consist of thin alternating layers of shale and sand and, oftentimes, the layers are so thin that due to the insufficient resolution of the conventional logging tool they cannot be detected individually. In this case the average conductivity of the formation is evaluated.  
         [0007]     Conventional induction well logging techniques employ antennas wound on an insulating mandrel. One or more transmitter antennas are energized by an alternating current. The oscillating magnetic field produced by this arrangement results in the induction of currents in the formations which are nearly proportional to the conductivity of the formations. These currents, in turn, contribute to the voltage induced in one or more receiver antenna. By selecting only the voltage component which is in phase with the transmitter current, a signal is obtained that is approximately proportional to the formation conductivity. In conventional induction logging apparatus, the basic transmitter antenna and receiver antenna has axes which are aligned with the longitudinal axis of the well logging device. This arrangement tends to induce secondary current loops in the formations that are concentric with the vertically oriented transmitting and receiving antennas. The resultant conductivity measurements are indicative of the horizontal conductivity (or resistivity) of the surrounding formations. There are, however, various formations encountered in well logging which have a conductivity that is anisotropic. Anisotropy results from the manner in which formation beds were deposited by nature. For example, “uniaxial anisotropy” is characterized by a difference between the horizontal conductivity, in a plane parallel to the bedding plane, and the vertical conductivity, in a direction perpendicular to the bedding plane. When there is no bedding dip, horizontal resistivity can be considered to be in the plane perpendicular to the bore hole, and the vertical resistivity in the direction parallel to the bore hole. Conventional induction logging devices, which tend to be sensitive only to the horizontal conductivity of the formations, do not provide a measure of vertical conductivity or of anisotropy.  
         [0008]     In a transverse induction logging tools the response of transversal antenna arrays is also determined by an average conductivity, however, the relatively lower conductivity of hydrocarbon-bearing sand layers dominates in this estimation. In general, the volume of shale/sand in the formation can be determined from gamma-ray or nuclear well logging measurements. Then a combination of the conventional induction logging tool with transmitters and receivers oriented along the well axis and the transversal induction logging tool can be used for determining the conductivity of individual shale and sand layers.  
         [0009]     One, if not the main, difficulties in interpreting the data acquired by a transversal induction logging tool is associated with vulnerability of its response to borehole conditions. Among these conditions is the presence of a conductive well fluid as well as wellbore fluid invasion effects  
         [0010]     In the induction logging instruments the acquired data quality depends on the formation electromagnetic parameter distribution (conductivity) in which the tool induction receivers operate. Thus, in the ideal case, the logging tool measures magnetic signals induced by eddy currents flowing in the formation. Variations in the magnitude and phase of the eddy currents occurring in response to variations in the formation conductivity are reflected as respective variations in the output voltage of receivers. In the conventional induction instruments these receiver induction antenna voltages are conditioned and then processed using analog phase sensitive detectors or digitized by digital to analog converters and then processed with signal processing algorithms. The processing allows for determining both receiver voltage amplitude and phase with respect to the induction transmitter current or magnetic field waveform.  
         [0011]     There are a few hardware margins and software limitations that impact a conventional transversal induction logging tool performance and result in errors appearing in the acquired data.  
         [0012]     The general problems encountered are discussed in U.S. Pat. No. 6,734,675 and U.S. Pat. No. 6,586,939 to Fanini et al., both having the same assignee as the present application and the contents of which are incorporated herein by reference. Fanini &#39;939 discloses a transverse induction logging tool having a transmitter and receiver for downhole sampling of formation properties, the tool having a symmetrical shielded split-coil transmitter antenna and a bucking coil interposed between the split transmitter coils to reduce coupling of the transmitter time varying magnetic field into the receiver. The tool provides symmetrical shielding of the coils and grounding at either the transmitter or receiver end only to reduce coupling of induced currents into the received signal. The tool provides an insulator between receiver electronics and the conductive receiver housing having contact with conductive wellbore fluid, to reduce parasitic current flowing in a loop formed by the upper housing, feed through pipe, lower housing and wellbore fluid adjacent the probe housing or mandrel. An internal verification loop is provided to track changes in transmitter current in the real and quadrature component of the received data signal.  
         [0013]     Fanini &#39;675 discloses a transverse induction logging tool having a transmitter and receiver for downhole sampling of formation properties, the tool having a symmetrical shielded split-coil transmitter antenna and a bucking coil interposed between the split transmitter coils to reduce coupling of the transmitter time varying magnetic field into the receiver. The tool provides symmetrical shielding of the coils and grounding at either the transmitter or receiver end only to reduce coupling of induced currents into the received signal. The tool provides an insulator between receiver electronics and the conductive receiver housing having contact with conductive wellbore fluid, to reduce parasitic current flowing in a loop formed by the upper housing, feed through pipe, lower housing and wellbore fluid adjacent the probe housing or mandrel. An internal verification loop is provided to track changes in transmitter current in the real and quadrature component of the received data signal.  
       SUMMARY OF THE INVENTION  
       [0014]     One embodiment of the invention is an apparatus for evaluating an induction logging tool for use in a borehole. The logging tool includes a current source which activates a transmitter antenna on the logging tool and a receiver antenna spaced apart axially from the transmitter antenna wherein the receiver antenna produces a signal in response to the activation of the transmitter coil. The apparatus includes at least one conducting loop which magnetically coupled to the transmitter antenna and/or the receiver antenna. The signal produced by the receiver coil is indicative of a misalignment between the transmitter antenna and the receiver antenna. A single conducting loop may encompass both the transmitter antenna and the receiver antenna. Two electrically connected conducting loops may be used with one of the loops encompassing the transmitter antenna and the other loop encompassing the receiver antenna. The transmitter antenna may have an axis substantially parallel to or substantially orthogonal to a longitudinal axis of the logging tool. The receiver antenna may have an axis substantially parallel to or substantially orthogonal to a longitudinal axis of the logging tool. The apparatus may further include a support which rotates the logging tool through a plurality of angles with the transmitter being activated at each of the angles, and a processor which estimates from the signals at each of the rotational angles the angle of misalignment. The misalignment angle may be estimated based on a rotational angle at which the signal is substantially zero.  
         [0015]     Another embodiment of the invention is a method of evaluating an induction logging tool for use in a borehole. A transmitter antenna on the tool is activated. A signal is provided using a receiver antenna in response to the activation of the transmitter antenna. Magnetic coupling is provided between a conducting loop and the transmitter antenna and/or receiver antenna. From the signal, a misalignment angle between the transmitter coil and the receiver coil. The method includes using at least one conducting loop for axially encompassing the transmitter antenna and/or the receiver antenna. The encompassing may be done by using a single conducting loop. The encompassing may be done by using a first loop for encompassing the transmitter antenna and a second loop for encompassing the receiver antenna. The transmitter antenna may have an axis that is substantially parallel to or orthogonal to a longitudinal axis of the tool. The receiver antenna may have an axis that is substantially parallel to or orthogonal to a longitudinal axis of the tool. The logging tool may be rotated through a plurality of angles with the transmitter being activated at each of the angles, and the misalignment angle may be estimated from the signals at each of the angles. The misalignment angle may be estimated from an angle at which the signal is substantially zero.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]     The present invention is best understood with reference to the accompanying figures in which like numerals refer to like elements and in which:  
         [0017]      FIG. 1  (prior art) shows schematically a wellbore extending into a laminated earth formation, into which wellbore an induction logging tool as used according to the invention has been lowered;  
         [0018]      FIG. 2A  (prior art) illustrates a conventional resistivity measurement in the vertical direction;  
         [0019]      FIG. 2B  (prior art) illustrates a resistivity measurement in the horizontal direction;  
         [0020]      FIG. 3  is an overall flow chart of the procedures of the present invention;  
         [0021]      FIG. 4  illustrates an assembly for calibrating of transverse arrays in a logging tool;  
         [0022]      FIG. 5  illustrates an assembly for calibrating longitudinal arrays in a logging tool;  
         [0023]      FIGS. 6-7  illustrate assemblies for calibrating XY cross-component arrays; and  
         [0024]      FIGS. 8-9  illustrate assemblies for calibrating XZ cross-component arrays. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0025]     The instrument structure provided by the present invention enables increased stability and accuracy in an induction wellbore logging tool and its operational capabilities, which, in turn, results in better quality and utility of wellbore data acquired during logging. The features of the present invention are applicable to improve the structure of a majority of known induction tools.  
         [0026]     The invention will now be described in more detail and by way of example with reference to the accompanying drawings.  FIG. 1  schematically shows a wellbore  1  extending into a laminated earth formation, into which wellbore an induction logging tool as used according to the present invention has been lowered. The wellbore in  FIG. 1  extends into an earth formation which includes a hydrocarbon-bearing sand layer  3  located between an upper shale layer  5  and a higher conductivity than the hydrocarbon bearing sand layer  3 . An induction logging tool  9  used in the practice of the invention has been lowered into the wellbore  1  via a wire line  11  extending through a blowout preventor  13  (shown schematically) located at the earth surface  15 . The surface equipment  22  includes an electric power supply to provide electric power to the set of coils  18  and a signal processor to receive and process electric signals from the receiver coils  19 . Alternatively, the power supply and/or signal processors are located in the logging tool.  
         [0027]     The relative orientation of the wellbore  1  and the logging tool  9  with respect to the layers  3 ,  5 ,  7  is determined by two angles, one of which θ as shown in the  FIG. 1 . For determination of these angles see, for example, U.S. Pat. No. 5,999,883 to Gupta, et al. The logging tool  9  is provided with a set of transmitter coils  18  and a set of receiver coils  19 , each set of coils  18 ,  19  being connected to surface equipment  22  via suitable conductors (not shown) extending along the wire line  11 .  
         [0028]     Each set of coils  18  and  19  includes three coils (not shown), which are arranged such that the set has three magnetic dipole moments in mutually orthogonal directions, that is, in x, y and z directions. The three-coil transmitter coil set transmits T x , T y  and T z . The receiver coil receives R x , R y  and R z  plus the cross components, R xy , R xz  and R zy . Thus, coil set  18  has magnetic dipole moments  26   a ,  26   b ,  26   c , and coil set  19  has magnetic dipole moments  28   a ,  28   b ,  28   c . In one embodiment the transmitter coil set  18  is electrically isolated from the receiver coil set  19 . In an alternative embodiment, each coil in transmitter coil set  18  electrically isolated from each other and each coil in receiver coil set  19  electrically isolated from each other. The coils with magnetic dipole moments  26   a  and  28   a  are transverse coils, that is they are oriented so that the magnetic dipole moments are oriented perpendicular to the wellbore axis, whereby the direction of magnetic dipole moment  28   a  is opposite to the direction of magnetic dipole moment  26   a . Furthermore the sets of coils  18  and  19  are positioned substantially along the longitudinal axis of the logging tool  9 .  
         [0029]     As shown in  FIG. 2A , conventional induction logging tools provide a single transmitter and receiver coil that measure resistivity in the horizontal direction. In the conventional horizontal mode, as shown in  FIG. 2A , the resistivities of adjacent high resistivity sand and low resistivity shale layers appear in parallel, thus the resistivity measurement is dominated by low resistivity shale. As shown in  FIGS. 1 and 2 B, in the present invention a transverse coil is added to measure resistivity in the vertical direction. In the vertical direction, the resistivity of the highly resistive sand and low resistivity shale are appear in series and thus the vertical series resistivity measurement is dominated by the resistivity of the highly resistive sand.  
         [0030]     For ease of reference, normal operation of the tool  9 , as shown in  FIGS. 1 and 2 B, will be described hereinafter only for the coils having dipole moments in the x-direction, i.e. dipole moments  26   a  and  28   a . During normal operation an alternating current of a frequency f 1  is supplied by the electric power supply of surface equipment  22  to transmitter coil set  18  so that a magnetic field with magnetic dipole moment  26   a  is induced in the formation. In an alternative embodiment, the frequency is swept through a range f 1  through f 2 . This magnetic field extends into the sand layer  3  and induces a number of local eddy currents in the sand layer  3 . The magnitude of the local eddy currents is dependent upon their location relative to the transmitter coil set  18 , the conductivity of the earth formation at each location, and the frequency at which the transmitter coil set  18  is operating. In principle the local eddy currents act as a source inducing new currents, which again induce further new currents, and so on. The currents induced into the sand layer  3  induces a response magnetic field in the formation, which is not in phase with the transmitted magnetic field, but which induces a response current in receiver coil set  19 . The magnitude of the current induced in the sand layer  3  depends on the conductivity of the sand layer  3 , the magnitude of the response current in receiver coil set  19 . The magnitude also depends on the conductivity and thereby provides an indication of the conductivity of the sand layer  3 . However, the magnetic field generated by transmitter coil set  18  not only extends into sand layer  3 , but also in the wellbore fluid and in the shale layers  5  and  7  so that currents in the wellbore fluid and the shale layers  5  and  7  are induced.  
         [0031]     The overall procedures of the present invention used to ensure proper functioning of a deployed multicomponent induction logging tool is summarized in  FIG. 3 . Calibration of the instrument&#39;s arrays is done, particularly estimating its transfer coefficient  101 . Subsequently, a final verification of the tuning and calibration consistency is performed  103 .  
         [0032]     Turning now to  FIG. 4 , one arrangement of the alignment loop is discussed. Shown therein is an alignment loop  501  surrounding an array characterized by the transmitter antenna  504  directed along an X direction (T x ) and the receiver antenna  508  directed along the X direction (R x ). Bucking coil B x    506  is also shown. This array is denoted as XX, using a nomenclature in which the first letter signifies the orientation direction of the transmitter antenna and the last letter signifies the orientation direction of the receiver antenna. This nomenclature is generally used herein. The XX and YY arrays in the multi-component tool are ideally aligned at 90° from each other. When this alignment is not met, the response of the cross components (XY, YX) are affected by part of the reading of the related main component. The alignment measuring method of the present invention is based on analyzing the output of the cross-component system when the tool is rotated inside of an alignment loop. The alignment loop is magnetically coupled to the transmitter antenna and the receiver antenna.  
         [0033]     The alignment loop  501  is a stationary loop, lying so that the longitudinal axis of the loop and the longitudinal axis of the well-logging tool are substantially aligned. Its dimensions are such as to obtain substantial inductive coupling with the transmitter as well as with the receiver of both XX and YY arrays. An important aspect of the present invention is that no portion of either the transmitter or the receiver coil extends beyond the loop. This is in contrast to prior art devices in which this condition is not satisfied. When this condition is not satisfied, the resulting calibration is sensitive to the position of the calibration loop relative to the transmitter and receiver antennas, and is hence suspect. The arrangement shown in  FIG. 5  uses a single calibration loop where this condition is satisfied. The single calibration loop axially encompasses the transmitter coil and the receiver coil. A detailed analysis of the signals is given later in this document. The logging tool is supported within the alignment loop by suitable support (not shown) that has the capability of rotating the logging tool about its axis through known angles.  
         [0034]      FIG. 5  illustrates a loop alignment assembly usable for aligning ZZ arrays in a testing device. Transmitter TZ  601 , bucking coil BZ  603  and receiver RZ  605  are disposed along the feed-through pipe  615  and have a common longitudinal axis. Alignment loop  610  is substantially coaxial with receiver RZ  605  and substantially centered on RZ. As with the arrangement of  FIG. 5 , the receiver coil is axially encompassed by d the calibration loop  610 .  
         [0035]     Cross component array calibration is discussed next.  FIG. 6  illustrates an embodiment for calibration of an XY array using a calibration box. This functions in the same manner as a calibration loop, and may be considered to be one. Transmitter  701  and bucking coil  703  are disposed along the feed-through pipe oriented to produce a magnetic moment in an X-direction. Receiver  705  is disposed along the same feed-through pipe having an orientation so as to receive components of a magnetic moment in a is disposed along the same feed-through pipe having an orientation so as to receive components of a magnetic moment in Y-direction. The alignment loop  710  is disposed at an angle of 45° so as to be oriented halfway between the X-direction and the Y-direction. To simplify the illustration, the box has been depicted without showing it as extending beyond the transmitter and receiver coils.  
         [0036]     Those skilled in the art would recognize that the alignment loop shown in  FIGS. 4 and 6  would be bulky and possible difficult to manage under field conditions. An embodiment of the present invention that addreses this problem is discussed next.  FIG. 7  illustrated an alternate embodiment for aligning an XY array. Alignment loop  815  is located at the TX  801 , and alignment loop  810  is positioned at the RXY cross-component receiver  805 . Both alignment loops are oriented along the same direction as their respective transmitter/receiver. A wire  820  electrically couples alignment loop  810  and alignment loop  815 . The individual loops  810  and  815  are easier to handle than a single large box, and by use of the electrical connection  820 , are functionally equivalent to box  501  of  FIG. 4 . In the configuration of  FIG. 7 , the loop  815  axially encompasses the transmitter coil  801  and the loop  810  axially encompasses the receiver coil.  
         [0037]      FIG. 8  illustrates an assembly for orienting of the XZ cross-component array. Transmitter TX  901  and bucking coil BX  903  are disposed along the feed-through pipe oriented so as to produce a magnetic moment along an X-direction. The receiver RZ  905  is disposed along the feed-through pipe and oriented so as to be receptive to Z-components of magnetic moments. The alignment loop  920  can be positioned centrally between main X-transmitter  901  and Z-cross-component receiver  905  and tilted 45° with respect to the tool longitudinal axis  910 . The assembly of  FIG. 8  displays small signals during XZ array calibration. This signal tends to display a high sensitivity to the angle.  
         [0038]      FIG. 9  illustrates an alternate embodiment for aligning the XZ cross-component array. As in the apparatus shown in  FIG. 7 , two loops are used. Transmitter TX  1001  and bucking coil BX  1003  are disposed along the feed-through pipe oriented so as to produce a magnetic moment along an X-direction. The receiver RZ  1005  is disposed along the feed-through pipe and oriented so as to be receptive to Z-components of magnetic moments. Alignment loop  1010  is centered on transmitter TX  1001 , and alignment loop  1015  is coaxial with receiver RZ  1005 . A wire  1020  electrically couples alignment loop  1010  and alignment loop  1015 . In contrast to the assembly of  FIG. 8 , calibration using two alignment devices displays a large signal for the XZ array calibration.  
         [0039]     We next discuss in detail the use of the alignment loop for establishing the coil orientation. When examining a cross-component array, the XY or YX response obtained by rotating the tool inside of the alignment loop has a zero-crossing each time that either a transmitter or a receiver coil is perpendicular to the plane of the loop. Whichever coil (transmitter or receiver) is substantially aligned with the loop (enclosed in the same plane) experiences a maximum coupling with the alignment loop. When the position of the aligned coil is varied around the point of alignment with the alignment loop, the coupling response between them undergoes a slow change corresponding to the variation. The non-aligned coil experiences a minimum coupling with the alignment loop. When the position of the non-aligned coil is varied around this point of minimal coupling, the coupling experiences an abrupt change. The coupling becomes zero when the non-aligned coil achieves perpendicularity with the alignment loop. A practitioner in the art would recognize that the zero-crossings of the coupling response are significantly affected by the coil that is at right angle to the alignment loop, regardless of whether the perpendicular coil is a receiver or a transmitter. The substantially aligned coil plays little or no role in the production of a zero-crossing. The angle between successive zero crossings thereby represents an alignment angle between the two related coils.  
         [0040]     Mathematically, the inductive coupling between two coils resembles a cosine function of the angle between them. Thus, the coupling response system of coils made by an aligned system of cross components and an alignment loop is given by the following expression:  
                 R   ⁡     (   ϕ   )       =     K   ·     cos   ⁡     (   ϕ   )           ⁣     ·       cos   ⁡     (     ϕ   -     π   2       )       .               (   1   )             
 
 Applying trigonometric identities, Eq. (1) can be simplified to  
                 R   ⁡     (   ϕ   )       =     K   ·     cos   ⁡     (   ϕ   )       ·     sin   ⁡     (   ϕ   )           ,     
     ⁢     and   ⁢           ⁢   since             (   2   )                     sin   ⁡     (   ϕ   )       ·     cos   ⁡     (   ϕ   )         =       1   2     ⁢     sin   ⁡     (     2   ·   ϕ     )           ,     
     ⁢     it   ⁢           ⁢   follows   ⁢           ⁢   that             (   3   )                 R   ⁡     (   ϕ   )       =     K   ·     1   2     ·       sin   ⁡     (     2   ·   ϕ     )       .               (   4   )             
 
 Eqn. (4) illustrates that there are two cycles of variation for each cycle of tool rotation. 
 
         [0041]     By considering a misalignment angle β between transmitter and receiver, the response function can now be expressed as  
                 R   ⁡     (     ϕ   ,   β     )       =     K   ·     cos   ⁡     (   ϕ   )       ·     cos   ⁡     (     ϕ   -     π   2     +   β     )           ,           (   5   )             
 
 where each cosine function characterizes the response of the individual cross component coils. It is easy to see that  
                   R   ⁡     (     ϕ   ,   β     )       =   0     ,     
     ⁢   when     ⁢     
     ⁢     ϕ   =     n   ·     π   2         ⁢     
     ⁢     or   ⁢           ⁢   when             (   6   )                   ϕ   -     π   2     +   β     =         n   ·     π   2       ⁢           ⁢   with   ⁢           ⁢   n     =     ±   1         ,   2   ,   3   ,   …           Eq   .           ⁢     (   7   )               
 
 According to eqn. (7), the angle between successive zero-crossings represents the alignment angle among the cross component coils. An intuitive graphical approach can therefore be used to measure the misalignment angle between transmitter and receiver. 
 
         [0042]     Alternatively, the misalignment angle can be obtained simply by using a trigonometric regression function to analyze the response of the system. Applying trigonometric identities to Eqn. (5), the response of the misaligned system can be written as  
                 R   ⁡     (     ϕ   ,   β     )       =       K   ·     cos   ⁡     (   ϕ   )       ·     sin   ⁡     (   ϕ   )       ·     cos   ⁡     (   β   )         +     K   ·       cos   2     ⁡     (   ϕ   )       ·     sin   ⁡     (   β   )             ⁢     
     ⁢       R   ⁡     (     ϕ   ,   β     )       =       K   ·     1   2     ·     sin   ⁡     (     2   ·   ϕ     )       ·     cos   ⁡     (   β   )         +     K   ·       cos   2     ⁡     (   ϕ   )       ·     sin   ⁡     (   β   )             ⁢     
     ⁢       R   ⁡     (     ϕ   ,   β     )       =         K   2     ·     sin   ⁡     (       2   ·   ϕ     +   β     )         +       K   2     ·     sin   ⁡     (   β   )                     (   8   )             
 
 The last expression in eqn. (8) indicates that a graphical representation of the coupling response of the misaligned cross component system resembles a sinusoidal function. The period of this sinusoid equals 180° and has offsets on both the abscissa and the ordinate. The offset on the abscissa is β, and the offset on the ordinate is (K/2)sin(β). Also, the coupling response is of the form A sin(x+B)+C, where A=K/2, B=β and C=(K/2)(sin(β). The coefficient B obtained with such fitting represents the misalignment angle. The cross component response can thus be fit to this curve. 
 
         [0043]     Implicit in the control and processing of the data is the use of a computer program on a suitable machine readable medium that enables the processor to perform the control and processing. The machine readable medium may include ROMs, EPROMs, EEPROMs, Flash Memories and Optical disks.  
         [0044]     While the foregoing disclosure is directed to the preferred embodiments of the invention, various modifications will be apparent to those skilled in the art. It is intended that all variations within the scope and spirit of the appended claims be embraced by the foregoing disclosure.  
         [0045]     The following definitions are helpful in understanding the scope of the invention: 
    alignment: the proper positioning or state of adjustment of parts in relation to each other;     calibrate: to standardize by determining the deviation from a standard so as to ascertain the proper correction factors;     coil: one or more turns, possibly circular or cylindrical of a current-carrying conductor capable of producing, a magnetic field;     EAROM: electrically alterable ROM;     Encompass: to enclose completely     EPROM: erasable programmable ROM;     flash memory: a nonvolatile memory that is rewritable;     machine readable medium: something on which information may be stored in a form that can be understood by a computer or a processor;     misalignment: the condition of being out of line or improperly adjusted;     Optical disk: a disc shaped medium in which optical methods are used for storing and retrieving information;     Position: an act of placing or arranging; the point or area occupied by a physical object     Quadrature: 90° out of phase; and     ROM: Read-only memory.