Abstract:
A detector for calculating a depth of a buried conductor is provided. The detector includes first, second and third antennas and a microprocessor. The second antenna has an axis parallel to an axis of the first antenna and is spaced a distance s from the first antenna. The third antenna has an axis parallel to the axes of the first and second antennas and is spaced a distance 2s from the first antenna and a distance s from the second antenna. The microprocessor is configured to compare magnetic fields at the first and second antennas to produce a first compared value, compare magnetic fields at the first and third antennas to produce a second compared value, and calculate the depth of said buried conductor based on the first and second compared values.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to United Kingdom Patent Application GB 0803992.7, filed on Mar. 3, 2008, and entitled “A Detector for Calculating a Depth of a Buried Conductor,” the disclosure of which is incorporated herein by reference in its entirety. 
     FIELD OF THE INVENTION 
     The present invention relates to a detector for calculating a depth of a buried conductor. 
     BACKGROUND OF THE INVENTION 
     Before commencing excavation or other work where electrical cables, fibre optic cables or other utilities ducts or pipes are buried, it is important to determine the location of such buried cables or pipes to ensure that they are not damaged during the work. Once a buried utility is located the depth of the utility can be calculated to determine a safe excavation depth. 
     Current carrying conductors emit electromagnetic radiation which can be detected by an electrical antenna. If fibre optic cables or non-metallic utilities ducts or pipes are fitted with a small electrical tracer line, an alternating electrical current can be induced in the tracer line which in turn radiates electromagnetic radiation. It is known to use detectors to detect the electromagnetic field emitted by conductors carrying alternating current. 
     One type of such detector works in one of two modes, namely ‘active’ or ‘passive’ modes. Each mode has its own frequency bands of detection. 
     The passive mode comprises ‘power’ mode and ‘radio’ mode. In power mode, the detector detects the magnetic field produced by a conductor carrying an AC mains power supply at 50/60 Hz, or the magnetic field re-radiated from a conductor as a result of a nearby cable carrying AC power, together with higher harmonics up to about 5 KHz. In radio mode, the detector detects very low frequency (VLF) radio energy which is re-radiated by buried conductors. The source of the original VLF radio signals is a plurality of VLF long wave transmitters, both commercial and military. 
     In the active mode, a signal transmitter produces an alternating magnetic field of known frequency and modulation, which induces a current in a nearby buried conductor. The signal transmitter may be directly connected to the conductor or, where direct connection access is not possible, a signal transmitter may be placed near to the buried conductor and a signal may be induced in the conductor. The buried conductor re-radiates the signal produced by the signal transmitter. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention advantageously provide a detector for calculating a depth of a buried conductor, and an associated method. 
     According to a first aspect of the invention there is provided a detector for calculating a depth of a buried conductor, the detector comprising: a first antenna; a second antenna having its axis parallel to an axis of the first antenna and spaced a distance s from the first antenna; a third antenna having its axis parallel to the axes of the first and second antennas and spaced a distance 2s from the first antenna and a distance s from the second antenna; means for comparing magnetic fields at the first and second antennas to produce a first compared value; means for comparing magnetic fields at the second and third antennas to produce a second compared value; and means for calculating the depth of said buried conductor based on the first and second compared values. 
     The magnetic fields at the first and second antennas and the magnetic fields at the second and third antennas may be compared using the relationship: 
     
       
         
           
             R 
             = 
             
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   M 
                 
               
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   T 
                 
               
             
           
         
       
     
     where:
         B B  is the magnetic field at the first antenna   B M  is the magnetic field at the second antenna; and   B T  is the magnetic field at the third antenna       

     and the depth d of said conductor below the first antenna may be calculated using the relationship: 
     
       
         
           
             d 
             = 
             
               
                 2 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   s 
                   ⁡ 
                   
                     ( 
                     
                       1 
                       - 
                       R 
                     
                     ) 
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   R 
                 
                 - 
                 1 
               
             
           
         
       
     
     Each antenna may output an analogue field strength signal representative of the electromagnetic field at the antenna. The detector may further comprise means for amplifying the field strength signals. 
     The detector may further comprise: means for converting the analogue field strength signals into digital signals; and means for processing the digital signals to isolate signals of predetermined frequency bands. 
     The means for converting the analogue field strength signals into digital signals may be a delta-sigma stereo CODEC. 
     Each pair of first and second antennas and second and third antennas may be calibrated to an accuracy of at least 1 part in 600,000. 
     According to a second aspect of the invention there is provided a method of calculating a depth of a buried conductor, the method comprising: providing a first antenna; providing a second antenna having its axis parallel to an axis of the first antenna and spaced a distance s from the first antenna; providing a third antenna having its axis parallel to the axes of the first and second antennas and spaced a distance 2s from the first antenna and a distance s from the second antenna; comparing magnetic fields at the first and second antennas to produce a first compared value; comparing magnetic fields at the second and third antennas to produce a second compared value; and calculating the depth of said buried conductor based on the first and second compared values. 
     The magnetic fields at the first and antennas and the magnetic fields at the second and third antennas may be compared using the relationship: 
     
       
         
           
             R 
             = 
             
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   M 
                 
               
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   T 
                 
               
             
           
         
       
     
     where:
         B B  is the magnetic field at the first antenna   B M  is the magnetic field at the second antenna; and   B T  is the magnetic field at the third antenna       

     and the depth d of said conductor below the first antenna may be calculated using the relationship: 
     
       
         
           
             d 
             = 
             
               
                 2 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   s 
                   ⁡ 
                   
                     ( 
                     
                       1 
                       - 
                       R 
                     
                     ) 
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   R 
                 
                 - 
                 1 
               
             
           
         
       
     
     Each antenna may output an analogue field strength signal representative of the electromagnetic field at the antenna. The method may further comprise amplifying the field strength signals. 
     The method may further comprise: converting the analogue field strength signals into digital signals; and processing the digital signals to isolate signals of predetermined frequency bands. 
     Each pair of first and second antennas and second and third antennas may be calibrated to an accuracy of at least 1 part in 600,000. 
     According to a third aspect of the invention there is provided a carrier medium carrying computer readable code for controlling a microprocessor to carry out the method described above. 
     According to a fourth aspect of the invention there is provided a detector for calculating a depth of a buried conductor, the detector comprising: a first antenna; a second antenna having its axis parallel to an axis of the first antenna and spaced a distance s from the first antenna; a third antenna having its axis parallel to the axes of the first and second antennas and spaced a distance 2s from the first antenna and a distance s from the second antenna; and a microprocessor, wherein the microprocessor is configured to: compare magnetic fields at the first and second antennas to produce a first compared value; compare magnetic fields at the second and third antennas to produce a second compared value; and calculate the depth of said buried conductor based on the first and second compared values. 
     The magnetic fields at the first and second antennas and the magnetic fields at the second and third antennas may be compared using the relationship: 
     
       
         
           
             R 
             = 
             
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   M 
                 
               
               
                 
                   B 
                   B 
                 
                 - 
                 
                   B 
                   T 
                 
               
             
           
         
       
     
     where:
         B B  is the magnetic field at the first antenna   B M  is the magnetic field at the second antenna; and   B T  is the magnetic field at the third antenna       

     and the depth d of said conductor below the first antenna may be calculated using the relationship: 
     
       
         
           
             d 
             = 
             
               
                 2 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   s 
                   ⁡ 
                   
                     ( 
                     
                       1 
                       - 
                       R 
                     
                     ) 
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   R 
                 
                 - 
                 1 
               
             
           
         
       
     
     Each antenna may output a field strength signal representative of the electromagnetic field at the antenna. The detector may further comprise amplifiers arranged to amplify the field strength signals. 
     The detector may further comprise: analogue to digital converters to convert the field strength signals into digital signals; and a digital signal processor arranged to process the digital signals and to isolate signals of predetermined frequency bands. The analogue to digital converter may be a delta-sigma stereo CODEC. 
     Each pair of first and second antennas and second and third antennas may be calibrated to an accuracy of at least 1 part in 600,000. 
     There has thus been outlined, rather broadly, certain embodiments of the invention in order that the detailed description thereof herein may be better understood, and in order that the present contribution to the art may be better appreciated. There are, of course, additional embodiments of the invention that will be described below and which will form the subject matter of the claims appended hereto. 
     In this respect, before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of embodiments in addition to those described and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein, as well as the abstract, are for the purpose of description and should not be regarded as limiting. 
     As such, those skilled in the art will appreciate that the conception upon which this disclosure is based may readily be utilized as a basis for the designing of other structures, methods and systems for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a detector according to an embodiment of the invention. 
         FIG. 2  is a schematic representation of two horizontal antennas of a known detector. 
         FIG. 3  is a schematic representation of three of the antennas of the detector of  FIG. 1 . 
         FIG. 4  is a block diagram of part of the detector of  FIG. 1  which processes the signals detected by the antennas of  FIG. 3 . 
         FIG. 5  is a schematic representation of two of the antennas of the detector of  FIG. 1 . 
         FIG. 6  is a schematic representation of a further two of the antennas of the detector of  FIG. 1 . 
         FIG. 7  is a block diagram of part of the digital signal processing block of the detector of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     The invention will now be described with reference to the drawing figures, in which like reference numerals refer to like parts throughout. 
       FIG. 1  is a block diagram of a portable detector  1  according to an embodiment of the invention. The detector  1  comprises five antennas  3  for detecting an electromagnetic signal radiated by a current carrying conductor. Each antenna  3  converts the electromagnetic field at the antenna into a field strength signal  5  which is output from the antenna  3 . 
     Each antenna output is passed to a pre-amplification and switching stage  7 . If the strength of the field strength signal  5  is low then the output from the antenna  3  is amplified and filtered with an equalization filter. If the field strength signal  5  output from the antenna  3  is adequate then the signal is fed directly into the next stage of the detector  1 . In addition to the outputs from the antennas  3 , other inputs can be directly applied to the detector  1  for example from accessories such as clamps, stethoscopes, underwater-probes and an A-frame for fault finding. 
     The output from the pre-amplification and switching stage  7  is fed into a super-heterodyne mixer  9 . The mixer circuit is designed to recover full magnitude and phase information from the carrier. 
     The output from the mixers  9  are fed into a CODEC  11 . The CODEC  11  is a 24-bit stereo delta-sigma analogue to digital converter (ADC). This is a relatively cheap device and has a poor absolute accuracy of ±1% but excellent ratiometric accuracy. However, the way that the CODEC  11  is used in the present invention makes it an ideal ADC as described below. The CODEC  11  over-samples the field strength signals at up to 96 KHz. The output of the CODEC  11  is fed into a digital signal processing block  13  which is comprised of a digital signal processor (DSP) and a field programmable date array (FPGA). 
     The detector  1  further comprises a power supply unit (PSU)  15  comprising a power source such as batteries and power management circuitry. A communications module  17  is provided to allow the detector  1  to be connected to a personal computer (PC) or personal digital assistant (PDA) to upload data stored in the detector  1  and to allow download from the PC/PDA to the detector  1 , for example software updates. The detector  1  further comprises a memory module  19  and a user interface module  21 . The user interface module  21  may comprise one or more of a display for displaying information to the operator of the device, input devices such as a keypad or a touch sensitive screen and audible output devices such as a speaker or beeper. The components of the portable detector  1  are housed in a housing (not shown). 
       FIG. 2  is a schematic representation of two horizontal vertically spaced antennas B, T of a known detector within an elongate vertically held housing (not shown). In use the detector is held vertical on ground  23  in which a current carrying conductor  25  is buried with the bottom antenna B close to the surface of the ground  23 . The axes of the antennas are parallel and the separation between the bottom antenna B and the top antenna T is 2s. The conductor  25  is buried at a depth d below the surface of the ground  23  (and below the bottom antenna B) and the horizontal displacement between the antennas B and T and the conductor  25  is x. 
     When alternating current flows in the conductor  25  the conductor  25  radiates an electromagnetic field. The magnetic flux density or magnetic field at the bottom antenna B B  and the top antenna B T  due to the electromagnetic field produced by the current carrying conductor  25  are respectively given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         B 
                         B 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           d 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           id 
                         
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   d 
                                   2 
                                 
                                 + 
                                 
                                   x 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       + 
                       C 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   and 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       B 
                       T 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         d 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         
                           i 
                           ⁡ 
                           
                             ( 
                             
                               d 
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   ( 
                                   
                                     d 
                                     + 
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       s 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               
                                 x 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where:
         μ 0  is the permeability of free space;   i is the current flowing in the conductor  25 ; and   C is a frequency dependent variable, known as the common mode field distortion.       

     Common mode field distortion is distortion of the electromagnetic field produced by the buried current carrying conductor  25  due to the complex impedance of the material in which the current carrying conductor  25  is buried. As the ground has a distributed complex impedance, the common mode field distortion results is a homogenous distortion of the signal due to return current through the ground. The complex impedance of the ground varies for different materials such as dry soil, wet clay and sand. For example, at a frequency of 83 KHz when the conductor is buried at a depth of 1.7 m in wet clay the contribution of C gives a 34% variation to the theoretical value of B. 
     The depth of a buried conductor based on magnetic flux density measurements B B  and B T  is: 
     
       
         
           
             
               
                 
                   d 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       s 
                     
                     
                       
                         
                           
                             B 
                             B 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               d 
                             
                             ) 
                           
                         
                         
                           
                             B 
                             T 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               d 
                             
                             ) 
                           
                         
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Substituting equations (1) and (2) into equation (3) when x=0, i.e., when the detector is directly above the current carrying conductor  25  gives: 
     
       
         
           
             
               
                 
                   d 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       s 
                     
                     
                       
                         
                           
                             
                               
                                 μ 
                                 0 
                               
                               ⁢ 
                               i 
                             
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               d 
                             
                           
                           + 
                           C 
                         
                         
                           
                             
                               
                                 μ 
                                 0 
                               
                               ⁢ 
                               i 
                             
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 π 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     + 
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           C 
                         
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     As can be seen from equation (4), the depth calculation using two antennas is dependent on the common mode field distortion which leads to practical difficulties in determining the depth of a buried conductor. This difficulty is mitigated in conventional apparatus by deploying a compensation algorithm which approximates the common mode field distortion based on measurements from different sites to give a function C for an ‘average’ soil type. This approximation is not satisfactory due to the significant difference in measurements of up to 35% between wet clay and dry sand, which in general leads to an underestimate of the depth of a buried current carrying conductor. 
       FIG. 3  is a schematic representation of three horizontal vertically spaced antennas T, M, B of the detector  1  of  FIG. 1 . The axes of the antennas are parallel. The middle antenna M is disposed midway between the bottom antenna B and top antenna T at a separation s from each antenna so that the separation between the bottom antenna B and the top antenna T is 2s. As in  FIG. 2 , the conductor  25  is buried at a depth d below the surface of the ground  23  (and below the bottom antenna B) and the horizontal displacement between the antennas T, M, B and the conductor is x. The magnetic flux density at the middle antenna B M  is given by: 
     
       
         
           
             
               
                 
                   
                     
                       B 
                       M 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         d 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         
                           i 
                           ⁡ 
                           
                             ( 
                             
                               d 
                               + 
                               s 
                             
                             ) 
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   ( 
                                   
                                     d 
                                     + 
                                     s 
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               
                                 x 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In practice, the depth of a current carrying conductor is calculated when the antennas are vertically above the conductor, i.e., when the lateral displacement, x, is zero. Equations (1), (2) and (5) become: 
     
       
         
           
             
               
                 
                   
                     B 
                     B 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         i 
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         d 
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     B 
                     T 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         i 
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               d 
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     B 
                     M 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         i 
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               d 
                               + 
                               s 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     A convenient ratio R to consider is given by: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         B 
                         B 
                       
                       - 
                       
                         B 
                         M 
                       
                     
                     
                       
                         B 
                         B 
                       
                       - 
                       
                         B 
                         T 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Replacing equations (6), (7) and (8) into equation (9) gives. 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           i 
                         
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           d 
                         
                       
                       + 
                       C 
                       - 
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           i 
                         
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 d 
                                 + 
                                 s 
                               
                               ) 
                             
                           
                         
                       
                       + 
                       C 
                     
                     
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           i 
                         
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           d 
                         
                       
                       + 
                       C 
                       - 
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           i 
                         
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 d 
                                 + 
                                 s 
                               
                               ) 
                             
                           
                         
                       
                       + 
                       C 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The ratio R is in effect a second derivative gradient term and is independent of the common mode distortion C. Simplifying equation (10) gives: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         
                           1 
                           d 
                         
                         - 
                         
                           1 
                           
                             d 
                             + 
                             s 
                           
                         
                       
                       
                         
                           1 
                           d 
                         
                         - 
                         
                           1 
                           
                             d 
                             + 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               s 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           1 
                           
                             d 
                             + 
                             s 
                           
                         
                         
                           2 
                           
                             d 
                             + 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               s 
                             
                           
                         
                       
                       = 
                       
                         
                           d 
                           + 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             s 
                           
                         
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               d 
                               + 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Solving equation (11) for d gives the three antenna depth equation: 
     
       
         
           
             
               
                 
                   d 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         s 
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             R 
                           
                           ) 
                         
                       
                     
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         R 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Hence, equations (9) and (12) provide a means of calculating the depth of a current carrying conductor  25  by comparing the magnetic field densities at the three antennas. By using the ratiometric term R, which is independent of the complex impedance of the substance in which the current carrying conductor is buried, equations (9) and (12) dispense with the need to compensate for the common mode field effect of the substance in which the current carrying conductor  25  is buried and these equations provide an improved method of calculating the depth of a buried conductor. 
     Equations (1), (2) and (5) apply to an infinite conductor carrying uniform current and giving a perfect radial field in a vacuum. When such a conductor is buried in soil with finite conductivity a secondary current and magnetic field are generated which is induced in the soil. An alternative model to equations (1), (2) and (5) for the field produced by a current carrying conductor is given below, which shows how equations (1), (2) and (5) depart from the theoretical pure radial field: 
     
       
         
           
             
               
                 
                   B 
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         i 
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         d 
                       
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         ( 
                         
                           - 
                           
                             d 
                             
                               Δ 
                               ⁡ 
                               
                                 ( 
                                 f 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where: 
     
       
         
           
             
               Δ 
               ⁡ 
               
                 ( 
                 f 
                 ) 
               
             
             = 
             
               503.8 
               
                 
                   
                     δ 
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   γ 
                 
               
             
           
         
       
         
         
           
             μ 0  is the permeability of free space; 
             i is the current flowing in the conductor  25 ; 
             δ is the ground conductivity; and 
             γ is a variable to allow for ground conductivity variation with frequency 
           
         
       
    
     Assuming that the soil conductivity is homogenous, if equation (13) is substituted into equation (9) for each of the antennas it can be shown that the exponential terms cancel and that common mode field effect is eliminated in the ratiometric analysis. 
     A prerequisite of this ratiometric calculation is accurate calibration of the three horizontal antennas T, M, B to an accuracy of around 1 part in 600,000. The calibration of the antennas is performed with respect to the relative performance of the top and middle antennas T, M and the relative performance of the middle and bottom antennas M, B. After assembly of the detector, each antenna is in turn placed within a known magnetic field and the magnitude and phase of the field strength signal output from the antennas is measured over a range of frequencies. A calibration value for the performance ratio of the top and middle antennas and the middle and bottom antennas is calculated and stored in the memory  19  of the detector  1  so that a ratiometric calculation of the field strength signals output from the pairs of antennas is consistently accurate to around 1 part in 600,000. 
       FIG. 4  is a block diagram of part of the detector  1  of  FIG. 1  which processes the signals detected by the antennas  3  of  FIG. 3 . 
     If the signal detected by antennas T, M, B is weak, the analogue output from each of the three antennas T, M, B is fed through an equalisation filter  7  and amplified by a factor G(w); otherwise the outputs from the antennas T, M, B are fed directly into the next stage  9  of the circuit. The next stage  9  comprises two multiplexors, the first multiplexor combining the signals from the top antenna T and middle antenna M and the second multiplexor combining the signals from the middle antenna M and the bottom antenna B. 
     The output from each multiplexor is then fed into a delta-sigma CODEC  11 . Delta-sigma CODECs are ideal CODECs to digitise the outputs of the pairs of antennas because they provide almost perfect ratiometric accuracy (around 1 part in 2 24  across the sampling bandwidth from 4 KHz to 96 KHz). Hence the implementation of equation (9) comprises feeding the output from the middle antenna M into two delta-sigma CODECs  11 . 
     With reference to  FIG. 4 , when the outputs of the antennas T, M, B are not amplified equation (9) becomes: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         
                           B 
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         
                           M 
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     
                       
                         
                           B 
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       - 
                       
                         
                           T 
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     where:
         B is the output from the bottom antenna;   M is the output from the middle antenna;   T is the output from the top antenna;   C 1  is the transfer function of codec 1; and   C 2  is the transfer function of codec 2.       

     By dividing through by C 2 , equation (14) becomes: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                           
                       
                       ⁢ 
                       
                         B 
                         - 
                         M 
                       
                     
                     
                       
                           
                       
                       ⁢ 
                       
                         
                           B 
                           · 
                           
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         - 
                         T 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The ratio C 1 /C 2  is evaluated by comparing the output from the middle antenna M through both CODECs  11  which allows R to be calculated. 
     When the outputs of the antennas T, M, B are amplified equation (9) becomes: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         
                           B 
                           · 
                           
                             G 
                             B 
                           
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         
                           M 
                           · 
                           
                             G 
                             M 
                           
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     
                       
                         
                           B 
                           · 
                           
                             G 
                             B 
                           
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       - 
                       
                         
                           T 
                           · 
                           
                             G 
                             T 
                           
                           · 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where:
         G B , G M  and G T  are the gain of the amplifiers for the amplified bottom, middle and top antennas respectively.       

     By dividing through by C 2  and B.G B , equation (16) becomes: 
     
       
         
           
             R 
             = 
             
               
                 
                   1 
                   - 
                   
                     
                       M 
                       · 
                       
                         G 
                         M 
                       
                     
                     
                       B 
                       · 
                       
                         G 
                         B 
                       
                     
                   
                 
                 ⁢ 
                 
                     
                 
               
               
                 
                   
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   
                     
                       T 
                       · 
                       
                         G 
                         T 
                       
                     
                     
                       B 
                       · 
                       
                         G 
                         B 
                       
                     
                   
                 
                 ⁢ 
                 
                     
                 
               
             
           
         
       
     
     By accurately calibrating M.G M /B.G B  and T.G T /B.G B  and by calculating the ratio C 1 /C 2  by comparing the output from the middle antenna through both CODECs  11 , R can be calculated. 
     There is also provided a method of calculating the common mode field distortion of an electromagnetic field produced by a current carrying conductor  25  due to the complex impedance of the material in which the conductor is buried. As stated above, different ground materials, such as sand, dry and wet soil and dry and wet clay, have different complex impedances. By comparing the depth measurements using the two antenna depth equation (3) and the three antenna depth equation (12) the common mode field distortion can be calculated. 
     In addition to common mode field distortion described above, an electromagnetic signal radiated by a current carrying conductor  25  may be distorted by secondary coupling onto a nearby conductor. Unlike common mode field distortion which is homogenous, field distortion due to coupling onto a nearby conductor leads to a non-radial field gradient and cannot be exactly compensated for. 
     If there is no or little distortion due to secondary coupling then the common mode field distortion calculation resulting from comparison of the two antenna depth equation (3) and the three antenna depth equation (12) should give a common mode field distortion, C, of &lt;10% of the detected signal. 
     If the distortion due to secondary coupling is significant then this will affect the accuracy of some measurements and it is useful to warn the operator of significant secondary coupling distortion which results in the lessened integrity of readings made by the detector. If the common mode field distortion is calculated as ≧10% of the detected signal then this is an indication of the presence of secondary distortion and the operator of the detector  1  can be warned by a visual or audible alarm. 
     For conventional detectors, depth data is presented to an operator by pressing a ‘calculate depth’ button on the detector once the detector has been placed in the correct position. The correct position for calculating the depth is when the antennas are vertically above the conductor and the axes of the antennas are perpendicular to the axis of the buried conductor. 
     In practice the correct location is found by moving the detector from side to side across the conductor and rotating the detector about a vertical axis. When the detector is correctly positioned a peak response is detected by a horizontal antenna having its axis perpendicular to the axis of the conductor and a null response is detected by a vertical antenna and a horizontal antenna having their axis parallel to the axis of the conductor. 
     To correctly and efficiently perform depth calculation the operator must have sufficient skill and experience to accurately locate the detector vertically above and aligned with the conductor at which point the depth of the buried conductor can be accurately calculated. An inexperienced or careless operator may be presented with an erroneous depth calculation if the calculate depth button is pressed when the detector is not correctly positioned relative to the buried conductor. 
     The optimum location for calculating the depth of a buried conductor can be considered as a depth calculation “sweet spot”. The present invention addresses the difficulty of locating the sweet spot by presenting the result of the depth calculation only when predetermined criteria are satisfied. 
       FIG. 5  is a schematic representation of two antennas B, V at the bottom of the detector  1  of  FIG. 1 . The detector  1  is located at a horizontal displacement x from the buried conductor  25  which is at a depth d below ground level  23 . The bottom two antennas B, V of the detector are placed in close proximity to each other at the foot of the detector  1 , one antenna B being disposed horizontally as described above and the other antenna V behind disposed vertically (when the detector  1  is held vertical), orthogonal to the bottom antenna B. A line  27  joining the buried conductor to the bottom antennas B, V is inclined at an angle θ to the vertical. 
     When an electromagnetic field is emitted by the buried conductor  25 , current is induced in the bottom antenna B and the vertical antenna V. As these antennas are orthogonal the current induced in the antennas can be considered as representing the resolved respective horizontal and vertical components of the electromagnetic field radiated by the conductor  25 . Hence, the angle θ can be calculated by considering the equation: 
     
       
         
           
             θ 
             = 
             
               
                 tan 
                 
                   - 
                   1 
                 
               
               ⁡ 
               
                 ( 
                 
                   
                     B 
                     V 
                   
                   
                     B 
                     B 
                   
                 
                 ) 
               
             
           
         
       
     
     where:
         B B  is the magnetic flux density at the bottom antenna; and   B V  is the magnetic flux density at the vertical antenna.       

     When the detector  1  is moved horizontally close to conductor  25 , i.e., as the horizontal displacement x decreases, B V /B B  decreases and the arctangent, θ, also decreases towards zero. 
       FIG. 6  is a schematic representation of a further two of the antennas M, M 90  of the detector  1  of  FIG. 1  viewed from above showing the first middle horizontal antenna M and a second middle horizontal antenna M 90 . The middle two antennas M, M 90  of the detector are placed in close proximity to each other in the middle of the detector  1 , both antennas M, M 90  being disposed horizontally (when the detector  1  is held vertical) at right angles to each other. The detector  1  is oriented relative to the buried conductor  25  such that the middle antennas M, M 90  are horizontal and the angle between the axis of the conductor  25  and the second horizontal middle antenna M 90 , i.e., the angle between the axis of the conductor and a plane perpendicular to the axis of the middle antenna M, is φ. For a peak response the axis of the first middle antenna M should be oriented vertically above and orthogonal to the buried conductor  25 . 
     When an electromagnetic field is emitted by the buried conductor  25 , current is induced in the first horizontal middle antenna M and the second horizontal middle antenna M 90 . As these antennas are orthogonal the current induced in the antennas can be considered as representing the resolved horizontal orthogonal components of the electromagnetic field produced by the conductor  25 . Hence, the angle φ can be calculated by considering the equation: 
             ϕ   =       tan     -   1       ⁡     (       B     M   ⁢           ⁢   90         B   M       )             
when the M 90  is antenna is oriented “in phase” with the conductor and:
 
             ϕ   =       180   ⁢   °     -       tan     -   1       ⁡     (       B     M   ⁢           ⁢   90         B   M       )               
when the M 90  is antenna is oriented “out of phase” with the conductor,
 
     where:
         B M90  is the magnetic flux density at the second horizontal middle antenna M 90  and   B M  is the magnetic flux density at the first horizontal middle antenna M.       

     As the detector  1  is rotated about a vertical axis so that the second middle antenna M 90  becomes more aligned with the conductor  25 , B V /B B  decreases and the arctangent, θ, also decreases towards zero. 
     By monitoring the current induced in the two middle antennas M, M 90  and the two bottom antennas B, V the angles θ and φ can be calculated. These angle calculations can be used to determine if the detector  1  is located in the depth calculation sweet spot where a depth calculation can be accurately undertaken. If it is determined that the detector  1  is located in the sweet spot then the detector  1  displays the result of the depth calculation to the user on the display  21 . 
     Predetermined criteria indicating that the detector  1  is in the sweet spot are when the angles θ and φ are within ±10°, preferably within ±5° and preferably within ±2°. 
     Further parameters can be considered to verify the integrity of the depth calculation. If the parameters satisfy predetermined criteria then the depth calculation will be displayed on the display  21  of the detector  1 . One or more of the following parameters may be considered and preferably all of the following parameters are evaluated and should satisfy predetermined criteria. These parameters may be considered for depth calculation based on measurements using two or three horizontal antennas, i.e., using equations (3) or (12). 
       FIG. 7  is a block diagram of part of the digital signal processing block  13  of the detector  1  of  FIG. 1 . The field strength signals  5  from the antennas  3  are sampled in the CODEC  11  of  FIG. 1  and mixed with cos and sin components of the frequency of interest to produce in-phase “I” and quadrature “Q” components of the field strength signals detected at the antenna  3 . Further details of this operation are provided in U.S. Pat. No. 6,977,508, assigned to Radiodetection Limited on its face, the contents of which are incorporated herein by reference. 
     The I and Q components are passed to a sinc 5  decimating filter  29 . Further details of the operation of the sinc 5  decimating filter are provided in U.S. Pat. No. 6,968,296, assigned to Radiodetection Limited on its face, the contents of which are incorporated herein by reference. 
     The output of the sinc 5  decimating filter is down-sampled  31  and low-pass filtered through a finite impulse response (FIR) filter. This process results in obtaining the complex phase and magnitude of the antenna signals defined in a narrow bandwidth, typically 10 Hz. Further details of the operation of the DSP&#39;s tasks are provided in U.S. Pat. No. 6,777,923, assigned to Radiodetection Limited on its face, the contents of which are incorporated herein by reference, in U.S. Pat. No. 7,184,951, assigned to Radiodetection Limited on its face, the contents of which are incorporated herein by reference, and in U.S. Pat. No. 6,977,508 (noted above). 
     The magnitude of the second derivative of the phase of the signals detected by the antennas, i.e. |d 2 ∠U/dt 2 | is a parameter which can be considered to verify the integrity of the depth calculation. This parameter is effectively a measure of the uncorrelated noise across the bandwidth of the FIR filter and should be less than 0.5°/s 2 , preferably less than 0.2°/s 2  and preferably less than 0.1°/s 2 . 
     A further parameter that can be considered to verify the integrity of the depth calculation is the standard deviation of the depth calculation. This parameter indicates that the depth calculation is stable and not unduly fluctuating due to noise. The standard deviation of the depth calculation referred to a 10 Hz bandwidth should be less than 5%, preferably less than 2% and preferably less than 1%. 
     A further parameter which may be considered to verify the integrity of the depth calculation is that all signals input to the CODEC are within the dynamic range of the CODEC. If the signals input to the CODEC are found to be outside the dynamic range of the CODEC then this will result in inaccurate sampling by the CODEC. 
     A further parameter which may be considered to verify the integrity of the depth calculation is the first derivative of the magnitude of the signals detected at the antennas, i.e., dU/dt. This parameter ensures that the instrument is being held still at the time that the depth is calculated so that this parameter acts as an anti-ballistic filter. The first derivative of the magnitude of the detected signal should be less than 5% of the signal/s, preferably less than 2% of the signal/s and preferably less than 1% of the signal/s. 
     A further parameter which may be considered to verify the integrity of the depth calculation is the phase correlation across the (two or three) antennas used to detect the signal radiated by the buried conductor. The phase difference between the antennas should be less than 5°, preferably less than 2° and preferably less than 1°. 
     One or more of the above parameters may be considered to determine that the depth calculation has good integrity. The values of the thresholds described above are dependent on the signal strength, the computing bandwidth of the FIR filters and the depth of the conductor being detected. 
     Various modifications will be apparent to those in the art and it is desired to include all such modifications as fall within the scope of the accompanying claims. 
     In the present embodiment the detector continuously calculates the depth of the buried conductor but only displays the calculated depth when predetermined criteria are satisfied. In other embodiments the detector may display an icon on its user interface or make an audible sound to inform the operator that the predetermined criteria are satisfied. Alternatively, the detector may be configured such that depth is only calculated when the predetermined criteria are satisfied. 
     Aspects of the present invention can be implemented in any convenient form, for example using dedicated hardware, or a mixture of dedicated hardware and software. The processing apparatuses can comprise any suitably programmed apparatuses such as a general purpose computer, personal digital assistant, mobile telephone (such as a WAP or 3G-compliant phone) and so on. Since the present invention can be implemented as software, each and every aspect of the present invention thus encompasses computer software implementable on a programmable device. The computer software can be provided to the programmable device using any conventional carrier medium. The carrier medium can comprise a transient carrier medium such as an electrical, optical, microwave, acoustic or radio frequency signal carrying the computer code. An example of such a transient medium is a TCP/IP signal carrying computer code over an IP network, such as the Internet. The carrier medium can also comprise a storage medium for storing processor readable code such as a floppy disk, hard disk, CD ROM, magnetic tape device or solid state memory device. 
     The many features and advantages of the invention are apparent from the detailed specification, and, thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and variations will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and, accordingly, all suitable modifications and equivalents may be resorted to that fall within the scope of the invention.