Abstract:
Vibration transducers, sensors including the vibration transducers, and methods for manufacturing the same. The vibration transducer may include a magnet. The vibration transducer may include a bobbin disposed about the magnet. The vibration transducer may include a first coil disposed about the bobbin. The vibration transducer may include a controllable damping coil disposed about the bobbin. The first coil is movable relative to the magnet. The magnet is polarized with respect to the axis of the vibration transducer.

Description:
BACKGROUND 
       [0001]    The present disclosure relates to geophone devices for sensing vibrations in earth formations, and may be applicable to other types of vibration transducers, either in sensing or transmitting operation. More specifically, the present disclosure relates to a damping controlled geophone. 
         [0002]    In seismic exploration, vibrations in the earth resulting from a source of seismic energy may be sensed at discrete locations by sensors and the output of the sensors used to image underground structures, or to locate seismic events. The source of seismic energy can be natural, such as earthquakes and other tectonic activity, subsidence, volcanic activity or the like, or man-made such as acoustic noise from surface or underground operations, or from deliberate operation of seismic sources at the surface or underground. Seismic sensors fall into two categories: hydrophones that sense the pressure field resulting from a seismic source, or geophones that sense vibration arising from a seismic source. 
         [0003]    An oscillatory geophone is shown in  FIG. 1-1 . The geophone  10  includes a housing  24 , a top cap  27  and a bottom cap  28  that are affixed to the housing  24 , a magnet  15  having a pair of pole pieces  16 ,  18  that are respectively affixed to the top and bottom caps  27 ,  28 , a moving coil that includes two coil windings  12 ,  13  and a bobbin  14  with suspension springs  20 ,  22  as shown in  FIG. 1-1 . The magnet  15 , along with its two pole pieces  16 ,  18 , can move with the housing  24 . Pole pieces  16 ,  18  and housing  24  are made of magnetically permeable material and form a magnetic flux  25  in which the moving coil is suspended. The caps  27 ,  28  are made of magnetically impermeable material. In this particular embodiment as shown, the coil windings  12 ,  13  are connected in series to form a continuous coil. The windings  12 ,  13  may be disposed about the bobbin  14  in opposite directions, so that the windings  12 ,  13  can generate voltage in a common direction. The windings  12 ,  13  of the moving coil are commonly mounted and move together. As illustrated, the magnetic flux  25  passes out one winding from inside to outside near the north of the magnet  15 , and then out the other winding from outside to inside near the south of the magnet  15 . 
         [0004]    When the earth moves due to the seismic energy propagating either directly from the source or via an underground reflector, the geophone  10 , which can be located at the earth&#39;s surface or on the wall of a borehole penetrating the earth, moves in the direction of the particle motion resulting from propagation of the energy. If the axis of the geophone  10  is aligned with the direction of motion, however, the coil windings  12 ,  13  mounted on the springs  20 ,  22  inside the geophone  10  stay in the same position causing relative motion of the moving coil with respect to the magnetic flux  25  that moves with the housing  24 . When the moving coil moves in the magnetic field, a measurable voltage is induced in the moving coil, which is proportional to the velocity of the relative motion between the moving coil and the magnetic flux  25 . 
         [0005]    Variations of geophones are described in U.S. Pat. No. 7,099,235 to Kamata, U.S. Publication 2011/0007608 to Woo, and U.S. Pat. No. 4,159,464 to Hall. 
       SUMMARY 
       [0006]    In at least one aspect, the disclosure relates to a vibration transducer with controlled damping. The vibration transducer may include a magnet. The vibration transducer may include a bobbin disposed about the magnet. The vibration transducer may include a first coil disposed about the bobbin. The vibration transducer may include a controllable damping coil disposed about the bobbin. The first coil is movable relative to the magnet. The magnet is polarized with respect to the axis of the vibration transducer. 
         [0007]    In at least one aspect, the disclosure relates to a seismic sensor. The seismic sensor includes controlled damping. The seismic sensor may include a magnet. The seismic sensor may include a bobbin disposed about the magnet. The seismic sensor may include a first coil disposed about the bobbin. The seismic sensor may include a controllable damping coil disposed about the bobbin. The first coil is movable relative to the magnet. The magnet is polarized with respect to the axis of the seismic sensor. The seismic sensor may also include a sensor housing. The seismic sensor may also include at least one signal output connectable to a data processing system. 
         [0008]    In at least one aspect, the disclosure relates to a method of manufacturing a vibration transducer. The method may include providing a housing having a magnet structure disposed in the housing, and a bobbin and moving coil disposed about the magnet structure and resiliently mounted relative to the housing and the magnet structure. The method may also include providing a damping coil disposed concentrically about the bobbin adjacent to the moving coil. 
         [0009]    This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    Embodiments of systems, apparatuses, and methods for a controlled damping geophone are described with reference to the following figures. Like numbers are used throughout the figures to reference like features and components. 
           [0011]      FIG. 1-1  is a cross-sectional view of a geophone; 
           [0012]      FIG. 1-2  shows a schematic of displacement of the geophone of  FIG. 1-1  while sensing; 
           [0013]      FIG. 2  shows a plot of an amplitude response for a unit velocity against frequency in Hertz for the geophone of  FIG. 1-1 ; 
           [0014]      FIG. 3  shows a plot of a phase response in degrees against frequency in Hertz for the geophone of  FIG. 1-1 ; 
           [0015]      FIG. 4  shows a plot of natural frequency f 0 , open circuit sensitivity S 0 , and open circuit damping D 0 , normalized at 20 degrees, versus temperature in degrees Celsius for the geophone of  FIG. 1-1 ; 
           [0016]      FIG. 5  shows a plot of geophone response over time for different temperatures for the geophone of  FIG. 1-1 ; 
           [0017]      FIG. 6  shows side view of a current flow in a metallic bobbin implemented in a geophone; 
           [0018]      FIG. 7-1  shows a moving coil having an independent damping coil added to each end of a dual coil in an embodiment of the present disclosure; 
           [0019]      FIG. 7-2  shows corresponding winding directions of the coils of the geophone of  FIG. 7-1 ; 
           [0020]      FIG. 8  shows an embodiment of a metallic slotted bobbin implemented in a geophone; 
           [0021]      FIG. 9  shows an embodiment of a slotted bobbin reinforced with insulation rings; 
           [0022]      FIG. 10  shows an embodiment of a slotted bobbin shorted with a chip resistor; 
           [0023]      FIG. 11  shows a cross-section of a geophone having metal deposition on a plurality of independent insulation rings on a slotted metallic bobbin; 
           [0024]      FIG. 12  shows a cross-section of a geophone having a damping coil embedded in a plastic bobbin; 
           [0025]      FIG. 13  shows an embodiment for damping coil as a thin metallic foil around a slotted bobbin; 
           [0026]      FIG. 14  shows an embodiment for damping coil as metal disposed on a plastic bobbin under a geophone coil; 
           [0027]      FIG. 15  shows a geophone in accordance with the present disclosure disposed on a sea bed cable; 
           [0028]      FIG. 16  shows a geophone in accordance with the present disclosure disposed on a land cable; and 
           [0029]      FIG. 17  shows geophones in accordance with the present disclosure disposed on a borehole tool. 
       
    
    
     DETAILED DESCRIPTION 
       [0030]    In the following description, numerous details are set forth to provide an understanding of the present disclosure. However, it will be understood by those skilled in the art that the present disclosure may be practiced without these details and that numerous variations or modifications from the described embodiments are possible. 
         [0031]    Currents can be induced in a geophone bobbin to dampen oscillating motion of the bobbin relative to the remainder of the geophone as the coils move in a magnetic field. Damping caused in the bobbin may be accounted for, and controlled, by implementing a short circuit damping coil and temperature insensitive wire, such as Constantan. The damping coil can be controlled to produce effective damping (e.g., approximately 70%) without an external shunt resistor. In an embodiment, the damping coil may be manufactured of Constantan wire to limit temperature dependency. 
         [0032]    Referring now to  FIG. 1-1 , a cross-section of a geophone  10  is shown. The geophone  10  includes a moving coil with windings  12 ,  13  mounted on a bobbin  14 , a magnet  15 , a pair of pole pieces  16 ,  18  with suspension springs  20 ,  22  and a housing  24  as shown in  FIG. 1-1 . The pole pieces  16 ,  18  and the housing  24  are made of magnetically permeable material and form a magnetic field in which the moving coil is suspended. 
         [0033]    Referring now to  FIG. 1-2 , a schematic of the displacement of the geophone of  FIG. 1-1  while sensing is shown. R s  represents an external shunt resistor, and r represents a DC resistance of the coil, as above. The moving coil has a moving mass m and its neutral position relative to the housing is x 0 . The displacement of the ground motion is u, which can be measured with reference to the neutral position x 0 . x is the displacement of the coil while sensing, which can also be measured with reference to the neutral position x 0 . The output is connected to the external shunt resistor R s  to adjust the total damping factor D. The external shunt resistor R s  may be varied to control the damping of the coil movement. 
         [0034]    As the coil moves in the magnetic flux  25 , the coil generates signal e g , which can be defined by: 
         [0000]      e g =Blv  Equation 1
 
         [0000]    where B represents the magnetic flux density, l represents the length of the coil, v represents the velocity of the moving coil relative to the magnetic field, and u represents the displacement of the ground motion. The product, Bl, represents the conversion factor of a geophone from velocity of ground motion to the electric signal, e g , and can be defined as open circuit sensitivity, S 0 . 
         [0035]    The current i flowing out of the coil and returned through the shunt resistor R s  can be defined by: 
         [0000]    
       
         
           
             
               
                 
                   i 
                   = 
                   
                     
                       e 
                       g 
                     
                     
                       r 
                       + 
                       
                         R 
                         s 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0036]    Current in the coil causes a force f to limit the motion of the coil, which can be defined by: 
         [0000]      f=S 0 i  Equation 3
 
         [0037]    A spring force acting on the moving mass m is proportional to the difference between the coil displacement x and the ground displacement u and can be defined by: 
         [0000]      −k(x−u)  Equation 4
 
         [0000]    where k is the spring constant. 
         [0038]    A damping force is related to the velocity of the coil in the magnetic field and can be defined by: 
         [0000]    
       
         
           
             
               
                 
                   
                     - 
                     c 
                   
                    
                   
                     
                        
                       
                         ( 
                         
                           x 
                           - 
                           u 
                         
                         ) 
                       
                     
                     
                        
                       t 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   5 
                 
               
             
           
         
       
     
         [0000]    where c is the friction factor proportional to the velocity, t is time. One cause of damping may be the current flowing in the metallic bobbin, as friction of the moving mass in the air and the loss in the spring can be negligibly small. 
         [0039]    Motion of the moving coil can be described in an equation of motion: 
         [0000]    
       
         
           
             
               
                 
                   
                     m 
                      
                     
                       
                         
                            
                           2 
                         
                          
                         x 
                       
                       
                          
                         
                           t 
                           2 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         - 
                         c 
                       
                        
                       
                         
                            
                           
                             ( 
                             
                               x 
                               - 
                               u 
                             
                             ) 
                           
                         
                         
                            
                           t 
                         
                       
                     
                     - 
                     
                       k 
                        
                       
                         ( 
                         
                           x 
                           - 
                           u 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         S 
                         0 
                       
                        
                       i 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
         [0040]    From Equations 1 and 2, current can be defined as: 
         [0000]    
       
         
           
             
               
                 
                   i 
                   = 
                   
                     
                       
                         e 
                         g 
                       
                       
                         r 
                         + 
                         
                           R 
                           s 
                         
                       
                     
                     = 
                     
                       
                         
                           S 
                           0 
                         
                         
                           r 
                           + 
                           
                             R 
                             s 
                           
                         
                       
                        
                       
                         
                            
                           ξ 
                         
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
         [0041]    A relative position of the moving coil to the ground motion in the housing can be defined as: 
         [0000]      ξ= x−u   Equation 8
 
         [0042]    A natural frequency ω 0  and a controlled damping D 0  can be defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     ω 
                     0 
                   
                   = 
                   
                     
                       k 
                       m 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   9 
                 
               
             
             
               
                 
                   
                     D 
                     0 
                   
                   = 
                   
                     c 
                     
                       2 
                        
                       
                           
                       
                        
                       m 
                        
                       
                           
                       
                        
                       
                         ω 
                         0 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   10 
                 
               
             
           
         
       
     
         [0043]    Equation 6 can be rewritten as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           2 
                         
                          
                         ξ 
                       
                       
                          
                         
                           t 
                           2 
                         
                       
                     
                     + 
                     
                       2 
                        
                       
                         ω 
                         0 
                       
                        
                       
                         D 
                         0 
                       
                        
                       
                         
                            
                           ξ 
                         
                         
                            
                           t 
                         
                       
                     
                     + 
                     
                       
                         ω 
                         0 
                         2 
                       
                        
                       ξ 
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           
                              
                             2 
                           
                            
                           u 
                         
                         
                            
                           
                             t 
                             2 
                           
                         
                       
                     
                     - 
                     
                       
                         
                           S 
                           0 
                           2 
                         
                         
                           m 
                            
                           
                             ( 
                             
                               r 
                               + 
                               
                                 R 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         
                            
                           ξ 
                         
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
         [0044]    The total damping D can be defined as: 
         [0000]    
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       D 
                       0 
                     
                     + 
                     
                       
                         S 
                         0 
                         2 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         m 
                          
                         
                             
                         
                          
                         
                           
                             ω 
                             0 
                           
                            
                           
                             ( 
                             
                               r 
                               + 
                               
                                 R 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
         [0045]    The equation of motion for the moving mass can be rewritten as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           2 
                         
                          
                         ξ 
                       
                       
                          
                         
                           t 
                           2 
                         
                       
                     
                     + 
                     
                       2 
                        
                       
                         ω 
                         0 
                       
                        
                       D 
                        
                       
                         
                            
                           ξ 
                         
                         
                            
                           t 
                         
                       
                     
                     + 
                     
                       
                         ω 
                         0 
                         2 
                       
                        
                       ξ 
                     
                   
                   = 
                   
                     - 
                     
                       
                         
                            
                           2 
                         
                          
                         u 
                       
                       
                          
                         
                           t 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
         [0046]    Assuming that ground motion u may be governed by: 
         [0000]        u=a  sin(ω t )  Equation 14
 
         [0000]    where a denotes the amplitude and ω is the angular frequency of the ground motion. 
         [0047]    Then: 
         [0000]    
       
         
           
             
               
                 
                   ξ 
                   = 
                   
                     
                       
                         
                           a 
                            
                           
                             ( 
                             
                               ω 
                               
                                 ω 
                                 0 
                               
                             
                             ) 
                           
                         
                         2 
                       
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   
                                     ω 
                                     0 
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 D 
                                  
                                 
                                   ω 
                                   
                                     ω 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             ω 
                              
                             
                                 
                             
                              
                             t 
                           
                           - 
                           ϕ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   15 
                 
               
             
           
         
       
     
         [0000]    where the phase delay φ of the coil motion is 
         [0000]    
       
         
           
             
               
                 
                   
                     tan 
                      
                     
                       ( 
                       ϕ 
                       ) 
                     
                   
                   = 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       D 
                        
                       
                         ω 
                         
                           ω 
                           0 
                         
                       
                     
                     
                       1 
                       - 
                       
                         
                           ω 
                           2 
                         
                         
                           ω 
                           0 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   16 
                 
               
             
           
         
       
     
         [0048]    The electric signals can be governed by: 
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     g 
                   
                   = 
                   
                     
                       
                         a 
                          
                         
                             
                         
                          
                         ω 
                          
                         
                             
                         
                          
                         
                           
                             
                               S 
                               0 
                             
                              
                             
                               ( 
                               
                                 ω 
                                 
                                   ω 
                                   0 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                       
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   
                                     ω 
                                     0 
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 D 
                                  
                                 
                                   ω 
                                   
                                     ω 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             ω 
                              
                             
                                 
                             
                              
                             t 
                           
                           - 
                           ϕ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
         [0049]    In a first example, a geophone has response parameters shown in Table 1. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 f 0  [Hz] 
                 10 
               
               
                   
                 S 0  [V/(m/s)] 
                 40 
               
               
                   
                 D 0  [—] 
                 0.2 
               
               
                   
                 r [ohm] 
                 400 
               
               
                   
                 m [kg] 
                 0.01 
               
               
                   
                   
               
             
          
         
       
     
         [0050]    The total damping factor D is adjusted by shunt resistors R s  to adjust Case 1 (D=0.3), Case 2 (D=0.7) and Case 3 (D=1.0) according to Equation 12 as shown in Table 2. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Case 1 
                 Case 2 
                 Case 3 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 R s  [ohm] 
                 12286 
                 2145 
                 1192 
               
               
                   
                 D [—] 
                 0.30 
                 0.70 
                 1.00 
               
               
                   
                 S [V/(m/s)] 
                 38.7 
                 33.7 
                 29.9 
               
               
                   
                   
               
             
          
         
       
     
         [0051]    The output signal can be reduced by the shunt resistance and coil resistance, and the overall sensitivity S can be governed by: 
         [0000]    
       
         
           
             
               
                 
                   S 
                   = 
                   
                     
                       S 
                       0 
                     
                      
                     
                       
                         R 
                         s 
                       
                       
                         r 
                         + 
                         
                           R 
                           s 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   18 
                 
               
             
           
         
       
     
         [0052]    The amplitude response of the geophone with the response parameters shown in Table 1 for unit velocity against frequency in Hertz is calculated using Equation 17 for different cases of shunt resistor shown in Table 2. The plot  200  in  FIG. 2  shows the geophone amplitude response (measured in V/(m/s)) over a plurality of frequencies (measured in Hz). The total damping factor is 0.3 for the frequency response line  202 , 0.7 for the frequency response line  204 , and 1.0 for the frequency response line  206 , showing a suppression of resonance at the natural frequency via the shunt resistor. 
         [0053]    The phase response  300  resulting from Equation 16 is shown in  FIG. 3  for Case 1, Case 2, and Case 3, plotting phase in degrees against frequency in Hertz. As in  FIG. 2 , for the three responses plotted, the damping factor is 0.3 for the frequency response line  302 , 0.7 for the frequency response line  304 , and 1.0 for the frequency response line  306 . 
         [0054]    In an example embodiment, the coil resistance r is a function of temperature. Typically the coil can be made of copper magnetic wire and the temperature dependency is found in an empirical relation as: 
         [0000]        r=r   0 {1+0.00393( T−T   0 )} 
         [0000]    where T is the operating temperature, T 0  is the room temperature, typically 20 degrees Celsius, and r 0  is the resistance at the room temperature. 
         [0055]    The natural frequency f 0 , open circuit damping D 0 , and open circuit sensitivity S 0  may change with temperature.  FIG. 4  is a plot  400  of natural frequency f 0 , open circuit sensitivity S 0 , and open circuit damping D 0 , versus temperature in degrees Celsius. The parameters are normalized by the values at 20 degrees Celsius. As can be seen in  FIG. 4 , the natural frequency, f 0  changes slightly with temperature due to the change in the Young&#39;s modulus of the spring material. The open circuit sensitivity S 0  changes due to the change of the demagnetizing curve of the permanent magnet. The open circuit damping D 0  changes with temperature. The open circuit damping is reduced by about 30% at 175 degrees Celsius. This is due to the increase of resistance of the bobbing and the reduction of the open circuit sensitivity. 
         [0056]    For an example geophone with response parameters: f 0 =15 Hz; S 0 =52; D 0 =0.57; r=2400 ohm; m=0.0078 kg; the total damping is about 70% with R s =11672 ohm. The controlled damping is reduced by about 30% while the reduction of the open circuit sensitivity is about 5%. The coil resistance increases by about 61% at 175 degrees Celsius. Assume that the shunt resistance does not change with temperature, then the total damping is reduced by about 28% at 175 degrees Celsius by using Equation 12 with the temperature dependencies shown in  FIG. 4 . From Equation 18, the output sensitivity with the shunt resistor is reduced by about 14%. Table 3 summarizes the response of the geophone at 20 degrees Celsius and at 175 degrees Celsius. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
             
             
               
                   
                   
               
               
                   
                 T [degC.] 
                   
               
             
          
           
               
                   
                 20 
                 175 
               
               
                   
                   
               
             
          
           
               
                   
                 f 0  [Hz] 
                 15 
                 15 
               
               
                   
                 S 0  [V/(m/s)] 
                 52 
                 49.4 
               
               
                   
                 D 0  [—] 
                 0.57 
                 0.399 
               
               
                   
                 m [kg] 
                 0.0078 
                 0.0078 
               
               
                   
                 r [ohm] 
                 2400 
                 3862 
               
               
                   
                 R s  [ohm] 
                 11672 
                 11672 
               
               
                   
                 D [—] 
                 0.70 
                 0.51 
               
               
                   
                 S [V/(m/s)] 
                 43.1 
                 37.1 
               
               
                   
                   
               
             
          
         
       
     
         [0057]      FIG. 5  shows a plot  500  for simulated results of time responses of the geophone described above for temperature at 20 degrees Celsius and at 175 degrees Celsius. The input is an impulse that is band limited between 3 Hz and 60 Hz. Line  502  is the time response of the geophone at 20 degrees Celsius and line  504  is at 175 degrees Celsius. The amplitude of the response at 175 degrees Celsius is reduced and ringing is longer compared to the response at 20 degrees Celsius. 
         [0058]    The resistance of the bobbin may be taken into account in order to control damping. The magnet wire is wound on a metallic bobbin  614  as shown in  FIG. 6 , illustrating a coil wrapped bobbin  600 . As shown in  FIG. 6 , the coil  612  is wound concentrically around the outer surface of the bobbin  614 , such that the coil  612  moves with the bobbin  614  in the magnetic flux field, relative to the housing (not shown). Current i b    650  is induced in the bobbin  614 , and in turn in the coil  612 , when the coil  612  moves in the magnetic flux field. The resistance of the bobbin  614 , r b , is 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     b 
                   
                   = 
                   
                     ρ 
                      
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           d 
                           b 
                         
                       
                       
                         H 
                          
                         
                             
                         
                          
                         τ 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   19 
                 
               
             
           
         
       
     
         [0000]    where ρ represents specific electrical resistance; H represents the height of the bobbin  614 ; τ represents the thickness of the bobbin  614 ; d b  represents the diameter of the bobbin  614 . 
         [0059]    The equation of motion (of the bobbin  614  and the moving coil  612 ) can be rewritten to include the damping caused in the bobbin  614 , accordingly: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           2 
                         
                          
                         ξ 
                       
                       
                          
                         
                           t 
                           2 
                         
                       
                     
                     + 
                     
                       2 
                        
                       
                         ω 
                         0 
                       
                        
                       
                         D 
                         0 
                       
                        
                       
                         
                            
                           ξ 
                         
                         
                            
                           t 
                         
                       
                     
                     + 
                     
                       
                         ω 
                         0 
                         2 
                       
                        
                       ξ 
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           
                              
                             2 
                           
                            
                           u 
                         
                         
                            
                           
                             t 
                             2 
                           
                         
                       
                     
                     - 
                     
                       
                         
                           S 
                           0 
                           2 
                         
                         
                           mr 
                           b 
                         
                       
                        
                       
                         
                           
                              
                             2 
                           
                            
                           ξ 
                         
                         
                            
                           
                             t 
                             2 
                           
                         
                       
                     
                     - 
                     
                       
                         
                           S 
                           0 
                           2 
                         
                         
                           m 
                            
                           
                             ( 
                             
                               r 
                               + 
                               
                                 R 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         
                           
                              
                             2 
                           
                            
                           ξ 
                         
                         
                            
                           
                             t 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   20 
                 
               
             
           
         
       
     
         [0000]    where D r  is the damping unrelated to the current in the bobbin  614 , such as the friction in surrounding air and/or the friction in the spring material. The controlled damping in turn, can take the form: 
         [0000]    
       
         
           
             
               
                 
                   
                     D 
                     0 
                   
                   = 
                   
                     
                       D 
                       r 
                     
                     + 
                     
                       
                         S 
                         0 
                         2 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         m 
                          
                         
                             
                         
                          
                         
                           ω 
                           0 
                         
                          
                         
                           r 
                           b 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   21 
                 
               
             
           
         
       
     
         [0000]    Then the total damping can be governed by: 
         [0000]    
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       D 
                       r 
                     
                     + 
                     
                       
                         S 
                         0 
                         2 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         m 
                          
                         
                             
                         
                          
                         
                           ω 
                           0 
                         
                          
                         
                           r 
                           b 
                         
                       
                     
                     + 
                     
                       
                         S 
                         0 
                         2 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         m 
                          
                         
                             
                         
                          
                         
                           
                             ω 
                             0 
                           
                            
                           
                             ( 
                             
                               r 
                               + 
                               
                                 R 
                                 s 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   22 
                 
               
             
           
         
       
     
         [0060]    In comparison, a controllable damping coil added to a geophone may provide controlled damping without using the bobbin as the element to cause the damping, and thus, without an external shunt resistor. In an embodiment, the damping coil may be made of Constantan wire to limit the temperature dependency. 
         [0061]      FIG. 7-1  shows a side view schematic of a dual coil geophone  700  having a damping coil added to each end of the coils. Underlying the geophone components, a bobbin (shown in shadow) is provided, about which additional geophone materials are disposed. The bobbin  714  may be made of various materials, including conductive metal or insulating plastic. A pair of coil windings  712 ,  713  is disposed concentrically about the bobbin  714 , spaced apart from one another by a spacer  733 . The spacer  733  may be made of, for example, an insulating material. At opposing ends of the geophone  700 , a damping coil  730  is added to the bobbin  714  on the upper and lower ends of the moving coils  712 ,  713 , respectively, and insulation rings  732  cap either end of the geophone  700  adjacent to each damping coil  730 .  FIG. 7-2  shows the relative winding directions of the moving coils  712 ,  713 , and the damping coils  730 . 
         [0062]    Various aspects of the bobbin and/or the damping coil may be designed to achieve particular results. For example, the thickness of the bobbin may be reduced by high precision machining, but there may be a limit to the effect of thickness. In an embodiment, the bobbin, when manufactured of a conductive metal, may be slotted as shown in  FIG. 8  to stop current flowing in the slotted bobbin  814 , as described in U.S. Pat. No. 7,099,235, commonly assigned with the present disclosure. 
         [0063]    In an embodiment, a sheet metal may be employed to manufacture the bobbin, as described in U.S. Pat. No. 7,099,235. In an embodiment, the bobbin is formed from a simple tube of suitable thickness and material. For example, a plastic tube might be 0.15 mm thick and have a mass of about 2 g, which can be extruded or formed in any suitable manner. Optionally, the bobbin  814  may be formed from a flat sheet into a tubular shape with a slot  826  down one side ( FIG. 8 ), in which case aluminum having a thickness of 0.1 mm might be used. When the bobbin  814  is a continuous metal tube, currents can be set up which damp the motion of the moving coil. If the tube is incomplete (as shown in  FIG. 8 ), currents may be prevented. 
         [0064]    In  FIG. 9 , an embodiment of the geophone  900  includes the moving coil  912  shown disposed and wrapped concentrically about the bobbin  914 . An insulation ring  932  is additionally wrapped or placed over the end of the bobbin  914  so as to be positioned concentrically about the bobbin  914  at either end such that the moving coil  912  is layered between rings of insulation  932  at either end. 
         [0065]    In an embodiment, insulation material may be cladded to the bobbin as shown in  FIG. 10 . In  FIG. 10 , an embodiment of the geophone  1000  includes the moving coils  1012 ,  1013  shown disposed and wrapped concentrically about the bobbin  1014  (shown in shadow). Insulation  1032  is cladded in a layer directly onto the outer surface of the bobbin  1014  at either end such that the moving coils  1012 ,  1013  are layered between insulation  1032  at either end. 
         [0066]    In the case that optimal damping resistance is high relative to the resistance of the bobbin, the damping resistance may dominate the total resistance, so the temperature dependency can be controlled by a chip resistor. As seen in  FIG. 10 , a slotted bobbin  1014  may underlay additional geophone components. A pair of moving coils  1012 ,  1013  is disposed and wrapped concentrically about the slotted bobbin  1014 , spaced apart by an open space lacking insulation or slot. In the open space separating the pair of moving coils  1012 ,  1013 , a damping resistance  1035 , such as a chip resistor, may be employed. Capping either end of the bobbin  1014 , insulation  1032  (disposed as a ring or cladded directly to the bobbin  1014 ) is provided. 
         [0067]    In still another embodiment, an embodiment of the geophone  1100  includes one or more independent damping coil(s), as shown in  FIG. 11 . In an embodiment, each independent damping coil  1130  can be a one-turn coil of metal deposited onto the insulation ring  1132 , at either end of the moving coil  1112 . In the embodiment of  FIG. 11 , a temperature insensitive wire material may be used for the one-turn damping coil  1130 , such as Constantan whose resistance is constant across a wide range of temperatures to reduce temperature dependence. The damping coil  1130  may be formed of a metal added to the outside of insulation  1132  (in ring form, or cladded directly to the bobbin as described above), forming a one-turn coil disposed on top of insulation  1032  at either end of the bobbin. 
         [0068]    The resistance of the bobbin r b  may be calculated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     b 
                   
                   = 
                   
                     
                       ρ 
                        
                       
                         
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             d 
                             b 
                           
                            
                           n 
                         
                         
                           π 
                            
                           
                               
                           
                            
                           
                             
                               d 
                               w 
                               2 
                             
                             / 
                             4 
                           
                         
                       
                     
                     = 
                     
                       ρ 
                        
                       
                         
                           8 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             d 
                             b 
                           
                            
                           n 
                         
                         
                           π 
                            
                           
                               
                           
                            
                           
                             d 
                             w 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   23 
                 
               
             
           
         
       
     
         [0000]    where d w  is the wire diameter of the damping coil, d b  is the diameter of the bobbin, ρ is the resistivity of the bobbin, and n is the number of turns of the damping coil. 
         [0069]    By implementing a damping coil with an open circuit response when output terminals are open, the amount of damping and temperature coefficient can be controlled. In turn, the controlled damping may be optimized to a particular degree of damping, for example, to about 70%, as would be achieved in a conventional geophone using external shunt resistor. By using temperature insensitive wire, such as Constantan, the temperature effects on the controlled damping can be reduced at high temperatures (for example, about 175 degrees Celsius and higher). Demagnetization of the magnet may affect the efficacy of damping, but to a lesser degree than in conventional geophones. 
         [0070]    Alternatively, in an embodiment of geophone  1200 , a damping coil  1236  can also be embedded in the material of a plastic bobbin  1214  as shown in  FIG. 12 . In the embodiment of  FIG. 12 , the bobbin  1214  is made of an insulating plastic material, with a recess into which the moving coil  1212  is wound concentrically about the bobbin  1214 . In a groove (or second recess) disposed about the bobbin  1214  in the insulating plastic both above and below the recess in which the moving coil  1212  is disposed, a metal material may be disposed, thereby forming the damping coil  1236  embedded in the plastic bobbin  1214  material. 
         [0071]    Alternatively, in an embodiment of geophone  1300 , an equivalent effect may be achieved by wrapping thin metallic foil as the damping coil  1338  around a slotted bobbin  1314  after providing insulation  1340  on the bobbin  1314 , such as insulation sheet or an anodic oxidation coating on the bobbin  1314  as shown in  FIG. 13 . The insulation  1340  and the conductive foil damping coil  1338  can be sufficiently thin as to not reduce the space allowed for the sensing moving coil  1312 . As shown in  FIG. 13 , a slotted bobbin (as shown in  FIG. 8 ) may have a thin layer of insulation  1341 , added by cladding, layering, or sputtering onto the bobbin  1314 . On top of the conductive thin layer, the moving coil(s)  1312  may be concentrically wound about the bobbin as described previously. Insulation  1332  in the form of material disposed to the bobbin  1314  by cladding, or slipped over the ends of the bobbin in ring-form, spans the outer ends of the bobbin around the moving coil(s). The same effect can be obtained by depositing metal as the damping coil  1452  on to a non-conductive plastic bobbin  1414  underneath the sensing moving coil  1412 , as shown in the geophone  1400  of  FIG. 14 . 
         [0072]    Geophones of the present disclosure find particular applications in seismic surveying equipment.  FIG. 15  shows a marine seismic survey  1500  having a sea bed cable  200  which includes a number of geophone packages  202  spaced at regular intervals and connected through the cable  200  to processing equipment  204 .  FIG. 16  shows a land seismic survey  1600  having a land cable  200 ′ which has a similar configuration as the sea bed cable with geophones  202 ′ spaced apart and connected to processing equipment  204 ′. 
         [0073]      FIG. 17  shows a borehole seismic survey  1700  having a downhole tool comprising a tool body  220  which can be lowered into a borehole  222  on a wireline cable  224  connected to surface processing equipment  226 . The tool body  220  includes an operable arm  228  which can be caused to bear against the borehole wall  230 , and a sensor package  232  which is forced against the borehole wall  230  due to the action of the arm  228 . The sensor package  232  contains three orthogonally oriented geophones  234   x,    234   y,    234   z  (x,y,z directions) which can receive seismic signals and pass data back to the surface via the wireline cable  224 . 
         [0074]    Although a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this disclosure. Accordingly, such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not simply structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of the claims herein, except for those in which the claim expressly uses the words ‘means for’ together with an associated function.