Patent Publication Number: US-2021184355-A1

Title: Toroidally-wound toroidal winding antenna for high-frequency applications

Description:
TECHNICAL FIELD 
     The exemplary embodiments disclosed herein relate generally to sensors used for measuring formation properties and, more specifically, to sensors and sensing methods that employ antennas having toroidally-wound toroidal windings (TWTW) to make high-frequency measurements. 
     BACKGROUND 
     Formation properties such as resistivity and permittivity are used in the oil and gas industry to assess the likelihood that hydrocarbon may be present in a subterranean formation. Electromagnetic logging tools are available that can estimate the resistivity and permittivity of a volume of interest in the formation. These logging tools typically operate by causing an electromagnetic wave to propagate from a wellbore into the formation. The logging tools often employ a sensor in the form of an antenna to receive electromagnetic waves returning from the formation. The received electromagnetic waves induce voltages in the antenna that may be logged (i.e., recorded) and processed to obtain an estimation of the resistivity, permittivity, and other properties of the volume being investigated. 
     One type of antenna often used with electromagnetic logging tools is a toroid antenna. A toroid antenna is essentially a wire wound in a helical pattern around a core having the shape of a toroid (i.e., a surface of revolution obtained by revolving a circle around a central axis). The toroid core is typically made of a ferromagnetic material, such as iron, steel, cobalt, nickel, and the like, that is insulated from the wire. The toroid antenna is typically mounted coaxially on a section of tubing or pipe, such as a mandrel of the logging tool or a drill collar (e.g., within an annular recess thereof). A single toroid antenna may be used as both transmitter and receiver antenna in some applications, or multiple toroid antennas may be used as transmitter and/or receiver antennas in some applications. It is also possible to use a combination of toroidal antennas and non-toroidal antennas in some applications. 
     However, while existing toroid antennas have generally been satisfactory as sensors in downhole logging tools, these toroid antennas can be somewhat sensitive to low-frequency and midrange frequency noise and other interference, either from other downhole logging tools operating in the wellbore and/or from the subterranean formation at large. Thus, there continues to be a need for an improved antenna that may be used as a sensor in downhole logging applications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the exemplary disclosed embodiments, and for further advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings in which: 
         FIG. 1A  illustrates an exemplary well in which a toroidally-wound toroidal winding antenna may be used according to the disclosed embodiments; 
         FIG. 1B  illustrates another exemplary well in which a toroidally-wound toroidal winding antenna may be used according to the disclosed embodiments; 
         FIG. 2  illustrates an exemplary formation evaluation system that may be used with a toroidally-wound toroidal winding antenna; 
         FIG. 3  illustrates an exemplary toroidally-wound toroidal winding antenna according to the disclosed embodiments; 
         FIG. 4  illustrates an exemplary toroidally-wound toroidal winding antenna according to the disclosed embodiments; 
         FIG. 5  illustrates another exemplary toroidally-wound toroidal winding antenna according to the disclosed embodiments; 
         FIG. 6  illustrates electric and magnetic fields for an exemplary toroidally-wound toroidal winding antenna according to the disclosed embodiments; 
         FIG. 7  illustrates an exemplary multi-axial configuration of toroidally-wound toroidal winding antennas according to the disclosed embodiments; 
         FIG. 8  illustrates an exemplary bucking configuration of toroidally-wound toroidal winding antennas according to the disclosed embodiments; 
         FIG. 9  illustrates an exemplary radial configuration of toroidally-wound toroidal winding antennas according to the disclosed embodiments; 
         FIG. 10  illustrates a method of designing an exemplary toroidally-wound toroidal winding antenna according to the disclosed embodiments; 
         FIG. 11  illustrates an exemplary frequency response of a toroidally-wound toroidal winding antenna according to the disclosed embodiments; and 
         FIG. 12  illustrates another exemplary frequency response of a toroidally-wound toroidal winding antenna according to the disclosed embodiments. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     The following discussion is presented to enable a person skilled in the art to make and use the exemplary disclosed embodiments. Various modifications will be readily apparent to those skilled in the art, and the general principles described herein may be applied to embodiments and applications other than those detailed below without departing from the spirit and scope of the disclosed embodiments as defined herein. Accordingly, the disclosed embodiments are not intended to be limited to the particular embodiments shown, but are to be accorded the widest scope consistent with the principles and features disclosed herein. 
     The embodiments disclosed herein relate to improved sensors and sensing methods for use in evaluating the resistivity and permittivity of a subterranean formation. The disclosed sensors and sensing methods advantageously employ antennas having toroidally-wound toroidal windings (“TWTW”) to make high-frequency measurements. The TWTW antennas are able to act as natural high-pass filters to suppress low-frequency and midrange frequency noise and other interference. Such antennas allow a logging tool to sense or detect high-frequency signals, or the high-frequency component of a signal, more clearly and accurately. Multiple TWTW antennas may be used in multiple different configurations, including a multi-axial configuration, bucking configuration, radial configuration, and the like. The TWTW antennas are particularly useful in applications like dielectric logging (including logging/measurement while drilling (L/MWD) operations), short hop communications, waterflood monitoring, and the like. 
     Referring now to  FIG. 1A , a drilling rig  100   a  is shown in which the sensors and sensing methods disclosed herein may be used to determine formation resistivity, permittivity, and other formation properties. The drilling rig  100   a  is located above a borehole  102  that has been drilled through a subterranean formation  104  from a surface location  106 . The surface location  106  is depicted here as an onshore location, but may also be an offshore location or any other location from which the borehole  102  may be drilled. A drill string  108  composed of a continuous length of assembled pipe segments  110  is suspended from the drilling rig  100   a . The drill string  108  typically has a bottom-hole-assembly (BHA) attached at the end thereof that includes a rotary drilling motor  112  connected to a drill bit  114 . A non-exclusive list of BHA components includes: drill pipe, drill collars, agitators, exciters, jars, stabilizers, reamers, hole openers, filter subs, circulation subs, monel or non-magnetic drill collars, crossovers, mud motor, the aforementioned drill bit, and the like. The drill string  108  may further include a downhole tool  116 , such as a logging/measurement while drilling (L/MWD) tool, that can be used to assess formation resistivity and other formation properties. 
     Other conveyances in addition to the drill string  108  may also be used to convey the downhole tool  116 , as depicted in the drilling rig  100   b  of  FIG. 1B . These conveyances may include, for example, a wireline, slickline, coiled tubing, pipe, tractor, and the like, including conveyances that comprise a conductor where tool measurements may be conveyed to the surface by telemetry along the conveyance, as well as conveyances that do not comprise a conductor. In the latter case, tool measurements may be transmitted to the surface acoustically, electromagnetically, or via mud pulse telemetry, or stored in memory and subsequently retrieved at the surface. In the example of  FIG. 1B , a wireline  117  is used as the conveyance for the downhole tool  116 . 
     In accordance with the disclosed embodiments, one or more TWTW antenna sensors  118  are mounted on the downhole tool  116 , for example, on a mandrel of the logging tool  116  (e.g., within an annular recess thereof). These TWTW antenna sensors  118  receive electromagnetic waves returning from the formation, allowing them to be logged as voltages by the downhole tool  116 . The recorded voltages are then communicated, typically in real time, to a data processing unit  120  located either near the drilling rig  100   a ,  100   b  and/or at another location where they are processed (e.g., filtering, analog-to-digital conversion, etc.) as needed. It is also possible to locate the data processing unit  120  downhole on the drill string  108 , for example, in the logging tool  116 , for in-situ processing of the sensor data from the sensors  118 . Alternatively, a portion of the data processing unit  120  may be located downhole and a portion located on the surface as needed to optimize processing of the sensor data. The data processing unit  120  thereafter sends the processed data to a formation evaluation system  122  via a communication link  124  to derive an estimation of the formation resistivity, permittivity, and other properties of the formation. 
     In the embodiment of  FIGS. 1A and 1B , the one or more TWTW antenna sensors  118  are shown as coaxially mounted on the downhole tool  116 . Other embodiments may employ alternative arrangements, such as a radial mounting configuration, without departing from the scope of the disclosed embodiments. A conventional antenna (not expressly shown) may be used in some embodiments to transmit the electromagnetic waves into the formation  104 , or one or more of the TWTW antenna sensors  118  may be used as both a transmitter and a receiver in some embodiments. Single-sensor embodiments as well as embodiments that use multiple sensors  118  are contemplated. It is also possible to use a combination of TWTW antenna sensors  118  and conventional antenna sensors to receive the electromagnetic waves in some embodiments. 
       FIG. 2  illustrates an exemplary implementation of the formation evaluation system  122  according to the embodiments disclosed herein. The formation evaluation system  122 , which is depicted as a surface level system (see  FIGS. 1A and 1B ) for ease of reference, may include a conventional computing system, such as a workstation, desktop, or laptop computer, indicated at  200 , or it may include a custom computing system developed for a particular application. In a typical arrangement, the computing system  200  includes a bus  202  or other communication pathway for transferring information among other components within the computing system  200 , and a CPU  204  coupled with the bus  202  for processing the information. The computing system  200  may also include a main memory  206 , such as a random access memory (RAM) or other dynamic storage device coupled to the bus  202  for storing computer-readable instructions to be executed by the CPU  204 . The main memory  206  may also be used for storing temporary variables or other intermediate information during execution of the instructions by the CPU  204 . 
     The computing system  200  may further include a read-only memory (ROM)  208  or other static storage device coupled to the bus  202  for storing static information and instructions for the CPU  204 . A computer-readable storage device  210 , such as a nonvolatile memory (e.g., Flash memory) or magnetic disk drive, may be coupled to the bus  202  for storing information and instructions for the CPU  204 . The CPU  204  may also be coupled via the bus  202  to a display  212  for displaying information to a user. One or more input devices  214 , including alphanumeric and other keyboards, mouse, trackball, cursor direction keys, and so forth, may be coupled to the bus  202  for transferring information and command selections to the CPU  204 . A communications interface  216  may be provided for allowing the computing system  200  to communicate with an external system or network. 
     The term “computer-readable instructions” as used above refers to any instructions that may be performed by the CPU  204  and/or other components. Similarly, the term “computer-readable medium” refers to any storage medium that may be used to store the computer-readable instructions. Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media may include, for example, optical or magnetic disks, such as the storage device  210 . Volatile media may include dynamic memory, such as main memory  206 . Transmission media may include coaxial cables, copper wire and fiber optics, including the wires of the bus  202 . Transmission itself may take the form of electromagnetic, acoustic or light waves, such as those generated for radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media may include, for example, magnetic medium, optical medium, memory chip, and any other medium from which a computer can read. 
     A formation resistivity evaluation application  218 , or the computer-readable instructions therefor, may also reside on or be downloaded to the storage device  210  for execution. The formation resistivity evaluation application  218  may be a standalone tool or it may be part of a larger suite of tools that may be used to obtain an overall evaluation of the formation  116 . This evaluation application  218  may be implemented in any suitable computer programming language or software development package known to those having ordinary skill in the art, including various versions of C, C++, FORTRAN, and the like. Users may then use the evaluation application  218  to analyze the data from the one or more TWTW antenna sensors  118  to estimate resistivity, permittivity, and other formation properties. 
     Referring now to  FIG. 3 , a toroidally-wound electrical conductor  300  is shown that may be used in the one or more TWTW antenna sensors  118  according some embodiments. The toroidally-wound electrical conductor  300  is composed mainly of a wire  302  or similar electrical conductor that is wound in a helical or spiral pattern around a core  304 . The core  304  may simply be an air core, but is typically made of a ferromagnetic material, such as iron, steel, cobalt, nickel, and the like, and is usually insulated from the wire or electrical conductor  302 . The toroidally-wound electrical conductor  300  (and the core  304  therein) may then be formed into a toroidally-wound toroidal winding similar to the one shown in  FIG. 4  by winding the electrical conductor  300  in a helical pattern around a toroid shaped core. 
       FIG. 4  shows an exemplary TWTW antenna  400  that may be constructed from a toroidally-wound electrical conductor (see  FIG. 3 ) according to the disclosed embodiments. As can be seen, the antenna  400  is composed of a primary core  402  in the shape of a toroid and a secondary core  404  wound in a helical or spiral pattern around the primary core  402 . A wire  406  or similar electrical conductor is wound in a helical or spiral pattern around the secondary core  404 , forming a toroidally-wound electrical conductor  408  that is structurally and electrically similar to the toroidally-wound electrical conductor  300  of  FIG. 3 . This toroidally-wound electrical conductor  408  also follows the path of the secondary core  404  around the primary core  402 , thus forming a toroidally-wound toroidal winding, indicated generally at  410 , around the primary core  402 . The thusly constructed TWTW antenna  400  may then be used as or in the sensor  118  (i.e., as a receiver antenna) in accordance with the disclosed embodiments. 
     The primary core  402  is typically made of a ferromagnetic material, such as iron, steel, cobalt, nickel, and the like, and is normally insulated from the toroidally-wound electrical conductor  408 , which may itself be a copper wire, for example. The secondary core  404  is also typically made of a ferromagnetic material, such as iron, steel, cobalt, nickel, and the like, and is also normally insulated from the toroidally-wound electrical conductor  406 . The material used for the primary core  402 , secondary core  404 , and electrical conductor  406 , as well as any insulating material, should be carefully selected to allow the antenna  400  to withstand harsh downhole environmental conditions, including high temperatures and pressures. It is of course possible in some embodiments for either the primary core  402  or the secondary core  404 , or both, to be air cores (see  FIG. 5 ) as needed depending on the particular application. 
       FIG. 5  depicts an alternative TWTW antenna  500  where the toroidally-wound toroidal winding itself is the TWTW antenna  500 . In this embodiment, both the primary core and the secondary core may be air cores such that the TWTW antenna  500  is composed only (or primarily) of a toroidally-wound electrical conductor  502  wound in a helical or spiral pattern to form the toroidally-wound toroidal winding  500 . 
     Operation of the TWTW antenna as a receiver may be described with reference to  FIG. 6  and the well-known Maxwell equations: 
     
       
         
           
             
               
                 
                   
                     ∇ 
                     
                       · 
                       D 
                     
                   
                   = 
                   ρ 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     ∇ 
                     
                       · 
                       B 
                     
                   
                   = 
                   0 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ∇ 
                     
                       × 
                       E 
                     
                   
                   = 
                   
                     - 
                     
                       
                         ∂ 
                         B 
                       
                       
                         ∂ 
                         t 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ∇ 
                     
                       × 
                       H 
                     
                   
                   = 
                   
                     
                       
                         ∂ 
                         D 
                       
                       
                         ∂ 
                         t 
                       
                     
                     + 
                     J 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     where E is electric field, H is magnetic field, D is electric displacement field, B is magnetic flux density, ρ is free electric charge density, and J is free current density. In phasor form for a time harmonic field and assuming a simple medium with dielectric permittivity of E and magnetic permeability of μ, Maxwell&#39;s equations become: 
     
       
         
           
             
               
                 
                   
                     
                       ∇ 
                       
                         · 
                         E 
                       
                     
                     = 
                     
                       ρ 
                       ɛ 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ∇ 
                       
                         · 
                         H 
                       
                     
                     = 
                     0 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ∇ 
                       
                         × 
                         E 
                       
                     
                     = 
                     
                       
                         - 
                         jw 
                       
                        
                       
                           
                       
                        
                       μ 
                        
                       
                           
                       
                        
                       H 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ∇ 
                       
                         × 
                         H 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             jw 
                              
                             
                                 
                             
                              
                             ɛ 
                           
                           + 
                           σ 
                         
                         ) 
                       
                        
                       E 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In general, these equations explain that a magnetic field passing through the cross-section of a coil will induce an electric field in the circumferential direction on the coil. This electric field will generate an electromotive force that will in turn create a voltage difference in the coil that may be measured. 
     Referring to  FIG. 6 , the Maxwell equations may be applied to a TWTW antenna as follows. A TWTW antenna may be considered as comprising a primary turn 600 (i.e., the toroid core), secondary turns 602 (i.e., the secondary core), and tertiary turns 604 (i.e., the toroidally-wound electrical conductor). The primary turn 600 may have radius r a , the secondary turns 602 may have radius r b , the tertiary turns 604 may have radius r a . An incident magnetic field H i  passing through the cross-section of the primary turn 600 induces an electric field E p  in the primary turn. This electric field E p  induces a magnetic field H s  in the secondary turns 602, which creates an electric field E p  in the tertiary turns 604. The electric field E t  in the tertiary turns 604 creates a voltage on the tertiary turns equal to the integral of the electric field along the length of the turns. 
     As it can be seen from Equation (2), assuming a coil antennas source, the induced electric and magnetic fields for the primary turn 600 are proportional to the angular frequency co. However, the induced fields in the secondary turns 602 are proportional to ω 2 , while the induced fields in the tertiary turns 604 are proportional to ω 3 . Thus, as co increases, the strength of a signal in a TWTW antenna may increase proportionately to ω 3  compared to co for a conventional coil antenna (i.e., an improvement of ω 2 ). 
     It should be understood, however, that the improved signal strength increase (i.e., improved receiver gain) may not be clearly noticeable at low frequencies. The reason is because the TWTW antenna is a combination of primary, secondary, and tertiary turns, and thus it can pick up the same signals that would normally be picked up by a conventional coil antenna. The signals received by the conventional coil antenna usually dominate at low frequencies (i.e., Earth fields) and will swamp the signals received by the tertiary turns at low frequencies. Once the frequency increases above a certain cutoff frequency where the signals received by the conventional coil antenna no longer dominate, then the improved receiver gain of the tertiary turns becomes more apparent. Simulations have shown in some instances that the improved receiver gain of the tertiary turns becomes apparent at about 10 MHz, with the highest receiver gains seen at about 1 GHz. 
     The improved signal strength increase as co increases allows the TWTW antenna to be used as a natural high-pass filter that can eliminate the effects of lower frequency noise, such as interference from tools working at lower frequencies, while strengthening higher frequency signals. This ability to suppress lower frequency noise and strengthen higher frequency signals makes the TWTW antenna particularly effective for use in sensors for dielectric logging applications and the like. Other downhole applications that may benefit from the TWTW antenna based sensors include short hop communication systems and fiber optic communication systems, such as those used for monitoring waterflood operations. 
       FIG. 7  illustrates an exemplary downhole application in which multiple TWTW antennas  700 ,  702 ,  704 , and  706  may be used in a multi-axial configuration. In this application, the TWTW antennas  700 - 706  are coaxially mounted along the axis of a downhole tool  116  (e.g., on a mandrel thereof) within a wellbore  102  in a subterranean formation  104 . The first TWTW antenna  700  operates as a transmitter while the remaining TWTW antennas  702 - 706  serve as receivers. As can be seen, the TWTW transmitter antenna  700  is spaced apart from the TWTW receiver antennas  702 - 706  by a distance “d 1 ” that is greater than the distance “d 2 ” by which the TWTW receiver antennas  702 - 706  are spaced apart from one another. In general, the spacing between a transmitter antenna and a receiver antenna, as well as the frequency of operation, determines the volume of investigation for any antenna pair. Thus, the spacing d 1  between the TWTW transmitter antenna  700  and the TWTW receiver antennas  702 - 706  may be adjusted as needed to target a specific volume of interest. Information obtained from the multi-axial antenna configuration may then be used in an inversion process to obtain a radial and/or vertical permittivity profile of the formation in a manner known to those having ordinary skill in the art. 
       FIG. 8  illustrates another exemplary antenna configuration in which two TWTW receiver antennas  800  and  802  are coaxially mounted on the downhole tool  116  in a bucking configuration. This bucking configuration is useful when there is a strong direct coupling between a transmitter antenna and a receiver antenna. The direct coupling may overwhelm and/or distort any signals received by the receiver antenna from the formation  104 , making it difficult to accurately determine the properties of the volume of interest. To counter such coupling, the TWTW antennas  800 - 802  may be arranged as a main antenna  800  and a bucking antenna  802  connected to the main TWTW antenna  800  so that the two antennas have opposite polarizations (i.e., wound in opposite directions). The precise position of the bucking antenna  802  relative to the main antenna  800  and the number of turns of the bucking antenna  802  may be adjusted such that the bucking antenna cancels any direct coupling on the main antenna  800  by the transmitter (not expressly shown). This ensures that any signals picked up by the main antenna  800 , to a very good approximation, do not contain any direct field contribution from the transmitter antenna. 
       FIG. 9  illustrates yet another exemplary antenna configuration in which two TWTW antennas  900  and  902  may be used to approximate a gradient (i.e., spatial derivative) of an electromagnetic field (or voltage which is proportional to the field). The information obtained from the gradient may be used to obtain a radial gradient of the voltage signal, which is useful in a variety of applications, including ranging operations. In  FIG. 9 , the two TWTW antennas  900  and  902  are located along radially opposite sides of the tool  116 . By subtracting the voltages measured by the radially opposing antennas  900  and  902  and dividing by the distance between them, the gradient of the measurement in the radial direction may be obtained. This is mathematically shown in Equation 3 below, where the component of the gradient of the voltage (V) in the radial direction (i) may be approximated by taking the difference in the voltages measured by antenna  1  (i.e., antenna  900 ) and antenna  2  (i.e., antenna  902 ), divided by the radial distance between them. 
     
       
         
           
             
               
                 
                   
                     
                       ∇ 
                       V 
                     
                     · 
                     
                       r 
                       → 
                     
                   
                   ≈ 
                   
                     
                       
                         V 
                         1 
                       
                       - 
                       
                         V 
                         2 
                       
                     
                     
                       Δ 
                        
                       r 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In a similar manner, although not expressly depicted, a gradient in the axial direction may also be obtained by coaxially mounting two TWTW antennas on a downhole tool. This configuration resembles the bucking configuration from  FIG. 8  except that the purpose of the second TWTW antenna is not to cancel the direct field contribution of a transmitter antenna, but rather to measure the rate of change of the measured electromagnetic field with respect to axial distance. This information may then be used to obtain an axial or vertical gradient of the voltage signal. 
       FIG. 10  illustrates an exemplary method  1000  that may be used to design a TWTW antenna for the foregoing downhole applications. The method  1000  allows the TWTW antenna to have any suitable size and gain characteristic needed for a particular application. The main parameters used to design the TWTW antenna are the primary turn radius r a , the secondary turn radius r b , the tertiary turn radius r c , the number Nb of secondary turns, and the number N c  of tertiary turns in a single secondary turn (see  FIG. 6 ). As an example, a typical TWTW antenna that may be used with a conventional downhole tool may have a primary turn radius r a  of about 2.5 inches, secondary turn radius r b  of about 0.75 inches, tertiary turn radius r c  of about 0.25 inches, secondary turn number Nb of about 9 turns, and tertiary turn number N c  of about 42 turns in a single secondary turn. 
     As can be seen in  FIG. 10 , designing a TWTW antenna begins in some embodiments by generating a first circle having radius r a  at block  1002 . A second circle having radius r b  is revolved around the first circle at block  1004 . Then, a line (wire) is wound around the surface of revolution from the block  1004  to form Nb evenly spaced turns at block  1006 . Thereafter, a third circle having radius r c  is revolved around the second circle at block  1008 . And last but not least, a line is wound around the surface of revolution from block  1008  to form N b ×N c  evenly spaced turns at block  1010 . Note that while the method  1000  of  FIG. 10  is shown using a number of discrete blocks, those having ordinary skill in the art will understand that any individual block may be divided into two or more constituent blocks, and that any two or more blocks may be combined to form a superblock, without departing from the scope of the disclosed embodiments. 
     Any individual turn of a TWTW antenna designed as set forth above may be described mathematically by Equations (4)-(7) below, where x, y and z are the set of points that describe the TWTW antenna: 
         x 1= ra ×cos(Φ)
 
         y 1= ra ×sin(Φ)
 
         z 1=0  (4)
 
         x 2= rb ×cos(1× N   b )×cos(Φ)
 
         y 2= rb ×cos( b×N   b )×sin(Φ)
 
         z 2= rb ×sin(Φ× N   b )  (5)
 
         x 3= rc ×cos(Φ× Nc×N   b )×cos(Φ× N   b )×cos(Φ)− rc ×sin(Φ× Nc×N   b )×sin(Φ)
 
         y 3= rc ×cos(Φ× Nc×N   b )×cos(Φ× N   b )×sin(Φ)+ rc ×sin(Φ× Nc×N   b )×cos(Φ)
 
         z 3= rc ×cos(Φ× Nc×N   b )×sin(Φ× N   b )  (6)
 
         x=x 1+ x 2+ x 3 
         y=y 1+ y 2+ y 3 
         z=z 1+ z 2+ z 3  (7)
 
     In the above equations, ϕ is a radial angle between 0 and 360 degrees, N b  is the number of turns of the toroidal windings (i.e., secondary turns); N c  is the number of turns in the toroidal windings (i.e., tertiary turns); r b  is the radius of the winding of the toroidal windings; r c  is the radius of the toroidal windings; r a  is the radius of the overall TWTW antenna; x1, y1 and z1 are displacements of the main (single) loop in the X, Y and Z Cartesian directions, respectively; x2, y2 and z2 are displacements of the winding of the toroidal windings in the X, Y and Z Cartesian directions, respectively; and x3, y3 and z3 are displacements of the toroidal windings in the X, Y and Z Cartesian directions, respectively. The Equations (4)-(7) thus allow each point on the TWTW antenna to be defined in the Cartesian coordinate system. 
     To demonstrate the behavior of the TWTW antenna, a simulation was performed and the results are displayed in  FIG. 11  for an exemplary TWTW antenna. In  FIG. 11 , a chart  1100  is shown in which the vertical axis represents measured voltage, the horizontal axis represents frequency (Hz), line  1102  represents voltage measured by a conventional coil receiver antenna, and line  1104  represents voltage measured by a TWTW receiver antenna. The simulation was performed using conventional coil transmitter coaxially mounted about 200 inches from the TWTW receiver antenna and assuming a vacuum medium. The radius of both the coil transmitter and the primary turn of the TWTW antenna (r a ) is 10 inches, the radius of the secondary turns (r b ) is 4 inches, the number of secondary turns (N b ) is 16, the radius of tertiary turns (r c ) is 1.75 inches, and the number of tertiary turns (N c ) is 1024. The simulation also assumed that magnetic moment vector of the coil transmitter and the primary turn of the TWTW antenna are aligned. Receiver gain was normalized to 1 at a frequency of 1 GHz. 
     As  FIG. 11  shows, the voltage measured by the coil antenna (line  1102 ) is proportional to the frequency until around 10 MHz, at which point it becomes proportional to the square of the frequency (i.e., the ω 2  term becomes dominant). The TWTW antenna shows a similar behavior until around 30 MHz when the ω 3  term starts to become dominant for the TWTW antenna. Importantly, it can be seen that the TWTW antenna has about the same gain as the coil antenna up to 1 GHz, but is able to suppress lower frequencies (e.g., up to 10 MHz) about 700 times (or more) better than the coil antenna. 
     In the simulation of  FIG. 11 , the main factor affecting the gain of the TWTW receiver antenna is the size of the antenna. Thus, the gain of the antenna may be adjusted by changing one or more of the radii of the antenna, for example the radius r c  of the tertiary turns (i.e., toroidally-wound electrical conductor), or the radius r b  of the secondary turns (i.e., toroidally-wound toroidal winding). The effect on antenna gain from the changes to the one or more of the radii can be seen in  FIG. 12 , which shows the result of a simulation performed for a TWTW antenna with dimensions that are 4 times smaller. 
     In  FIG. 12 , a chart  1200  is shown that is otherwise the same as the chart  1100  from  FIG. 11  line, except a line  1202  has been added representing voltage measured by a TWTW receiver antenna dimensions that are 4 times smaller. Specifically, the TWTW antenna represented by line  1202  has a primary turn radius (r a ) of 2.5 inches, a secondary turn radius (r b ) of 1 inch, and a tertiary turn radius (r c ) of 0.4375 inches. The secondary turn number (N b ) and the tertiary turn number (N c ) are the same as in the previous simulation (i.e., N b =16, N c =1024). 
     As  FIG. 12  shows, the gain of the conventional coil antenna (line  1102 ) is unchanged from the previous simulation when normalized at 1 GHz. Similarly, the smaller TWTW antenna (line  1202 ) behaves like the conventional coil antenna up to around 100 MHz when the ω 3  term starts to become dominant for the TWTW antenna. However, the ability of the smaller TWTW antenna (line  1202 ) to suppress low frequencies (e.g., up to 10 MHz) is almost 10 times worse compared to the larger TWTW antenna (line  1104 ). 
     As can be deduced from the above simulations (and from Equation (2)), electromagnetic sensors working at low frequencies are primarily sensitive to the resistivity of the medium. However, as the frequency of operation increases, the contribution from the higher frequencies, which also relates to the dielectric permittivity, becomes more dominant. The operational frequencies of downhole tools used to measure dielectric permittivity are in the order of gigahertz. Moreover, during logging, many different tools may be stacked together. These tools generally have different frequencies of operation and different sensitivity regions. However, interference between the tools remain an area of concern. Electronic circuitry to prevent such interference by filtering frequency components out of the tool&#39;s band of operation are often needed. The TWTW antenna disclosed herein may naturally perform some of the interference filtering for dielectric logging applications. As described above (see  FIGS. 11 and 12 ), sensors that are based on the TWTW antenna disclosed herein may provide filtering in the order of hundreds of times better compared to a traditional coil antenna. Thus, such an antenna would reduce the need for additional filtering, simplifying design and reducing cost. 
     The TWTW antenna disclosed herein may also be advantageously employed in short hop communication systems. Communication is the transfer of information and it is generally understood that a higher rate of information may be transferred at higher frequencies. Thus, the disclosed TWTW antenna may also be useful in transmitting and receiving data for high-frequency communication systems while again eliminating interference. At higher frequencies, signals attenuate faster, which suggest that short hop communication systems where transmit-receive spacing is low would be most likely to benefit from the TWTW antenna disclosed herein. 
     And as mentioned above, waterflood monitoring applications would also benefit from using TWTW antenna-based sensors. In waterflood monitoring, water is injected from one well to increase the production in a separate production well. Permanent sensors based on TWTW antennas in the production well may be used to estimate the position of the water. This information may in turn be used to optimize the water injection and maximize production. Fiber optic lines are generally used to transmit information from the sensors to the surface in these applications. Several such sensors at different frequencies may operate at the same time to increase information about the waterflood in these systems. 
     Accordingly, as set forth above, the embodiments disclosed herein may be implemented in a number of ways. For example, in general, in one aspect, the disclosed embodiments may relate to an antenna for a downhole logging tool. The antenna may comprise, among other things, a toroid core mountable on the downhole logging tool and a toroidally-wound electrical conductor wound around the toroid core in a helical pattern, thereby forming a toroidally-wound toroidal winding, the toroidally-wound toroidal winding having a predetermined number of turns around the toroid core. The antenna may further comprise an insulating material disposed between the toroidally-wound toroidal winding and the toroid core, the insulating material electrically insulating the toroidally-wound toroidal winding from the toroid core. The insulating material, the toroidally-wound toroidal winding, and the toroid core are composed of materials that allow the antenna to operate under downhole environmental conditions. 
     In accordance with any one or more of the foregoing embodiments, the antenna is operated as one of: a transmitter antenna, or a receiver antenna. 
     In accordance with any one or more of the foregoing embodiments, the antenna is operated as both a transmitter antenna and a receiver antenna. 
     In accordance with any one or more of the foregoing embodiments, the toroid core is one of: a ferromagnetic core, a wire mesh core, or an air core. 
     In accordance with any one or more of the foregoing embodiments, the toroidally-wound electrical conductor has one of: a ferromagnetic core, a wire mesh core, or an air core. 
     In accordance with any one or more of the foregoing embodiments, the antenna allows frequencies higher than a cutoff frequency to pass and suppresses frequencies lower than the cutoff frequency, the cutoff frequency being between about 10 MHz and about 1 GHz. 
     In general, in another aspect, the disclosed embodiments may relate to a method of sensing an electromagnetic signal in a downhole logging tool. The method comprises, among other things, receiving the electromagnetic signal at an antenna mounted on the downhole logging tool, the electromagnetic signal inducing a voltage signal having multiple frequency components in the antenna. The antenna comprises a toroid core and a toroidally-wound electrical conductor wound around the toroid core in a helical pattern, thereby forming a toroidally-wound toroidal winding, the toroidally-wound toroidal winding having a predetermined number of turns around the toroid core. The method further comprises allowing certain frequency components of the voltage signal to pass through the antenna and logging the voltage signal that is outputted by the antenna using the logging tool. 
     In accordance with any one or more of the foregoing embodiments, allowing certain frequency components of the voltage signal to pass through the antenna comprises allowing frequency components higher than a cutoff frequency to pass, the cutoff frequency being between about 10 MHz and about 1 GHz. 
     In accordance with any one or more of the foregoing embodiments, allowing certain frequency components of the voltage signal to pass through the antenna further comprises suppressing frequency components lower than the cutoff frequency. 
     In accordance with any one or more of the foregoing embodiments, the method further comprises adjusting the cutoff frequency of the antenna by changing one or more of: a radius of the toroidally-wound electrical conductor, or a radius of the toroidally-wound toroidal winding. 
     In general, in yet another aspect, the disclosed embodiments may relate to a downhole logging tool for determining a property of a subterranean formation. The downhole logging tool comprises, among other things, a tool body and at least one toroidally-wound toroidal winding antenna mounted on the tool body. The at least one toroidally-wound toroidal winding antenna comprises a toroid core and a toroidally-wound electrical conductor wound around the toroid core in a helical pattern to form a toroidally-wound toroidal winding, the toroidally-wound toroidal winding having a predetermined number of turns around the toroid core. The downhole logging tool further comprises a signal processing unit connected to the at least one toroidally-wound toroidal winding antenna, the signal processing unit operable to log a voltage signal outputted by the at least one toroidally-wound toroidal winding antenna. 
     In accordance with any one or more of the foregoing embodiments, the at least one toroidally-wound toroidal winding antenna comprises multiple toroidally-wound toroidal winding antennas coaxially mounted on the tool body and having a predefined spacing therebetween. 
     In accordance with any one or more of the foregoing embodiments, the predefined spacing is selected based on a volume of interest in the subterranean formation. 
     In accordance with any one or more of the foregoing embodiments, the voltage signal outputted by the multiple toroidally-wound toroidal winding antennas contains information that may be used to obtain one of: a radial permittivity profile for the volume of interest, or vertical permittivity profile for the volume of interest. 
     In accordance with any one or more of the foregoing embodiments, the voltage signal outputted by the coaxially mounted multiple toroidally-wound toroidal winding antennas contains information that may be used to obtain an axial gradient of the voltage signal. 
     In accordance with any one or more of the foregoing embodiments, the multiple toroidally-wound toroidal winding antennas coaxially mounted on the tool body are arranged in a bucking configuration in which the toroidally-wound electrical conductor of one antenna is wound around the toroid core of said antenna in a direction opposite from the toroidally-wound electrical conductor of a second antenna. 
     In accordance with any one or more of the foregoing embodiments, the voltage signal outputted by the radially mounted multiple toroidally-wound toroidal winding antennas contains information that may be used to obtain a radial gradient of the voltage signal. 
     In accordance with any one or more of the foregoing embodiments, the tool body comprises a mandrel of the logging tool. 
     While the invention has been described with reference to one or more particular embodiments, those skilled in the art will recognize that many changes may be made thereto without departing from the spirit and scope of the description. Each of these embodiments and obvious variations thereof is contemplated as falling within the spirit and scope of the claimed invention, which is set forth in the following claims.