Patent Publication Number: US-2011071762-A1

Title: Method of determining a transient electromagnetic response of a formation

Description:
TECHNICAL FIELD 
     This invention relates generally to signal processing in the context of geological exploration and, more specifically, to determining the transient electromagnetic response of a region of an earth formation. 
     BACKGROUND 
     Electromagnetic investigation tools are often used to take measurements at points along the length of a borehole in an earth formation. In many instances, the tools are attached to or associated with a support structure such as a mandrel, bar, shaft, spindle, housing, cable or wire line. For example, in measuring while drilling (MWD) applications, also known as logging while drilling (LWD) applications, measurement tools may be attached to a high strength support structure that supports a drill bit as the drill bit forms a borehole. The high strength structure can cause the formation response measurements to be disrupted as the high strength structure is typically formed from an electrically conductive material, such as steel or another metal. Therefore, it is desirable to have a system and method that facilitate the removal or reduction of the contribution of the support structure to the measurement so as to reveal information that is provided by a formation response signal. 
     SUMMARY 
     The various embodiments of the present invention overcome the shortcomings of the prior art by providing a system and method for determining an electromagnetic response from a region in an earth formation. Raw response signals are measured with receivers at different offset distances from one or more transmitters. The receivers are electromagnetically coupled to the one or more transmitters by a support structure. The raw signals are adjusted according to an exemplary method to provide an adjusted signal where the effect of the support structure on the raw response signals is removed or reduced. The adjusted signal can be interpreted to determine information that is masked in the raw response signals. In other words, the adjusted signal reflects the electromagnetic response from the region of the earth formation. 
     An exemplary method for determining an electromagnetic response from a region in an earth formation is now described. A measurement tool is conveyed into a borehole formed in the earth formation. The measurement tool can include multiple transmitters and multiple receivers. For example, the measurement tool can include a transmitter, a first receiver, and a second receiver, each positioned on or near an electrically conductive support structure. Here, the first receiver is positioned at a first distance from the transmitter and the second receiver is positioned at a second distance from the transmitter. One of the first receiver and the second receiver can be selected as a primary receiver and the other receiver can be selected as a secondary receiver, as described herein. 
     Once the measurement tool is positioned in the borehole, a source signal is transmitted from the transmitter. The source signal incites a first raw signal in the first receiver and a second raw signal in the second receiver. A data acquisition unit measures the first raw signal and the second raw signal and the raw signals are stored in a memory of a computing unit. The raw response signals exhibit an effect from the support structure coupling the transmitters to the receivers such that in a masked time interval the raw response signals do not reflect formation response signals. 
     The computing unit includes a processor unit that calculates an adjusted signal by determining a first function of the first raw signal, a second function of the second raw signal, a third function of the first distance, and a fourth function of the second distance. The third function and the fourth function relate the first function and the second function. The computing unit then modifies at least one of the first function and the second function according to the relationship between the third function and the fourth function and subtracts one of the resulting first and second functions from the other of the resulting first and second functions. 
     According to one aspect of the disclosure, the first function is the first raw signal, the second function is the second raw signal, the third function is the inverse of the first distance cubed, and the fourth function is the inverse of the second distance cubed. 
     According to another aspect of the disclosure, the first function is the first raw signal, the second function is the second raw signal, the third function is the average of the first raw signal over the masked time interval, and the fourth function is a the average of the second raw signal over the masked time interval. 
     In certain of the exemplary methods, a first reference signal and a second reference signal are respectively obtained at the first distance and the second distance in a reference medium having a resistivity that is higher than that of the region in the earth formation. For example, the reference medium can have a resistivity that is at least ten times that of the earth formation. 
     The computing unit can include memory that stores the first reference signal and the second reference signal. 
     According to an aspect of the disclosure, the first function is the first raw signal, the second function is the second raw signal, the third function is the first reference signal, and the fourth function is the second reference signal. 
     According to another aspect of the disclosure, the first function is a first calibrated signal that is determined by subtracting the first reference signal from the first raw signal, the second function is a second calibrated signal that is determined by subtracting the second reference signal from the second raw signal, the third function is the first distance, and the fourth function is the second distance. 
     According to another aspect of the disclosure, the first function is a first calibrated signal that is determined by subtracting the first reference signal from the first raw signal, the second function is a second calibrated signal that is determined by subtracting the second reference signal from the second raw signal, the third function is the average of the first calibrated signal over the masked time interval, and the fourth function is the average of the second calibrated signal over the masked time interval. 
     According to another aspect of the disclosure, the first function is a first calibrated signal that is determined by subtracting the first reference signal from the first raw signal, the second function is a second calibrated signal that is determined by subtracting the second reference signal from the second raw signal, the third function is the cube root of the first reference signal, and the fourth function is the cube root of the second reference signal. 
     The adjusted signal can be interpreted to determine information about the formation that is masked by the raw response signals. For example, the number of layers present in the region in the formation may be determined by calculating the slope of the adjusted signal in the masked time interval. 
     It is envisaged that the method can be performed by the system where computer executable instructions are contained on a computer readable medium. For example, a processor unit of the computing unit can execute the instructions. 
     The foregoing has broadly outlined some of the aspects and features of the present invention, which should be construed to be merely illustrative of various potential applications of the invention. Other beneficial results can be obtained by applying the disclosed information in a different manner or by combining various aspects of the disclosed embodiments. Accordingly, other aspects and a more comprehensive understanding of the invention may be obtained by referring to the detailed description of the exemplary embodiments taken in conjunction with the accompanying drawings, in addition to the scope of the invention defined by the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of a system for determining an electromagnetic response from a region of an earth formation. 
         FIG. 2  is an illustration of the system of  FIG. 1  in a homogenous region of the formation. 
         FIGS. 3 and 4  are illustrations of the system of  FIG. 1  in two layer regions of the formation. 
         FIG. 5  is a graph illustrating signals relating to the homogeneous region of  FIG. 2 . 
         FIGS. 6 and 7  are graphs illustrating signals relating to the two layer regions of  FIGS. 3 and 4 . 
         FIG. 8  is a graph illustrating calibrated signals relating to the regions of  FIGS. 2-4 . 
         FIG. 9  is a graph illustrating adjusted signals relating to the regions of  FIGS. 2-4 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     As required, detailed embodiments of the present invention are disclosed herein. It must be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms, and combinations thereof. As used herein, the word “exemplary” is used expansively to refer to embodiments that serve as illustrations, specimens, models, or patterns. The figures are not necessarily to scale and some features may be exaggerated or minimized to show details of particular components. In other instances, well-known components, systems, materials, or methods have not been described in detail in order to avoid obscuring the present invention. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention. 
     Systems and methods are described herein in the context of determining a transient electromagnetic response in a region of an earth formation. The electromagnetic formation response can be interpreted to determine characteristics of the formation, such as the resistivity or conductivity of regions of the formation and the locations of boundaries. However, it is envisaged that the systems and methods taught herein can be applied to other environments and other parameters. 
     Measurement System 
     Referring to  FIG. 1 , a system  10  is configured to drill a borehole  12  in a formation  14  and to take measurements while drilling (MWD). In alternative embodiments, a borehole is drilled, the drill string is removed, and a measurement tool is then lowered into the borehole by a cable or other suitable suspension means. 
     To drill borehole  12 , a drill bit  16  is positioned at the end of a series of tubular elements, referred to as a drill string  18 . Drill bit  16  can be directed by a steering system  20 , such as a rotatable steering system or a sliding steering system. In certain applications, measurements facilitate directing drill bit  16 , for example, toward a hydrocarbon fluid reservoir. 
     System  10  includes a measurement tool  24  that is generally described as an array of transmitters and receivers and a corresponding support structure. In the illustrated embodiment, the support structure is a part of drill string  18 . The support structure provides a foundation to which the transmitters and receivers are attached or otherwise houses the array. Hereinafter, the support structure will be described as a mandrel  32 . However, the support structure could be any number of structures for supporting and positioning the array including a cable, housing, drill string element, combinations thereof, and the like. 
     Illustrated measurement tool  24  includes a transmitter  26 , a first receiver  28 , and a second receiver  30  that are each positioned along the length of mandrel  32 . As best shown in  FIGS. 2-4 , first receiver  28  is positioned at a first transmitter-receiver (TR) offset distance L 1  from transmitter  26  and second receiver  30  is positioned at a second transmitter-receiver offset distance L 2  from transmitter  26 . In the exemplary embodiment, each of transmitter  26  and receivers  28 ,  30  includes a coil antenna that is wound around mandrel  32 . Transmitter  26  and receivers  28 ,  30  are thereby arranged to be substantially coaxial. This arrangement is used for purposes of teaching. However, in alternative embodiments, transmitters and/or receivers can be multi-axial so as to send and receive signals along multiple axes. Further, in alternative embodiments, the measurement tool can include multiple transmitters and multiple receivers. 
     Generally described, a measurement tool includes a primary receiver and one or more secondary receivers. Various amounts of the responses from the secondary receivers are used to adjust the response of the primary receiver so as to minimize or reduce the mandrel effect, that is, the response due to electromagnetic coupling of transmitters and receivers by a mandrel or support structure. In other words, an adjusted signal can be the sum of the response of a primary receiver and responses of the secondary receivers where the responses of the secondary receivers are scaled, altered, or modified according to certain relationships. 
     In an exemplary embodiment described herein, first receiver  28  is selected as the primary receiver and second receiver  30  is selected as the secondary receiver. The formulations of adjusted signals reflect this selection. However, in alternative embodiments, second receiver  30  may be selected as the primary receiver and first receiver  28  may be selected as the secondary receiver. 
     System  10  further includes a data acquisition unit  40  and a computing unit  50 . Data acquisition unit  40  controls output of transmitter  26  and collects the response at receivers  28 ,  30 . The response and/or data representative thereof are provided to computing unit  50  to be processed according to the adjustment methods described herein. Computing unit  50  includes computer components including a data acquisition unit interface  52 , an operator interface  54 , a processor unit  56 , a memory  58  for storing information, and a bus  60  that couples various system components including memory  58  to processor unit  56 . 
     Computing unit  50  can be positioned at the surface or at a remote location such that information collected by measurement tool  24  while in borehole  12  is readily available. For example, a telemetry system can connect measurement tool  24 , data acquisition unit  40 , and computing unit  50 . In alternative embodiments, data acquisition unit  40  and/or computing unit  50  is combined with or integral to measurement tool  24  and processes signals while in borehole  12 . 
     Method of Measuring a Transient Electromagnetic Response 
     An exemplary method of measuring an electromagnetic response of a region of formation  14  is now described. The response is measured with measurement tool  24 . A transient electromagnetic (TEM) response is useful, for example, in deep reading electromagnetic (DEM) well logging applications to identify the boundaries and properties of layers of a region of a formation  14  at relatively large distances from borehole  12 . 
     To begin, data acquisition unit  40  causes a current to flow through transmitter  26  so as to generate a magnetic field. The source signal or input to transmitter  26  may vary. According to an exemplary method, current is passed through transmitter  26  for a time that is long enough to induce a substantially stable magnetic field. This magnetic field permeates both the region of formation  14  and mandrel  32 . 
     Then, the current is abruptly shut off and the changing magnetic fields of the region of formation  14  and mandrel  32  induce currents in receivers  28 ,  30 . Signals that are measured at receivers  28 ,  30  over time are termed raw response signals V raw . Raw response signals V raw  include contributions from both the region of formation  14  and mandrel  32 . Raw response signals V raw  may be subjected to one or more operations such as noise suppression, pre-amplification, filtering, or transformation, prior to or as part of a method of adjusting the raw response signal. 
     In any event, mandrel  32  electromagnetically couples transmitter  26  to receivers  28 ,  30  so as to mask the electromagnetic response of the region of formation  14 . 
     Mandrel Effect Observed in Raw Signals 
     Referring to  FIGS. 2-7 , the effect of mandrel  32  is observed by comparing raw response signal V raw  to a formation response signal V f , which represents the response of a region of formation  14  in the absence of mandrel  32 . Formation response signal V f  is substantially fully attributed to the region of formation  14 . 
     Referring to  FIGS. 2-4 , exemplary regions of the formation  14  are illustrated.  FIG. 2  illustrates measurement tool  24  positioned in a homogeneous region N 1  of formation  14  that has a resistivity R 1 .  FIGS. 3 and 4  illustrate measurement tool  24  in a heterogeneous region N 2  of formation  14  having two layers  100 ,  102 . In  FIG. 3 , layers  100 ,  102  have resistivities R 2 , R 3 , respectively, and in  FIG. 4 , layers  100 ,  102  have resistivities R 3 , R 2 , respectively. For purposes of teaching, resistivity R 3  is substantially greater than resistivity R 2 . A boundary  104  between layers  100 ,  102  is a distance D from measurement tool  24 . 
     Raw response signal V raw  and formation response signal V f  illustrated in  FIG. 5  relate to homogeneous region N 1  of  FIG. 2 . Raw response signal V raw  and formation response signal V f  of  FIG. 6  relate to heterogeneous region N 2  of  FIG. 3  where measurement tool  24  is positioned in first layer  100  having resistivity R 2 . Raw response signal V raw  and formation response signal V f  of  FIG. 7  relate to heterogeneous region N 2  of  FIG. 4  where measurement tool  24  is positioned in first layer  100  having resistivity R 3 . 
     In each case, the contribution of mandrel  32  to raw response signal V raw  causes raw response signal V raw  to deviate from formation response signal V f . Mandrel  32  contributes to raw response signal V raw  during a time interval that is referred to as a masked time interval M. For example, masked time interval M may be approximately 10 −5 s&lt;t&lt;10 −2 s. 
     At sufficiently late time, formation response signal V f  decays essentially as t −5/2  (when plotted on a double logarithmic graph). During masked time interval M, raw response signal V raw  decays substantially as t −1/2 . After the mandrel contribution dies out, raw response signal V raw  decays essentially as t −5/2  and reflects formation response signal V f . Raw response signal V raw  may also reflect formation response signal V f  at times before masked time interval M depending on the resistivity of the formation. 
     Adjustment Methods for Reducing the Mandrel Effect 
     During masked time interval M, it is difficult to interpret raw response signal V raw , as raw response signal V raw  does not reflect formation response signal V f . Adjustment methods can be applied to raw response signals V raw  to reduce the contribution of mandrel  32 . Resulting adjusted signals V adj  better reflect formation response signals V f  or provide information about formation  14  that is present in the masked time interval M. Adjusted signals V adj  can be analyzed to facilitate determining the parameters of a model of formation  14 , for example, the number of layers of formation  14 . Generally, adjusted signals V adj  can be determined based on a relationship between raw response signals V raw  or between raw response signals V raw  and reference signals V ref . 
     Reference signals V ref  that are used in certain methods of adjusting are now described. Reference signals V ref  are measured by receivers  28 ,  30  in a test environment. Typically, reference signals V ref  are collected to calibrate measurement tool  24  and are stored in memory  58 . One example of a test environment is a substantially homogeneous reference medium that has a resistivity that is high relative to the resistivity of a region of formation  14  from which an electromagnetic response is to be determined. For example, the resistivity of a suitable test environment can be at least ten times greater than the resistivity of the region of formation  14 . An example of a widely used test environment is air. 
     Reference signals V ref  are collected in the same manner as raw response signals V raw  with the difference being that reference signals V ref  are collected in a test environment and raw response signals V raw  are collected in a region of formation  14 . Where the resistivity of the test environment is relatively high, the contribution of mandrel  32  to reference signal V ref  is relatively high compared to the contribution of the test environment. Thus, reference signal V ref  approximates the mandrel contribution. 
     Generally, the measurement tool that is used to obtain reference signals V ref  is the same that is used to measure raw response signals V raw . Here, TR offset distances L 1 , L 2  are the same in both the test environment and formation  14  to provide a relationship between reference signals V ref  and raw signals V raw  that have the same offset. In alternative embodiments, reference signals V ref  measured by one measurement tool can be used to adjust raw response signals V raw  measured by another measurement tool. For example, this may be acceptable where the different measurement tools have substantially equivalent conductive structures and arrays. In either case, reference signals V ref  and raw response signals V raw  that have the same offset can be related. 
     A calibrated signal V cal  that relates raw response signal V raw  and reference signal V ref  is now described. Calibrated signal V cal  is given by 
         V   cal ( t )= V   raw ( t )− V   ref ( t ).
 
     Referring to  FIGS. 5-7 , calibrated signal V cal  reduces the dominant mandrel effect of raw response signal V raw  and decays essentially as t −3/2  for the masked time interval M. This decay is slower than that of formation response signal V f  and is nearly proportional to the formation conductivity σ f . 
     Certain of the methods of adjusting are based on a relationship between raw response signals at different offset distances along the length of mandrel  32 . These methods are termed “raw signal adjustment methods.” Other of the methods of adjusting are based on a relationship between calibrated signals at different offset distances along the length of mandrel  32 . These methods are termed “calibrated signal adjustment methods.” 
     Raw Signal Adjustment Methods 
     Relationships between raw response signals V raw  at different offset distances L 1 , L 2  and corresponding raw signal adjustment methods are now described. Raw response signal V raw  measured by one of receivers  28 ,  30  depends not only on the resistivity of mandrel  32  and mandrel  32  geometry (e.g., diameter), but also strongly on TR offset distance L 1 , L 2 . Raw response signal V raw  is nearly independent of the TR offset distance L 1 , L 2  if there is no mandrel  32 . A combination of raw response signals V raw  measured at multiple TR offset distances L 1 , L 2  can be used to reduce the mandrel effect and better reflect formation response signal V f . 
     A first relationship between raw response signals V raw  measured at TR offset distances L 1 , L 2  is now described. For large offsets, by comparing raw response signals V raw  measured at different TR offset distances L 1 , L 2 , it is observed that raw response signal V raw  is approximately inversely proportional to the cube of TR offset distance L 1 , L 2 . Thus, a large offset approximation of the relationship between raw response signal V raw  at first offset distance L 1  and raw response signal V raw  at second offset distance L 2  is given by 
     
       
         
           
             
               
                 
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     As this relationship relates the contributions of mandrel  32  at different offsets L 1 , L 2  but does not proportionally or directly relate the contributions of formation  14  at different offsets L 1 , L 2 , first adjusted signal V adj,1  can be determined whereby the first relationship is used to cancel out much of the mandrel contribution and better reflect formation response signal V f . First adjusted signal V adj,1  is given by 
     
       
         
           
             
               
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     For smaller TR offset distances L 1 , L 2 , the first relationship described above is less applicable. A second adjusted signal V adj,2  can be given by 
         V   adj,2 ( t,L   1   ,L   2 )= V   raw ( t,L   1 )− P   adj,2 ( L   1   ,L   2 ) V   raw ( t,L   2 )
 
     where modifying function P adj,2 (L 1 ,L 2 ) represents an observed or experimentally determined relationship found by analyzing the ratio of raw response signal V raw  at first offset distance L 1  to raw response signal V raw  at second offset distance L 2 . For example, modifying function P adj,2 (L 1 ,L 2 ) can be determined by taking the average of the ratio over masked time interval M. In alternative embodiments, modifying function P adj,2 (L , ,L 2 ) is also a function of time. 
     The first relationship described above is equally applicable to reference signals V ref  at different offset distances L 1 , L 2 . Accordingly, a third relationship between reference signals V ref  at offset distances L 1 , L 2  and raw response signals V raw  at the same offset distances L 1 , L 2  is given by 
     
       
         
           
             
               
                 
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     This third relationship can similarly be used to provide a third adjusted signal V adj,3  that cancels out much of the mandrel contribution and reflects a formation signal. Third adjusted signal V adj,3  is given by 
     
       
         
           
             
               
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     Calibrated Signal Adjustment Methods 
     Relationships between calibrated signals V cal  at different offset distances L 1 , L 2  and corresponding calibrated signal adjustment methods are now described. For large offset distances, it is observed that calibrated signal V cal  is approximately inversely proportional to offset distance L 1 , L 2 . For large offset distance, a fourth relationship between calibrated signal V cal  at first offset distance L 1  and calibrated signal V cal  at second offset distance L 2  is given by 
     
       
         
           
             
               
                 
                   
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     A fourth adjusted signal V adj,4  that incorporates the fourth relationship is given by 
     
       
         
           
             
               
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     Similar to the second adjusted signal V adj,2  above, a fifth adjusted signal V adj,6  can accordingly be given by 
         V   adj,5 ( t,L   1   ,L   2 )= V   cal ( t,L   1 )− P   adj,5 ( L   1   ,L   2 ) V   cal ( t,L   2 )
 
     where modifying function P adh,5 (L 1 ,L 2 ) represents an observed or experimentally determined relationship found by analyzing the ratio of calibrated signal V cal  at first offset distance L 1  to calibrated signal V cal  at second offset distance L 2 . 
     Based on a relationship between first adjusted signal V adj,1  and third adjusted signal V adj,3 , a sixth adjusted signal V adj,6  can be similarly related to the fourth adjusted signal V adj,4 . Sixth adjusted signal V adj,6  is given by 
     
       
         
           
             
               
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     where f 1  is a function of raw response signal V raw  at offset distance L 1 , f 2  is a function of raw response signal V raw  at offset distance L 2 , f 3  is a function of first distance L 1 , and f 4  is a function of second distance L 2 . With respect to the adjusted signals described above, functions f 1 , f 2  may be raw response signals V raw  or calibrated signals V cal  and functions f 3 , f 4  may be offset distances L 1 , L 2 , reference signals V ref , raw response signals V raw , and variations thereof raised to an exponent. In any event, functions f 3 , f 4  relate functions f 1 , f 2  to one another. 
     Functions f 3 , f 4  can be constant functions of offset distances L 1 , L 2 , respectively, or functions of both time and offset distances L 1 , L 2 , respectively. 
     Referring again to  FIGS. 5-7 , the graphs conceptually illustrate formation response signals V f , raw response signals V raw , calibrated signals V cal , and adjusted response signals V adj  measured or calculated for each situation illustrated in  FIGS. 2-4 . For purposes of teaching, only one adjusted response signal V adj  is shown in each of  FIGS. 5-7 . Calibrated signal V cal  and adjusted response signal V adj  of each formation reduce the mandrel contribution of the raw response signal V raw  although neither fits formation response signal V f  during masked time interval M. 
     In general, during masked time interval M, raw response signals V raw  decay essentially as t −1/2 , calibrated signals V raw  decay essentially as t −3/2 , adjusted raw response signals V raw  decay essentially as t −3/2 , and adjusted calibrated response signals V cal  decay essentially as t −5/2 . For calibrated signals V cal  and adjusted signals V adj , the mandrel contribution is particularly difficult to reduce toward the end of masked time interval M where deviations from a substantially constant decay are observed. The signals V cal , V adj  may not provide useful information at this time although they can provide useful information at other times within and outside of masked time interval M. 
     Interpretation of Adjusted Signal 
     Within masked time interval M, adjusted response signal V adj  reflects formation response signal V f  better than calibrated signal V cal . To illustrate this, referring first to  FIG. 8 , calibrated signals for V cal  comparing homogeneous and heterogeneous regions N 1 , N 2  are shown on the same graph. Here, for purposes of clarity, calibrated signals V cal  will be represented with unique element numbers. A first calibrated signal C 1  is determined from raw response signal V raw  measured in homogeneous region N 1  where resistivity R 1  is equal to resistivity R 2 . A second calibrated signal C 2  is determined from raw response signal V raw  measured in homogeneous region N 1  where resistivity R 1  is equal to resistivity R 3 . A third calibrated signal C 3  is determined from raw response signal V raw  measured in heterogeneous region N 2  where measurement tool  24  is positioned in first layer  100  having resistivity R 2 , as shown in  FIG. 3 . A fourth calibrated signal C 4  is determined from raw response signal V raw  measured in heterogeneous region N 2  where measurement tool  24  is positioned in first layer  100  having resistivity R 3 , as shown in  FIG. 4 . 
     The difference between calibrated signals C 2 , C 4  due to the different regions N 1 , N 2  is mainly observed in the form of a shift of the overall response. As this difference is similar to the difference that is observed between calibrated signals C 1 , C 2  due to the difference in resistivity R 2 , R 3  in the same region N 1 , it is difficult to determine whether calibrated signal C 4  represents heterogeneous region N 2  or homogeneous region N 1 . In other words, the calibrated signal C 3 , C 4  of heterogeneous region N 2  may be wrongly interpreted as that of homogeneous region N 1 . 
     In the case of  FIG. 4  where measurement tool  24  is located in the more conductive layer of heterogeneous region N 2 , a shift to less conductive layer is not readily observed. Accordingly, there is little difference between calibrated signals C 1 , C 3 . In either case, calibrated signal V cal  alone does not delineate the presence of a second layer. 
     Referring to  FIG. 9 , adjusted signals V adj  measured in different homogeneous and heterogeneous regions N 1 , N 2  are shown on the same graph. Here, for purposes of clarity, adjusted signals V adj  will be represented with unique element numbers. A first adjusted signal A 1  is determined from raw response signal V raw  measured in homogeneous region N 1  where resistivity R 1  is equal to resistivity R 2 . A second adjusted signal A 2  is determined from raw response signal V raw  measured in homogeneous region N 1  where resistivity R 1  is equal to resistivity R 3 . A third adjusted signal A 3  is determined from raw response signal V raw  measured in heterogeneous region N 2  where measurement tool  24  is positioned in first layer  100  having a resistivity R 2 , as shown in  FIG. 3 . A fourth adjusted signal A 4  is determined from raw response signal V raw  measured in heterogeneous region N 2  where measurement tool  24  is positioned in first layer  100  having a resistivity R 3 , as shown in  FIG. 4 . 
     Here, the adjusted signals A 3 , A 4  measured in heterogeneous regions N 2  transition from the adjusted signals A 1 , A 2  measured in homogeneous region N 1  thereby clearly delineating the presence of a second layer. When measurement tool  24  is located in more a conductive layer, adjusted signal A 3  is more difficult to distinguish from adjusted signal A 1 . 
     Without prior knowledge of region N 1 , N 2  in which raw response signal V raw  is determined, raw response signal V raw  can be adjusted according to methods of adjusting described herein to provide adjusted response signal V adj . Adjusted response signal V adj  at different points along the length of borehole  12  can be compared to one another to gain information about the formation  14  that is present in masked time interval M of each. For example, at one point along the length of the borehole, masked time interval M of adjusted response signal V adj  may have a certain slope in a substantially homogeneous region and, at another point along the length of borehole, masked time interval M of adjusted response signal V adj  may have a slope that transitions from that of the other adjusted response signal V adj  thereby indicating the presence of at least a second layer. 
     As the contribution of mandrel  32  has not been removed from adjusted signal V adj  toward the end of the masked time interval M, transitions from a constant slope line near this time may not delineate the presence of an additional layer. 
     The law does not require and it is economically prohibitive to illustrate and teach every possible embodiment of the present disclosure. Hence, the above-described embodiments are merely exemplary illustrations of implementations set forth for a clear understanding of the principles of the invention. Variations, modifications, and combinations may be made to the above-described embodiments without departing from the scope of the claims. All such variations, modifications, and combinations are included herein by the scope of this disclosure and the following claims.