Patent Publication Number: US-11643920-B2

Title: Dip correction for non-circular borehole and off-center logging

Description:
TECHNICAL FIELD 
     The disclosure generally relates to the field of subsurface formation evaluation, and more particularly to formation dip correction for non-circular boreholes and off-center logging tools. 
     BACKGROUND 
     Accurate characterization of structural and stratigraphic bedding features of subsurface formations allows for increased hydrocarbon recovery from such formations. This characterization includes measuring the magnitude and direction of the formation dip. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the disclosure may be better understood by referencing the accompanying drawings. 
         FIG.  1    depicts an example wireline system, according to some embodiments. 
         FIG.  2    depicts an example drilling system, according to some embodiments. 
         FIGS.  3 - 4    depict flowcharts of operations for dip correction for non-circular boreholes and off-center logging, according to some embodiments. 
         FIG.  5    depicts a graph of a borehole with slant layers, according to some embodiments. 
         FIG.  6    depicts a graph of a reconstructed (elliptical) borehole from measurements obtained from the borehole, according to some embodiments. 
         FIG.  7    depicts a graph of a top view of non-circular borehole, according to some embodiments. 
         FIG.  8    depicts a graph of a top view of non-circular borehole with the logging tool off-center, according to some embodiments. 
         FIG.  9    depicts an unrolled borehole image corresponding to the non-circular borehole depicted in  FIG.  7   , according to some embodiments. 
         FIG.  10    depicts an unrolled borehole image corresponding to the non-circular, off-center borehole depicted in  FIG.  8   , according to some embodiments. 
         FIG.  11    depicts a graph of a borehole ellipse that is transformed to a unit circle with a new center, according to some embodiments. 
         FIG.  12    depicts a graph of a reconstructed (elliptical) borehole of  FIG.  6    transformed into a circular borehole, according to some embodiments. 
         FIG.  13    depicts a top view of the borehole of  FIG.  7    after being transformed into a circular borehole, according to some embodiments. 
         FIG.  14    depicts a top view of the borehole of  FIG.  8    after being transformed into a circular borehole, according to some embodiments. 
         FIG.  15    depicts an unrolled borehole image corresponding to the transformed borehole depicted in  FIG.  13   . 
         FIG.  16    depicts an unrolled borehole image corresponding to the transformed borehole depicted in  FIG.  14   . 
         FIG.  17    depicts an example computer, according to some embodiments. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The description that follows includes example systems, methods, techniques, and program flows that embody embodiments of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. For instance, this disclosure refers to dip correction based on changing a shape of a borehole from elliptical to circular in illustrative examples. Embodiments of this disclosure can be also applied to any other non-circular borehole shape. In other instances, well-known instruction instances, protocols, structures and techniques have not been shown in detail in order not to obfuscate the description. 
     Downhole logging tool (such as a resistivity imaging tool) may be used to determine the resistivity of the borehole layers. These tools can be used to perform formation evaluation. Such formation evaluation can include identification a wide range of characteristics from the magnitude and direction of the formation dip, thinly laminated beds, lithology, porosity, fluid profile, flow potential, and presence of permeability barriers, sand attributes, clasts, vugs, etc. For example, these downhole logging tools can capture borehole images that can then be used to perform the formation evaluation. 
     In an ideal borehole condition with the logging tool centralized, these dipping formation beds appear as non-distorted sine waves when viewed on an image log. However, in non-ideal borehole conditions these sinusoidal features can become distorted which create problems in detecting and characterizing formation dips. Various embodiments provide for correction of the borehole images to remove distortion of formation dips caused by either a non-circular borehole shape or a logging tool that is off-center in the borehole. Various embodiments include detection and processing of images of subsurface formations to provide for accurate characterization of structural and stratigraphic bedding features of these formations. This characterization can include measuring the magnitude and direction of the formation dip. Once the images are corrected, the formation dips can be identified and fitted. Additionally, the results of interpolation using the formation dips can be enhanced. 
     Example Systems 
       FIGS.  1 - 2    depict an example wireline system and a drilling system, respectively. In these examples, the boreholes are non-circular, and the logging tools are not centered in the borehole during logging. Either condition can result in distortion of formation dips of borehole images captured during logging. Various embodiments (described below) provide for removal of this distortion of the captured borehole images that is caused by at least one of the borehole being non-circular and the logging tool not being centered during logging. 
       FIG.  1    depicts an example wireline system, according to some embodiments. In particular,  FIG.  1    depicts an example wireline system that includes a logging tool  110  disposed in a wellbore  102  drilled through earth formations. In some embodiments, the logging tool  110  can be an induction well logging tool. The earth formations are shown generally at  106 ,  107 ,  108 ,  109 ,  112 ,  113  and  114 . The logging tool  110  is typically lowered into the wellbore  102  at one end of a conveyance  122  by means of a winch  128  or similar device. The conveyance  122  may be one or more of a slickline, wireline, coiled tubing, pipe, etc. Conveyance  122  may at times provide power, telemetry, or both power and telemetry. 
     The logging tool  110  can include a signal processor device  120  (device  120 ). The device  120  can include a source of alternating current (not shown separately). The alternating current is generally conducted through a transmitter  116  disposed on the logging tool  110 . Receivers  118 A- 118 F can be disposed at axially spaced apart locations along the logging tool  110 . The device  120  can include receiver circuits (not shown separately) connected to the receivers  118 A- 118 F for detecting voltages induced in each of the receivers  118 A- 118 F. The device  120  can also impart signals to the cable  122  corresponding to the magnitude of the voltages induced in each of the receivers  118 A- 118 F. It is to be understood that there can be a different number of transmitters and receivers and different relative geometries of the transmitter  116  and the receivers  118 A- 118 F than those shown in  FIG.  1   . 
     The alternating current passing through the transmitter  116  induces eddy currents in the earth formations  106 ,  107 ,  108 ,  109 ,  112 ,  113 ,  114 . The eddy currents correspond in magnitude both to the electrical conductivity of the earth formations  106 ,  107 ,  108 ,  109 ,  112 ,  113 ,  114  and to the relative position of the particular earth formation with respect to the transmitter  116 . The eddy currents in turn induce voltages in the receivers  118 A- 118 F, the magnitude of which depends on both the eddy current magnitude and the relative position of the earth formation with respect to the individual receiver  118 A- 118 F. 
     The signals, corresponding to the voltages induced in each receiver  118 A- 118 F, can be transmitted along the cable  122  to a computer  124 . The computer  124  can include detectors (not shown separately) for interpreting the signals transmitted from the logging tool  110 . The computer  124  can also include a processor  126  to perform the process the signals (as further described below). In some embodiments, some or all of the processing of the signals can be performed by the device  120  downhole. 
     The voltages induced in each receiver  118 A- 118 F correspond to apparent electrical conductivity of the media surrounding the logging tool  110 . The media comprise the earth formations  106 ,  107 ,  108 ,  109 ,  112 ,  113 ,  114  and the drilling mud  104  in the wellbore  102 . The degree of correspondence between the voltages induced in a particular receiver, and the electrical conductivity of the particular earth formation axially disposed between the particular receiver and the transmitter  116 , can depend on the relative inclination of the layers of the earth formations, such as formation  112 , and the axis of the logging tool  110 . 
     In some embodiments, the imaging can be captured by a Measurement While Drilling (MWD) or Logging While Drilling (LWD) logging tool as part of a drilling system. An example of such a drilling system is now described.  FIG.  2    depicts an example drilling rig system, according to some embodiments. 
     In  FIG.  2    it can be seen how a system  264  can include a drilling rig  202  located at the surface  204  of a well  206 . Drilling of oil and gas wells is commonly carried out using a string of drill pipes connected together so as to form a drilling string  208  that is lowered through a rotary table  210  into a wellbore or borehole  112 . Here a drilling platform  286  is equipped with the derrick  202  that supports a hoist. 
     The drilling rig  202  may thus provide support for the drill string  208 . The drill string  208  may operate to penetrate the rotary table  210  for drilling the borehole  112  through subsurface formations  211 ,  213 ,  214 . Subsurface formations can include layers of differing resistivities. The drill string  208  may include a Kelly  216 , drill pipe  218 , and a bottom hole assembly  220 , perhaps located at the lower portion of the drill pipe  218 . 
     The bottom hole assembly  220  may include drill collars  222 , a down hole tool  224 , and a drill bit  226 . The drill bit  226  may operate to create the borehole  112  by penetrating the surface  204  and subsurface formations  211 ,  213 ,  214 . The down hole tool  224  may comprise any of a number of different types of tools including MWD tools, LWD tools, and others. In some embodiments, the down hole tool  224  includes an NMR logging tool (as described herein). 
     During drilling operations, the drill string  208  (perhaps including the Kelly  216 , the drill pipe  218 , and the bottom hole assembly  220 ) may be rotated by the rotary table  210 . In addition to, or alternatively, the bottom hole assembly  220  may also be rotated by a motor (e.g., a mud motor) that is located down hole. The drill collars  222  may be used to add weight to the drill bit  226 . The drill collars  222  may also operate to stiffen the bottom hole assembly  220 , allowing the bottom hole assembly  220  to transfer the added weight to the drill bit  226 , and in turn, to assist the drill bit  226  in penetrating the surface  204  and subsurface formations  211 ,  213 ,  214 . 
     During drilling operations, a mud pump  232  may pump drilling fluid (sometimes known by those of ordinary skill in the art as “drilling mud”) from a mud pit  234  through a hose  236  into the drill pipe  218  and down to the drill bit  226 . The drilling fluid can flow out from the drill bit  226  and be returned to the surface  204  through an annular area  240  between the drill pipe  218  and the sides of the borehole  112 . The drilling fluid may then be returned to the mud pit  234 , where such fluid is filtered. In some embodiments, the drilling fluid can be used to cool the drill bit  226 , as well as to provide lubrication for the drill bit  226  during drilling operations. Additionally, the drilling fluid may be used to remove subsurface formation  211 ,  213 ,  214  cuttings created by operating the drill bit  226 . It is the images of these cuttings that many embodiments operate to acquire and process. 
     The eddy currents induced by the transmitter coils tend to flow in circular paths that are coaxial with the transmitter coils. For a vertical borehole traversing horizontal formations, each line of current flow ideally remains in the same formation along its entire flow path, and never crosses a bed boundary. Thus, one simplifying assumption that is made in relating the receiver voltage measurements to the conductivity of the earth formations is that the ground loops are positioned entirely within a portion of the earth formation having substantially circumferentially uniform conductivity. This assumption fails in cases where layers of the earth formations are not perpendicular to, but are inclined with respect to, the axis of the wellbore (and consequently the axis of the instrument). A boundary separates two layers which can have different conductivities. When the ground loops cross one or more bed boundaries, errors are introduced into the tool response. This is known as the “dipping effect.” 
     The dipping effect is classified into two components: the charge component and the volumetric component. The charge component is caused by an electric charge buildup when the induced eddy currents flow across inclined formation interfaces. Quantitatively, the charge component depends on the inner product of the electric field vector and the directional derivative of the formation conductivity. The volumetric component is caused by the fact that eddy currents take paths through formations of different conductivities. 
     Another tool error is commonly known as the “nonlinear shoulder effect.” As the logging tool traverses the wellbore it commonly approaches, crosses, and then passes bed boundaries between formation layers. While the logging tool is proximate these bed boundaries, a portion of the receiver response comes from the bed or beds adjacent the bed in which the logging tool lies, introducing error into the measurements. It has been established that a portion of this tool response error in the regions proximate bed boundaries is non-linear. This nonlinearity makes it difficult to evaluate exactly the response portion that is from the adjacent bed, leading to an incorrect evaluation of the conductivity of the bed of interest. 
     Thus, a logging tool at an angle to a formation bed produces a series of inaccurate measurements. The larger the dip angle, the less accurate is the measurement with depth. Further, the log includes polarization “horns”, which correspond to the charge effect. 
     The measurements from logging tools can be used to create formation resistivity well logs. Formation resistivity well logs are commonly used to map subsurface geologic structures and to infer the fluid content within pore spaces of earth formations. Formation resistivity well logs include electromagnetic induction logs. Of course, if not corrected for, the dipping error and shoulder bed error made in the raw measurements are reflected by inaccuracies in the formation resistivity well logs. The borehole shape may be elliptical thereby distorting the sinusoidal nature of the unrolled bed boundary borehole image. To correct for this distortion, the borehole shape may be transformed onto a unit circle through a linear transformation method. 
     Example Operations 
       FIGS.  3 - 4    depict flowcharts of operations for dip correction for non-circular boreholes and off-center logging, according to some embodiments. Flowcharts  300  and  400  of  FIGS.  3 - 4    include operations that can be performed by hardware, software, firmware, or a combination thereof. For example, at least some of the operations can be performed by a processor executing program code or instructions. In some embodiments, such operations can be performed downhole in a logging tool and/or in a computer at the surface. Operations depicted in the flowchart  300  continue to operations depicted in the flowchart  400  through transition point A. 
     At block  302 , a logging tool is deployed in a borehole created in a subsurface formation. For example, with reference to  FIGS.  1 - 2   , the logging tool  110  is deployed in the borehole  112 . The logging tool  110  can be any type of tool that captures imaging of the surrounding subsurface formation (e.g., the formations  106 ,  107 ,  108 ,  109 ,  112 ,  113  and  114 ) to characterize the borehole. For example, the logging tool  110  can be a micro-resistivity imaging tool such as Oil Mud Reservoir Imager Tool. 
     At block  304 , a current is emitted, by the logging tool, into the subsurface formation. For example, with reference to  FIGS.  1 - 2   , one or more transmitters of the logging tool  110  can emit a current into the subsurface formations. 
     At block  306 , a response to the current being emitted into the subsurface formation is detected. For example, with reference to  FIGS.  1 - 2   , one or more sensors of the logging tool  110  detects a response to the current being emitted into the subsurface formation. To illustrate, the logging tool  110  can include multiple caliper arms that are in two axes. Each caliper arms can be equipped with a pad containing resistivity sensors able to provide resistivity measurements circumferentially around the borehole wall  112  and provide the angle and distance between the center of the logging tool  110  and their points of contact with the wall of the borehole  112 . 
     At block  308 , a wall of the borehole  112  is characterized based on the response to the current. For example, the characteristic of the wall of the borehole  112  can be a combination of the angle and distance of the borehole from the center of the tool and their associated resistivity. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation where the response to a current obtained by the logging tool  110  can be interpreted to distinguish layers of the subsurface formation based on the resistivity and other properties of the subsurface formation. Based on different resistivity a graph depicting the stratified layers of the subsurface formation can be generated. 
     To illustrate,  FIG.  5    depicts a graph of a borehole with slant layers, according to some embodiments. In particular,  FIG.  5    depicts a graph  500  that includes an x-axis, y-axis, and a z-axis as shown in inches. The Z-axis corresponds to the depth in the borehole. The graph  500  includes a number of ellipses  504  and  506 . Each of the ellipses  504  and  506  represents a subsurface formation layer of differing resistivities. Thickness of ellipses  504  and  506  correspond to the thickness of the corresponding subsurface formation layer. For example, with reference to  FIG.  1   , the thickness of the ellipses  504  and  506  can correspond to the thickness of the formations  106 ,  107 ,  108 ,  109 ,  112 ,  113  and  114 . A flat non-slanted ellipse  502  is added to the graph to help visualize by contrast that ellipses  504  and  506  traverse multiple depths when unrolled. 
     At block  310 , the wall of the borehole is reconstructed into a series of non-circular (e.g., ellipses) shapes based on the detected response to the logging tool such as the tool arms extending to contact the inner borehole surface and the current emitted into the subsurface formation. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation. As described above, the logging tool  110  can include multiple caliper arms that are in two axes. Each caliper arm can be equipped with a pad containing resistivity sensors that are used to provide the angle and distance between the center of the logging tool and their points of contact with the wall of the borehole  112 . These points and their associated angle and distance from the center can be used to determine the x-y coordinates of the points of contacts between the borehole wall and the arms of the logging tool. To illustrate,  FIG.  6    depicts a graph of a reconstructed (elliptical) borehole from measurements obtained from the borehole, according to some embodiments.  FIG.  6    depicts a graph  600  that includes six groups of points of different shades  602 ,  604 ,  606 ,  608 ,  610 , and  612  that represent contact points obtained by six different calipers of the logging tool  110 . Graph  600  includes an x-axis, y-axis, and a z-axis as shown in inches. 
     The groups of caliper contact points  602 ,  604 ,  606 ,  608 ,  610 , and  612  on the x-y axis are then used to reconstruct the borehole into series of non-circular shapes that correspond to various subsurface formation layers of different resistivities. In the graph  600 , the non-circular shapes are ellipses  614 ,  616 . In some embodiments, a best-fit function is applied over the points to reconstruct the borehole into a series of non-circular shapes. Alternatively, or in addition, the equation of the non-circular shape can be solved to reconstruct the borehole into a series of non-circular shapes. 
     The general equation for a conic section, including an ellipse, in a Cartesian coordinate system can be described by Equation (1) where x and y are the coordinate location of the point that are obtained from the logging tool  110 , and a 1  . . . a 5  are constants that define the nature of the conic section.
 
 x   2   +a   1   y   2   +a   2   xy+a   3   x+a   4   y+a   5 =0  (1)
 
     Various points in the x-y axis are then used to solve for Equation (1). By using six points selected from each group of caliper contact points  602 ,  604 ,  606 ,  608 ,  610 , and  612  in the same subterranean layer and their x and y coordinates derived from the logging tool, a series of ellipse equations, Equation (2), can be generated and the five constants a 1  . . . a 5  as solved. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     The constants a 1  . . . a 5  as solved by Equation (2) identifies the ellipse equation that corresponds to contact points selected from the same subterranean layer. Series of ellipse equations that are associated with each subterranean layer can be obtained during this step. In other instances where the points do not lie evenly in an ellipse, the ellipses  614 ,  616  and their corresponding ellipse equations can be obtained by applying a best fit function over various contact points in each subterranean layer. The differing shades of ellipse  614 ,  616  represents the differing resistivities of subterranean layers. 
       FIG.  7    depicts a graph of a top view of non-circular borehole, according to some embodiments. 
     In particular,  FIG.  7    depicts a graph  700  that lies in the x-y plane. An ellipse  702  includes a position  704  of the logging tool  110  at the same position as the center of the borehole. As shown, the borehole image is non-circular (elliptical) even when the logging tool  110  is centered in the borehole. In some examples, the borehole image captured is non-circular because the borehole itself is non-circular. Before the transformation, the x-axis and the y-axis has the corresponding units (inches). 
     Other embodiments may include non-circular reconstruction of the wall of the borehole  112  where the logging tool is off center. To illustrate,  FIG.  8    depicts a graph of a top view of non-circular borehole with the logging tool off-center, according to some embodiments. In particular,  FIG.  8    depicts a graph  800  that lies in the x-y plane. An ellipse  802  includes a position  804  of the logging tool  110  that is at a different position from a center of the borehole  806 . In some examples, the borehole image captured is non-circular because the borehole itself is non-circular. 
     At block  312 , an unrolled borehole image is generated from the reconstructed borehole wall. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation.  FIG.  9    depicts an unrolled borehole image corresponding to the non-circular borehole depicted in  FIG.  7   , according to some embodiments. An unrolled borehole image  900  includes a number of lines, wherein each line is derived by unrolling an ellipse. Each ellipse can represent a subsurface formation layer of a differing resistivity. For example, with reference to the different ellipses depicted in  FIG.  5   , each line of the borehole image  900  can correspond to an ellipse depicted in the graph  500 . The x-axis is a view angle as measured from the position  704  of the logging tool  110  and the y-axis is the borehole depth. For example, with reference to  FIG.  5   , the lines  902  and  904  of the unrolled borehole image  900  can be generated by plotting the ellipses  504  and  506 , respectively, from 0° to 360° with their associated depths. With reference to  FIG.  5   , plotting non-circular shapes such as ellipses  504  and  506  will result in the lines  902  and  904  departing from the desired sinusoidal shape. Also, with reference to  FIG.  5   , a flat line  906  is derived from the non-slanted ellipse  502  and is added to the graph to help visualize by contrast that lines  902  and  904  traverse multiple depths. Other embodiments may include unrolled borehole image generated from the reconstructed borehole wall wherein the logging tool off-center. 
     To further illustrate,  FIG.  10    depicts an unrolled borehole image corresponding to the non-circular borehole with the off-center logging tool depicted in  FIG.  8   , according to some embodiments. An unrolled borehole image  1000  that includes a number of lines, wherein each line is derived by unrolling an ellipse. Each ellipse can represent a subsurface formation layer of a differing resistivity. For example, with reference to the different ellipses depicted in  FIG.  5   , each line of the borehole image  1000  can correspond to an ellipse depicted in the graph  500 . The x-axis consists of the view angle as measured from the off-center position  804  of the logging tool  110  and the y-axis consists of the borehole depth. For example, with reference to  FIG.  5   , the lines  1002  and  1004  of the unrolled borehole image  1000  can be generated by plotting the ellipses  504  and  506 , respectively, from 0° to 360° with their associated depths. With reference to  FIG.  5   , plotting non-circular shapes such as ellipses  504  and  506  will result in the lines  1002  and  1004  departing from the desired sinusoidal shape. Furthermore, with reference to  FIG.  13   , the lines  1002  and  1004  further diverge from the desired sinusoidal shape because of the off-centered nature of logging tool position  804 . Also, with reference to  FIG.  5   , a flat line  1006  is derived from the non-slanted ellipse  502  and is added to the graph to help visualize by contrast that lines  1002  and  1004  traverse multiple depths. 
     At block  314  the non-circular to circular transformation matrix is determined using the constants from the ellipse equation of the reconstructed borehole image. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation. To illustrate, the ellipse equations from block  310  can be used to obtain the corresponding transformation matrix. With the constants a 1  . . . a 5  as solved for by the series of ellipse equations at block  310 , the points (x,y) from block  308  may now be transformed into points (u,v) on a unit circle through a purely linear transformation. The relationship between the measured point and the transformed point (u,v) would be governed by Equation (3). 
     
       
         
           
             
               
                 
                   
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     The transformation matrix M can be defined as the matrix below, where u and v are the various basis vectors that govern the linear transformation, Equation (4). 
     
       
         
           
             
               
                 
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     The basis vectors defining the relationship between an ellipse and a circle are given by the sets of equations below, Equations (5)-(7). 
     
       
         
           
             
               
                 
                   
                     
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     Lastly, to transform the circle into a unit circle, the transformation matrix M has the radius defined by Equation (8), divided from its basis vectors as shown in Equation (9). This results in the final matrix multiplication to be solved, Equation (10). 
     
       
         
           
             
               
                 
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                     radius 
                   
                 
               
               
                 
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     Each ellipse would solve for its own Equations (5)-(7) by using the set of a 1  . . . a 5  constants obtained at block  310 . With the solutions from Equations (5)-(7), the transformation matrix, Equation (4) can be completed for each ellipses  614 ,  616 . The ellipses  614 ,  616  may further be transformed into unit circles by dividing the radius of the circle, Equation (8), from its basis vectors, Equation (9). The final matrix multiplication, Equation (10) describes the transformation of reconstructed borehole wall ellipses  614 ,  616  into unit circles. Operations of the flowchart  300  continue at transition point A, which continues at transition point A of the flowchart  400 . From the transition point A of the flowchart  400 , operations continue at block  402 . 
     At block  402  the reconstructed borehole image is transformed into a circular borehole image based on the non-circular to circular transformation matrix. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation. To illustrate, the ellipses  614 ,  616  and the corresponding caliper contact points  602 ,  604 ,  606 ,  608 ,  610 , and  612  on the x-y plane are transformed into circles with points on the u-v plane.  FIG.  11    depicts a graph of a borehole ellipse that is transformed to a unit circle with a new center, according to some embodiments. In particular,  FIG.  11    illustrates a graph  1100  of a borehole ellipse  1110  that is transformed to a circular borehole  1112  using the operations described at block  314 . Applying the final matrix multiplication described in Equation (10) to caliper contact point  1106  results in a transformed contact point  1108 . This transformation would be applied to the reconstructed elliptical borehole  1110  to generate a transformed circular borehole  1112 . The transformed circular borehole  1112  would be generated around the logging tool position  1105  making this position the new transformed borehole center  1104  from the borehole center  1102 . 
       FIG.  12    depicts a graph of a reconstructed (elliptical) borehole of  FIG.  6    transformed into a circular borehole, according to some embodiments. In particular,  FIG.  12    depicts a graph  1200  of a transformed circular borehole derived from  FIG.  6   . Applying the final matrix multiplication described in Equation (10) to the six groups of caliper contact points  602 ,  604 ,  606 ,  608 ,  610 , and  612  of differing shades generates a new transformed caliper contact points  1202 ,  1204 ,  1206 ,  1208 ,  1210 , and  1212  on the u-v plane. These transformed points are then used to reconstruct the borehole into circular shapes  1214 ,  1216  that correspond to various subsurface formation layers of different resistivities. 
       FIG.  13    depicts a top view of the borehole of  FIG.  7    after being transformed into a circular borehole, according to some embodiments. In particular,  FIG.  13    depicts a graph  1300  that lies in the u-v plane. For example, with reference to  FIG.  7   , a transformed circle  1302  is generated by applying the final matrix multiplication described in Equation (10) to the ellipse  702 . The circle  1302  includes a position  1304  of the logging tool  110  that continues to remain at the same position as the center of the borehole. Other embodiments may include transformation of non-circular reconstruction of the wall of the borehole  112  where the logging tool is off-center. For example,  FIG.  14    depicts a top view of the borehole of  FIG.  8    after being transformed into a circular borehole, according to some embodiments. In particular,  FIG.  14    depicts a graph  1400  that lies in the u-v plane. With reference to  FIG.  8   , a transformed circle  1402  is generated by applying the final matrix multiplication defined by Equation (10) to the ellipse  802 . The circle  1402  includes a position  1404  of the logging tool  110  that is now at the center of the borehole. 
     At block  404 , an unrolled borehole image is generated from the transformed circular borehole wall  1014 ,  1016 . For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation. To illustrate,  FIG.  15    depicts an unrolled borehole image corresponding to the transformed circular borehole depicted in  FIG.  13   , according to some embodiments. An unrolled borehole image  1500  includes a number of lines, wherein each line is derived by unrolling a transformed circle. The circles can represent a subsurface formation layer of a differing resistivity associated with the corresponding ellipses from which the circles were generated. For example, with reference to  FIG.  5   , each line of the borehole image  1500  can correspond to a transformed circle derived from an ellipse depicted in the graph  500 . The x-axis is a view angle as measured from the position  1304  of the logging tool  110  and the y-axis is the borehole depth. For example, with reference to  FIG.  5   , the lines  1502  and  1504  of the unrolled borehole image  1500  can be generated by plotting the transformed circles derived from ellipses  504  and  506 , from 0° to 360° with their associated depths. The lines  1502  and  1504  are in sinusoidal form having been unrolled from a circular shape. Also, with reference to  FIG.  5   , a flat line  1506  is derived from the non-slanted ellipse  502  and is added to the graph to help visualize by contrast that lines  1502  and  1504  traverse multiple depths. 
     Other embodiments may include unrolled borehole image corresponding to the transformed circular borehole that has corrected an off-center logging tool.  FIG.  16    depicts an unrolled borehole image corresponding to the non-circular borehole depicted in  FIG.  14   , according to some embodiments. An unrolled borehole image  1600  includes a number of lines, wherein each line is derived by unrolling a transformed circle. The circles can represent a subsurface formation layer of a differing resistivity associated with the corresponding ellipses from which the circles were generated. For example, with reference to  FIG.  5   , each line of the borehole image  1600  can correspond to a transformed circle derived from an ellipse depicted in the graph  500 . The x-axis is a view angle as measured from the position  1404  of the logging tool  110  and the y-axis is the borehole depth. For example, with reference to  FIG.  5   , the lines  1602  and  1604  of the unrolled borehole image  1600  can be generated by plotting the transformed circles derived from ellipses  504  and  506 , from 0° to 360° with their associated depths. With reference to  FIG.  14   , the lines  1602  and  1604  are in sinusoidal form having been unrolled from a circular shape with the centralized logging tool position  1404 . Also, with reference to  FIG.  5   , a flat line  1606  is derived from the non-slanted ellipse  502  and is added to the graph to help visualize by contrast that lines  1602  and  1604  traverse multiple depths. 
     At block  406 , properties of the subsurface formation are evaluated based on the corrected borehole image. For example, with reference to  FIGS.  1 - 2   , a processor downhole and/or at the surface can perform this operation. Such formation evaluation can include identification of a wide range of characteristics from formation dip magnitude and direction, lamination, porosity, fluid profile, flow potential, sand attributes, and presence of permeability barriers, clasts, vugs, etc. For example, with reference to  FIG.  1   , the device  120  can perform this operation. 
     At block  408 , a hydrocarbon recovery operation based on evaluation of the subsurface formation can be performed. Examples of a hydrocarbon recovery operation can include hydraulic fracturing, perforation operations, well flooding and/or additional drilling on the current borehole, drilling a new borehole, etc. 
     Example Computer 
       FIG.  17    depicts an example computer, according to some embodiments. The computer includes a processor  1701  (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer includes memory  1707 . The memory  1707  may be system memory (e.g., one or more of cache, SRAM, DRAM, zero capacitor RAM, Twin Transistor RAM, eDRAM, EDO RAM, DDR RAM, EEPROM, NRAM, RRAM, SONOS, PRAM, etc.) or any one or more of the above already described possible realizations of machine-readable media. The computer system also includes a bus  1703  (e.g., PCI, ISA, PCI-Express, HyperTransport® bus, InfiniBand® bus, NuBus, etc.) and a network interface  1705  (e.g., a Fiber Channel interface, an Ethernet interface, an internet small computer system interface, SONET interface, wireless interface, etc.). 
     The computer also includes an image processor  1711  and a controller  1715 . The image processor  1711  can perform processing of the borehole images to remove distortion (as described above). The controller  1715  can control the different operations that can occur in the response to results from processing of the borehole images. For example, the controller  1715  can communicate instructions to the appropriate equipment, devices, etc. to alter the cementing operations, drilling operations. Any one of the previously described functionalities may be partially (or entirely) implemented in hardware and/or on the processor  1701 . For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the processor  1701 , in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in  FIG.  17    (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor  1701  and the network interface  1705  are coupled to the bus  1703 . Although illustrated as being coupled to the bus  1703 , the memory  1707  may be coupled to the processor  1701 . 
     The flowcharts are provided to aid in understanding the illustrations and are not to be used to limit scope of the claims. The flowcharts depict example operations that can vary within the scope of the claims. Additional operations may be performed; fewer operations may be performed; the operations may be performed in parallel; and the operations may be performed in a different order. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by program code. The program code may be provided to a processor of a general purpose computer, special purpose computer, or other programmable machine or apparatus. 
     It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by program code. The program code may be provided to a processor of a general purpose computer, special purpose computer, or other programmable machine or apparatus. 
     As will be appreciated, aspects of the disclosure may be embodied as a system, method or program code/instructions stored in one or more machine-readable media. Accordingly, aspects may take the form of hardware, software (including firmware, resident software, micro-code, etc.), or a combination of software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” The functionality presented as individual modules/units in the example illustrations can be organized differently in accordance with any one of platform (operating system and/or hardware), application ecosystem, interfaces, programmer preferences, programming language, administrator preferences, etc. 
     Any combination of one or more machine readable medium(s) may be utilized. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable storage medium may be, for example, but not limited to, a system, apparatus, or device, that employs any one of or combination of electronic, magnetic, optical, electromagnetic, infrared, or semiconductor technology to store program code. More specific examples (a non-exhaustive list) of the machine-readable storage medium would include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a machine-readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable storage medium is not a machine-readable signal medium. 
     A machine-readable signal medium may include a propagated data signal with machine readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A machine-readable signal medium may be any machine-readable medium that is not a machine-readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a machine-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as the Java® programming language, C++ or the like; a dynamic programming language such as Python; a scripting language such as Perl programming language or PowerShell script language; and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on a stand-alone machine, may execute in a distributed manner across multiple machines, and may execute on one machine while providing results and or accepting input on another machine. 
     The program code/instructions may also be stored in a machine-readable medium that can direct a machine to function in a particular manner, such that the instructions stored in the machine-readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     Plural instances may be provided for components, operations or structures described herein as a single instance. Finally, boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure. 
     As used herein, the term “or” is inclusive unless otherwise explicitly noted. Thus, the phrase “at least one of A, B, or C” is satisfied by any element from the set {A, B, C} or any combination thereof, including multiples of any element. 
     Example Embodiments 
     Example embodiments include the following: 
     Embodiment 1: A method comprising: deploying a logging tool in a borehole formed in a subsurface formation, the logging tool having a transmitter and a receiver; emitting, by the transmitter, a signal into subsurface formation; detecting, by the receiver, a response to the signal being propagated through the subsurface formation; creating, from the response, a borehole image that includes distorted features representing bedding dips in the subsurface formation; and correcting the distorted features, wherein correcting the distorted features comprises mapping points of a non-circular shape in the borehole image to points on a circular shape. 
     Embodiment 2: The method of Embodiment 1, wherein creating the borehole image comprises: reconstructing a wall of the borehole image into a series of non-circular shapes based on the response to create a reconstructed borehole image. 
     Embodiment 3: The method of Embodiments 1 or 2, wherein mapping the points comprises: determining a non-circular to circular transformation matrix using at least one constant from a non-circular equation of the reconstructed borehole image; and transforming the reconstructed borehole image into a circular borehole image based on the non-circular to circular transformation matrix. 
     Embodiment 4: The method of any one of Embodiments 1-3, wherein the non-circular shape comprises an elliptical shape. 
     Embodiment 5: The method of any one of Embodiments 1-4, wherein the distorted features comprise distorted sinusoidal features. 
     Embodiment 6: The method of any one of Embodiments 1-5, wherein a shape of the borehole is at least partially non-circular. 
     Embodiment 7: The method of any one of Embodiments 1-6, wherein deploying the logging tool comprises deploying the logging tool in an off-center position in the borehole. 
     Embodiment 8: The method of any one of Embodiments 1-7, further comprising performing an evaluation of the subsurface formation based on the borehole image after correcting of the distorted features. 
     Embodiment 9: The method of any one of Embodiments 1-8, further comprising performing a hydrocarbon recovery operation based on the evaluation of the subsurface formation. 
     Embodiment 10: A system comprising: a logging tool configured to be positioned in a borehole formed in a subsurface formation, wherein the logging tool comprises, a transmitter to emit a signal into the subsurface formation; a receiver to detect a response to the signal being propagated through the subsurface formation; a processor; and a machine-readable medium having instructions stored thereon that are executable by the processor to cause the processor to, create, from the response, a borehole image that includes distorted features representing bedding dips in the subsurface formation; and correct the distorted features, wherein the instructions executable by the processor to cause the processor to correct the distorted features comprises instructions executable by the processor to cause the processor to map points of a non-circular shape in the borehole image to points on a circular shape. 
     Embodiment 11: The system of Embodiment 10, wherein the instructions executable by the processor to cause the processor to create the borehole image comprises instructions executable by the processor to cause the processor to: reconstruct a wall of the borehole image into a series of non-circular shapes based on the response to create a reconstructed borehole image. 
     Embodiment 12: The system of Embodiments 10 or 11, wherein the instructions executable by the processor to cause the processor to map the points comprises instructions executable by the processor to cause the processor to: determine a non-circular to circular transformation matrix using at least one constant from a non-circular equation of the reconstructed borehole image; and transform the reconstructed borehole image into a circular borehole image based on the non-circular to circular transformation matrix. 
     Embodiment 13: The system of any one of Embodiments 10-12, wherein the non-circular shape comprises an elliptical shape. 
     Embodiment 14: The system of any one of Embodiments 10-13, wherein the distorted features comprise distorted sinusoidal features. 
     Embodiment 15: The system of any one of Embodiments 10-14, wherein a shape of the borehole is at least partially non-circular. 
     Embodiment 16: The system of any one of Embodiments 10-15, wherein the logging tool is positioned at an off-center position in the borehole during detection of the response. 
     Embodiment 17: The system of any one of Embodiments 10-16, wherein the instructions comprise instructions executable by the processor to cause the processor to perform an evaluation of the subsurface formation based on the borehole image after correcting of the distorted features. 
     Embodiment 18: One or more non-transitory machine-readable media comprising instructions executable by a processor to cause the processor to: create, from a response to a signal being propagated through a subsurface formation from a borehole in the subsurface formation, a borehole image that includes distorted features representing bedding dips in the subsurface formation; and correct the distorted features, wherein the instructions executable by the processor to cause the processor to correct the distorted features comprises instructions executable by the processor to cause the processor to map points of a non-circular shape in the borehole image to points on a circular shape. 
     Embodiment 19: The one or more non-transitory machine-readable media of Embodiment 18, wherein the instructions executable by the processor to cause the processor to create the borehole image comprises instructions executable by the processor to cause the processor to: reconstruct a wall of the borehole image into a series of non-circular shapes based on the response to create a reconstructed borehole image. 
     Embodiment 20: The one or more non-transitory machine-readable media of Embodiments 18 or 19, wherein the instructions executable by the processor to cause the processor to map the points comprises instructions executable by the processor to cause the processor to: determine a non-circular to circular transformation matrix using at least one constant from a non-circular equation of the reconstructed borehole image; and transform the reconstructed borehole image into a circular borehole image based on the non-circular to circular transformation matrix.