MXPA01000427A - Method and apparatus for imaging earth formation - Google Patents

Abstract

The borehole imaging apparatus of the present invention includes a tool having an array of voltage electrode buttons (32a, b, ...) mounted on a non-conductive pad (30). A current source (34, 38) and a current return (36, 40) are preferably located on the non-conductive pads at opposite ends thereof. The locations of the current source (34, 38) and return (36, 40) are designed to force a current to flow in the formation parallel to the pad face and non-parallel to the formation boundary layers. According to a method of the invention, the voltage difference between a pair of buttons in the array is proportional to the resistivity of the formation bed adjacent to the buttons. The ratio of voltage differences between two nearby pairs of electrode buttons provides a quantitative measurement of the ratio of shallow resistivity. The resolution of the image produced by the new tool is determined only by the spacing of the buttons.

Description

METHOD AND APPARATUS TO REPRESENT THE IMAGE OF A TERRESTRIAL FORMATION This application is related to U.S. Patent No. 4,468,623 which is a co-property, U.S. Patent No. 4,567,759 in co-ownership and U.S. Patent No. 4,692,908 in co-ownership. The complete description of each of these co-owned US Patents is hereby incorporated by reference.

BACKGROUND OF THE INVENTION Field of the invention The present invention relates to the investigation of terrestrial formations. More specifically, the invention relates to methods and apparatuses for electrically representing wall images of a perforation.

STATE OF THE ART When analyzing a hydrocarbon well, it is desirable to identify the characteristics of the land formation at different depths of the drilling. Some of the characteristics of the formation that are desirable to identify include fine stratifications and facies, the heterogeneity of the carbonate deposits and the structure of the fractures. The detection of the stratifications includes the detection of the slate sandstone sequences where the slates establish a base contact for each sequence. The identification of the facies includes the identification of the lithology between basal contacts. The analysis of carbonates includes the detection of inhomogeneous characteristics such as those due to irregular cementation, variations in pore sizes, changes in small-scale lithology, etc. Fractures play an important role in the flow characteristics of productive rock. Therefore, the measurement or detection of the characteristics, the determination of their orientations, density, height, vertical and lateral continuity is highly desirable. U.S. Patent No. 4,468,623, co-owned by Gianzero et al. (Patent '623) describes a tool for the investigation of land formation that can detect characteristics of the perforation wall that are only millimeters in size. As shown in Figures 1 and 2 of the prior art, the tool 10 includes an array 12 of small topographic electrodes (buttons) 14a-141 mounted on a conductive pad 16 that is pressed against the wall of the perforation 18. A source constant current is coupled to each button so that the current flows out from each button 14 to the adjacent formation, perpendicular to the wall of the perforation 18 as illustrated in Figure 1 by the arrows Ei, E2. The current returns to an electrode (not shown) that is located on or near the surface, or in another part of the tool 10. The currents of the individual buttons are checked and recorded (by a processor on top of the perforation 20) as the tool 10 moves through the perforation. The currents of the buttons measured are proportional to the conductivity of the material in front of each button. The conductivities are plotted as a function of the depth to form a "wavy trace" (or record) which can be analyzed to identify the characteristics of the formation at different depths of the borehole. U.S. Patent No. 4,567,759, co-owned, by E strom et al. (the '759 patent) describes a method and apparatus for producing a high resolution image from the data collected by the tool described in the' 623 patent. According to the methods of the '759 patent, signals from a conductivity measuring tool are processed to compensate for conditions such as variation. in the speed of the tool, variation in the environment of the perforation, etc. This processing allows subsequent improvements in the signal with which the signals can be displayed in a manner that approximates the nature of a visual image of the bore wall taken from within the bore. In view of the fact that the human eye is highly perceptive, the fine high resolution characteristics of the hole wall can be discerned and interpreted visually. These features include small variations in the perforation wall in the circumferential as well as vertical directions. The characteristics that can be differentiated from the image include drusen, small stratigraphic beds with their variations in circumferential thickness, small-scale lithological changes, pore sizes, fractures with their density, height, vertical and lateral continuity, and so on. Other improvements to the methods and apparatus of the '623 patent and the' 759 patent are described in co-owned US Patent No. 4,692,908 to Ekstrom et al. (the '908 patent). The '908 patent describes an acoustic method and apparatus for measuring the distance between the electrode buttons and the perforation wall. It is very likely that this distance will change as the tool moves through the hole. Distance measurements are made according to the '908 patent, recorded and used to correct the conductivity measurements if deemed necessary. As described in the '623 patent, the size and spacing of the electrode buttons is important to obtain good resolution and signal-to-noise ratio. In particular, the buttons must be tightly placed for high resolution and in a small area for good spatial bandwidth. However, if the buttons are too small, the signal-to-noise ratio (SNR) is adversely affected. This is demonstrated by analyzing the current flow through the buttons in the formation. For example, as shown in Figure 1 of the prior art, buttons 14a and 14b are located on opposite sides of a bed contour B that separates beds having different resistivities Ri and R2. Assuming that the pad 16 is in perfect contact with the wall of the perforation 18, the electric field near the pad 16 is perpendicular to the face of the pad or parallel to the contour of the B bed. The parallel component of the electric field is continuous to through the two different media as shown by: Ei = E2 (1) where Ei and E2 are the electric fields on the two sides of the contour of Bed B. In an ideal case, with an infinitely long pad, the equipotential surfaces near the center of the pad are all parallel to the face of the pad and the field electrical is constant. The density of the stream jx flowing to each bed is proportional to the conductivity sx of the bed as shown in accordance with: If the conductivity s of the formation is continuously variable, then the density of the current j can be expressed as: j = Is (3) The electric current Ib flowing to a button is, therefore, the integral of the current density over the area of the bobon according to: Ib = I j Ada = E Al s da The electric field E depends on the distribution of the conductivity away from the pad and is not calibrated. Therefore, the button current is not a quantitative measure of local conductivity. However, if the ratio of the button currents at two nearby points is calculated, the unknown E's are canceled. Thus, the ratio of the currents passing through two nearby buttons is a quantitative measurement of the surface conductivities ratio. From the aforementioned, it will be appreciated that the size and separation of the electrode buttons will control the resolution and the SNR, and that the resolution can be increased only at the expense of decreasing the SNR. The methods and apparatuses thus far described with reference to patents 759 and 623 in co-property are known in the art as FMI ™, a registered trademark of Schlumberger and an abbreviation for "formation micro imager" (micro imager in one training). The IMF ™ has been very successful in the production of precise perforation images when used in wells that have been drilled with water-based mud (WBM). However, the IMF ™ produces lower quality images in wells that have been drilled with oil-based mud (OBM). Currently there are no tools available that can produce images of perforations in an OBM well and that are comparable in quality with the images produced by the IMF ™ in a WBM well. Despite this fact, the use of OBM in well drilling is increasingly popular.

It is considered that a non-conductive mud cake from an OBM well between the conductive buttons and the borehole wall interferes with the conductivity measurements.

SUMMARY OF THE INVENTION Therefore, an object of the invention is to provide the methods and apparatuses for forming accurate images of a wall of a hole in an OBM well. In accordance with this objective which will be described in more detail below, the image forming apparatus of the present invention includes a tool similar to the FMI ™ tool having an array of electrode buttons mounted on a pad. However, according to the invention, the pad is non-conductive and the buttons are voltage electrodes instead of current electrodes. In the preferred embodiment, the current source and a current return are located at opposite ends of the non-conductive pad; although the source of current and the return of the current may be located outside the pad. However, whether they are located inside or outside the pad, the locations of the source and the return of the current are designed to force a current flow in the formation parallel to the face of the pad, preferably orthogonal to the layers. boundary of the formation. According to a method of the invention, the voltage difference between a pair of buttons in the array is proportional to the resistivity of the formation bed adjacent to the buttons. The relationship of the voltage differences between two close pairs of electrode buttons provides a quantitative measurement of the ratio of surface resistivity in the beds. The resolution of the image produced by the new tool is only determined by the separation of the buttons. The tool according to the invention produces much better images than the FMI ™ tool when used in OBM wells. To ensure that the flow of the stream is not tangential to the contours of the bedIt is preferred that the non-conductive pad be provided with a pair of current sources and current returns that are substantially non-parallel (eg, orthogonal). According to a currently preferred embodiment of the invention, the voltage electrodes are arranged in a matrix having displaced rows and the measurements are made for adjacent electrodes in two dimensions. Additional objects and advantages of the invention will be apparent to those skilled in the art with reference to the detailed description taken in conjunction with the figures provided.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a schematic illustration of an image forming tool of a prior art perforation; Figure 2 is a schematic illustration of the electrode pad of the prior art tool of Figure 1; Figure 3 is a schematic illustration of a pad electrodes of an image forming tool according to the invention; Figure 4a is partly schematic and partly a block diagram of an image forming tool according to the invention; Figure 4b is a schematic illustration of vertical current flow parallel to the electrode pad of the invention. Figure 5 is a graph showing five traces of current versus depth in a conductive bed covered with resistive mud cakes of different resistivity, having made current measurements with an FMI ™ tool of the prior art; Figure 6 is a graph similar to Figure 5 where the measurements have been taken in a resistive bed; Figure 7 is a graph showing five voltage traces against depth in a conductive bed covered with resistive cement cakes of different resistivity, having made the voltage measurements with a tool according to the invention; Figure 8 is a graph similar to Figure 7 where the measurements have been taken in a resistive bed; Figure 9 is a schematic illustration of an alternative, less preferred embodiment of the invention with the current flow properly aligned orthogonal to the boundaries of the léche. Figure 10 is a schematic illustration of the embodiment of Figure 1 where the current flow is tangential to the contours of the bed; Figure 11 is a schematic illustration of the most preferred embodiment (also illustrated in Figure 3) with two-dimensional current flow; Figure 12 is a view similar to Figure 11 of a currently most preferred embodiment of the invention having an optimized array of electrodes; and Figure 13 is a schematic illustration of a matrix of voltage sampling points used to form a resistivity image according to the invention. DETAILED DESCRIPTION OF THE PREFERRED MODALITIES Now refer to Figures 1-3 and 4a, the training apparatus of the present invention includes a tool similar to the FMI ™ tool shown in Figure 1 of the prior art but having an array of voltage electio buttons mounted on a non-conductive pad. According to the invention, a non-conductive pad 30 preferably made of rubber or ceramic is provided with an arrangement of voltage electrodes 32a-32t. In the preferred embodiment, a current source 34 and a current return 36 are located at opposite ends (upper and lower part) of the non-conductive pad 30. In the alternative modes (not shown) the source and current return they are located in centralizers above and below the pad, or on adjacent pads. Regardless of whether the current source 34 and the current return 36 are located in the non-conductive pad 30, the locations of the source 34 and the return 36 of the current are designed to force a current flow in the parallel array. to the face of the pad and not parallel to the boundary layers of the formation. As described in more detail below with reference to Figures 9-12, due to the nature of the boundary layers of the formation, it is preferable to provide a second current source 38 and a second current return 40 which are arranged as along a line that is orthogonal to the line along which the first current source 34 and the current return 36 are arranged. The first source of current and current return and the second source of current and current return preferably they are at different times. If desired, a single switched current supply can be used to supply both current sources; or, if desired, it is possible to provide separate current supplies. As can be seen in Figure 4a, the voltages measured at the voltage electrodes are used to provide the measurements and images as described below. In particular, voltages of adjacent voltage electrodes 32 (for example 32a and 32c, 32c and 32e) are provided to a bank of amplifiers 37 that amplify voltage differences (although a single switched amplifier can be used). As is known in the art, the outputs of the amplifiers 37 can be sampled in sequence and converted A / D by the sampler / converter block 51. In turn, the output of the block 51 is preferably processed by the signal processor 55. and recorded by the registrar 57. The output of the recorder 57 can be a log (s) or record, an image (s) or data without processing.

The basic operating theory of the invention is explained with reference to Figure 4b. Figure 4b is a schematic illustration of a pad 30 according to the invention in perfect contact with the wall 42 of a perforation in a formation having four beds with different resistivities Ri, R2, R3, R4. A current supply 35 is coupled to the electrodes 30, 36 and a voltage feeder circuit (amplifier) 37 is coupled to the pairs of the electrodes 32, for example, 32a, 32b. According to the invention, the current flows from the source 34 to the return 36 so that the density of the current near the pad 30 is substantially parallel to the face of the pad and (in many situations) substantially perpendicular to the contours of the pad. bed. According to the laws of physics, the perpendicular component of the current density j remains constant across the formation beds: The voltage difference (dV) x between a pair of electrodes located in the same bed is given by: (dV) x = DjRx (6) where D is the distance between the two electrodes, j is the constant current density, and Rx is the resistivity of the lousy j_ecno # 5] the electrodes are each located in a different bed , then the voltage difference between the electrodes is the one-dimensional integral: dV = jlRdl (7) where di is the distance between the two electrodes. The current density j depends on the distribution of the resistivity away from the pad 30, and it is not easy to calibrate it. Therefore, the voltage difference (dV) is not a quantitative measurement of the local resistivity. However, according to a method of the invention, the ratio of the voltage difference (dV) i and the voltage difference (dV) between two close pairs of electrode buttons provides a quantitative measurement of the surface resistivity ratio. As can be seen from the relations 6 and 7, the resolution of the image produced by the image-forming tool of the invention is only determined by the separation of the buttons. Those skilled in the art will appreciate that ratios 6 and 7 (as well as 4) assume an infinitely long pad in perfect contact with the array. However, as demonstrated by the prior art FMI ™ tool and in the subsequent tests of the present inventors, the finite size of the pad and the imperfect contact of the pad do not significantly impede the tool's ability to invention to make meaningful measurements. The reason why the FMI ™ tool produces bad images in an OBM well is considered to be that the highly resistive mud cakes in the perforation walls interfere with the current measurements. Returning now to Figures 5-8, the effects of the resistive mud cakes were measured with respect to the FMI image forming tool (Figures 5 and 6) and with respect to the tool according to the invention (Figure 7 and £) As seen in Figures 5 and 6, the contrast resolved by the FMI imager on both conductive and resistive beds is significantly affected by the resistive slurry cake. As the resistive relationship (resistivity of the mud cake: bed resistivity) increases, the ability of the FMI ™ tool to detect changes in currents under study deteriorates. When the ratio is 100 or greater, the FMI tool is practically incapable of resolving any image. As seen in Figures 7 and 8, however, the resolution of the image forming tool of the present invention actually improves in the presence of the slurry cake. The results shown in Figures 7 and 8 refer to mud cakes approximately 0.05 inches (1.27 mm) thick. Similar tests were performed with thinner mud cakes (0.025 inch, 0.64 mm) and similar results were obtained. In addition, similar tests were performed with thicker mud cakes (0.10 inches, 2.54 mm) and similar results were obtained in the resistive beds. In conductive beds with thick mud cakes (0.10 inches, 2.54 mm), slightly different results were obtained, however. In conductive beds with thick mud cake (0.10 inches, 2.54 mm), an appreciable loss of 50% was observed. However, on the contrary, this loss is not crucial and is expected not to occur in OBM wells. The tests described above were performed with mud cakes having a uniform thickness and resistivity. It is expected that in practice there are mud cakes of varying thickness and resistivity. Thus, additional tests were performed with random variations in thickness and resistivity of the mud cake. The results of these tests are not drastically different from the results described above. As already mentioned, the numerical analyzes presented heretofore assume that the current flows substantially normal to the contours of the bed. In such an ideal situation, a simplified pad 30 ', as shown in Figure 9, is sufficiently provided with a single current source 34' and a single current return 36 '. However, in practice, a one-dimensional current flow can not guarantee that the current will always flow substantially normal to the contours of the bed. For example, as shown in Figure 10, it is possible that the contours of the bed may be aligned parallel to the flow of the stream, for example, in a deviated or horizontal well. If this happens, the current flowing through the different beds will not be equal and the voltage differences measured by two pairs of electrodes on opposite sides of a bed contour will not be significant. Those skilled in the art will also appreciate that if some of the beds shown in Figure 9 are infinitely resistive, measurements will not be possible. It is known that highly resistive veins or veins occur in terrestrial formations and if these veins are between the current source and the current return, a current field will not be generated and voltages will not be detected. To ensure that the current flow is not tangential to the contours of the bed and is not interrupted by a highly resistive vein, it is preferred that the tool be provided with a pair of current sources and non-parallel current returns (eg, orthogonal ) as shown in Figures 3 and 11. Figure 11 also illustrates a complicated bed structure where the beds are inclined and are divided by an inclined fracture of high angle shown schematically by the dark black line marked "F". Under these circumstances, it does not matter if the current source 38 or 38 is operated, nor will it give rise to a current flow that is substantially perpendicular to the contours of the bed. To take this alignment into account, one method of the invention is to measure the voltage drop in two directions and perform a vector analysis. For example, the measurement of the voltage drop across the electrodes 32k and 321 as well as the voltage drop across 32m and 32k can be used as vector components to calculate the current vector that is perpenoicular to the contours of the bed. This technique is also improved by arranging the voltage electrodes in a matrix having displaced rows as shown in Figure 12. Turning now to Figure 12, a currently more preferred non-conductive sensing pad 130 is similar to the pad 30 described above with reference numbers siirilares referring to the similar structure.

The sensing pad 130 differs from the pad 30 in that its individual electrodes 132 are arranged in three rows with one row being displaced from the other rows. The voltage drop across two orthogonal pairs of electrodes such as 132k, 1321 and 132j, 132m are used as vector components to calculate the current vector that is perpendicular to the contours of the bed. It will be noted that the arrangement of Figure 12 includes four voltage measurements for each sampling point in the perforation wall. These four voltage measurements combine to produce a single resistivity value for each element of the image in an image of the wall of the perforation. Now returning to Figure 13, the elements of the image that correspond to nine sampling points separated at regular intervals are shown as schema using Cartesian coordinates (i, j). However, it will be noted that, in practice, the ordinate "i" will follow a circular path around the perforation wall. For the purpose of illustration, it is assumed that the vector of the current flow that is perpendicular to the contours of the bed lies along the line "L" in Figure 13 and passes through the points (i, j) y (i + l, j ') where j < j '< j + l, and the point (i + l, j ') is not a sampling point. Based on the relationship (7) above, it will be observed that the ratio of the voltage drop at the point (i, j) in comparison with the voltage drop at the point (i + l, j ') must be equal to The relation of the resistivities in these points according to the following relation (8), where • indicates voltage drop and R indicates resistivity: ? 1/3 R?,: According to a method of the invention, paca logarithms are used to reconstruct the resistivity image of four independent measurements. For example, if Y is the natural logarithm of R, and S is the natural logarithm of • [sic], the ratio of the relation (8) can be expressed as equality: Yi,] ~ Y? +1,] '= Sj., -, - S1 +?, - j' (9) With the relationship between the voltage drop and the resistivity expressed in terms of logarithms, it is possible to apply a linear interpolation logarithm to determine the values of Y and S at the point (i + l, j ') from the values really measured at nearby sampling points. If the fractional component of j 'is called a, such that j' = j + a and 0 < a < L, then the values of Y and S at the point (i + l, j ') can be expressed in terms of the values at the nearby sampled points according to: Y1 + III = (l-a) Y1 +? / D + Y1 + 1, D +? (10) S? +? FD '= (l-a) S1 +? F3 + aS1 + ?, 3+? (eleven) By replacing the values of the relations (10) and (11) in (9), you get the following: Ylf3- (l-a) Y1 +? LD-aY? + ?, 3+? = Slf3- (l-a) S1 + ?, 3-aS1 + ?, 3+? (12) Those skilled in the art will appreciate that the solution of the ratio (12) for each voltage drop measurement is difficult by the number of unknowns. Thus, to obtain a better solution for the relation (12), it is preferable to reduce to the minimum the following cost function that contains the term ll? Ilf3 = [Y1 / 3- (1-a) Y1 +? 3-aY1 +? 3 +? - Slf3- (1-a) S1 +? 3-aS1 +? 3+?] 2 (13) The relation (13) represents only one of eight possible solutions depending on the slope of the "L" line in the Figure 13. In view of the fact that the coordinates (i, j) only increase by one unit, the relation (13) applies only to the case where the slope of the line "L" is between 0 ° and 45 °. To cover the case where the slope of the "L" line is between 45 ° and 90 °, the index (i + l, j) in the relation (13) must change to (i + l, j + l) and the index (i + l, j + l) in relation (13) must change to (i + l, j). Those skilled in the art, in this way, will appreciate that the appropriate indices of the form (i ± 1, j ± 1) must be replaced in relation (13) to create a separate equation of each of the 45 ° octants that they sprinkle point (i, j) in Figure 13. The function of cost to minimize it is provided in relation (14) where the first sum is taken over two different pairs of current source and current return, and the Second sum is taken from all sampled points: 1 = 3 3 I1 / 3 (14) The image of the resistivity is constructed by minimizing the cost function I in the relation (14) with respect to Yi (3. The result of the minimization is a series of linear equations in Y1 / D that can be solved according to any known technique For a given row "j", Y?, D is only coupled only to the given row j and two adjacent rows j + 1. Therefore, the linear equations can be established as an equation of a tridiagonal block matrix where each block consists of Ylí3 for a given row, and the equation of the tridiagonal block matrix can be solved according to well-known techniques Some modalities of a method and apparatus for electrically analyzing a perforation have been described and illustrated herein. which penetrates a terrestrial formation Although particular embodiments of the invention have been described, the invention is not intended to be limited thereto, since it is intended The invention must be extended in its scope as permitted by the technique and in the same way that the specification is read. Thus, although numbers of specific electrode buttons have been described, it will be appreciated that it is possible to use other numbers with consequent increase. Also, although a specific tool for carrying the electrode pad (s) of the invention has been shown, it will be recognized that it is possible to use another type of drilling tools obtaining similar results. Furthermore, although specific configurations have been described with reference to the state of the art for signal processing, it will be appreciated that it is possible to use other configurations as well. For example, it will be understood that voltage measurements made at the bottom of the bore may be transmitted up the bore (with or without compression) for processing at the top of the bore, or some or all of the signal processing It can be carried out at the bottom of the borehole with partial or final results transmitted upwards from the borehole. In addition, although specific circuits and specific processing techniques were described, it will be appreciated that it is possible to use different circuits and / or computer programs. Therefore, the person skilled in the art will realize that it is possible to make other modifications to the invention provided without deviating from its spirit and scope as claimed.

Claims (20)

1. An appliance for use with a tool to investigate a hole, which can be moved through the hole to investigate the wall of the hole, the apparatus consists of: a) a non-conductive pad adapted to be pressed against the wall of the perforation; b) a matrix of voltage electrodes carried in the non-conductive pad and adapted to detect voltages in the perforation wall; c) a first electrode of the current source adapted to inject a current in the perforation wall; and d) a first current return electrode adapted to brake current from the wall of the perforation to a location separate from the first electrode of the current source, the matrix of the voltage electrodes being located between the first electrode of the current source and the first current return electrode. The apparatus according to claim 1, wherein: at least the first electrode of the current source or the first current return electrode is carried in the non-conductive pad. 3. The apparatus according to claim 1, further comprising: e) a current supply coupled to the first electrode of the current source and to the first current return electrode; and f) a grid for measuring the voltage coupled to the matrix of the voltage electrodes to measure the voltage differences between the electrodes in the matrix of the voltage electrodes. The apparatus according to claim 1, further comprising: e) a second electrode of the current source and adapted to inject a current to the perforation wall; and f) a second current return electrode adapted to drain current from the perforation wall to a location separate from the second electrode of the current source, the second electrode of the current source and the second current return electrode being located substantially not parallel to the first electrode of the current source and the first current return electrode. The apparatus according to claim 4, wherein: at least the first electrode of the current source, the second electrode of the current source, the first current return [sic] or the second current return electrode It is carried on the non-conductive pad. The apparatus according to claim 4, wherein: the first electrode of the current source, the second electrode of the current source, the first current return and the second return electrode and current are carried on the pad not conductive The apparatus according to claim 4, further comprising: g) a current supply coupled to the first electrode of the current source, the first current return electrode, the second electrode of the current source and the second electrode current return; and h) the means for measuring the voltage coupled to the matrix of the voltage electrodes to measure voltage differences between the electrodes in the matrix of the voltage electrodes. The apparatus according to claim 7, wherein: the matrix of the voltage electrodes includes three rows of electrodes, each row having a plurality of electrodes arranged in columns, at least one of the rows having columns offset from the columns from another of the rows. The apparatus according to claim 8, wherein: the means for measuring the voltage includes the means for determining the difference in voltage between an electrode in one row and an electrode in another row, as well as the means for determining the difference in the voltage between two electrodes of the same row. 10. The apparatus according to claim 9, further comprising: h) the signal processing means coupled to the means for measuring the voltage to generate a resistivity image based on the voltage differences measured by the means for measuring the voltage . 11. The apparatus according to claim 10, where: the signal processing means generates the resistivity image by comparing pairs of voltage differences. 1

2. An apparatus for forming the electric image of the wall of a perforation in a terrestrial formation having a plurality of beds separated by contours of the beds, the apparatus corsiste in: a) the means to generate current to generate a current flow to through a portion of the formation so that the current density near the wall of the perforation adjacent to the formation portion is substantially not parallel to the contours of the bed; b) the means to measure the voltage, to measure the voltage in the perforation wall; and c) the means for signal processing coupled to the means for measuring the voltage to generate a resistivity image of the perforation wall based on the voltage measured by the means for measuring the voltage. The apparatus according to claim 12, wherein: the means for measuring the voltage includes the first, second, third and fourth electrodes, and the means for comparing the voltage difference between the first and second electrodes and the difference of voltage between the third and fourth electrode. The apparatus according to claim 13, wherein: the first and second electrodes are separated from each other in a first direction, and the second and third electrodes are separated from each other in a second direction that is substantially not parallel to the first one. address. The apparatus according to claim 12, wherein: the current generating means includes the means for generating the current flow through the formation portion in two substantially non-parallel directions. 16. The apparatus according to claim 13, wherein: the first electrode is in a first row of electrodes, the second electrode is in a second row of electrodes, the third and fourth electrodes are in a third row of electrodes. electrodes, and the third row is located between the first row and the second row. 17. A method for forming the electrical image of the wall of a perforation in a land formation having a plurality of beds separated by the contours of the beds using a tool having a plurality of electrodes, the method comprising: a) generating a flow current through a portion of the formation so that the current density near the wall of the perforation adjacent to the formation portion is substantially not parallel to the contours of the beds; b) use the electrodes, measure voltages in the perforation wall; and c) generating a resistivity image of the perforation wall based on the measured voltages. 18. The method according to claim 17, wherein: the step to measure is to compare the voltage difference between a first and second electrode of the plurality of electrodes with the voltage difference between a third and fourth electrode of the plurality of electrodes. The method according to claim 18, wherein: the first and second electrodes are separated from each other in a first direction, and the second and third electrodes are separated from each other in a second direction that is substantially not parallel to the first address. The method according to claim 17, wherein: the step of generating a current flow includes generating the current flow through the portion of the formation in two substantially non-parallel directions.