Geomembrane defect identification and positioning method based on dipole electric field method
Through the geomembrane defect identification and positioning method based on the dipole electric field method, using three-dimensional scanning technology and the dipole electric field method, combined with terrain and soil resistivity, the accuracy and positioning problems of geomembrane defect detection are solved, and high-precision three-dimensional spatial positioning and multi-defect detection are achieved.
Patent Information
- Application Number
- CN202510877668.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-27
- Publication Date
- 2025-09-16
AI Technical Summary
Existing geomembrane defect detection methods have problems such as low detection efficiency, poor accuracy, and inability to accurately locate. In particular, the uneven electric field distribution and single data processing method in complex environments lead to large detection errors.
A geomembrane defect identification and positioning method based on the dipole electric field method is adopted. A three-dimensional map of the detection area is constructed through three-dimensional point cloud scanning, and the optimal power supply points and detection points are planned. Combined with the terrain conditions and soil resistivity, the average voltage difference and fluctuation coefficient are calculated to determine the defect location.
It achieves high-precision positioning of geomembrane defects in complex environments, reduces detection errors, and supports three-dimensional spatial positioning of multiple defects.
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Figure CN120651916A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of geomembrane defect detection, and in particular to a geomembrane defect identification and positioning method based on a dipole electric field method. Background Art
[0002] As an important anti-seepage material, geomembranes are widely used in projects such as landfills, reservoirs, and dams. However, due to mechanical damage, aging, or external stress during construction, geomembranes can develop defects, leading to leachate leakage and posing a serious threat to the environment and project safety. Traditional geomembrane defect detection methods, such as visual inspection and tracer methods, suffer from low efficiency, poor accuracy, and inability to accurately locate defects.
[0003] Although existing electrical detection technology can achieve preliminary detection of defects, it still has the following shortcomings: Uneven electric field distribution: A single electric field mode is difficult to adapt to complex environments, resulting in large defect positioning errors.
[0004] Single data processing method: The influence of the surrounding soil environment on the detection accuracy is not considered during the actual processing and detection process, resulting in large errors in the collected electric field data and large errors in the detection.
[0005] Therefore, it is urgent to propose a new method for identifying and locating geomembrane defects based on the dipole electric field method. Summary of the Invention
[0006] To address the above-mentioned shortcomings of the existing technology, the present invention provides a method for identifying and locating geomembrane defects based on the dipole electric field method. This method comprehensively considers the impact of the ground environment on detection accuracy, effectively reduces detection errors, and uses longitude and latitude positioning to locate the geomembrane defect.
[0007] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for identifying and locating geomembrane defects based on a dipole electric field method is provided, which comprises the following steps: S1: Determine the detection area for geomembrane defects, use 3D point cloud scanning equipment to scan the terrain data of the detection area, determine the installation position of the electric field release device based on the terrain data, and locate the optimal power supply point in the detection area; S2: The optimal power point is used as the midpoint to determine the detection range. The electric field release device releases the set voltage at the optimal power point into the detection range. Detection points are arranged on the detection latitude within the detection range to obtain the central voltage around the detection points. S3: Obtain the center voltage corresponding to each detection point, then draw detection meridians within the detection range, calculate the average voltage difference on the detection meridians, and calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian; S4: Based on the fluctuation coefficient of the average voltage difference, determine that the geomembrane defect is located in the fan-shaped area surrounded by two detection meridians, and determine the detection latitude range where the geomembrane defect is located based on the voltage difference fluctuation coefficient between two adjacent detection points on the same detection meridian; determine the location of the geomembrane defect through the detection latitude range and the fan-shaped area surrounded by the detection meridian.
[0008] Furthermore, step S1 includes: S11: Scan the inspection area using a three-dimensional point cloud scanning device, construct a three-dimensional topographic map of the inspection area, and establish a three-dimensional coordinate system within the three-dimensional topographic map; S12: Grid the surface of the three-dimensional terrain map and obtain the coordinates of each grid center in the three-dimensional coordinate system , n is the grid number, according to the area of the detection area S As well as the rated voltage of the electric field release device, plan the number of power points in the detection area M ; ; in, Rated voltage released by the electric field release device, The minimum voltage that the voltage detection terminal can detect. d is the electric field diffusion radius, is the average attenuation rate of voltage with distance in the detection area; S13: According to the vertical coordinate of each grid Size, filter out M grid high points within the detection area, M The vertical coordinate value corresponding to the grid high point is the first one in the descending order of the grid vertical coordinate values. M The center coordinates of the grid high point are used as the reference high point coordinates. , m is the number of the reference high point; S14: Take discrete distributions evenly on the terrain surface of the three-dimensional terrain map M power reference points and obtain the coordinates of each power reference point , u Number the power reference point and filter the two closest reference high points and the power reference point. The filtering constraints are: ; in, are the collection of reference high point and power reference point respectively, The maximum voltage that the electric field release device can release; S15: If the power reference point u There is a reference high point around mIf the constraint condition is met, the reference high point m As the best power source in the nearby area, if the power reference point u There is no reference high point around m If the constraints are met, the power reference point u As the best power source in the surrounding area; S16: After all the optimal power supply points in the detection area are determined, an electric field release device is installed on the optimal power supply point according to the position of the coordinates corresponding to the optimal power supply point in the detection area, and the positive pole of the electric field release device is buried above the geomembrane and the negative pole is buried below the geomembrane.
[0009] Furthermore, step S2 includes: S21: Take the optimal power point as the midpoint, Determine the detection range for the radius, and evenly select several detection latitudes within the detection range, and evenly distribute them on each detection latitude. P At each detection point p Several pairs of electrode points are evenly arranged around the periphery, and each pair of electrode points is symmetrically arranged with the detection point as the symmetrical point, and detection terminals are inserted into the electrode points; S22: The electric field release device releases the set voltage within the detection range at the optimal power point The detection terminals on the electrode points detect the voltage at their locations, and the detection points are calculated using the voltage detected by each pair of detection terminals. p Center voltage at the location ; ; in, e For detection point p The electrode point pairs set around are numbered. E For detection point p The number of electrode pairs set around, They are the voltage values detected by a pair of electrode points.
[0010] Furthermore, in step S2, the optimal distance between the terminals is detected. The calculation method is: ; in, d 0 means the detection terminal has the best sensitivity under ideal geological conditions The basic distance can be obtained through experiments, Ra is the terrain roughness between each pair of electrode points, are the heights of the grids where the two electrode points in each pair of electrode points are located, is the height of the grid where the power point is located. The height of the electrode point can be expressed by the vertical coordinate corresponding to the grid. is the resistivity gradient corresponding to each pair of electrode points, is the maximum resistivity gradient between each pair of electrode points, express x Direction and y Directional resistivity gradient component, is the resistivity gradient, is the influence coefficient of terrain roughness on the sensitivity of the detection terminal, is the influence coefficient of resistivity on the sensitivity of the detection terminal, the influence coefficient and influence coefficient , can be obtained through experimental testing.
[0011] Furthermore, the optimal sensitivity The calculation method is: ; in, is the minimum voltage error detected by the detection terminal under test conditions, The minimum voltage error designed for the detection terminal.
[0012] Furthermore, step S3 includes: S31: Obtain the center voltage corresponding to each detection point. Then, take the power point as the starting point and the detection points on the same direction of different detection latitudes as the passing points as the detection meridians, and calculate the average value of the voltage difference between two adjacent detection points on the same detection meridian. ; ; in, w To detect the number of detection points on the meridian, To detect the first w The central voltage corresponding to each detection point; S32: Calculate the average voltage difference of the detection area around the power point based on the average voltage difference corresponding to each detection meridian ; f To detect the number of the meridian, F To detect the number of longitudes, For the f Average voltage difference of the detection meridians; S33: Calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian ; .
[0013] Furthermore, step S4 includes: S41: Setting the Fluctuation Coefficient Threshold ,like , then the detection meridian is determinedw There are defects in the geomembrane on both sides of the area, otherwise, the detection warp is determined w There are no geomembrane defects in the areas on both sides; When it is determined that two adjacent detection meridians w 、 w If there are geomembrane defects in the areas on both sides of -1, it means that the geomembrane defects are located in the fan-shaped area surrounded by two adjacent detection meridians, and step S42 is executed; S42: Based on the voltage difference between two adjacent detection points on the same detection line , calculate the voltage difference fluctuation coefficient between two adjacent electrode points ; Set the voltage difference fluctuation coefficient threshold ,like , it is determined that the geomembrane defect is located at the detection point w and w -1 is within the range between the detection latitudes; Utilize detection points w and w The location of the geomembrane defect is determined by the overlapping area between the detection latitude line of -1 and the fan-shaped area surrounded by two adjacent detection meridians.
[0014] The beneficial effects of the present invention are as follows: the present invention utilizes 3D scanning technology to construct a 3D map of the detection area, and uses the grid data of the 3D map to accurately plan the detection points within the detection area. Furthermore, the influence of terrain conditions and soil resistivity on detection accuracy is comprehensively considered, effectively reducing the error in the acquired electric field data. Furthermore, the present invention also plans precision lines and latitudes to locate geomembrane defects, and uses the dipole electric field method to perform potential analysis at the defect location. This method has excellent error and interference immunity, can achieve 3D spatial positioning, and supports simultaneous detection of multiple defects. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 This is the principle diagram of the geomembrane defect identification and location method based on the dipole electric field method.
[0016] Figure 2 This is the principle diagram for planning and positioning of longitude and latitude lines within the detection range. DETAILED DESCRIPTION
[0017] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.
[0018] like Figure 1 As shown, a method for identifying and locating geomembrane defects based on a dipole electric field method comprises the following steps: S1: Determine the detection area for geomembrane defects, use 3D point cloud scanning equipment to scan the terrain data of the detection area, determine the installation location of the electric field release device based on the terrain data, and locate the optimal power supply point in the detection area. Specifically, the following steps are included: S11: Scan the inspection area using a three-dimensional point cloud scanning device, construct a three-dimensional topographic map of the inspection area, and establish a three-dimensional coordinate system within the three-dimensional topographic map; S12: Grid the surface of the three-dimensional terrain map and obtain the coordinates of each grid center in the three-dimensional coordinate system , n is the grid number, according to the area of the detection area S As well as the rated voltage of the electric field release device, plan the number of power points in the detection area M ; ; in, Rated voltage released by the electric field release device, The minimum voltage that the voltage detection terminal can detect. d is the electric field diffusion radius, is the average attenuation rate of voltage with distance in the detection area; S13: According to the vertical coordinate of each grid Size, filter out M grid high points within the detection area, M The vertical coordinate value corresponding to the grid high point is the first one in the descending order of the grid vertical coordinate values. M The center coordinates of the grid high point are used as the reference high point coordinates. , m is the number of the reference high point; S14: Take discrete distributions evenly on the terrain surface of the three-dimensional terrain map M power reference points and obtain the coordinates of each power reference point , u Number the power reference point and filter the two closest reference high points and the power reference point. The filtering constraints are: ; in, are the collection of reference high point and power reference point respectively, The maximum voltage that the electric field release device can release; S15: If the power reference point u There is a reference high point around mIf the constraint condition is met, the reference high point m As the best power source in the nearby area, if the power reference point u There is no reference high point around m If the constraints are met, the power reference point u As the best power source in the surrounding area; S16: After all the optimal power supply points in the detection area are determined, an electric field release device is installed on the optimal power supply point according to the position of the coordinates corresponding to the optimal power supply point in the detection area, and the positive pole of the electric field release device is buried above the geomembrane and the negative pole is buried below the geomembrane.
[0019] Ridges create an electric field "focusing effect," with current density locally enhanced at the ridge crest. Valleys create an electric field "attenuation trap," significantly reducing the electric field intensity at the base. Furthermore, the electric field spreads more rapidly downhill, while forming an electric field "shadow zone" uphill. Therefore, the present invention utilizes the aforementioned method to maximize the selection of topographic high points within the detection area for releasing the electric field. This selection, while minimizing the uniformity and density of the power source distribution within the detection area, promotes the diffusion of the electric field to the surrounding area, thereby increasing the sensitivity of the electrodes to sensing electric field changes.
[0020] S2: The optimal power point is used as the midpoint to determine the detection range. The electric field release device releases the set voltage at the optimal power point into the detection range. The detection points are arranged on the detection latitude within the detection range to obtain the center voltage around the detection points. Step S2 specifically includes: S21: Take the optimal power point as the midpoint, Determine the detection range for the radius, and evenly select several detection latitudes within the detection range to ensure that the distances between the detection latitudes are equal. Reasonable setting of the density of the detection latitudes can effectively improve the positioning accuracy of geomembrane defects while reducing the difficulty of detection, and each detection latitude is evenly distributed. P At each detection point p Several pairs of electrode points are evenly arranged around the periphery, and each pair of electrode points is symmetrically arranged with the detection point as the symmetrical point, and detection terminals are inserted into the electrode points; Optimal distance between detection terminals The calculation method is: ; in, d 0 means the detection terminal has the best sensitivity under ideal geological conditions The basic distance can be obtained through experiments. R a is the terrain roughness between each pair of electrode points, are the heights of the grids where the two electrode points in each pair of electrode points are located, is the height of the grid where the power point is located. The height of the electrode point can be expressed by the vertical coordinate corresponding to the grid. is the resistivity gradient corresponding to each pair of electrode points, is the maximum resistivity gradient between each pair of electrode points, express x Direction and y Directional resistivity gradient component, is the resistivity gradient, is the influence coefficient of terrain roughness on the sensitivity of the detection terminal, is the influence coefficient of resistivity on the sensitivity of the detection terminal, the influence coefficient and influence coefficient , can be obtained through experimental testing.
[0021] Optimal sensitivity The calculation method is: ; in, is the minimum voltage error detected by the detection terminal under test conditions, Minimum voltage error designed for detection terminals; The larger the terrain roughness value, the more uneven the terrain between each pair of electrode points, and the greater its impact on the voltage transmission between the electrode points. It is necessary to reduce the error caused by the terrain effect by shortening the distance between each pair of electrode points. The resistivity gradient has a similar effect on the sensitivity between the detection terminals.
[0022] S22: The electric field release device releases the set voltage within the detection range at the optimal power point The detection terminals on the electrode points detect the voltage at their locations, and the detection points are calculated using the voltage detected by each pair of detection terminals. p Center voltage at the location ; ; in, e For detection point p The electrode point pairs set around are numbered. E For detection point p The number of electrode pairs set around, They are the voltage values detected by a pair of electrode points.
[0023] S3: Obtain the center voltage corresponding to each detection point, then draw detection meridians within the detection range, calculate the average voltage difference on the detection meridians, and calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian. Step S3 specifically includes: S31: Obtain the center voltage corresponding to each detection point. Then, take the power point as the starting point and the detection points on the same direction of different detection latitudes as the passing points as the detection meridians, and calculate the average value of the voltage difference between two adjacent detection points on the same detection meridian. ; ; in, w To detect the number of detection points on the meridian, To detect the first w The central voltage corresponding to each detection point; S32: Calculate the average voltage difference of the detection area around the power point based on the average voltage difference corresponding to each detection meridian ; f To detect the number of the meridian, F To detect the number of longitudes, For the f Average voltage difference of the detection meridians; S33: Calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian ; .
[0024] S4: Based on the fluctuation coefficient of the average voltage difference, determine that the geomembrane defect is located in the fan-shaped area surrounded by two detection meridians, and based on the voltage difference fluctuation coefficient between two adjacent detection points on the same detection meridian, determine the detection latitude range where the geomembrane defect is located; determine the geomembrane defect location through the detection latitude range and the fan-shaped area surrounded by the detection meridian. Step S4 specifically includes: S41: Setting the Fluctuation Coefficient Threshold ,like , then the detection meridian is determined w There are defects in the geomembrane on both sides of the area, otherwise, the detection warp is determined w There are no geomembrane defects in the areas on both sides; When it is determined that two adjacent detection meridians w 、 w If there are geomembrane defects in the areas on both sides of -1, it means that the geomembrane defects are located in the fan-shaped area surrounded by two adjacent detection meridians, and step S42 is executed; S42: Based on the voltage difference between two adjacent detection points on the same detection line , calculate the voltage difference fluctuation coefficient between two adjacent electrode points ; Set the voltage difference fluctuation coefficient threshold ,like , it is determined that the geomembrane defect is located at the detection point w andw -1 is within the range between the detection latitudes; Utilize detection points w and w The location of the geomembrane defect is determined by the overlapping area between the detection latitude line of -1 and the fan-shaped area surrounded by two adjacent detection meridians.
[0025] like Figure 2 As shown in the figure, a principle diagram of locating geomembrane defects using detection latitudes and detection longitudes is given. By rationally planning the number of detection points on the detection latitudes, high-precision geomembrane defect positioning can be achieved, and the geomembrane defect position can be determined within the area surrounded by the longitude and latitude lines.
[0026] The present invention utilizes 3D scanning technology to construct a 3D map of the inspection area, and uses the grid data of the 3D map to accurately plan the inspection points within the inspection area. The method also comprehensively considers the impact of terrain conditions and soil resistivity on inspection accuracy, effectively reducing the error in the acquired electric field data. Furthermore, the present invention also plans precision lines and latitudes to locate geomembrane defects, and uses the dipole electric field method to analyze the potential of the defect location. This method has excellent error-resistance and interference-resistant capabilities, can achieve 3D spatial positioning, and supports simultaneous detection of multiple defects.
Claims
1. A method for identifying and locating geomembrane defects based on the dipole electric field method, characterized in that: The following steps are involved: S1: Determine the detection area for geomembrane defects, use 3D point cloud scanning equipment to scan the terrain data of the detection area, determine the installation position of the electric field release device based on the terrain data, and locate the optimal power supply point in the detection area; S2: The optimal power point is used as the midpoint to determine the detection range. The electric field release device releases the set voltage at the optimal power point into the detection range. Detection points are arranged on the detection latitude within the detection range to obtain the central voltage around the detection points. S3: Obtain the center voltage corresponding to each detection point, then draw detection meridians within the detection range, calculate the average voltage difference on the detection meridians, and calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian; S4: Based on the fluctuation coefficient of the average voltage difference, determine that the geomembrane defect is located in the fan-shaped area surrounded by two detection meridians, and determine the detection latitude range where the geomembrane defect is located based on the voltage difference fluctuation coefficient between two adjacent detection points on the same detection meridian; determine the location of the geomembrane defect through the detection latitude range and the fan-shaped area surrounded by the detection meridian.
2. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 1 is characterized in that: The step S1 comprises: S11: Scan the inspection area using a three-dimensional point cloud scanning device, construct a three-dimensional topographic map of the inspection area, and establish a three-dimensional coordinate system within the three-dimensional topographic map; S12: Grid the surface of the three-dimensional terrain map and obtain the coordinates of each grid center in the three-dimensional coordinate system , n is the grid number, according to the area of the detection area S As well as the rated voltage of the electric field release device, plan the number of power points in the detection area M ; ; in, Rated voltage released by the electric field release device, The minimum voltage that the voltage detection terminal can detect. d is the electric field diffusion radius, is the average attenuation rate of voltage with distance in the detection area; S13: According to the vertical coordinate of each grid Size, filter out M grid high points within the detection area, M The vertical coordinate value corresponding to the grid high point is the first one in the descending order of the grid vertical coordinate values. M The center coordinates of the grid high point are used as the reference high point coordinates. , m is the number of the reference high point; S14: Take discrete distributions evenly on the terrain surface of the three-dimensional terrain map M power reference points and obtain the coordinates of each power reference point , u Number the power reference point and filter the two closest reference high points and the power reference point. The filtering constraints are: ; in, are the collection of reference high point and power reference point respectively, The maximum voltage that the electric field release device can release; S15: If the power reference point u There is a reference high point around m If the constraint condition is met, the reference high point m As the best power source in the nearby area, if the power reference point u There is no reference high point around m If the constraints are met, the power reference point u As the best power source in the surrounding area; S16: After all the optimal power supply points in the detection area are determined, an electric field release device is installed on the optimal power supply point according to the position of the coordinates corresponding to the optimal power supply point in the detection area, and the positive pole of the electric field release device is buried above the geomembrane and the negative pole is buried below the geomembrane.
3. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 2, characterized in that: The step S2 comprises: S21: Take the optimal power point as the midpoint, Determine the detection range for the radius, and evenly select several detection latitudes within the detection range, and evenly distribute them on each detection latitude. P At each detection point p Several pairs of electrode points are evenly arranged around the periphery, and each pair of electrode points is symmetrically arranged with the detection point as the symmetrical point, and detection terminals are inserted into the electrode points; S22: The electric field release device releases the set voltage within the detection range at the optimal power point The detection terminals on the electrode points detect the voltage at their locations, and the detection points are calculated using the voltage detected by each pair of detection terminals. p Center voltage at the location ; ; in, e For detection point p The electrode point pairs set around are numbered. E For detection point p The number of electrode pairs set around, They are the voltage values detected by a pair of electrode points.
4. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 3 is characterized in that: In step S2, the optimal distance between the terminals is detected. The calculation method is: ; in, d 0 means the detection terminal has the best sensitivity under ideal geological conditions The basic distance can be obtained through experiments. R a is the terrain roughness between each pair of electrode points, are the heights of the grids where the two electrode points in each pair of electrode points are located, is the height of the grid where the power point is located. The height of the electrode point can be expressed by the vertical coordinate corresponding to the grid. is the resistivity gradient corresponding to each pair of electrode points, is the maximum resistivity gradient between each pair of electrode points, express x Direction and y Directional resistivity gradient component, is the resistivity gradient, is the influence coefficient of terrain roughness on the sensitivity of the detection terminal, is the influence coefficient of resistivity on the sensitivity of the detection terminal, the influence coefficient and influence coefficient , can be obtained through experimental testing.
5. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 4 is characterized in that: The optimal sensitivity The calculation method is: ; in, is the minimum voltage error detected by the detection terminal under test conditions, The minimum voltage error designed for the detection terminal.
6. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 3 is characterized in that: The step S3 comprises: S31: Obtain the center voltage corresponding to each detection point. Then, take the power point as the starting point and the detection points on the same direction of different detection latitudes as the passing points as the detection meridians, and calculate the average value of the voltage difference between two adjacent detection points on the same detection meridian. ; ; in, w To detect the number of detection points on the meridian, To detect the first w The central voltage corresponding to each detection point; S32: Calculate the average voltage difference of the detection area around the power point based on the average voltage difference corresponding to each detection meridian ; f To detect the number of the meridian, F To detect the number of longitudes, For the f Average voltage difference of the detection meridians; S33: Calculate the fluctuation coefficient of the average voltage difference corresponding to each detection meridian ; 。 7. The method for identifying and locating geomembrane defects based on the dipole electric field method according to claim 6, characterized in that: The step S4 comprises: S41: Setting the Fluctuation Coefficient Threshold ,like , then the detection meridian is determined w There are defects in the geomembrane on both sides of the area, otherwise, the detection warp is determined w There are no geomembrane defects in the areas on both sides; When it is determined that two adjacent detection meridians w 、 w If there are geomembrane defects in the areas on both sides of -1, it means that the geomembrane defects are located in the fan-shaped area surrounded by two adjacent detection meridians, and step S42 is executed; S42: Based on the voltage difference between two adjacent detection points on the same detection line , calculate the voltage difference fluctuation coefficient between two adjacent electrode points ; Set the voltage difference fluctuation coefficient threshold ,like , it is determined that the geomembrane defect is located at the detection point w and w -1 is within the range between the detection latitudes; Utilize detection points w and w The location of the geomembrane defect is determined by the overlapping area between the detection latitude line of -1 and the fan-shaped area surrounded by two adjacent detection meridians.