A method for rapid imaging of full-space apparent resistivity based on point source attenuation field

Abstract

The present invention discloses a method for rapid imaging of full-space apparent resistivity based on the attenuation field of a point source, which utilizes the concentric diffusion attenuation distribution characteristics of the equipotential surface of the point source in space, converts the two-pole apparent resistivity calculation method into a three-pole apparent resistivity calculation between two adjacent acquisition electrodes, and groups them by positive and negative direction symbols, and grids the detection area at the same time, obtains the apparent resistivity data of multiple point sources in each grid, and finally screens to obtain the unique apparent resistivity value of each network, so as to realize rapid imaging of the detection area; this method provides higher resolution and sensitivity, so that it can more accurately identify small-scale geological features and abnormal bodies, thereby improving the reliability and accuracy of monitoring results. In addition, this method avoids complex matrix calculations, can realize almost instant data processing, improves the time efficiency of imaging, and meets the needs of rapidly changing underground environment monitoring.

Description

Technical Field

[0001] The invention relates to a full-space apparent resistivity fast imaging method based on a point power supply attenuation field, and belongs to the field of geophysical exploration data processing. Background Art

[0002] Detecting the resistivity change characteristics of overburden during coal mining is one of the reliable means to achieve dynamic monitoring of roof rock deformation and damage. Combining specific electrode configurations with efficient data acquisition technology, by optimizing electrode layout and increasing data acquisition frequency, it is possible to capture resistivity changes in real time and improve monitoring speed and spatial resolution. The potential data after collection is mainly processed in two ways. One of them is resistivity inversion imaging, which provides higher resolution and accurate resistivity distribution through a specific calculation process and is suitable for fine analysis. However, due to its complex calculation, it takes a long time to complete. The other is to directly use apparent resistivity imaging. Although this method can shorten the calculation time and improve the detection efficiency, its imaging resolution is low, and it is difficult to capture small geological features or abnormal bodies, resulting in insufficient imaging results. The imaging range is limited and cannot meet the regional coverage. Since the existing resistivity imaging technology has its own shortcomings in real-time and efficiency, it can no longer meet the needs of rapidly changing underground environment monitoring.

[0003] In response to the above problems, how to provide a new method for rapid apparent resistivity imaging, which can perform imaging in a shorter time after acquiring potential data, with higher imaging precision and larger coverage area, so as to meet the needs of rapidly changing underground environment monitoring, is the research direction required by the present invention. Summary of the invention

[0004] In view of the problems existing in the above-mentioned prior art, the present invention provides a full-space apparent resistivity rapid imaging method based on point source attenuation field, which does not require complex matrix calculations, thereby reducing the calculation time and improving the time efficiency of imaging. At the same time, the two-pole apparent resistivity calculation method is converted into a three-pole apparent resistivity calculation between two adjacent acquisition electrodes, thereby obtaining higher resolution and sensitivity, thereby meeting the needs of rapidly changing underground environment monitoring.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a method for rapid imaging of full-space apparent resistivity based on point source attenuation field, the specific steps are:

[0006] Step 1: Data acquisition: Use an electrical data acquisition device to perform electrical detection on the required detection area and obtain the corresponding potential data.

[0007] Step 2, calculate the normalized potential and grouping: for the potential data collected in step 1, assume that the position of the reference electrode B is infinite, and define the positive and negative signs in space: there are two three-dimensional fixed points E and F in space, and one three-dimensional free point G. It is defined that the sign of point G is positive when ∠GEF≤90°, and the sign of point C is negative when ∠GEF>90°; when the point power supply p is supplying power, the position of the point is fixed, and the position of the reference electrode B is also fixed, which is equivalent to the fixed points E and F respectively; at the same time, the position of each collecting electrode q is continuously changing, which is equivalent to the three-dimensional free point G. The potential is normalized and calculated according to the following formula, and the obtained apparent resistivity is grouped according to the subscript p.

[0008]

[0009] Where: N is the number of electrodes used as point power sources; U p,q ,I p,q They are respectively the potential and current data collected by the qth collecting electrode when the pth point power supply is supplied; ∠qpB is the angle formed between the pth point power supply, the qth collecting electrode and the reference electrode B.

[0010] Step 3: Curve correction: Assuming that the resistivity in space is continuously distributed, p,q± According to the positive and negative signs, the data can be divided into two groups: positive and negative directions. p,q+ ,L}、{u p,q- ,L}; at the same time, p,q+ ,u p,q- The data were calibrated separately, and the calibration principle was to ensure that u p,q+ and u p,q- The absolute values ​​of each are negatively correlated with the distance L, where L is the distance between the collection electrode q and the point power source p.

[0011] Step 4: Calculate the potential gradient for each set of data corrected in step 3:

[0012] ① For each set of data, u of two adjacent acquisition electrodes p,q Perform gradient calculation.

[0013] δu p，q± =|u p，q1± -u p，q2± |

[0014] Where: u p,q1± 、u p,q2± When the point power source p is used for power supply, the potential difference between two adjacent collection electrodes q1 and q2 in the two sets of data in the positive and negative directions is calculated respectively.

[0015] ② Calculate the apparent resistivity on the equipotential surface:

[0016] ρL± =K ± ·δu p,q±

[0017] in: L p,q1± , L p,q2± When power is supplied to a point power source p, the distances between two adjacent collection electrodes q1 and q2 in the two sets of data in the positive and negative directions to the point power source p respectively.

[0018] ③After calculations in steps ① and ②, the distance L from the point source p is obtained ± The apparent resistivity distribution on the equipotential surface {L ± , ρ L±}; where: L ± =(L p,q1± +L p,q2± ) / 2.

[0019] Step 5: Gridding the imaging area: Grid the area to be imaged in the underground space.

[0020] Step 6: Spatial superposition:

[0021] Ⅰ. Calculate the distance D from each grid center point in the space to the first power supply point p p,s± ; Where: p is the serial number of the point power supply, and s is the serial number of the center point of each grid.

[0022] Ⅱ. Data fitting: linear interpolation is used according to (L ± , ρ L± ) for each grid center point D p,s± In (0, max (L ± )] to calculate the ρ in each grid. p,s If D p,s± Greater than max(L ± ), then the interpolation result of the current point power p in the grid is recorded as empty.

[0023] III. Repeat steps Ⅰ to Ⅱ to calculate the ρ of each point power source p in each grid. p,s .

[0024] Step 7: After step 6, multiple apparent resistivity values ​​are obtained in each grid, and the unique apparent resistivity value of each grid is determined by adopting the same screening method.

[0025] Step 8: Since the coordinates of each network center point are known, the apparent resistivity values ​​of each grid obtained in step 7 are marked at the corresponding network coordinate positions, thereby obtaining the apparent resistivity profile imaging of the required detection area.

[0026] Furthermore, the electrical data acquisition device includes multiple electrodes and an electrical detector. The multiple electrodes are arranged in the required detection area, and the position coordinates of each electrode are recorded. The electrical detector is connected to each electrode and is used to power some electrodes as a point power supply. The remaining electrodes are used as collection electrodes to receive and collect potential data, and a reference electrode B is arranged at a farther position.

[0027] Furthermore, the specific screening method in step seven is: averaging multiple apparent resistivity values ​​in each grid, and using the average value as the unique apparent resistivity value of each grid.

[0028] Furthermore, the specific screening method in step seven is: in the process of step six, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the F apparent resistivity data in each grid are averaged, and the average value is used as the unique apparent resistivity value of each grid.

[0029] Furthermore, the specific screening method in step seven is: in the process of step six, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the maximum or minimum value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

[0030] Furthermore, the specific screening method in step seven is: in the process of step six, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the median value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

[0031] Furthermore, the specific screening method in step seven is: in the process of step six, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and for the F apparent resistivity data in each grid, the apparent resistivity value obtained by the center point of each network and the point power source closest to it is selected, and this value is used as the unique apparent resistivity value of each grid.

[0032] The working principle of the present invention is as follows: assuming that the entire space of the detection area is a uniform medium, the point power source is distributed in a concentric circle on the equipotential surface of the space, and the apparent resistivity value on a certain equipotential surface is calculated according to the two-pole apparent resistivity calculation formula, which means that the apparent resistivity values ​​at all points on this equipotential surface are calculated at the same time, and the apparent resistivity is continuously distributed in the uniform medium space. Even if the equipotential surface is not continuously distributed, the potential distribution on any equipotential surface can be determined by interpolation, and its apparent resistivity can be calculated; if there are several point power sources in the space, then there is an intersection point of different point power sources at any position in the space, and several apparent resistivity values ​​can be calculated within a limited range of the intersection point. By interpolating the apparent resistivity values ​​within the limited range of the intersection point, the comprehensive response of several point power sources at this point can be obtained, and then the space is gridded to calculate the apparent resistivity distribution in the detection area. In order to achieve higher sensitivity (or resolution), the curve is calculated for gradient, and the two-pole apparent resistivity calculation method is converted into a three-pole apparent resistivity calculation between two adjacent acquisition points to obtain higher resolution and sensitivity.

[0033] Compared with the prior art, the present invention utilizes the concentric diffusion attenuation distribution characteristics of the equipotential surface of the point source in space, converts the two-pole apparent resistivity calculation method into a three-pole apparent resistivity calculation between two adjacent acquisition electrodes, and groups them by positive and negative direction symbols, and grids the detection area at the same time, obtains the apparent resistivity data of multiple point sources in each grid, and finally screens to obtain the unique apparent resistivity value of each network, so as to realize rapid imaging of the detection area; this method provides higher resolution and sensitivity, so that it can more accurately identify small-scale geological features and abnormal bodies, thereby improving the reliability and accuracy of the monitoring results. And this method avoids complex matrix calculations and can realize almost instant data processing, which is crucial for real-time monitoring and ensures rapid response to potential dangers. In addition, this method is not only suitable for roof monitoring during coal mining, but also can be extended to multiple fields such as geological disaster monitoring, groundwater resource assessment, and mineral resource development, and has wide practicality and potential market value. The present invention does not need to improve the equipment, and still adopts the existing electrical data acquisition device and its acquisition method. By optimizing the electrode configuration and acquisition frequency of the existing device, it can adapt to the underground environment monitoring needs of different geological conditions and rapid changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the overall process of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be further described below.

[0036] like Figure 1 As shown, the specific steps of the present invention are:

[0037] Step 1, data acquisition: Use an electrical data acquisition device to perform electrical detection on the required detection area and obtain corresponding potential data; the electrical data acquisition device uses existing equipment, which includes multiple electrodes and an electrical detector. The multiple electrodes are arranged in the required detection area, and the position coordinates of each electrode are recorded. The electrical detector is connected to each electrode to supply power to some electrodes as a point power supply, and the remaining electrodes are used as collection electrodes to receive and collect potential data, and a reference electrode B is arranged at a farther position.

[0038] Step 2, calculate the normalized potential and grouping: for the potential data collected in step 1, assume that the position of the reference electrode B is infinite, and define the positive and negative signs in space: there are two three-dimensional fixed points E and F in space, and one three-dimensional free point G. It is defined that the sign of point G is positive when ∠GEF≤90°, and the sign of point C is negative when ∠GEF>90°; when the point power supply p is supplying power, the position of the point is fixed, and the position of the reference electrode B is also fixed, which is equivalent to the fixed points E and F respectively; at the same time, the position of each collecting electrode q is continuously changing, which is equivalent to the three-dimensional free point G. The potential is normalized and calculated according to the following formula, and the obtained apparent resistivity is grouped according to the subscript p.

[0039]

[0040] Where: N is the number of electrodes used as point power sources; U p,q ,I p,q They are respectively the potential and current data collected by the qth collecting electrode when the pth point power supply is supplied; ∠qpB is the angle formed between the pth point power supply, the qth collecting electrode and the reference electrode B.

[0041] Step 3: Curve correction: Assuming that the resistivity in space is continuously distributed, p,q± According to the positive and negative signs, the data can be divided into two groups: positive and negative directions. p,q+ ,L}、{u p,q- ,L}; at the same time, p,q+ ,u p,q- The data were calibrated separately, and the calibration principle was to ensure that u p,q+ and u p,q- The absolute values ​​of each are negatively correlated with the distance L, where L is the distance between the collection electrode q and the point power source p.

[0042] Step 4: Calculate the potential gradient for each set of data corrected in step 3:

[0043] ① For each set of data, u of two adjacent acquisition electrodes p,q Perform gradient calculation.

[0044] δu p，q± =|up，q1± -u p，q2± |

[0045] Where: u p,q1± 、u p,q2± When the point power source p is used for power supply, the potential difference between two adjacent collection electrodes q1 and q2 in the two sets of data in the positive and negative directions is calculated respectively.

[0046] ② Calculate the apparent resistivity on the equipotential surface:

[0047] ρ L± =K ± ·δu p,q±

[0048] in: L p,q1± , L p,q2± When power is supplied to a point power source p, the distances between two adjacent collection electrodes q1 and q2 in the two sets of data in the positive and negative directions to the point power source p respectively.

[0049] ③After calculations in steps ① and ②, the distance L from the point source p is obtained ± The apparent resistivity distribution on the equipotential surface {L ± , ρ L±}; where: L ± =(L p,q1± +L p,q2± ) / 2.

[0050] Step 5: Gridding the imaging area: Grid the area to be imaged in the underground space.

[0051] Step 6: Spatial superposition:

[0052] Ⅰ. Calculate the distance Dp,s from each grid center point in the space to the first power supply point p ± ; Where: p is the serial number of the point power supply, and s is the serial number of the center point of each grid.

[0053] Ⅱ. Data fitting: linear interpolation is used according to (L ± , ρ L± ) for each grid center point Dp,s ± In (0, max (L ± )] to calculate the ρ in each grid. p,s If D p,s± Greater than max(L ± ), then the interpolation result of the current point power p in the grid is recorded as empty.

[0054] III. Repeat steps Ⅰ to Ⅱ to calculate the ρ of each point power source p in each grid. p,s .

[0055] Step 7: After step 6, multiple apparent resistivity values ​​are obtained in each grid, and the multiple apparent resistivity values ​​in each grid are averaged for screening, and the average value is used as the unique apparent resistivity value of each grid.

[0056] Step 8: Since the coordinates of each network center point are known, the apparent resistivity values ​​of each grid obtained in step 7 are marked at the corresponding network coordinate positions, thereby obtaining the apparent resistivity profile imaging of the required detection area.

[0057] As an improvement of the present invention, the screening method in step 7 is replaced by one of the following methods:

[0058] 1. In step 6, during step 2, the distance between some grid center points and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the F apparent resistivity data in each grid are averaged, and the average value is used as the unique apparent resistivity value of each grid.

[0059] 2. In step 6, during step 2, the distance between some grid center points and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the maximum or minimum value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

[0060] 3. In step 6, during step 2, the distance between some grid center points and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the median value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

[0061] 4. In step 6, during step ②, the distance between some grid center points and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and for the F apparent resistivity data in each grid, the apparent resistivity value obtained by the center point of each network and the point power source closest to it is selected, and this value is used as the unique apparent resistivity value of each grid.

[0062] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for rapid imaging of full-space apparent resistivity based on point source attenuation field, characterized in that: The specific steps are: Step 1: Data acquisition: Use an electrical data acquisition device to perform electrical detection on the required detection area and obtain corresponding potential data; Step 2, calculate normalized potential and group: the potential data collected in step 1 is assumed to be at infinity, and the potential is normalized according to the following formula, and the obtained apparent resistivity is grouped according to the subscript p; p=1,2…N Where: N is the number of electrodes used as point power sources; U p,q ,I p,q are the potential and current data collected by the qth collection electrode when the pth point power supply is powered; ∠qpB is the angle formed between the pth point power supply, the qth collection electrode and the reference electrode B; Step 3: Curve correction: Assuming that the resistivity in the space is continuously distributed, the up,q ± According to the positive and negative signs, the data can be divided into two groups: positive and negative directions. p,q+ ,L}、{u p,q- ,L}; at the same time, p,q+ ,u p,q- The data were calibrated separately, and the calibration principle was to ensure that u p,q+ and u p,q- The absolute values ​​of each are negatively correlated with the distance L, where L is the distance between the collection electrode q and the point power source p; Step 4: Calculate the potential gradient for each set of data corrected in step 3: ① For each set of data, u of two adjacent acquisition electrodes p,q Perform gradient calculation: δu p，q± =|u p，q1± -u p，q± | Where: up,q 1± 、up,q 2± When the point power source p is used for power supply, the potential difference between two adjacent collection electrodes q1 and q2 in the two respective data sets in the positive and negative directions is calculated respectively; ② Calculate the apparent resistivity on the equipotential surface: r L± =K ± ·you p,q± in: L p,q1± , L p,q2± When the point power source p is powered, the distances between the two adjacent collection electrodes q1 and q2 in the two sets of data in the positive and negative directions to the point power source p; ③After calculations in steps ① and ②, the distance L from the point source p is obtained ± The apparent resistivity distribution on the equipotential surface {L ± , ρ L± }; where: L ± =(L p,q1± +L p,q2± ) / 2; Step 5: Gridding the imaging area: Gridding the area to be imaged in the underground space; Step 6: Spatial superposition: Ⅰ. Calculate the distance D from each grid center point in the space to the first power supply point p p,s± ; Where: p is the serial number of the point power supply, s is the serial number of the center point of each grid; Ⅱ. Data fitting: linear interpolation is used according to (L ± , ρ L± ) for each grid center point D p,s± In (0, max (L ± )] to calculate the ρ in each grid. p,s If D p,s± Greater than max(L ± ), then the interpolation result of the current point power source p in the grid is recorded as empty; III. Repeat steps Ⅰ to Ⅱ to calculate the ρ of each point power source p in each grid. p,s ; Step 7, after step 6, multiple apparent resistivity values ​​are obtained in each grid, and a unique apparent resistivity value of each grid is determined by adopting the same screening method; Step 8: Since the coordinates of each network center point are known, the apparent resistivity values ​​of each grid obtained in step 7 are marked at the corresponding network coordinate positions, thereby obtaining the apparent resistivity profile imaging of the required detection area.

2. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The electrical data acquisition device includes multiple electrodes and an electrical detector. The multiple electrodes are arranged in the required detection area and the position coordinates of each electrode are recorded. The electrical detector is connected to each electrode and is used to power some electrodes as a point power supply. The remaining electrodes are used as collection electrodes to receive and collect potential data, and a reference electrode B is arranged at a farther position.

3. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The specific screening method in step seven is: averaging multiple apparent resistivity values ​​in each grid, and using the average value as the unique apparent resistivity value of each grid.

4. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The specific screening method in step 7 is: in the process of step 6, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the F apparent resistivity data in each grid are averaged, and the average value is used as the unique apparent resistivity value of each grid.

5. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The specific screening method in step 7 is: in the process of step 6, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the maximum or minimum value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

6. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The specific screening method in step 7 is: in the process of step 6, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and the median value of the F apparent resistivity data in each grid is obtained, and this value is used as the unique apparent resistivity value of each grid.

7. The method for rapid full-space apparent resistivity imaging based on point source attenuation field according to claim 1 is characterized in that: The specific screening method in step 7 is: in the process of step 6, the distance between the center point of some grids and the point power source is greater than max(L ± ), resulting in the number of apparent resistivities in a single grid ≤ N; therefore, the number of coverages F is selected, and F ≤ N, and for the F apparent resistivity data in each grid, the apparent resistivity value obtained by the center point of each network and the point power source closest to it is selected, and this value is used as the unique apparent resistivity value of each grid.

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