WO2021068527A1 - Procédé de simulation numérique pour étude électromagnétique aéroportée à haute efficacité guidée par empreinte - Google Patents

Procédé de simulation numérique pour étude électromagnétique aéroportée à haute efficacité guidée par empreinte Download PDF

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WO2021068527A1
WO2021068527A1 PCT/CN2020/093495 CN2020093495W WO2021068527A1 WO 2021068527 A1 WO2021068527 A1 WO 2021068527A1 CN 2020093495 W CN2020093495 W CN 2020093495W WO 2021068527 A1 WO2021068527 A1 WO 2021068527A1
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footprint
area
station
calculation
green
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PCT/CN2020/093495
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Chinese (zh)
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刘嵘
柳卓
柳建新
王建新
郭荣文
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中南大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]

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  • the invention relates to the technical field of aviation electromagnetic forward modeling, in particular to a footprint-guided high-efficiency aviation electromagnetic method numerical simulation method.
  • the aerial electromagnetic observation device uses an airborne platform, which is characterized by high efficiency, and the detection area often covers tens of square kilometers to thousands of square kilometers.
  • Traditional numerical simulation methods require that the entire detection area be used as the calculation area. This large-area grid calculation will consume a lot of calculation memory and time.
  • the truncated boundary vector finite element method only requires the abnormal body in the detection area as the calculation area, which has the characteristics of high efficiency. However, in the face of the existence of a large range of abnormal bodies, a large number of Green's function calculations are required, which makes the efficiency of this method questionable.
  • the present invention provides a footprint-guided high-efficiency aviation electromagnetic method numerical simulation method, which combines the aviation electromagnetic method observation device with a limited footprint area (that is, the aviation electromagnetic method footprint Features) and the truncated boundary vector finite element method, the entire aerial electromagnetic detection area is subdivided into multiple sub-areas according to the station to calculate the electromagnetic field of the station measurement point one by one, which has the characteristics of proper calculation area and high calculation efficiency.
  • the specific technical solutions are as follows:
  • the present invention provides a footprint-guided high-efficiency aviation electromagnetic method numerical simulation method, which includes the following steps:
  • Step S100 Use a uniform grid to divide the aerial electromagnetic method to detect the area
  • Step S200 Calculate the extension scales of the footprint area of the aviation electromagnetic observation device used in the x, y, and z directions; the number of grids in the x and y directions of the footprint area is equal, and the number of grids in the z direction is x or Between 1/4 and 1/2 of the number of grids in the y direction; the specific number of grids is determined by the ratio between the analytical solution and the numerical solution of the electromagnetic field at the measurement point of the uniform half-space model;
  • Step S300 Use the truncated boundary vector finite element method to take the footprint corresponding to the first station as an abnormal body, calculate the scattered current in the footprint, and store the Green function generated during the calculation process for future use;
  • the Green function is generated when the truncated boundary vector finite element is used, and is used to calculate the electromagnetic field generated by the boundary of the truncated boundary vector finite element method in the calculation of the scattered current of the discrete elements in the footprint;
  • Step S400 Calculate the electromagnetic field response of the measuring point by using the scattered current of the discrete unit in the footprint of the first measuring station, and store the Green function generated in the calculation process for backup;
  • the Green's function is used to calculate the electromagnetic field generated by the scattered current of the discrete unit in the footprint at the observation point of the station;
  • Step S500 Repeat the Green's function stored in steps S300 and S400 at the first station for subsequent stations, first calculate the scattered current in the station footprint according to S300, and then calculate the electromagnetic field of the station footprint at the measurement point according to S400.
  • Green's function recorded in steps S300 and S400 of the present invention it can be seen that they essentially belong to two Green's functions with different purposes. Therefore, in order to better distinguish, the Green's function recorded in step S300 is named the first Green's function.
  • the Green function recorded in step S400 is named the second Green function.
  • the grid in the step S100 is a regular hexahedral grid.
  • step S200 specifically requires that the footprint area is centered on the projection of the emission source on the ground, and the number of grids in the x, y, and z directions is gradually increased at a ratio of 4:4:1 until the scattered current in the footprint is measured
  • the error between the electromagnetic field generated by the point and the analytical solution of the measurement point is less than 5%.
  • step S200 is specifically:
  • Step S210 Calculate the analytical solution of the secondary electromagnetic field generated by the aviation electromagnetic emission source at the receiving point;
  • the area A is an area of 400 ⁇ 400 ⁇ 100m 3 ;
  • Step S220 the relative error between the calculated numerical solution of the secondary magnetic field and the obtained analytical solution of the secondary magnetic field
  • Step S230 Determine the magnitude of the relative error. If the relative error between the real and imaginary parts of the magnetic field does not exceed 5%, the volume of area A in Step S210 is defined as the footprint of the aviation electromagnetic device;
  • the area A in S210 will be redefined according to the 4:4:1 ratio expansion and the excitation current in the area and the secondary excitation current generated by the aeronautical electromagnetic measuring device in the area will be calculated. Field value solution, return to step S220.
  • the use of the truncated boundary vector finite element method in the step S300 includes:
  • Step S310 The calculation area is defined as the footprint and an element thickness wrapper, the electric field is defined at the center point of the edge of the division element of the calculation area, and the vector finite element theory is used to establish a set of equations to be solved that the electric field satisfies;
  • Step S320 Calculate the Green function to connect the central current of the unit in the footprint with the boundary electric field of the calculation area, arrange the Green function in a matrix form, the number of rows is the number of edges of the calculation area, and the number of columns is the number of edges of the elements in the footprint area;
  • Step S330 Store the coefficient matrix of the relational equation group in step S320 for use;
  • Step S340 forming a relational equation group for the electric field at the edge center of the calculation area boundary and the electric field at the edge center of the internal element of the footprint;
  • Step S350 Replace the calculated area boundary electric field in step S310 with the expression in step S320 to form a truncated boundary vector finite element method control equation set;
  • Step S360 Solve the equations to obtain the electric field value at the center of the edge of the element in the footprint, and use linear interpolation to obtain the scattered current at the center of the element.
  • step S400 specifically includes the following steps:
  • Step S410 Calculate and connect the measuring point of the first measuring station with the scattered current Green's function of the discrete unit in the footprint of the first measuring station, and arrange it into a row matrix.
  • the number of matrix columns is the number of scattered currents, that is, the number of discrete units of the footprint;
  • Step S420 store the row matrix formed in step S410 for future use
  • Step S430 Multiply the row matrix of Green's function by the column matrix formed by the scattered current to obtain the magnetic field value of the measuring point.
  • the step S500 includes the following steps:
  • Step S510 Repeat step S310, call the Green function stored in step S330, repeat steps S340-S360, and obtain the scattered current of the unit in the footprint of the subsequent station;
  • Step S520 Call the Green function stored in step S420, repeat step S430, and obtain the magnetic field value of the subsequent measuring station.
  • the footprint-guided high-efficiency aviation electromagnetic method numerical simulation method provided by the present invention abandons the traditional numerical simulation method that requires all detection areas as calculation areas, and chooses to calculate the detection areas one by one according to the footprint of a single station, which greatly reduces the calculation area.
  • the footprint-guided high-efficiency aviation electromagnetic method numerical simulation method provided by the present invention uses uniform grid division, and all station footprints are composed of the same grid.
  • the Green function stored in the first station can be reused, which greatly improves the calculation efficiency of subsequent stations.
  • Fig. 1 is a schematic diagram of the numerical simulation method of the high-efficiency aviation electromagnetic method guided by the footprint in this embodiment
  • Figure 2 is a schematic diagram of the form of the station device and the uniform dissection of the uniform underground medium below (using a uniform grid to divide the detection area of the aerial electromagnetic method);
  • Figure 3a is the layout of the real part of the current in the underground homogeneous medium in the form of a coaxial device
  • Figure 3b is the layout of the imaginary part of the current in the underground homogeneous medium in the form of a coaxial device
  • Figure 4a is the layout of the real part of the current in the underground homogeneous medium in the form of a coplanar device
  • Figure 4b is the layout of the imaginary part of the current in the underground homogeneous medium in the form of a coplanar device
  • Figure 5 is a diagram of the evaluation process of the underground footprint area scale (the solid line box is the 400 ⁇ 400 ⁇ 100m 3 calculation area used in the first evaluation, and the dashed box is the subsequent calculation area after expansion according to 4:4:1);
  • Figure 6 is a schematic diagram of the calculation area required by different methods to calculate the large horizontally extending thin plate abnormal body (Box 1 is the calculation area required by the traditional differential method, Box 2 is the calculation area required by the traditional truncated boundary vector finite element method, and Box 3 is the calculation area required by the traditional truncated boundary vector finite element method. Footprint guided truncated boundary vector finite element method required calculation area);
  • Figure 7 is a schematic diagram of the footprint area of the subsequent station (the calculation area of the first station is shown by the solid black box, and the calculation area of the second station is shown by the dashed black box);
  • Figure 8 is a schematic diagram of a zigzag complex three-dimensional model (Box No. 1 is the calculation area of the first station in this embodiment, Box No. 2 is the calculation area of the station No. 45 in this embodiment, and Box No. 3 is the traditional truncated boundary vector finite element method. The calculation area required by the station);
  • Figure 9a is a comparison diagram of the imaginary part of the magnetic field numerical solution of the zigzag complex three-dimensional model using the method of this embodiment and the traditional truncated boundary vector finite element method when using a coaxial device (the black dot is the imaginary part of the calculation result of the method of this embodiment, and the black line is the traditional The imaginary part of the calculation result of the truncated boundary vector finite element method);
  • Fig. 9b is a comparison diagram of the numerical solution real part of the magnetic field of the zigzag complex three-dimensional model between the method of this embodiment and the traditional truncated boundary vector finite element method when a coaxial device is used (the circle is the real part of the calculation result of the method of this embodiment, and the dashed line is the traditional truncated boundary Real part of vector finite element method calculation results);
  • Figure 10a is a comparison diagram of the imaginary part of the magnetic field numerical solution of the complex three-dimensional model of the sawtooth between the method of this embodiment and the traditional truncated boundary vector finite element method when the coplanar device is used (the black dot is the imaginary part of the calculation result of the method of this embodiment, and the black line is the traditional The imaginary part of the calculation result of the truncated boundary vector finite element method);
  • Figure 10b is a comparison diagram of the numerical solution real part of the magnetic field of the zigzag complex three-dimensional model between the method of this embodiment and the traditional truncated boundary vector finite element method when a coplanar device is used (the circle is the real part of the calculation result of the method of this embodiment, and the dashed line is the traditional truncated boundary The real part of the calculation result of the vector finite element method).
  • a footprint-guided high-efficiency aviation electromagnetic method numerical simulation method includes the following steps:
  • Step S100 Use a uniform grid to subdivide the airborne electromagnetic method to detect the area.
  • the uniform grid used here is a regular hexahedral grid with the same scale in the x, y and z directions, and the size is equal to 5, 10 and Choose between 25 three numbers, the smaller the scale, the higher the accuracy.
  • Step S200 Calculate the extension scale of the footprint area of the aviation electromagnetic observation device used in the x, y, and z directions, which specifically includes the following steps:
  • the first step Calculate the uniform half-space analytical solution and the full-space analytical solution generated by the emission source of a single station at the measurement point, and use the half-space analytical solution to subtract the full-space analytical solution to obtain the secondary current generated by the uniform underground medium at the measurement point Analytical solution of magnetic field;
  • Step 2 Calculate the excitation current generated by the emission source of the aviation electromagnetic device at the center of the uniform grid unit in the uniform underground A area (400 ⁇ 400 ⁇ 100m 3 area) directly below it;
  • the third step Calculate the secondary field generated by the excitation current at the measuring device in the uniform grid unit of the defined volume area (400 ⁇ 400 ⁇ 100m 3 area) to superimpose, and obtain the numerical solution of the secondary magnetic field at the measuring point;
  • Step 4 Calculate the relative error between the numerical solution of the secondary magnetic field obtained in the third step and the analytical solution of the secondary magnetic field obtained in the first step;
  • Step 5 Determine the relative error size. If the relative error between the real and imaginary parts of the magnetic field does not exceed 5%, the volume of area A in the second step of the step is defined as the footprint of the aviation electromagnetic device;
  • Step S300 Use the truncated boundary vector finite element method to take the footprint corresponding to the first station as the target area, calculate the scattered current in the footprint, and store the Green function generated during the calculation process for use;
  • Step S310 The calculation area is defined as the footprint and an element thickness wrapper, the electric field is defined at the center point of the edge of the division element of the calculation area, and the vector finite element theory is used to establish a set of equations to be solved that the electric field satisfies;
  • Step S320 Calculate the Green function to connect the central current of the unit in the footprint with the boundary electric field of the calculation area, arrange the Green function in a matrix form, the number of rows is the number of edges of the calculation area, and the number of columns is the number of edges of the elements in the footprint area;
  • Step S330 Store the coefficient matrix of the relational equation group in step S320 for use;
  • Step S340 forming a relational equation group for the electric field at the edge center of the calculation area boundary and the electric field at the edge center of the internal element of the footprint;
  • Step S350 Replace the calculated area boundary electric field in step S310 with the expression in step S320 to form a truncated boundary vector finite element method control equation set;
  • Step S360 Solve the equations to obtain the electric field value at the center of the edge of the element in the footprint, and use linear interpolation to obtain the scattered current at the center of the element.
  • Step S400 Calculate the electromagnetic field response of the measuring point by using the scattered current of the discrete elements in the footprint of the measuring station. The steps are as follows:
  • Step S410 Calculate and connect the measuring point of the first measuring station with the scattered current Green's function of the discrete unit in the footprint of the first measuring station, and arrange it into a row matrix.
  • the number of matrix columns is the number of scattered currents, that is, the number of discrete units of the footprint;
  • Step S420 store the row matrix formed in step S410 for future use
  • Step S430 Multiply the row matrix of Green's function by the column matrix formed by the scattered current to obtain the magnetic field value of the measuring point.
  • Step S500 Repeat the Green's function stored in steps S300 and S400 at the first station for subsequent stations, first calculate the scattered current in the station footprint according to S300, and then calculate the electromagnetic field of the station footprint at the measurement point according to S400.
  • the specific S500 includes the following steps:
  • Step S510 Repeat step S310, call the Green function stored in step S330, repeat steps S340-S360, and obtain the scattered current of the unit in the footprint of the subsequent station;
  • Step S520 Call the Green function stored in step S420, repeat step S430, and obtain the magnetic field value of the subsequent measuring station.
  • the aviation electromagnetic method uses an airborne platform to carry an observation device, which is composed of a transmitting coil and a receiving coil.
  • an observation device which is composed of a transmitting coil and a receiving coil.
  • the transmitting coil and the receiving coil are horizontal coils, it is called a coplanar device form, and when the transmitting coil and the receiving coil are vertical coils, it is called a coaxial device form.
  • the altitude of the airborne electromagnetic method is between 40m and the route from right to left.
  • the source of the transmitting coil is located 7.5m in front of the receiving coil, and the transmitting frequency of the transmitting coil is 10000hz.
  • this embodiment uses a uniform grid underground medium.
  • the vertical coil (coaxial device) used in the aerial electromagnetic transmitter can be treated as a horizontal magnetic dipole source, and the horizontal coil used in the transmitter (coplanar device) can be treated as a vertical magnetic dipole source.
  • the time-harmonic factor e iwt set the rectangular coordinates, the ground surface is the xy plane, and the z coordinate is downward.
  • the emission source in the air is a unit horizontal magnetic dipole source (coaxial device).
  • the electric field expression generated at the receiving point (the center of the underground grid unit) satisfies the expression 1)-3):
  • i is the unit imaginary number
  • w is the angular velocity corresponding to the frequency of the emission source
  • ⁇ x and ⁇ y are the difference between the x and y coordinates of the receiving point (the center point of the underground grid) and the aviation electromagnetic emission source, respectively
  • r and ⁇ are the distance between the receiving point (the center point of the underground grid) and the dipole source and the horizontal projection distance
  • ⁇ is the spatial wave number
  • J 0 and J 1 are the first type 0-order and 1st-order Bessels, respectively Er function
  • ⁇ is the air permeability
  • ⁇ is the conductivity of the underground homogeneous medium.
  • the current distribution generated by the uniform underground emission source is as follows:
  • Figure 3a, Figure 3b, Figure 4a and Figure 4b respectively show the horizontal slice diagram and the vertical slice diagram of the current amplitude distribution of the horizontal magnetic dipole source (coaxial device) and the vertical magnetic dipole source (coplanar device) .
  • the second column of Fig. 3b and Fig. 4b shows the current distribution of the vertical section in the direction of the source horizontal dipole. The current is greater than 10 -9.5 A/m mainly in the depth of 100m underground.
  • Figure 3a, Figure 3b, Figure 4a and Figure 4b show that the underground current caused by the aviation electromagnetic emission source is mainly concentrated in the 400 ⁇ 400 ⁇ 100m 3 area directly below the emission source. In the process of footprint assessment, this area is first selected for calculation Numerical solution of the secondary magnetic field at the measuring point.
  • the uniform half-space model is selected, and the magnetic field generated by the underground medium at the measuring point is compared by comparing two different methods to define the size of the footprint area of the aviation electromagnetic method device.
  • the specifics are: First, the calculation of the emission source caused by the selected underground area After the current distribution; then, calculate the secondary magnetic field superimposition caused by the current in the selected area grid at the aviation electromagnetic observation point to obtain the numerical solution of the secondary magnetic field at the measurement point; finally, the obtained secondary magnetic field numerical solution is compared with the analytical solution to determine Whether the selected current area has reached the required scale.
  • the judgment criterion is that the secondary magnetic field analytical solution is the standard, and the numerical solution error of the secondary magnetic field is less than 5%.
  • the analytical solution is obtained by subtracting the full-space analytical solution from the uniform half-space analytical solution of the magnetic field at the measuring point.
  • the internal current of the grid cell is regarded as a uniform distribution, and when calculating the magnetic field generated at the measuring point, the grid cell is regarded as an electric dipole source.
  • the magnetic field generated by the unit electric dipole source in the whole space is the expression 7)-9):
  • the magnetic field generated by the unit electric dipole source in the whole space is the expression 10)-12):
  • i is the unit imaginary number
  • ⁇ 0 is the air conductivity
  • w is the angular velocity corresponding to the frequency of the emission source
  • ⁇ is the air permeability
  • the H subscript indicates the direction of the electric dipole
  • the superscript indicates the direction of the generated magnetic field
  • ⁇ x, ⁇ y , ⁇ z are the x, y, z coordinate differences between the grid center point of the underground unit and the measurement point of the aeronautical device
  • r is the distance between the grid center point of the underground unit and the receiving point of the aeronautical device.
  • the transmitting device uses the x-direction magnetic dipole source, and the receiving device measures the x-direction magnetic field.
  • the unit magnetic dipole transmitting source is in full space conditions.
  • the following expression for the magnetic field generated at the measuring point is expression 13):
  • Each parameter in expression 13) is consistent with each parameter in expression 7)-12).
  • Each parameter in expression 14) is consistent with each parameter in expressions 1)-6).
  • Use expression 14) Minus expression 15) The analytical solution of the secondary magnetic field generated by the emission source of the aerial electromagnetic method coaxial device at the measuring point can be obtained.
  • the transmitting device uses the z-direction magnetic dipole source, and the receiving device measures the z-direction magnetic field.
  • the magnetic field generated by the unit magnetic dipole transmitting source at the measuring point under the full space condition is expression 15):
  • Each parameter in expression 15) is consistent with each parameter in expression 7)-12).
  • Each parameter in expression 16) is consistent with each parameter in expression 1)-6).
  • Use expression 16) Minus expression 15) The analytical solution of the secondary magnetic field generated by the emission source of the airborne electromagnetic coplanar device at the measuring point can be obtained.
  • Figure 5 shows the process of gradually expanding the grid area so that the numerical solution of the secondary magnetic field at the measuring point gradually approaches the analytical solution, and obtaining the footprint area of the aviation electromagnetic device.
  • the first numerical solution calculation uses a 400 ⁇ 400 ⁇ 100m 3 area grid.
  • the network is expanded according to the ratio of 4:4:1 Grid area.
  • This embodiment is based on the quadratic electric field vector finite element method, and the finite element discrete grid element edge center electric field satisfies expression 17):
  • E p is the initial field emission sources uniformly generated in the ground, can be calculated by Expression 1) -6);
  • K is the overall stiffness matrix
  • S is the item related to the initial electric field generated by the emission source underground
  • SH is the Poynting vector item generated by the electromagnetic field at the boundary of the calculation area
  • K II is symmetric and sparse
  • K IB is asymmetric
  • the truncated boundary vector finite element method cuts the vector finite element method calculation area into anomalous body and its element thickness wrap.
  • the relationship between E Bs and E Is in expression 20) is established through Green's function.
  • the truncated boundary vector finite element method calculates the secondary electric field E Bs at the boundary of the region, which can be expressed by the internal element scattering current as expression 21):
  • g ee is the connection between the scattered current J I at the center of the internal unit and the electric field E Bs at the boundary of the calculation area.
  • E IP is the initial electric field at the edge of the internal unit
  • V is the internal unit volume
  • Ne is the linear interpolation operator
  • ⁇ * is the conductivity of the uniform underground medium
  • ⁇ is the conductivity of the underground medium.
  • G ee is the expression 24):
  • G ee g ee V( ⁇ - ⁇ * )n e 24);
  • the magnetic field generated by the center current J I of the discrete element of the abnormal body in the footprint at the measuring point can be regarded as the magnetic field generated in the air by a uniform underground electric dipole source.
  • the secondary magnetic field generated by the underground unit electric dipole source at the measuring point is expressed as expression 26)-28):
  • g em is the Green's function linking the underground current in a uniform half-space with the magnetic field at the measuring point of the aeronautical device.
  • the calculation of matrices g ee and g em in Expression 21) and Expression 32) includes Bessel integrals of the first kind, and such integral calculation requires a lot of time. Fortunately, the truncated boundary vector finite element method guided by the footprint of the present invention can be reused in subsequent stations after the matrix g ee and g em are calculated for the first station. As shown in Figure 7, the calculation area of the first station is a solid line frame, and the calculation area of the second station is a dashed frame.
  • the relative positional relationship between the discrete units within the calculation area of the second station and the boundary of the calculation area can be determined from the The relative positional relationship between the discrete unit within the calculation area of a station and the boundary of the calculation area can be found accordingly.
  • the second station can use the g ee of the first station.
  • the positional relationship between the discrete unit in the calculation area of the second station and the measurement point of the second station can be found in the position relationship between the discrete unit and the measurement point of the first station in the calculation area of the first station.
  • the second station can use the g em of the first station.
  • subsequent stations can reuse the matrices g ee and g em generated in the calculation process of the first station, which greatly speeds up the calculation of the secondary magnetic field response of the subsequent station.
  • the invention calculates a one-dimensional layered model, which has verified the calculation accuracy of the invention.
  • the aviation electromagnetic method uses the device shown in Figure 2, the transmitting coil and the receiving coil are separated by 7.5m, and the transmitting source receiving device is 40m away from the ground.
  • First use Figure 5 first use a uniform cubic grid to divide a 400 ⁇ 400 ⁇ 100m 3 calculation area, evaluate the secondary magnetic field generated by the discrete unit current in the area at the measuring point and the analytical solution error, so as to determine the area Whether to meet the footprint area requirements.
  • the calculation results show that when using a coaxial device, the excitation current in a volume of 400 ⁇ 400 ⁇ 100m 3 in the x direction of the measuring point has a secondary magnetic field response with a numerical solution error of 0% for the real part and 2% for the imaginary part; when using the same-plane device , The excitation current in the volume of 400 ⁇ 400 ⁇ 100m 3 in the z direction of the measuring point, the real part error of the numerical solution of the secondary magnetic field response is 3%, and the imaginary part error is 2%. Therefore, it is judged that the volume of 400 ⁇ 400 ⁇ 100m 3 is the footprint area of the aerial electromagnetic method device.
  • the dashed frame in Figure 6 is the footprint area of the aerial electromagnetic method device, and the internal line frame No.
  • Table 3 is the calculation area of the layered medium model by the truncated boundary vector finite element method guided by the footprint.
  • Table 1 shows the accuracy comparison between the numerical solution and the analytical solution of the truncated boundary vector finite element method (the method of the present invention) guided by the layered model footprint under different device forms. From the data in Table 1, it can be seen that under different device forms, the errors of the real and imaginary parts of the values are kept within 5%, which meets the accuracy requirements of the aviation electromagnetic method.
  • Hsx is the calculation result of the magnetic field in the x direction
  • Hsz is the calculation result of the magnetic field in the z direction.
  • the present invention calculates a relatively complex three-dimensional model to verify the high efficiency and accuracy of the present invention for the calculation of complex geological models.
  • the complex model is shown in Figure 8. There are two jagged low-resistance anomalies with different electrical conductivity underground.
  • the calculation area is shown in box No. 1 in Fig. 8.
  • the area size is 405 ⁇ 21 ⁇ 20m 3 , and the 3 ⁇ 3 ⁇ 4m 3 network is selected.
  • the grid is divided into the area.
  • the second station is located at 727.5m.
  • the mesh of the first station is moved 4 units to the left to obtain the calculation area of the second station.
  • subsequent stations move the grid one after another.
  • the calculation area is shown in the second box in Figure 8.
  • the calculation area of the model includes two anomalous conductive bodies and the wrapping layer.
  • the calculation area is shown in the third box in Figure 8.
  • the calculation area size is 834 ⁇ 21 ⁇ 20m 3
  • Table 2 compares the calculation efficiency of the method of the present invention and the traditional truncated boundary vector finite element method in calculating the data of the single station of the model.
  • the data in Table 2 show that the degree of freedom of the equations formed by the truncated boundary vector finite element method guided by the footprint, the required Green's function, and the calculation time are significantly less than the traditional truncated boundary vector finite element method.
  • the Green's function between the electric field of the element inside the contact area and the electric field of the boundary node in the two methods can be stored in a matrix form.
  • the truncated boundary vector finite element method guided by the footprints calculates the relative position of the area and the receiving device every time, it only needs to calculate the Green's function linking the electric field of the unit inside the calculation area with the magnetic field of the receiving point, which greatly reduces the calculation time.
  • Figures 9a, 9b, 10a and 10b show the numerical comparison between the truncated boundary vector finite element method based on a relatively complex three-dimensional model and the footprint guided truncated boundary vector finite element method (the present invention).
  • the calculated results of the secondary magnetic field response of the measuring point are plotted in parts per million (ppm) of the full-space magnetic field of the emission source, and the two methods are compared.
  • the real and imaginary parts of the horizontal magnetic field (Hsx) and vertical magnetic field (Hsz) calculated by the footprint-guided truncated boundary vector finite element method are the same as those of the traditional truncated boundary vector finite element method.
  • the results are consistent. This result further verifies that the calculation result of the present invention is correct and has universal applicability.
  • Step 1 Take a cube of the same size with a side length of 4m as the unit body, and divide the grid into 50 grids in the x and y axis directions and 25 grids in the z axis direction with the underground projection of the emission source as the center. 100 ⁇ 100 ⁇ 25 scale grid, the calculation area size is 400 ⁇ 400 ⁇ 100m 3 .
  • Step 2 Calculate the excitation current of the emission source in the center of the discrete grid within 400 ⁇ 400 ⁇ 100m 3 ; calculate the secondary magnetic field generated by the excitation current of the emission source in the center of each discrete grid at the receiving point, and combine the grids The magnetic field generated by the internal current at the measuring point is superimposed to form a numerical solution of the magnetic field at the measuring point.
  • Step 3 Calculate the analytical solution of the magnetic field generated by the uniform half-space underground medium at the measuring point, and use the analytical solution as the standard to calculate the numerical solution error.
  • the error is within 5%, and the footprint area of the aviation electromagnetic device is determined to be 400 ⁇ 400 ⁇ 100m 3 .
  • Step 4 Cut the infinitely extending low-resistance plate-shaped model into a finite-volume plate-shaped body of 400 ⁇ 400 ⁇ 4m 3.
  • the footprint-guided truncated boundary vector finite element method defines the calculation area as 400 ⁇ 400 ⁇ 12m 3 , and uses 4 ⁇ 4 ⁇ 4m 3 grid division.
  • Step 5 Use the truncated boundary vector finite element method to calculate the scattered current at the center of the discrete element in the area of 400 ⁇ 400 ⁇ 12m 3.
  • Step 6 Calculate the magnetic field generated by the scattered current from the center of the discrete unit in the 400 ⁇ 400 ⁇ 12m 3 area at the measuring point, and superimpose the magnetic field generated by each unit to obtain the numerical solution of the truncated boundary vector finite element method guided by the layered model footprint.

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Abstract

L'invention concerne un procédé de simulation numérique pour une étude électromagnétique aéroportée à haute efficacité guidée par empreinte. Le procédé comprend les étapes consistant à : diviser une région d'étude électromagnétique aéroportée à l'aide de grilles uniformes ; augmenter progressivement le nombre d'unités uniformes, et déterminer une taille d'empreinte d'un dispositif d'observation d'étude électromagnétique aéroportée ; calculer un courant de diffusion existant dans une empreinte d'une première station d'étude à l'aide d'un procédé d'élément fini de vecteur de limite tronqué, et stocker une fonction de Green obtenue à partir du calcul dans cette étape ; calculer une réponse de champ électromagnétique générée à un premier point d'étude par le courant de diffusion à l'intérieur de l'empreinte obtenue dans l'étape précédente, et mémoriser une fonction de Green obtenue à partir du calcul dans cette étape ; et répéter les deux étapes ci-dessus pour une station d'étude ultérieure. Dans la présente invention, le calcul est effectué pour une région d'étude successivement pour des empreintes de stations d'étude individuelles, réduisant ainsi de façon significative une région de calcul. De plus, l'invention utilise des grilles uniformes pour le partitionnement pour permettre à une fonction de Green d'être utilisée de façon répétée pour une station d'étude ultérieure lors de l'utilisation du procédé d'élément fini de vecteur de limite tronqué, ce qui permet d'améliorer considérablement l'efficacité de calcul pour des stations d'étude ultérieures.
PCT/CN2020/093495 2019-10-12 2020-05-29 Procédé de simulation numérique pour étude électromagnétique aéroportée à haute efficacité guidée par empreinte WO2021068527A1 (fr)

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