An efficient method for solving the electromagnetic field of the radiation source layer in a layered lossy medium

Abstract

The present invention relates to an efficient solution method for the electromagnetic field of the radiation source layer in a layered lossy medium. The secondary field is obtained by selecting the amplitude coefficient from the interface of the radiation layer, and then the electromagnetic field of the radiation source layer is obtained by superimposing it with the background field. Since the amplitude coefficient from the interface of the radiation layer has the smallest difference, the method has low requirements on the integration interval and the number of sampling points, and the background field can be directly obtained through theoretical formulas. Compared with the traditional method, the overall required memory and time are also greatly reduced, and the calculation efficiency is higher. The present invention reduces the calculation cost of the electromagnetic field of the radiation source layer in the layered lossy medium, improves the solution rate of the model, and thus ensures the efficient development of research such as marine electromagnetic detection. Compared with the traditional method, this method has a faster solution speed and lower requirements on computing resources.

Description

Technical Field

[0001] The invention belongs to electromagnetic field modeling and simulation, and relates to an efficient solution method for the electromagnetic field of a radiation source layer in a layered lossy medium. Background Art

[0002] The layered lossy medium model is widely used in marine electromagnetic detection, magnetotelluric forward modeling, underwater electromagnetic wave propagation characteristics and other studies due to its simple structure and clear physical properties. In these studies, the transceiver devices are mostly located in the same horizontal layer. Therefore, in order to ensure its smooth implementation, it is necessary to achieve efficient and accurate solution of the electromagnetic field in the radiation layer of the layered lossy medium model.

[0003] At present, the solution methods of layered lossy medium model are mainly divided into three categories: analytical approximation method, semi-analytical method and numerical method. Among them, the analytical approximation method obtains the approximate analytical solution under specific conditions by approximating the Sommerfeld integral equation. This method has a fast solution speed but is limited by the approximate conditions when applied; the numerical method refers to the finite difference method or the finite element method, which meshes the electromagnetic parameters in the model and solves the electromagnetic field based on the Maxwell equation. This type of method can solve electromagnetic waves in complex environments, but the calculation cost is high; the semi-analytical method numerically solves the Sommerfeld integral equation in the analytical solution. While ensuring accuracy and versatility, it also requires relatively few computing resources, so it is widely used.

[0004] However, unlike lossless media, electromagnetic waves have absorption losses in lossy media, which makes the upper and lower wave amplitudes of the received electromagnetic field in the radiation layer differ greatly, and the singularity of the radiation source makes the difference in wave amplitude in the radiation layer more prominent. In order to ensure the accuracy of the solution, the Sommerfeld integration interval must be expanded and the number of sampling points must be increased, which will greatly increase the solution cost of the electromagnetic field in the radiation source layer. Therefore, it is necessary to propose a method to reduce the solution cost and improve the solution efficiency.

[0005] In order to reduce the computational cost of the electromagnetic field of the radiation source layer in a layered lossy medium, improve the solution rate while ensuring the accuracy of the results, and ensure the efficient development of research such as marine electromagnetic detection, the method of the present invention is proposed.

[0006] Since the amplitude coefficients of the received electromagnetic field in the layered lossy medium radiation source layer vary greatly, the difficulty and cost of solving the traditional method are greatly increased. Summary of the invention

[0007] Technical issues to be solved

[0008] In order to avoid the shortcomings of the prior art, the present invention proposes an efficient solution method for the electromagnetic field of the radiation source layer in a layered lossy medium, the purpose of which is to reduce the computational cost of the electromagnetic field of the radiation source layer in a layered lossy medium, improve the solution rate of the model, and thus ensure the efficient development of research such as marine electromagnetic detection. Compared with traditional methods, this method has a faster solution speed and lower requirements for computing resources.

[0009] The main contents of the present invention are:

[0010] 1) According to the layered lossy medium model, the amplitude coefficient of the electromagnetic field in the radiation layer is solved, and some amplitude coefficients from the radiation source are discarded, while those from the upper and lower interfaces are retained, which are substituted into the electromagnetic field solution equation. Then, the Sommerfeld integral in the equation is solved using the direct method or the fast Fourier method. The electromagnetic field obtained is the secondary field composed of the side wave and the reflected wave. Since the amplitude coefficients selected have the smallest difference, there is no need to increase the integration interval and the number of sampling points, so the requirements for computing resources are relatively low, and the efficiency is also improved.

[0011] 2) Based on the field strength calculation formula generated by the radiation source in free space and combined with the electromagnetic parameters of the radiation source layer, the background field generated by the radiation source is solved.

[0012] 3) The calculated results of the secondary field and the background field in 1) and 2) are vector-added to obtain the electromagnetic field of the radiation source layer in the layered lossy medium.

[0013] Technical Solution

[0014] An efficient method for solving the electromagnetic field of a radiation source layer in a layered lossy medium is characterized by the following steps:

[0015] Step 1: The electromagnetic field in the radiation layer of the layered lossy medium model is expressed as the superposition of TE waves and TM waves, and the electromagnetic field expression of each component in the electromagnetic field is established;

[0016] Step 2: According to the boundary conditions of the electromagnetic field, the propagation matrix and the type of dipole antenna, the amplitude coefficient of the radiation layer when z ≥ 0 is obtained as:

[0017]

[0018] In the formula, IS is the magnetic dipole moment;

[0019] and the amplitude coefficient of the radiation layer when z≤0;

[0020]

[0021] Step 3: Select A with the smallest amplitude difference 0+ ,B 0- and C 0+ , D0- In the input electromagnetic field expression, each component electromagnetic field is solved to obtain the secondary field generated by the radiation layer interface of the component;

[0022] Step 4: Perform vector addition of the secondary field and the background field to obtain each component of the total electromagnetic field in the radiation layer.

[0023] The three-layer lossy medium model: the thickness of the 1st layer to the -1st layer is infinite; the 0th layer is the layer where the radiation source is located, the thickness is d, the radiating antenna is the horizontal magnetic dipole HMD, and the distance from the upper interface of the 0th layer is d1; the receiving point P is located in the cylindrical coordinate with the center of the HMD as the origin μ l ,ε l ,σ l They are the magnetic permeability, dielectric constant and conductivity of the lth (l=-1,0,1) layer respectively.

[0024] When the radiation source solved in step 1 is a horizontal magnetic dipole HMD, the expressions of the components of the electromagnetic field in the radiation layer are:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Where A0, B0, C0 and D0 are the amplitude coefficients of TM waves and TE waves in the radiation layer respectively; is the first-order Hankel function of the first kind; for The derivative of η; ξ0 satisfies The expression of the propagation constant k0 in the radiation layer is:

[0032] The secondary field in step 3 is:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] Each component of the total electromagnetic field in step 4 is:

[0040]

[0041]

[0042]

[0043] The background field is obtained directly from the theoretical formula:

[0044]

[0045] An application of an efficient solution method for the electromagnetic field of a radiation source layer in a layered lossy medium, characterized in that the secondary field of the radiation source layer is obtained by selecting the amplitude coefficient with the smallest amplitude difference, and then the total electromagnetic field of the radiation source layer is obtained after vector superposition with the background field; it is used to ensure the efficient development of marine electromagnetic detection research.

[0046] Beneficial Effects

[0047] The invention proposes an efficient solution method for the electromagnetic field of the radiation source layer in a layered lossy medium, which solves the problem of high calculation cost and low solution efficiency of the electromagnetic field of the radiation layer of the layered lossy medium. This method can realize low-cost and rapid solution of the electromagnetic field in the radiation layer of the lossy medium, which is conducive to the efficient development of research such as marine electromagnetic detection.

[0048] Innovation: Since the amplitude coefficients of the electromagnetic field in the radiation layer in the lossy medium model vary greatly, the traditional method needs to increase the integration interval and the number of sampling points to ensure the accuracy of the results, which will reduce the efficiency of solving the electromagnetic field in the radiation layer. Different from the calculation process of the traditional method, the method proposed in this application obtains the secondary field by selecting the amplitude coefficient from the radiation layer interface, and then superimposes it with the background field to obtain the electromagnetic field of the radiation source layer. Since the amplitude coefficients from the radiation layer interface differ the least, this method has lower requirements for the integration interval and the number of sampling points, and the background field can be directly obtained through theoretical formulas. Compared with the traditional method, the overall memory and time required are also greatly reduced, and the calculation efficiency is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 :Schematic diagram of three-layer lossy medium model

[0050] Among them, the thickness of layer 1 and layer -1 are both infinite; layer 0 is the layer where the radiation source is located, with a thickness of d, and the radiating antenna is a horizontal magnetic dipole (HMD), and the distance from the upper interface of layer 0 is d1; the receiving point P is located in the cylindrical coordinates with the center of the HMD as the origin μ l ,ε l ,σ l They are the magnetic permeability, dielectric constant and conductivity of the lth (l=-1,0,1) layer respectively.

[0051] Figure 2 :Comparison of TM wave amplitude coefficients in the radiation layer

[0052] (a) Real part, (b) Imaginary part. The curve in the figure shows the amplitude coefficients of TM waves in the radiation layer as a function of the integral variable k. ρ By comparing the changes in the amplitude coefficient A from the radiation source, we can find 0+ and B 0- The real and imaginary parts of are both greater than A from the upper and lower interfaces of the radiation layer. 0- and B 0+ Several orders of magnitude.

[0053] Figure 3 :Comparison of TM wave amplitudes in the radiation layer

[0054] The figure shows the amplitude ratio of the TM wave received in the radiation layer. As the receiving depth and the integral variable change, it can be seen from the figure that the amplitude ratio varies greatly, especially when the receiving point is near the plane where the radiation source is located, the TM wave amplitude difference exceeds 10 200 times or more.

[0055] Figure 4 :Comparison of electromagnetic field components obtained by this method and traditional methods under different integration intervals and sampling points

[0056] (a) Different integration intervals, number of sampling points 2 20 , (b) Different sampling points, integration interval [-4,4]. The figure takes the electromagnetic field components calculated by the finite element method as a reference, and shows the curves of the change of the electromagnetic field component intensity with horizontal distance calculated by this method and the traditional method under different integration intervals and sampling points. It can be seen from the figure that under the same number of sampling points, when the integration interval is small, the error of the traditional method is large, while this method maintains good accuracy in all integration intervals; the results obtained under the same integration interval and different sampling points are also similar.

[0057] Figure 5 :Comparison of computing resources required by this method and traditional methods

[0058] The figure shows the comparison of computing resources (memory, time) required for this method and traditional methods under the premise of ensuring the accuracy of the results through a bar graph. It can be found from the figure that under the simulation conditions in this application, this method can reduce more than 90% of the memory requirements and computing time compared with traditional methods. DETAILED DESCRIPTION

[0059] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0060] The present invention proposes an efficient solution method for the electromagnetic field of the radiation source layer in a layered lossy medium. The technical solution adopted can be divided into the following four steps:

[0061] 1. Solution of the amplitude coefficient of electromagnetic waves in the radiation layer of lossy media

[0062] like Figure 1 The figure shows a three-layer lossy medium model. The electromagnetic field in the radiation layer can be expressed as the superposition of TE waves and TM waves. When the radiation source is a horizontal magnetic dipole (HMD), the expression of each electromagnetic field component in the radiation source layer is:

[0063]

[0064] Where A0, B0, C0 and D0 are the amplitude coefficients of TM waves and TE waves in the radiation layer respectively; is the first-order Hankel function of the first kind; for The derivative of η; ξ0 satisfies The expression of the propagation constant k0 in the radiation layer is:

[0065] According to the boundary conditions, propagation matrix and dipole antenna type, the amplitude coefficient of the radiation layer when z ≥ 0 can be obtained as:

[0066]

[0067] In the formula, IS is the magnetic dipole moment.

[0068] When z≤0, the amplitude coefficient of the radiation layer is:

[0069]

[0070] like Figure 2 As shown in the figure, the amplitude coefficients of TM waves in the radiation layer vary greatly, among which A 0+ and B 0- is the amplitude coefficient from the radiation source, which is greater than A from the upper and lower interfaces of the radiation layer. 0- and B 0+ Several orders of magnitude. Figure 3As shown in Figure 1, due to the existence of absorption loss in the lossy medium, the ratio of the amplitudes of the uplink and downlink waves near the plane where the radiation source is located reaches 10 200 If the traditional method is used, A 0+ and B 0+ or A 0- and B 0- If we directly substitute into (1) to accurately solve the electromagnetic field, we must increase the integration interval and the number of sampling points, which will greatly increase the computational cost and reduce the solution efficiency.

[0071] 2. Solution of the secondary field generated by the upper and lower interfaces of the radiation layer

[0072] In order to reduce the computational cost and improve the efficiency of the algorithm, this method discards the amplitude coefficient from the radiation source and uses the A with the smallest amplitude difference. 0+ ,B 0- and C 0+ ,D 0- Solve the electromagnetic field. Since these four amplitude coefficients all represent the waves from the radiation layer interface, they are the superposition fields of the side waves and the reflected waves, that is, the secondary fields generated by the radiation layer interface, and their expressions are as follows:

[0073]

[0074] 3. Solution of background field generated by radiation source

[0075] The background field refers to the electromagnetic field generated by the radiation source in free space. The electromagnetic field parameters in free space are the same as those in the emission layer. The background field can be directly obtained from the theoretical formula, and the expression is as follows:

[0076]

[0077] 4. Calculate the total field of received electromagnetic waves

[0078] Combining the secondary field and background field in (4) and (5), the components of the total electromagnetic field in the radiation layer can be obtained as follows:

[0079]

[0080] Compared with the traditional method, this method only adds the calculation of the background field, but greatly reduces the requirements for the integration interval and the number of sampling points in the solution process, thereby reducing the calculation cost and improving the efficiency of the algorithm.

[0081] Embodiment Invention verification:

[0082] Taking a three-layer lossy medium model with a horizontal magnetic dipole antenna as a radiation source as an example, an example of the present invention is given. In order to verify the correctness and effective performance of the present invention, the inventors conducted a confirmatory theoretical simulation.

[0083] The simulation conditions are as follows: the radiation source is located in the second layer, 20m away from the interface between the 1st and 2nd layers, and the magnetic dipole moment of the antenna is 10A·m 2 , the height of the receiving point relative to the radiation source is 10m, the signal frequency is 10kHz, and the electromagnetic parameters in each layer of the medium are shown in Table 1. The positions of the radiation source and the receiving point under the simulation conditions are suitable for the constraints of the present invention.

[0084] Table 1 Electromagnetic parameters in each layer of medium

[0085]

[0086] all in all:

[0087] 1. The solution method is simple and clear

[0088] In the solution method proposed in this application, the background field can be obtained by theoretical formulas, and the secondary field is solved by directly selecting the amplitude coefficients of the upper and lower interfaces in the radiation layer, which reduces the difference in amplitude coefficients used to solve the electromagnetic field in the radiation layer. The whole process is simple and the physical meaning is clear.

[0089] 2. Feasibility of the solution

[0090] like Figure 4 As shown in , the electromagnetic fields obtained by the traditional method under higher integration intervals and sampling points are consistent with those obtained by the finite element method, while the present solution method can obtain accurate results under all conditions, which shows that the present method is feasible.

[0091] 3. Efficiency of the solution method

[0092] like Figure 5 As shown, under the premise of ensuring the accuracy of the results, this method is superior to other methods in terms of required computing space and time, which shows that this method requires less computing resources and has higher computing efficiency.

[0093] 4. According to the implementation examples:

[0094] The proposed method for efficiently solving the electromagnetic field of the radiation source layer in a layered lossy medium is feasible. While ensuring the accuracy of the calculation results, it reduces the demand for computing resources and improves the calculation efficiency. In addition, compared with the traditional method, this method only adds the solution of the background field, and the selection of the amplitude coefficient for calculating the electromagnetic field also corresponds to the principle of generating the secondary field. The whole process is simple and the physical meaning is clear.

Claims

1. An efficient method for solving the electromagnetic field of the radiation source layer in a layered lossy medium, characterized by Here are the steps: Step 1: The electromagnetic field in the radiation layer of the layered lossy medium model is expressed as the superposition of TE waves and TM waves, and the electromagnetic field expression of each component in the electromagnetic field is established; The layered lossy medium model has three layers of lossy medium models: the thickness of the 1st layer to the -1st layer is infinite; the 0th layer is the layer where the radiation source is located, the thickness is d, the radiating antenna is a horizontal magnetic dipole HMD, and the distance from the upper interface of the 0th layer is d1; the receiving point P is located in the cylindrical coordinates with the center of the HMD as the origin μ l ,ε l ,σ l are the magnetic permeability, dielectric constant, and conductivity of the lth (l = -1, 0, 1) layer respectively; Step 2: According to the boundary conditions of the electromagnetic field, the propagation matrix and the type of dipole antenna, the amplitude coefficient of the radiation layer when z ≥ 0 is obtained as: In the formula, IS is the magnetic dipole moment; and the amplitude coefficient of the radiating layer when z≤0; Step 3: Select A with the smallest amplitude difference 0+ ,B 0- and C 0+ , D 0- In the input electromagnetic field expression, each component electromagnetic field is solved to obtain the secondary field generated by the radiation layer interface of the component; Step 4: Perform vector addition of the secondary field and the background field to obtain each component of the total electromagnetic field in the radiation layer.

2. The method for efficiently solving the electromagnetic field of the radiation source layer in the layered lossy medium according to claim 1, characterized in that: When the radiation source solved in step 1 is a horizontal magnetic dipole HMD, the expressions of the components of the electromagnetic field in the radiation layer are: Where A0, B0, C0 and D0 are the amplitude coefficients of TM waves and TE waves in the radiation layer respectively; is the first-order Hankel function of the first kind; for The derivative of η; ξ0 satisfies The expression of the propagation constant k0 in the radiation layer is:

3. The efficient solution method for the electromagnetic field of the radiation source layer in the layered lossy medium according to claim 1 is characterized by: The secondary field in step 3 is:

4. The method for efficiently solving the electromagnetic field of the radiation source layer in the layered lossy medium according to claim 1, characterized in that: Each component of the total electromagnetic field in step 4 is:

5. The method for efficiently solving the electromagnetic field of the radiation source layer in the layered lossy medium according to claim 1, characterized in that: The background field is obtained directly from the theoretical formula:

6. An application of the method for efficiently solving the electromagnetic field of a radiation source layer in a layered lossy medium as claimed in any one of claims 1 to 5, characterized in that The secondary field of the radiation source layer is obtained by selecting the amplitude coefficient with the smallest amplitude difference, and then the total electromagnetic field of the radiation source layer is obtained by vector superposition with the background field; it is used to ensure the efficient development of marine electromagnetic detection research.

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