A method for anisotropic ionospheric very low frequency scattering at low altitude based on transfer matrix method

Abstract

The present invention belongs to the field of electromagnetic wave technology, and discloses a very low frequency scattering method of anisotropic ionosphere in medium and low altitude based on the transmission matrix method. The present invention establishes a low ionosphere layered model structure considering the anisotropy of the ionosphere. First, the transmission matrix of the anisotropic layered structure is derived and verified. Then, based on the transmission matrix, the scattering characteristics of the very low frequency electromagnetic waves in the above-mentioned ionosphere layered structure under different conditions are accurately calculated, and the propagation law is summarized. This work provides a reliable calculation model for the propagation of very low frequency in the low and medium ionosphere, and greatly improves the accuracy of its propagation and scattering parameter calculation. This has important guiding and reference value for studying the propagation of very low frequency electromagnetic waves in the atmosphere.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic waves, and in particular relates to a medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on a transmission matrix method. Background Art

[0002] Very low frequency (VLF) radio waves (3kHz–30kHz) are widely used in ultra-long-range navigation, communication, and earthquake prediction. The United States' Omega and Russia's Alpha systems are the most typical VLF navigation systems. VLF radio waves are a type of electromagnetic wave that propagates in the global "ground ionosphere" waveguide formed by the Earth's surface and the lower ionosphere. Due to the anisotropic dielectric properties of the lower ionosphere and its complex spatiotemporal variations, it is challenging to accurately predict its propagation characteristics, especially during periods of abnormal solar activity. The lower ionosphere and VLF propagation still lack more accurate algorithms, which has become a research hotspot in recent years.

[0003] The study of the propagation characteristics of very low frequency radio waves can be traced back to the 1960s. The classic absorption curve given by Helliwell (1965) calculated the energy attenuation of very low frequency waves passing through the ionosphere. This model was used by Inan (1984), Abel and Thorne (1998) and Starks (2008). Helliwell (1965) adopted an ionospheric D region model that is average and does not vary with latitude. However, the actual ionospheric D region electron density does vary with latitude and season, and undergoes complex physical changes. Therefore, this model is only suitable for preliminary qualitative analysis of some very low frequency electromagnetic wave propagation examples.

[0004] Considering that in the VLF band, the dielectric parameters of the lower ionosphere vary dramatically within a wavelength range, the ray theory is not applicable. However, it is possible to consider idealizing the ionosphere as a horizontally layered medium and using the full-wave solution method to obtain the solution. Budden (1985) summarized the early methods and pointed out that many of them faced challenges in maintaining numerical stability. Lehtinen and Inan (2009) improved the full-wave solution method, but the results still showed that the model's predictions greatly exceeded the very low frequency wave intensity measured at satellite altitude, magnifying the shortcomings of the model's low accuracy. Swati (2021) and Forrest (2021) both considered using the International Reference Ionosphere (IRI) model to simulate the reflection parameters of the lower ionosphere and verified the feasibility of the very low frequency band under the IRI model. Richardson and Cohen studied the seasonal changes in the D-region ionosphere and proposed a very low frequency propagation model based on machine learning.

[0005] Through the above analysis, the problems and defects of the prior art are as follows:

[0006] More accurate algorithms are still lacking for lower ionosphere and VLF propagation. Summary of the invention

[0007] In view of the problems existing in the prior art, the present invention provides a medium and low altitude anisotropic ionospheric very low frequency scattering method based on a transmission matrix method.

[0008] The present invention is achieved in that a medium and low altitude anisotropic ionospheric very low frequency scattering method based on a transmission matrix method comprises:

[0009] Step 1, the ionospheric anisotropy layered model structure of the lower ionosphere was established;

[0010] Step 2, the transmission matrix of the anisotropic layered structure is derived and verified;

[0011] Step three, based on the transmission matrix, calculate the scattering characteristics of very low frequency electromagnetic waves in the ionospheric layered structure under different conditions.

[0012] Further, the method for establishing the low ionosphere layered model structure of ionosphere anisotropy is as follows:

[0013] The ionosphere is divided into N layers with fixed thickness; the effective dielectric constant of each layer is expressed as a tensor, denoted as [εij] and [μij]; from the ground to the upper boundary of the ionosphere of 150 kilometers, it is divided into N layers according to altitude; ξ represents the direction cosines of the Earth's magnetic field, and the coordinate system is defined in the x, y, and z directions; represents the angle between the Earth's magnetic field and the z-axis, and φ represents the angle between the positive magnetic north and the positive x-axis.

[0014]

[0015] Furthermore, the dielectric constant tensor of each layer of the ionosphere can be expressed as:

[0016]

[0017] Where M is the electrical susceptibility matrix of each layer of the ionosphere, which is determined by the electron density and collision frequency in the ionosphere;

[0018]

[0019] represents the plasma angular frequency of the layer, ω represents the radio wave angular frequency of the layer, e represents the electron charge, Ne represents the electron density of the layer, ε0 represents the dielectric constant of air, ω H =eB0 / m e represents the electron rotation angular frequency, and υ represents the collision frequency of this layer.

[0020] Further, the transfer matrix method:

[0021] An N-layer anisotropic dielectric structure material, each layer shows electromagnetic anisotropy, and its dielectric constant and magnetic permeability can be expressed in tensor form: [εij], [μij] (i, j = 1, 2, 3); the thickness of each layer is equal to d; the electromagnetic wave is obliquely incident from free space into the structure, and its incident angle is θ, and the incident plane is the xoz plane; the eigenvalue equation of the electromagnetic field in the n-th layer of material can be obtained;

[0022]

[0023] The matrix A is:

[0024]

[0025] In the above formula, ε ij , μ ij (i, j = 1, 2, 3 ...) represents the electromagnetic parameters of this layer of material, and δ = sinθ; γ(M) represents the eigenvalue of equation (4), W(M) (a 4 × 4 matrix) represents its eigenvector, where: γ(M) = [γ(M)1, γ(M)2, γ(M)3, γ(M)4], and γ(M)1 = -γ(M)3, γ(M)2 = -γ(M)4; the field distribution in the material of the Mth layer region is:

[0026]

[0027] It is known that in the above formula, η=120π, the elements of the diagonal matrix X(M) are X(M)(j, j)=exp(k0γ(M)j(z+(M-1)d)), (j=1,2,3,4); G can be expressed as G(j, j)=exp(k0(xδ)); in the formula, u(M)1, v(M)1 and u(M)2, v(M)2 represent the amplitudes of the up and down waves of the first type wave and the up and down waves of the second type wave in the material M respectively;

[0028] It is deduced that the field distribution in the M-1th layer and the M+1th layer adjacent to the Mth layer of material can be expressed as:

[0029] Q=W(M)·X(M)·W(M)-1·P (6)

[0030] The total transmission matrix from layer 1 to layer N is:

[0031] T=T(1)×T(2)×…T(N-1)×T(N) (7)

[0032] In the above formula, the eigenvector in free space is:

[0033]

[0034] Where β = cosθ;

[0035] The relationship between the field in free space at z = -Nd and the field at z = 0 is:

[0036]

[0037] Then we have:

[0038]

[0039] In the above formula

[0040] Define the following relationship:

[0041]

[0042] The reflection matrix R can be obtained from equation (8);

[0043]

[0044] Furthermore, the R matrix represents a generalized reflection coefficient including multiple optical reflection processes.

[0045] Further, the method verification of the transfer matrix method is:

[0046] The layered medium is composed of layers of high refractive index (n3) and low refractive index (n2) films; the thickness of the high refractive index film is h3, the thickness of the low refractive index film is h2, and the refractive index of the entire film is n1; assume that all media are non-magnetic; therefore, the characteristic matrix M of the multilayer medium M is 2N (Nh) is as follows:

[0047]

[0048] in:

[0049]

[0050] The reflectance calculated by optical method is as follows:

[0051]

[0052] At the same time, according to the equivalent medium theory, if the thickness of the film is much smaller than the wavelength, the periodic multilayer film material can be equivalent to a uniaxial anisotropic medium, and the equivalent dielectric constant is ε = [εs, εs, εz,]; the total thickness of the material before and after the equivalence remains unchanged;

[0053]

[0054] Another object of the present invention is to provide a medium-low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method for implementing the medium-low altitude anisotropic ionospheric very low frequency scattering method based on the transmission matrix method as claimed in any one of claims 1 to 6, characterized in that the medium-low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method comprises:

[0055] Model module, used to establish the structure of the lower ionosphere layered model with ionospheric anisotropy;

[0056] Verification module, used to derive and verify the transmission matrix of anisotropic layered structures;

[0057] The calculation module is used to calculate the scattering characteristics of very low frequency electromagnetic waves in the ionosphere layered structure under different conditions based on the transmission matrix.

[0058] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method.

[0059] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method.

[0060] Another object of the present invention is to provide an information data processing terminal, which is used to implement the medium and low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method.

[0061] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0062] First, the present invention establishes a low ionosphere layered model structure that takes into account the anisotropy of the ionosphere. First, the transmission matrix of the anisotropic layered structure is derived and verified. Then, based on the transmission matrix, the scattering characteristics of the very low frequency electromagnetic waves in the above-mentioned ionosphere layered structure under different conditions are accurately calculated, and the propagation law is summarized. This work provides a reliable calculation model for the propagation of very low frequency in the lower ionosphere, and greatly improves the accuracy of its propagation and scattering parameter calculation. This has important guiding and reference value for studying the propagation of very low frequency electromagnetic waves in the atmosphere.

[0063] Second, the technical problems in the prior art solved by the present invention and the significant technical progress achieved are as follows:

[0064] Technical issues:

[0065] 1. The existing ionospheric scattering research methods fail to fully consider the anisotropic characteristics of the mid- and low-altitude ionosphere, resulting in deviations between the calculated results and the actual situation.

[0066] 2. When dealing with multi-layer ionospheric structures, traditional calculation methods have complex calculation processes and large amounts of calculation, making it difficult to obtain accurate results.

[0067] Technological advancements:

[0068] 1. The present invention establishes an ionospheric anisotropic low ionosphere layered model structure, fully considering the anisotropic characteristics of the medium and low altitude ionosphere, so that the calculation results are closer to the actual situation.

[0069] 2. By deriving and verifying the transmission matrix of the anisotropic layered structure, the calculation process of the multi-layer ionospheric structure is simplified, the amount of calculation is reduced, and the calculation efficiency is improved.

[0070] 3. The present invention calculates the scattering characteristics of very low frequency electromagnetic waves in the ionospheric layered structure under different conditions based on the transmission matrix method, which can more accurately predict and analyze the propagation characteristics of electromagnetic waves in the ionosphere, and provide strong support for related communication and detection technologies.

[0071] The present invention introduces the transfer matrix method to deal with the very low frequency scattering problem of the anisotropic ionosphere in the medium and low altitudes, which not only improves the accuracy and efficiency of the calculation, but also promotes the technical progress in the field of ionospheric scattering research.

[0072] Third, the present invention proposes a solution based on the transfer matrix method for the problem of anisotropic ionospheric very low frequency scattering in the medium and low altitudes. This technology solves several key problems in the prior art and brings about significant technological progress, which is mainly reflected in the following aspects:

[0073] ###Existing technical problems solved:

[0074] 1) Simplification of ionosphere model: Traditional ionosphere models often ignore its anisotropic characteristics, resulting in inaccurate calculation results. The present invention reflects the physical characteristics of the ionosphere more realistically by establishing a low ionosphere layered model structure with ionosphere anisotropy.

[0075] 2) Low computational efficiency: When dealing with multi-layer medium scattering problems, traditional methods usually need to calculate the scattering characteristics of each layer separately, which is computationally intensive and inefficient. The present invention introduces the transfer matrix method to calculate the scattering characteristics of the entire multi-layer medium at one time, greatly improving the computational efficiency.

[0076] 3) Difficulty in experimental verification: Due to the particularity of the ionospheric environment, traditional experimental verification methods are difficult to apply directly. The present invention provides an effective verification method for the study of ionospheric scattering characteristics through theoretical derivation and mathematical simulation.

[0077] ###Significant technological progress achieved:

[0078] 1) High-precision model: By establishing an ionospheric anisotropic low-ionosphere layered model structure, the present invention can more accurately simulate the physical characteristics of the ionosphere and provide a more accurate model basis for the scattering research of very low frequency electromagnetic waves.

[0079] 2) Efficient calculation method: By adopting the transfer matrix method, the present invention can calculate the overall scattering characteristics of the multi-layer medium at one time, avoiding the tedious process of layer-by-layer calculation in the traditional method and greatly improving the calculation efficiency.

[0080] 3) Wide applicability: The present invention is not only applicable to the study of ionospheric scattering problems in medium and low altitudes, but can also be extended to the study of other multi-layer medium scattering problems, and has wide applicability.

[0081] 4) Experimental verification feasibility: Through theoretical deduction and mathematical simulation, the present invention provides an effective verification method for the study of ionospheric scattering characteristics, overcoming the difficulties of experimental verification in traditional methods.

[0082] In summary, the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method proposed in the present invention not only solves the key problems in the prior art, but also brings significant technological progress, and provides new ideas and methods for the study of ionospheric scattering characteristics.

[0083] Fourth, the present invention solves multiple technical problems of the prior art through mathematical models and achieves significant technical progress. The following is a detailed explanation:

[0084] ###Existing technical problems solved:

[0085] 1) Insufficient model accuracy: Traditional ionospheric scattering models often ignore the anisotropic characteristics of the ionosphere, resulting in insufficient model accuracy and failure to accurately describe the actual scattering behavior of the ionosphere. The present invention significantly improves the accuracy of the model by constructing an ionospheric anisotropic low ionosphere layered model structure and deriving the corresponding transmission matrix.

[0086] 2) Low computational efficiency: For multi-layer dielectric structures, traditional computational methods usually require calculating the scattering characteristics of electromagnetic waves layer by layer, which is not only computationally intensive but also inefficient. The present invention uses the transfer matrix method to calculate the scattering characteristics of the multi-layer dielectric as a whole at one time, greatly reducing the amount of computation and improving computational efficiency.

[0087] 3) Difficulty in experimental verification: Due to the particularity of the ionospheric environment, there are many difficulties in experimentally verifying the ionospheric scattering model. The present invention provides an effective verification method through mathematical models and theoretical derivation, which can verify the accuracy of the model without relying on experimental conditions.

[0088] ###Significant technological progress achieved:

[0089] 1) High-precision model: The mathematical model of the present invention takes into account the anisotropic characteristics of the ionosphere. By constructing a low-ionosphere layered model structure and combining it with the transfer matrix method, it can more accurately describe the scattering behavior of the ionosphere, providing a high-precision model basis for the transmission and scattering research of very low frequency electromagnetic waves.

[0090] 2) Efficient calculation method: The transfer matrix method adopted in the present invention not only simplifies the calculation process, but also improves the calculation efficiency. By calculating the overall scattering characteristics of multi-layer media at one time, the tedious process of layer-by-layer calculation in the traditional method is avoided, providing an efficient calculation method for the study of ionospheric scattering characteristics.

[0091] 3) Wide applicability: The mathematical model of the present invention is not only applicable to the study of ionospheric scattering problems in the middle and low altitudes, but can also be extended to the study of scattering problems in other multi-layer media. By adjusting the model parameters and the transmission matrix, it can adapt to scattering problems in different scenarios and has wide applicability.

[0092] 4) Feasibility of experimental verification: Through mathematical models and theoretical derivation, the present invention provides an effective verification method for the study of ionospheric scattering characteristics. This verification method does not depend on experimental conditions and can be verified under different parameter settings, which improves the feasibility and flexibility of experimental verification.

[0093] In summary, the present invention solves multiple technical problems of the prior art through mathematical models, achieves significant technical progress, and provides new ideas and methods for the study of ionospheric scattering characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 It is a flow chart of a medium and low altitude anisotropic ionospheric very low frequency scattering method based on a transfer matrix method provided in an embodiment of the present invention.

[0095] Figure 2 It is a structural block diagram of a medium- and low-altitude anisotropic ionospheric very low frequency scattering system based on a transfer matrix method provided in an embodiment of the present invention.

[0096] Figure 3 It is a schematic diagram of a horizontal layered ionosphere model provided by an embodiment of the present invention.

[0097] Figure 4It is a schematic diagram of the structure of a multi-layer anisotropic thin film medium provided by an embodiment of the present invention.

[0098] Figure 5 1 is a graph of calculated reflection coefficients provided by an embodiment of the present invention. (a) Multilayer isotropic periodic medium before equivalence. (b) Equivalent multilayer anisotropic periodic medium.

[0099] Figure 6 The following are the results of calculations provided by the embodiments of the present invention. (a) A curve showing the reflection coefficient of a periodic layered medium changing with frequency at vertical incidence. (b) A curve showing the reflection coefficient of a periodic layered medium changing with frequency at oblique incidence.

[0100] Figure 7 This is a diagram of an IRI data export interface provided by an embodiment of the present invention.

[0101] Figure 8 It is a curve diagram of the reflection coefficient R11 changing with frequency under different limited thicknesses provided by an embodiment of the present invention.

[0102] Fig. 9 The electron density changes with altitude curves provided by the embodiments of the present invention are as follows: (a) The electron density changes with altitude curves during winter daytime and nighttime. (b) The electron density changes with altitude curves during summer and winter nighttime.

[0103] Fig.10 1. The reflection coefficient varies with frequency according to the embodiment of the present invention. (a) The reflection coefficient varies with frequency during the day and night in summer. (b) The reflection coefficient varies with frequency in summer and winter.

[0104] Fig.11 The collision frequency provided by the embodiment of the present invention is 107s -1 ,106s -1 and 105s -1 R11 change curve.

[0105] Fig.12 1 is a frequency variation curve provided by an embodiment of the present invention. (a) R11 variation curve when the incident angle is 0°, 30° and 60°. (b) R22 variation curve when the incident angle is 0°, 30° and 60°.

[0106] Fig.13 1 is a graph showing the change of the reflection coefficient R11 with the incident angle provided by the embodiment of the present invention. (a) A graph showing the change of R11 with the frequency when the incident angle is 0°, 30°, 60° and 75°. (b) A graph showing the change of R22 with the frequency when the incident angle is 0°, 30°, 60° and 75°. DETAILED DESCRIPTION

[0107] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0108] The following are two specific application examples of the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method:

[0109] Application Example 1: Single Frequency Very Low Frequency Scattering Simulation

[0110] Evaluate the scattering effect of a single frequency Very Low Frequency (VLF) signal through an anisotropic ionosphere.

[0111] 1) Model establishment:

[0112] Build an ionosphere model consisting of 5 layers, each with a thickness of 30 km.

[0113] The electron density and collision frequency of each layer are set according to actual observation data.

[0114] 2) Parameter setting:

[0115] Select a VLF signal with a fixed frequency, such as 30kHz.

[0116] Set the geomagnetic field parameters, for example, the angle between the geomagnetic field direction and the ground is 45 degrees.

[0117] 3) Transmission matrix calculation:

[0118] The transmission matrix is ​​calculated from the permittivity and permeability tensors of each layer.

[0119] The total transfer matrix from the first layer to the last layer is calculated using matrix multiplication.

[0120] 4) Scattering characteristics analysis:

[0121] By calculating the propagation of electromagnetic waves in the ionosphere, its scattering characteristics are analyzed.

[0122] Calculate and plot the attenuation and phase change of a signal.

[0123] The simulation results help us understand the propagation characteristics of single-frequency VLF signals under specific ionospheric conditions and provide a reference for further communication system design.

[0124] Application Example 2: Multi-frequency VLF scattering impact assessment

[0125] The scattering characteristics of VLF signals of various frequencies passing through the ionosphere are analyzed to study the effect of frequency on scattering.

[0126] 1) Ionosphere model:

[0127] An ionospheric model consisting of 10 layers with different dielectric constants and magnetic permeabilities is designed to simulate the real ionospheric environment.

[0128] The electron density and collision frequency of each layer are adjusted according to seasonal changes.

[0129] 2)Multi-frequency setting:

[0130] Different frequencies ranging from 10kHz to 100kHz were selected for testing.

[0131] Different incident angles are set to simulate the situation where the signal enters the ionosphere from different directions.

[0132] 3) Transmission matrix and scattering calculation:

[0133] The transmission matrix is ​​calculated for each frequency separately.

[0134] Analyze the scattering characteristics of electromagnetic waves of each frequency in the ionosphere.

[0135] 4) Comprehensive analysis:

[0136] Compare the scattering effects of different frequencies, including signal attenuation and phase shift.

[0137] The implications of the results for VLF communication system design are discussed.

[0138] This embodiment provides a deep understanding of the scattering characteristics of very low frequency signals of different frequencies in the ionosphere, which helps to optimize frequency selection and signal design in long-distance communications.

[0139] These two embodiments demonstrate how to evaluate the scattering characteristics of very low frequency signals in the ionosphere through numerical simulation methods, providing a theoretical basis and practical application guidance for communication technology.

[0140] The following are two specific embodiments of the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transmission matrix method:

[0141] Embodiment 1:

[0142] In a very low frequency communication experiment, it is necessary to predict the propagation characteristics of electromagnetic waves in the medium and low altitude ionosphere. According to the method of the present invention, firstly, an anisotropic low ionosphere layered model structure of the ionosphere is established, the ionosphere is divided into several layers according to the height, and the tensor form of the dielectric constant and permeability of each layer is considered. Then, the scattering characteristics of electromagnetic waves at different incident angles, different frequencies and different polarization modes are calculated using the derived transmission matrix of the anisotropic layered structure. By comparing the experimental results with the theoretical calculations, it is found that the calculation results of the present invention are highly consistent with the actual situation, and can accurately predict the propagation characteristics of electromagnetic waves in the ionosphere, providing an important reference for the design and optimization of very low frequency communication systems.

[0143] Embodiment 2:

[0144] In an ionospheric detection mission, it is necessary to analyze the scattering of very low frequency electromagnetic waves in the ionosphere. According to the method of the present invention, an anisotropic layered model of the ionosphere is first established, taking into account the differences in dielectric constant and magnetic permeability between different layers. Then, the transmission matrix of electromagnetic waves in the ionosphere is calculated using the transmission matrix method, and the scattering characteristics of electromagnetic waves in the ionosphere are obtained. By analyzing the calculation results, the researchers found the phenomenon of enhanced scattering at certain specific frequencies and incident angles, which helps to further understand the physical properties of the ionosphere and the propagation mechanism of electromagnetic waves. At the same time, these results also provide new ideas and methods for the development of ionospheric detection technology.

[0145] Example 3: Space communication link optimization

[0146] In the process of designing and optimizing space communication links, the low-altitude anisotropic ionospheric very low frequency scattering method based on the transmission matrix method can effectively improve the stability and reliability of communication. This embodiment specifically includes the following steps:

[0147] 1. Model establishment: According to the needs of space communication, a low-ionosphere layered model structure with ionospheric anisotropy is established. The model needs to take into account the actual space environment and the characteristics of the ionosphere, such as electron density, electromagnetic anisotropy, etc.

[0148] 2. Derivation of the transmission matrix: Based on the actual communication wavelength, the transmission matrix of the anisotropic layered structure suitable for the space communication link is derived to ensure that the model can accurately simulate the propagation and scattering of electromagnetic waves in the ionosphere.

[0149] 3. Scattering characteristics analysis: Use the transfer matrix method to calculate the very low frequency electromagnetic wave scattering characteristics in the ionosphere, provide a theoretical basis for communication link design, optimize link parameters, and ensure communication quality.

[0150] This embodiment is of great significance for the design and optimization of communication systems in deep space exploration missions, and can enhance the robustness of communication links and improve signal transmission efficiency.

[0151] Example 4: Polar Science Research Station Communication Support

[0152] In the communication support of polar scientific research stations, due to the extreme geographical environment and complex ionospheric conditions, the scattering method can effectively optimize the communication link. The specific steps include:

[0153] 1. Model establishment: Considering the unique geomagnetic field configuration and ionosphere characteristics of the polar regions, an anisotropic layered model for the polar ionosphere is established, and the electromagnetic parameters of each layer are described in detail.

[0154] 2. Application of transmission matrix: Based on the characteristics of the polar ionosphere, the transmission matrix is ​​derived to accurately calculate the propagation and scattering behavior of very low frequency electromagnetic waves in extreme environments.

[0155] 3. Communication link optimization: By analyzing the scattering characteristics under different conditions, we can guide the setting and adjustment of the polar research station communication system, such as the placement of antennas and the selection of communication frequency bands, to ensure the reliability and stability of the communication link.

[0156] This embodiment makes a significant contribution to improving the efficiency and stability of polar scientific research communications, ensuring that polar scientific researchers can transmit research data in a timely and effective manner and maintain communication with the outside world.

[0157] like Figure 1 As shown, a medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on a transmission matrix method provided by an embodiment of the present invention comprises the following steps:

[0158] S101, the structure of the layered model of the lower ionosphere with ionospheric anisotropy was established;

[0159] S102, the transmission matrix of anisotropic layered structures was derived and verified;

[0160] S103, calculating the scattering characteristics of very low frequency electromagnetic waves in the ionospheric layered structure under different conditions based on the transmission matrix.

[0161] The method for establishing a low ionosphere layered model structure for ionosphere anisotropy provided in an embodiment of the present invention is as follows:

[0162] The ionosphere is divided into N layers with fixed thickness; the effective dielectric constant of each layer is expressed as a tensor, denoted as [εij] and [μij]; from the ground to the upper boundary of the ionosphere of 150 kilometers, it is divided into N layers according to altitude; ξ represents the direction cosines of the Earth's magnetic field, and the coordinate system is defined in the x, y, and z directions; represents the angle between the Earth's magnetic field and the z-axis, and φ represents the angle between the positive magnetic north and the positive x-axis.

[0163]

[0164] The dielectric constant tensor of each layer of the ionosphere provided by the embodiment of the present invention can be expressed as:

[0165]

[0166] Where M is the electrical susceptibility matrix of each layer of the ionosphere, which is determined by the electron density and collision frequency in the ionosphere;

[0167]

[0168] represents the plasma angular frequency of the layer, ω represents the radio wave angular frequency of the layer, e represents the electron charge, Ne represents the electron density of the layer, ε0 represents the dielectric constant of air, ω H =eB0 / m e represents the electron rotation angular frequency, and υ represents the collision frequency of this layer.

[0169] The transmission matrix method provided by the embodiment of the present invention:

[0170] An N-layer anisotropic dielectric structure material, each layer shows electromagnetic anisotropy, and its dielectric constant and magnetic permeability can be expressed in tensor form: [εij], [μij] (i, j = 1, 2, 3); the thickness of each layer is equal to d; the electromagnetic wave is obliquely incident from free space into the structure, and its incident angle is θ, and the incident plane is the xoz plane; the eigenvalue equation of the electromagnetic field in the n-th layer of material can be obtained;

[0171]

[0172] The matrix A is:

[0173]

[0174] In the above formula, ε ij , μ ij (i, j = 1, 2, 3 ...) represents the electromagnetic parameters of this layer of material, and δ = sinθ; γ(M) represents the eigenvalue of equation (4), W(M) (a 4 × 4 matrix) represents its eigenvector, where: γ(M) = [γ(M)1, γ(M)2, γ(M)3, γ(M)4], and γ(M)1 = -γ(M)3, γ(M)2 = -γ(M)4; the field distribution in the material of the Mth layer region is:

[0175]

[0176] It is known that in the above formula, η=120π, the elements of the diagonal matrix X(M) are X(M)(j, j)=exp(k0γ(M)j(z+(M-1)d)), (j=1,2,3,4); G can be expressed as G(j, j)=exp(k0(xδ)); in the formula, u(M)1, v(M)1 and u(M)2, v(M)2 represent the amplitudes of the up and down waves of the first type wave and the up and down waves of the second type wave in the material M respectively;

[0177] It is deduced that the field distribution in the M-1th layer and the M+1th layer adjacent to the Mth layer of material can be expressed as:

[0178] Q=W(M)·X(M)·W(M)-1·P (6)

[0179] The total transmission matrix from layer 1 to layer N is:

[0180] T=T(1)×T(2)×…T(N-1)×T(N) (7)

[0181] In the above formula, the eigenvector in free space is:

[0182]

[0183] Where β = cosθ;

[0184] The relationship between the field in free space at z = -Nd and the field at z = 0 is:

[0185]

[0186] Then we have:

[0187]

[0188] In the above formula

[0189] Define the following relationship:

[0190]

[0191] The reflection matrix R can be obtained from equation (8);

[0192]

[0193] The R matrix provided in the embodiment of the present invention represents a generalized reflection coefficient including multiple optical reflection processes.

[0194] Method verification of the transfer matrix method provided by the embodiment of the present invention:

[0195] The layered medium is composed of layers of high refractive index (n3) and low refractive index (n2) films; the thickness of the high refractive index film is h3, the thickness of the low refractive index film is h2, and the refractive index of the entire film is n1; assume that all media are non-magnetic; therefore, the characteristic matrix M of the multilayer medium M is 2N (Nh) is as follows:

[0196]

[0197] in:

[0198]

[0199] The reflectance calculated by optical method is as follows:

[0200]

[0201] At the same time, according to the equivalent medium theory, if the thickness of the film is much smaller than the wavelength, the periodic multilayer film material can be equivalent to a uniaxial anisotropic medium, and the equivalent dielectric constant is ε = [εs, εs, εz,]; the total thickness of the material before and after the equivalence remains unchanged;

[0202]

[0203] like Figure 2 As shown, a medium- and low-altitude anisotropic ionospheric very low frequency scattering system based on a transmission matrix method provided by an embodiment of the present invention includes:

[0204] Model module, used to establish the structure of the lower ionosphere layered model with ionospheric anisotropy;

[0205] Verification module, used to derive and verify the transmission matrix of anisotropic layered structures;

[0206] The calculation module is used to calculate the scattering characteristics of very low frequency electromagnetic waves in the ionosphere layered structure under different conditions based on the transmission matrix.

[0207] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method.

[0208] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method.

[0209] Another object of the present invention is to provide an information data processing terminal, which is used to implement the medium and low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method.

[0210] The present invention is specifically implemented:

[0211] 1. The present invention establishes a low ionosphere layered model structure taking into account the anisotropy of the ionosphere. First, the transmission matrix of the anisotropic layered structure is derived and verified. Then, based on the transmission matrix, the scattering characteristics of the very low frequency electromagnetic waves in the above-mentioned ionosphere layered structure under different conditions are accurately calculated, and the propagation law is summarized. This work provides a reliable calculation model for the propagation of very low frequency in the lower ionosphere, and greatly improves the accuracy of its propagation and scattering parameter calculation. This has important guiding and reference value for studying the propagation of very low frequency electromagnetic waves in the atmosphere.

[0212] 2. Construction of ionospheric model

[0213] Considering the significant variation of electromagnetic parameters with altitude, the ionosphere is divided into horizontally layered inhomogeneous media. The ionosphere is divided into N layers with a fixed thickness

[18] . The effective dielectric constant of each layer is expressed as a tensor, denoted as [εij] and [μij]. From the ground to the upper boundary of the ionosphere (150 km), it is divided into N layers according to altitude. Here, ξ represents the direction cosines of the geomagnetic field, and the coordinate system is defined in the x, y, and z directions. represents the angle between the Earth's magnetic field and the z-axis, and φ represents the angle between the positive magnetic north and the positive x-axis.

[0214]

[0215] The dielectric constant tensor of each layer of the ionosphere can be expressed as

[0216]

[0217] where M is the electrical susceptibility matrix of each layer of the ionosphere, which is determined by the electron density and collision frequency in the ionosphere.

[0218]

[0219] Here. represents the plasma angular frequency of the layer, ω represents the radio wave angular frequency of the layer, e represents the electron charge, Ne represents the electron density of the layer, ε0 represents the dielectric constant of air, ω H =eB0 / m e represents the electron rotation angular frequency, and υ represents the collision frequency of this layer.

[0220] like Figure 3As shown in Figure 1, the ionosphere is considered as a layered anisotropic medium model. In the following chapters, the principle of the transfer matrix method will be used to systematically explain the model and derive the transfer matrix applicable to any anisotropic medium.

[0221] 3. Transfer Matrix Method

[0222] In the study of the anisotropic ionosphere, the electromagnetic propagation in anisotropic multilayer structures is analyzed in depth. Since the electromagnetic parameters of anisotropic multilayer media behave as tensors, they bring complexity to the electromagnetic fields within the structure, making the calculation of its electromagnetic properties a challenging task. To address this complexity, the concept of the transmission matrix is ​​utilized. This enables the detailed derivation of the electromagnetic wave transmission properties of multilayer structures containing arbitrary anisotropic materials. This is achieved through a comprehensive analysis and calculation of various anisotropic media.

[0223] like Figure 4 As shown in the figure, there is an N-layer anisotropic dielectric structure material, each layer shows electromagnetic anisotropy, so its dielectric constant and magnetic permeability can be expressed in tensor form: [εij], [μij] (i, j = 1, 2, 3). And the electromagnetic parameters between different media are expressed in different arbitrary tensor forms. For simplicity, it is assumed that the thickness of each layer is equal to d. Now the electromagnetic wave is obliquely incident from free space into the structure, with an incident angle of θ and an incident plane of the xoz plane. The eigenvalue equation of the electromagnetic field in the nth layer of material can be obtained.

[0224]

[0225] The matrix A is:

[0226]

[0227] In the above formula, ε ij , μ ij (i, j = 1, 2, 3...) represents the electromagnetic parameters of this layer of material, and δ = sinθ.

[0228] γ(M) represents the eigenvalue of equation (4), W(M) (a 4×4 matrix) represents its eigenvector, where: γ(M) = [γ(M)1, γ(M)2, γ(M)3, γ(M)4], and γ(M)1 = -γ(M)3, γ(M)2 = -γ(M)4. Therefore, the field distribution in the material of the Mth layer region can be written as:

[0229]

[0230] It is known that in the above formula, η = 120π, the elements of the diagonal matrix X(M) are X(M)(j, j) = exp(k0γ(M)j(z+(M-1)d)), (j = 1, 2, 3, 4); G can be expressed as G(j, j) = exp(k0(xδ)); in the formula, u(M)1, v(M)1 and u(M)2, v(M)2 represent the amplitudes of the up and down waves of the type I wave and the up and down waves of the type II wave in the material M respectively.

[0231] Similarly, it can be deduced that the field distribution in the M-1th layer and the M+1th layer adjacent to the Mth layer of material can be expressed as:

[0232] Q=W(M)·X(M)·W(M)-1·P (6)

[0233] Therefore, the matrix T(M) = W(M) · X(M) · W(M)-1 determines the field relationship on the two interfaces, so T(M) is called the transmission matrix of the Mth layer of the medium. For multi-layer medium structure materials, the transmission matrix connects the fields on any two medium interfaces. Therefore, as long as the transmission matrix of each layer of transmission medium is multiplied, the total transmission matrix of the multi-layer structure material can be obtained. That is, the total transmission matrix from the 1st layer to the Nth layer is:

[0234] T=T(1)×T(2)×…T(N-1)×T(N) (7)

[0235] In the above formula, the eigenvector in free space is:

[0236]

[0237] Where β = cosθ.

[0238] Since there is only a transmitted wave and no reflected wave at z = 0, the relationship between the field in free space at z = -Nd and the field at z = 0 is:

[0239]

[0240] Then we have:

[0241]

[0242] In the above formula

[0243] Define the following relationship:

[0244]

[0245] The reflection matrix R can be obtained from equation (8).

[0246]

[0247] The matrix R represents the generalized reflection coefficients including multiple optical reflection processes. In this matrix, there are four elements, all of which are complex. R11 and R22 represent the reflection coefficients of type I wave reflected to type I wave and type II to type II in a medium, respectively. R12 and R21 express the relationship coefficients of the mutual conversion between type I and type II reflected waves. These coefficients reflect the coupling characteristics between type I and type II waves.

[0248] Method validation

[0249] The correctness of the algorithm is verified by using the characteristics of periodic media and the principle of equivalent media. This rare layered medium consists of layers of high refractive index (n3) and low refractive index (n2) films. The thickness of the high refractive index film is h3, the thickness of the low refractive index film is h2, and the refractive index of the entire film is n1. Assume that all media are non-magnetic. Therefore, the characteristic matrix M of the multilayer medium M is 2N (Nh) is as follows:

[0250]

[0251] in:

[0252]

[0253] The reflectance calculated by optical method is as follows:

[0254]

[0255] At the same time, according to the equivalent medium theory, if the thickness of the film is much smaller than the wavelength, the periodic multilayer film material can be equivalent to a uniaxial anisotropic medium, and the equivalent dielectric constant is ε = [εs, εs, εz,]. The total thickness of the material remains unchanged before and after the equivalence.

[0256]

[0257] The reflection coefficient can be obtained by substituting the equivalent dielectric constant into the transmission matrix method in the previous section.

[0258] In the study of , a multilayer periodic medium was designed, such as Figure 5 As shown in Figure 2. For the two methods of calculating the reflection coefficient, two different methods are used: the optical method and the transfer matrix method. The results of these calculations are shown in Figure 2. Figure 6 It is worth noting that the results obtained from the two methods show a considerable degree of consistency, which provides strong support for the effectiveness and correctness of the transfer matrix method in this study.

[0259] 4. Numerical calculation and analysis

[0260] 4.1. Layer thickness selection

[0261] In actual radio wave propagation, the VLF band mainly depends on the lower ionosphere, and the dielectric parameters of the lower ionosphere change dramatically within the height range of one wavelength of VLF. Therefore, choosing the appropriate layering method, especially the layering thickness, is a key part of the calculation.

[0262] Ideally, a more detailed ionosphere model makes it closer to reality, resulting in higher calculation accuracy. However, this comes at the expense of increased computational complexity. In practical use, it is crucial to strike a balance between computational efficiency and accuracy to obtain the best solution. Taking a specific time and location as an example, the range of the lower ionosphere altitude is 60 km to 150 km. Based on the IRI model, the data acquisition interface is as follows: Figure 7 As shown, the ionospheric parameters with layer thickness d of 0.3km, 0.5km, 1km, 5km and 10km were obtained respectively. The model was established and the reflection coefficient R11 was calculated. R11 represents the modulus of R11, which is the absolute value of the reflection coefficient of type I wave reflected to type I wave.

[0263] like Figure 8 As shown in the figure, with other factors unchanged, as the thickness d decreases, the calculation results gradually converge. When d drops to 1 km or less, the reflection coefficient curves are basically consistent. Considering the calculation efficiency and the resistance to numerical overflow, it is reasonable to set the layer thickness d to 1 km.

[0264] 4.2 Calculation results and analysis

[0265] Once the thickness of the ionospheric model layer is determined, this section will proceed to build a model, calculate the reflection coefficient and study the VLF propagation law. Ionospheric parameters include electron density and collision frequency, while geomagnetic parameters include geomagnetic intensity, geomagnetic inclination and magnetic declination. These parameters vary with geographical location, altitude, season and local time. Therefore, the ionospheric parameters in the present invention are obtained based on the calculation results of the International Geomagnetic Reference Field (IGRF) and IRI.

[0266] like Fig. 9 As shown in Figure 1, the ionosphere height increases by about 20km at night. At the same height, the electron density in the lower ionosphere is much higher at night in winter than during the day. This phenomenon is related to direct sunlight. The stronger the solar radiation, the more active the ionosphere, resulting in a higher electron density.

[0267] from Fig.10 It can be seen that the reflection coefficient at night is significantly lower than that during the day, and the reflection coefficient in summer is slightly lower than that in winter. According to the electron density diagram, a higher electron density corresponds to a higher reflection coefficient. In other words, the propagation efficiency of the VLF band during the day is higher than that at night, and the propagation effect is better in summer than in winter.

[0268] When studying the effect of collision frequency on reflection coefficient, the geomagnetic inclination is fixed at 45°, the incident angle θ is 30°, and the collision frequency is 10 7 s -1 , 10 6 s -1 , 10 5 s - 1. On the other hand, when studying the effect of the incident angle on the reflection coefficient, the frequency was fixed at 5 kHz and the collision frequency was 10 6 s -1 , the incident angles are 0°, 30° and 60° respectively.

[0269] The main diagonal element R11 of the reflection matrix represents the reflection coefficient of TM wave reflected to TM wave, and R22 represents the reflection coefficient of TE wave reflected to TE wave.

[0270] like Fig.11 As shown in Figure 2, as the electron collision frequency and the incident wave frequency increase, the reflection coefficient R11 decreases. 5 s -1 Increase to 10 6 s -1 When the reflection coefficient decreases significantly, it indicates that the more active the ionosphere is, the worse the reflection effect of the ionosphere on electromagnetic waves in the VLF band is.

[0271] like Fig.12 As shown in the figure, the reflection coefficient of TM wave decreases with the increase of incident angle, while TE wave shows the opposite trend. This phenomenon is related to the polarization direction of the two electromagnetic waves.

[0272] Assume that the incident angle is the angle between the geomagnetic field and the vertical direction, which is complementary to the geomagnetic inclination. Fig.13 As shown in the figure, the reflection coefficient R11 increases as the incident angle increases from 0° to 180°. When the incident angle range is 0°-90°, the reflection coefficient increases as the incident angle increases and reaches a maximum value at 90°. This shows that the reflection effect is best at the magnetic equator and worst at the magnetic pole. For TE waves, when the incident angle changes, the reflection coefficient versus frequency curve is always a straight line, that is, the geomagnetic inclination has almost no effect on the reflection coefficient. The reflection coefficient of TE waves increases with the increase of the incident angle, which is opposite to the performance of TM waves. Fig.12 The trends shown are consistent.

[0273] In actual calculations, it is found that the values ​​of R12 and R21 in the reflection matrix are very small and can be ignored. In the VLF band, the coupling between TE waves and TM waves is minimal.

[0274] The present invention derives a transmission matrix method based on the full-wave method and establishes a more accurate anisotropic ionosphere model. Through calculation and verification, a more suitable layering method is determined. Through specific examples, the reflection coefficient of VLF band electromagnetic waves in the low ionosphere is calculated. The influence of incident wave frequency, incident angle, geomagnetic inclination, frequency, ionospheric electron density and electron collision frequency on the propagation of ionospheric radio waves is studied. This provides valuable insights for satellite navigation and very low frequency communications. However, this article still lacks consideration of the curvature of the earth, which will be further addressed in the future.

[0275] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0276] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A medium and low altitude anisotropic ionospheric very low frequency scattering method based on a transfer matrix method, characterized in that: The following steps are involved: Step 1, the ionospheric anisotropy layered model structure of the lower ionosphere was established; Step 2, the transmission matrix of the anisotropic layered structure is derived and verified; Step 3, based on the transmission matrix, calculate the scattering characteristics of very low frequency electromagnetic waves in the ionospheric layered structure under different conditions; The transfer matrix method: An N-layer anisotropic dielectric structure material, each layer shows electromagnetic anisotropy, and its dielectric constant and magnetic permeability can be expressed in tensor form: [εij], [μij], i, j = 1, 2, 3; the thickness of each layer is equal to d; the electromagnetic wave is obliquely incident from free space into the structure, and its incident angle is θ, and the incident plane is the xoz plane; the eigenvalue equation of the electromagnetic field in the n-th layer of material can be obtained; The matrix A is: In the above formula, ε ij , μ ij , i, j = 1, 2, 3, ..., represents the electromagnetic parameters of this layer of material, and δ = sinθ; γ(M) represents the eigenvalue of equation (4); W(M) represents its eigenvector, which is a 4 × 4 matrix, where: γ(M) = [γ(M)1, γ(M)2, γ(M)3, γ(M)4], and γ(M)1 = -γ(M)3, γ(M)2 = -γ(M)4; The field distribution in the material of the Mth layer region is: It is known that in the above formula, η=120π, the elements of the diagonal matrix X(M) are X(M)(j, j)=exp(k0γ(M)j(z+(M-1)d)), j=1,2,3,4; G can be expressed as G(j, j)=exp(k0(xδ)); in the formula, u(M)1, v(M)1 and u(M)2, v(M)2 represent the amplitudes of the up and down waves of the first type wave and the up and down waves of the second type wave in the material M respectively; It is deduced that the field distribution in the M-1th layer and the M+1th layer adjacent to the Mth layer of material can be expressed as: Q=W(M)·X(M)·W(M)-1·P(6) The total transmission matrix from layer 1 to layer N is: T=T(1)×T(2)×…T(N-1)×T(N)(7) In the above formula, the eigenvector in free space is: Where β = cosθ; The relationship between the field in free space at z = -Nd and the field at z = 0 is: Then we have: In the above formula Define the following relationship: The reflection matrix R can be obtained from equation (8); The R matrix represents the generalized reflection coefficients including multiple optical reflection processes; Method validation of the transfer matrix method: The layered medium is composed of layers of high refractive index (n3) and low refractive index (n2) films; the thickness of the high refractive index film is h3, the thickness of the low refractive index film is h2, and the refractive index of the entire film is n1; assume that all media are non-magnetic; therefore, the characteristic matrix M of the multilayer medium M is 2N (Nh) is as follows: in: The reflectance calculated by optical method is as follows: At the same time, according to the equivalent medium theory, if the thickness of the film is much smaller than the wavelength, the periodic multilayer film material can be equivalent to a uniaxial anisotropic medium, and the equivalent dielectric constant is ε = [εs, εs, εz,]; the total thickness of the material before and after the equivalence remains unchanged; 2. The medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method as claimed in claim 1, characterized in that: The method for constructing the low ionosphere layered model with ionosphere anisotropy is as follows: The ionosphere is divided into N layers with fixed thickness; the effective dielectric constant of each layer is expressed as a tensor, denoted as [εij] and [μij]; from the ground to the upper boundary of the ionosphere of 150 kilometers, it is divided into N layers according to altitude; ξ represents the direction cosines of the Earth's magnetic field, and the coordinate system is defined in the x, y, and z directions; represents the angle between the Earth's magnetic field and the z-axis, and φ represents the angle between the positive magnetic north and the positive x-axis.

3. The medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method as claimed in claim 2, characterized in that: The dielectric constant tensor of each layer of the ionosphere can be expressed as: Where M is the electrical susceptibility matrix of each layer of the ionosphere, which is determined by the electron density and collision frequency in the ionosphere; represents the plasma angular frequency of the layer, ω represents the radio wave angular frequency of the layer, e represents the electron charge, Ne represents the electron density of the layer, ε0 represents the dielectric constant of air, ω H =eB0 / m e represents the electron rotation angular frequency, and υ represents the collision frequency of this layer.

4. A medium- and low-altitude anisotropic ionospheric very low frequency scattering system based on the transfer matrix method for implementing the medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method as claimed in any one of claims 1 to 3, characterized in that: The medium and low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method comprises: Model module, used to establish the structure of the lower ionosphere layered model with ionospheric anisotropy; Verification module, used to derive and verify the transmission matrix of anisotropic layered structures; The calculation module is used to calculate the scattering characteristics of very low frequency electromagnetic waves in the ionosphere layered structure under different conditions based on the transmission matrix.

5. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the medium and low altitude anisotropic ionospheric very low frequency scattering method based on the transmission matrix method as described in any one of claims 1 to 3.

6. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the medium- and low-altitude anisotropic ionospheric very low frequency scattering method based on the transfer matrix method as described in any one of claims 1 to 3.

7. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the medium and low altitude anisotropic ionospheric very low frequency scattering system based on the transmission matrix method as described in claim 4.

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