CN114491987B - Modeling method for electromagnetic field during electromagnetic wave propagation in marine multilayer medium - Google Patents
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Abstract
The invention relates to a modeling method of electromagnetic field during electromagnetic wave propagation in a marine multilayer medium, which is a novel modeling method of respectively modeling two layers of medium and then superposing and synthesizing vectors. In the implementation process of the method, for example, when the radiation source is positioned in a seawater medium, modeling calculation is firstly carried out on an air-seawater two-layer medium, then modeling calculation is carried out on the seawater-seabed two-layer medium, and finally vector synthesis is carried out on respective model calculation results, so that the result when three layers of mediums are obtained. In this way, the calculation efficiency, the calculation accuracy and the physical interpretation of the result can be ensured while the modeling complexity is reduced. The results show that: compared with the complex process of electromagnetic wave propagation modeling in the traditional three-layer medium, the model derivation process is simple, the modeling flow is greatly simplified on the premise of ensuring the calculation efficiency and the result accuracy of the model, and all the obtained electric field and magnetic field components have definite physical meanings.
Description
Technical Field
The invention belongs to marine electromagnetic field calculation, and relates to a modeling method of electromagnetic field during electromagnetic wave propagation in a marine multilayer medium.
Background
Data can be transmitted and communicated wirelessly and remotely near the ocean interface using electromagnetic waves. The technology essentially utilizes the fact that when electromagnetic waves propagate in a layered conductive medium, surface wave components and side wave components exist across an interface, so that the propagation distance can be greatly increased (Wang Honglei, the research on the propagation characteristics of the electromagnetic waves across a sea-air interface, doctor's academic paper of northwest university, 2015). The physical phenomenon can be used for realizing wireless data transmission near the sea surface and near the sea bottom, such as wireless data transmission and communication between an underwater navigation body and a sea surface ship, wireless data transmission and communication between sensor nodes distributed at the sea bottom, and the like.
The propagation model of electromagnetic waves near the ocean interface and the calculation of the electromagnetic field intensity are the basic theories for realizing the wireless transmission and communication of data based on the electromagnetic waves. Propagation theory of electromagnetic waves in stratified conductive media is often used for modeling propagation of electromagnetic waves in marine stratified media (R.W.P. King, lateral Electromagnetic Waves: theory and Applications to Communications, geophysical Exploration, and Remote sensing, new York: springer London, limited, 1992). For modeling the propagation of electromagnetic waves in seawater, the space medium is generally divided into three layers of air-seawater-seabed conductive medium, as shown in fig. 1, the transmitting and receiving antennas can be positioned at any position in the three mediums, and the antennas can be in the form of electric dipoles or magnetic dipoles. According to the propagation theory of electromagnetic waves in the layered conductive medium, a Maxwell equation set in three areas (when a radiation source is positioned in a certain layer area, the Maxwell equation of the layer area is provided with more parameters of the radiation source) can be directly written, and then the boundary conditions near the interfaces of the sea surface and the upper layer and the lower layer of the seabed are combined to obtain the radiation electric field and the magnetic field at any position in the three-layer medium.
In general, the electric field and the magnetic field in the space can be obtained by combining the Maxwell equation set in each layer of medium and the boundary conditions near each interface. The two-layer medium is the most basic model, such as when only air-seawater two-layer medium is considered, there is only one interface and both layers are infinite half-spaces. When the number of layers of the medium exceeds two layers, such as the air-seawater-seabed three-layer medium, although the model is more in line with the actual ocean environment, the calculation result is more accurate, the number of solving equations is increased due to the increase of the number of layers, and meanwhile, the electromagnetic field between the layers has coupling influence, so that the difficulty of the model construction and solving process is greatly increased. To obtain the electric field and magnetic field strength, it is often necessary to approximate the expression or increase the computational resources, which may reduce the accuracy or computational efficiency of model calculation. Further, in order to accurately characterize the marine environment and improve the accuracy of model calculations, it is necessary to take into account the non-uniformity of the seawater, which is also considered as a multi-layer medium. The number of layers of the medium in the model constructed under the condition is far greater than three, as shown in fig. 2, the number of equations is more, the coupling between electromagnetic fields of all layers is more complex, the construction difficulty of the model based on the traditional layering theory is approximately increased in an exponential rule, the calculation efficiency and the calculation precision are greatly reduced, and meanwhile, the physical mechanism of electromagnetic field propagation caused by the complex coupling relation of all layers is difficult to explain.
In summary, how to reduce the difficulty of constructing an electromagnetic wave propagation model in a marine layered conductive medium, improve the calculation efficiency and calculation precision, and increase the physical interpretation of the calculation result becomes one of the hot problems in the research of the field.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a modeling method of an electromagnetic field during electromagnetic wave propagation in a marine multilayer medium, and provides a novel modeling method of modeling of two layers of mediums and then vector superposition synthesis for the propagation modeling of electromagnetic waves in an air-seawater-submarine three-layer medium. In the implementation process of the method, for example, when the radiation source is positioned in a seawater medium, modeling calculation is firstly carried out on an air-seawater two-layer medium, then modeling calculation is carried out on the seawater-seabed two-layer medium, and finally vector synthesis is carried out on respective model calculation results, so that the result when three layers of mediums are obtained. In this way, the calculation efficiency, the calculation accuracy and the physical interpretation of the result can be ensured while the modeling complexity is reduced.
Technical proposal
A modeling method of electromagnetic field during electromagnetic wave propagation in a marine multilayer medium is characterized in that: when the sea water depth D is greater than the skin depth delta, i.eWherein: the working frequency f, the seawater conductivity constant sigma and the seawater permeability constant mu are modeled as follows:
step 1, splitting an air-seawater-submarine three-layer medium into two-layer medium models:
1. an electromagnetic wave propagation model is constructed by using two layers of semi-infinite media of air and seawater, and vector potential F 'generated in the seawater' 1z The method comprises the following steps:
wherein ε is 1 Is the dielectric constant of seawater, I m Magnetic dipole moment of dl magnetic dipole, gamma 1 Is propagation constant in sea water, gamma 2 Is propagation constant in air, z is distance from receiving antenna to sea surface, d is distance from transmitting antenna to sea surface, lambda is integral variable, ρ is horizontal distance, J 0 Is a zero-order Bessel function;
2. constructing an electromagnetic wave propagation model by using two layers of semi-infinite media of sea water and seabed to obtain vector potential F' generated in sea water 1z The method comprises the following steps:
wherein D is sea water depth, gamma -1 Is a propagation constant in the sea floor;
step 2: superposing the two-layer medium model to obtain the result of the three-layer medium, and obtaining the vector potential F generated by the vertical magnetic dipole in the sea water in the air-sea water-submarine three-layer medium 1z The method comprises the following steps:
step 3: using the relationship between the vector potential and the electromagnetic field, deriving the expression of the electric field and the magnetic field:
wherein F is a vector potential, E is an electric field, H is a magnetic field, ω is an angular frequency, and v is a rotation operator.
When the radiation source is a horizontal magnetic dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when the three-layer medium is obtained, and a vector potential generated by the horizontal magnetic dipole in the sea water in the air-sea water-submarine three-layer medium is obtained; when the radiation source is a horizontal magnetic dipole, the vector potential has a z-direction component F 1z In addition, there is also an x-direction component F 1x ：
Wherein the method comprises the steps of J is the included angle between the field point and ρ 1 Is a first order Bessel function;
will vector potential F 1z And F 1x And (3) carrying out the step (3) to obtain the expression of the electric field and the magnetic field.
When the radiation source is a vertical electric dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when the three-layer medium is obtained, and a vector magnetic level A generated by the vertical electric dipole in the sea water in the air-sea-seabed three-layer medium is obtained 1z ：
Wherein mu 1 Is the magnetic permeability of sea water, idl is the electric dipole moment of the electric dipole;
will vector magnetic potential A 1z The following expression is taken to obtain the expressions of electric field and magnetic field:
wherein A is vector magnetic potential, E represents electric field, H represents magnetic field, and V is rotation operator.
When the radiation source is a horizontal electric dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when three-layer medium is obtained, and a vector magnetic level generated by the horizontal electric dipole in the sea water in the air-sea water-submarine three-layer medium is obtained; when the radiation source is a horizontal electric dipole, the vector magnetic potential has a z direction component A 1z In addition, there is also an x-direction component A 1x ：
Will vector magnetic potential A 1z And A 1x And carrying the vector magnetic potential and the electromagnetic field into the relational expression of the vector magnetic potential and the electromagnetic field to obtain the expression of the electric field and the magnetic field.
Advantageous effects
The invention provides a modeling method of electromagnetic field during electromagnetic wave propagation in a marine multilayer medium, which is a novel modeling method of respectively modeling two layers of medium and then superposing and synthesizing vectors. In the implementation process of the method, for example, when the radiation source is positioned in a seawater medium, modeling calculation is firstly carried out on an air-seawater two-layer medium, then modeling calculation is carried out on the seawater-seabed two-layer medium, and finally vector synthesis is carried out on respective model calculation results, so that the result when three layers of mediums are obtained. In this way, the calculation efficiency, the calculation accuracy and the physical interpretation of the result can be ensured while the modeling complexity is reduced.
In the invention, the following components are added:
1. the radiation source is positioned in any area of the air or the sea water or the sea floor, and the receiving point is positioned in any area of the air or the sea water or the sea floor. The radiation source may be an electric dipole or a magnetic dipole. The method is applicable under the condition that the sea water depth D is larger than the skin depth delta, namely D is larger than 1/[ pi ] [ mu ] sigma ], wherein pi is a circumference ratio, f is a working frequency (in Hz), mu is a sea water magnetic permeability constant (in H/m), and sigma is a sea water conductivity constant (in S/m).
2. The air-sea water-seabed three-layer medium is divided into an air-sea water two-layer medium and a sea water-seabed two-layer medium. The split air, sea water and sea floor space are all considered semi-infinite space. The remaining parameters were unchanged.
3. Firstly, modeling electromagnetic wave propagation aiming at an air-seawater two-layer medium, wherein the modeling theory adopted is Maxwell equation and boundary conditions at an air-seawater interface. The electric and magnetic field components at any location in air and sea water can be obtained by modeling, for example, when the radiation source is located in a sea water medium.
4. And modeling electromagnetic wave propagation aiming at the seawater-seabed two-layer medium, wherein the modeling theory adopted is Maxwell equation and boundary conditions at the seawater-seabed interface. The electric and magnetic field components at any location in the sea water and the sea floor can be obtained by modeling, for example when the radiation source is located in a sea water medium.
5. And vector superposition is carried out on electric field and magnetic field components in the air, the sea water and the sea bottom obtained by the two models. Note that in the process of superposition: the direct wave component can only be calculated once if the radiation source and the receiving point are located in the same layer of medium.
6. When the three-layer medium of air-sea water-seabed is provided by computer numerical simulation, the performance curves of electric field and magnetic field components generated by a radiation source in sea water are compared with the results of the traditional three-layer medium model, so that the accuracy of the calculation result of the invention is basically not lost, the modeling process is greatly simplified, the calculation efficiency of the model is effectively improved, and the physical mechanism of the result is clarified.
The invention provides a propagation modeling method of electromagnetic waves in an air-seawater-submarine three-layer medium, the principle and the implementation scheme of the method are verified by computer simulation, and the result shows that: compared with the complex process of electromagnetic wave propagation modeling in the traditional three-layer medium, the model derivation process is simple, the modeling flow is greatly simplified on the premise of ensuring the calculation efficiency and the result accuracy of the model, and all the obtained electric field and magnetic field components have definite physical meanings.
Drawings
FIG. 1 is a schematic illustration of electromagnetic wave propagation in an air-seawater-seafloor trilayer medium.
Fig. 2 considers a multi-layer medium after seawater is the non-uniform medium.
Fig. 3 is a schematic diagram of radiation field propagation paths in a three-layer medium.
Fig. 4 is a schematic illustration of a three-layer medium split into two-layer media.
Fig. 5 electromagnetic fields generated in seawater by vertical magnetic dipoles in seawater. a is the electric fieldAnd b is the magnetic field H ρ 。
FIG. 6 is a comparison of the results obtained by the modeling method of the present invention with those obtained by conventional modeling methods. a is the electric fieldAnd b is the magnetic field H ρ 。
Detailed Description
The invention will now be further described with reference to examples, figures:
the invention provides a method for modeling electromagnetic wave propagation in an air-seawater-submarine three-layer medium, which can reduce the complexity of model construction and improve the physical interpretation of results while ensuring the calculation efficiency and the calculation accuracy.
The invention solves the problem of high complexity of electromagnetic wave propagation modeling in an air-seawater-submarine three-layer medium, and the adopted technical scheme can be divided into the following 4 steps:
1) The application range of the technical method of the invention is determined, and the method mainly comprises the sea water depth and the working frequency range.
For the propagation problem of electromagnetic waves in an air-seawater-submarine three-layer medium, the electromagnetic field from the transmitting end to the receiving end is seen to comprise a plurality of propagation paths, and the case of the maximum paths is taken as an example for explanation. When the transmitting end and the receiving end are located in the sea water, the propagation path includes seven types: the schematic diagram of the direct wave, sea surface reflected wave, submarine reflected wave, sea surface side wave, submarine side wave, sea surface multiple reflected wave and sea bottom multiple reflected wave in the sea water is shown in fig. 3. When the areas of the transmitting end and the receiving end are changed, some paths in the seven paths are not present or are changed, for example, when the transmitting end is positioned in sea water and the receiving end is positioned in air, the direct wave path is not present, and the reflected wave paths of the upper interface and the lower interface are changed into the transmitted wave paths. It is the existence of multiple paths that makes the traditional modeling approach quite complex.
As is known, electromagnetic waves are attenuated as they propagate in sea water. The path loss PL (in dB) due to attenuation is positively correlated with the operating frequency f (in Hz) and the propagation distance r (in m). The expression is as follows:
where α is the decay constant, pi is the circumference ratio, μ is the seawater permeability constant (in H/m), and σ is the seawater conductivity constant (in S/m).
When the sea water depth is D, the path loss caused by the sea surface multi-reflection wave and the seabed multi-reflection wave has the following relation,
wherein PL is up Path loss for M reflections from sea surface, PL dw Path loss for N reflections off the ocean floor.
It can be seen that the propagation distances traveled by the two types of path loss are mxd and nxd, respectively. When the sea depth D is large, even if the values of M and N are equal to 1, the values of the two types of path losses are large. That is, the sea surface multiple reflection wave and the sea bottom multiple reflection wave have little contribution to the total field.
Therefore, we agree that when the sea water depth D is greater than the skin depth δ, the sea surface multiple reflection wave and the sea bottom multiple reflection wave are ignored. Therefore, the relation between the sea water depth and the working frequency which is suitable for the method is as follows:
for example, when the working frequency is 1kHz, the sea water depth is only more than 8m, and the method can be applied. Obviously, such sea water depth conditions are readily achieved.
2) After the condition in 1) is satisfied, the air-seawater-subsea three-layer medium is split into two-layer medium models, as shown in fig. 4. The specific contents are as follows:
i. for A in FIG. 4, an air-seawater two-layer semi-infinite medium is used for constructing an electromagnetic wave propagation model
According to the traditional method of the electromagnetic wave propagation theory in the two conductive media, a propagation model of the electromagnetic wave is constructed. The vertical magnetic dipole is illustrated as being located in a seawater medium. The vector potential F 'generated in the seawater can be directly obtained' 1z There is a formula of the following expression,
wherein ε is 1 Is the dielectric constant of seawater, I m Magnetic dipole moment of dl magnetic dipole, gamma 1 Is propagation constant in sea water, gamma 2 The meaning of z and d is marked in FIG. 4A for propagation constant in air, lambda is the integral variable, ρ is the horizontal distance, J 0 Is a zero order bessel function.
Aiming at B in fig. 4, constructing an electromagnetic wave propagation model by using a seawater-seabed two-layer semi-infinite medium
Similar to the method in step i, a propagation model of electromagnetic waves is constructed. For consistency, the vertical magnetic dipole is still illustrated as being in the seawater medium. The vector potential F' generated in the seawater can be directly obtained 1z There is a formula of the following expression,
wherein D is sea water depth, gamma -1 The remaining parameters are the same meaning as in equation (4) for propagation constants in the seafloor.
3) And 2) superposing the results of the two-layer medium model to obtain the results of the three-layer medium.
The vertical magnetic dipole is still described as being located in a seawater medium. Vector superposition of formulas (4) and (5) to obtain vector potential F generated by vertical magnetic dipole in sea water in air-sea water-submarine three-layer medium 1z ，
The meaning of the parameters in the formula is the same as that in the formulas (4) and (5). It is particularly noted that the first term in brackets in the equation is a direct wave component, which is present in both equations (4) and (5), but in practice the direct wave component can only be calculated once, so care should be taken in the superposition process.
4) On the basis of 3), the expression of the electric field and the magnetic field is deduced by utilizing the relation between the vector potential and the electromagnetic field.
Wherein F is a vector potential, E is an electric field, H is a magnetic field, ω is an angular frequency, and v is a rotation operator.
The above assumes that the radiation source is a vertical magnetic dipole and that the radiation source is located in the sea water, an electromagnetic field in the sea water is obtained. When the radiation source is a horizontal magnetic dipole or an electric dipole and is positioned in any area of air, sea water and seabed, the electromagnetic field in any area of air, sea water and seabed is solved, and the same steps as those in 1) to 4) are carried out, except that specific parameters are changed.
Taking a typical magnetic dipole in sea water as an example of radiating an electromagnetic field in sea water, a real-time example of the present invention is given. To verify the effective performance of the present invention, the inventors performed a theoretical simulation of the verifications.
Simulation conditions: air-sea-ocean bottom three-layer medium, the vertical magnetic dipoles in the sea generate electromagnetic fields in the sea. Magnetic dipole moment: 0.7854 A.m 2 The frequency is 100kHz, the sea depth is 100m, the magnetic dipole depth is 5m, and the underwater receiving depth is 2m. Conductivity: sigma (sigma) 1 ＝4(mho/m)，σ 2 ＝0，σ -1 =4e-2 (mho/m). Permeability μ, μ=4ρe-7 (H/m) is the same for all three media. Dielectric constant: epsilon 1 ＝81ε 2 -iσ 1 /ω(F/m)，ε 2 ＝8.85e-12(F/m)，ε -1 ＝8ε 2 -iσ 1 ω (F/m). The sea water depth and the operating frequency under the simulation conditions are applicable to the constraint conditions of the invention.
By electric field componentAnd magnetic field component H ρ An example is described.
1) The model construction process is simple and clear
The modeling method provided by the invention divides the air-seawater-seabed three-layer medium into the air-seawater two-layer medium and the seawater-seabed two-layer medium. When the electromagnetic fields radiated by the vertical magnetic dipoles in the two-layer medium are respectively modeled, the propagation model of the electromagnetic waves in the two-layer semi-infinite medium which is the most basic is adopted for calculation. The decoupling of the air and the submarine medium is equivalent, the joint influence of the two layers of medium on the electromagnetic wave propagation is ignored, and the most complex component of the three layers of medium is abandoned. The construction and subsequent calculation of the model are simplified.
2) Physical interpretability of model computation results
The modeling method provided by the invention can obtain the result of each component between the radiation source and the receiving point, as shown in fig. 5. The total field in the figure represents the superposition of the individual components, and at close distances (within about 10m in the figure) the total field almost overlaps the direct wave component; the total field almost overlaps with the sea surface side wave component at a long distance (outside about 10m in the figure). This shows that the direct wave component is the main contributor to the electromagnetic field at close distances and the sea surface side wave component is the main contributor to the electromagnetic field at long distances, which is also consistent with practical situations. The calculation result of the electromagnetic field model obtained by the invention has physical interpretability.
3) Accuracy of model calculation results
The results obtained by the modeling method provided by the invention are compared with the results obtained by the traditional three-layer medium model, as shown in fig. 6. The calculation result of the invention has good consistency with the calculation result of the traditional method, which shows the accuracy of the calculation result of the invention.
According to an embodiment example, it can be considered that: the modeling and calculating method for electromagnetic wave propagation in the air-seawater-submarine three-layer medium is feasible, reduces complexity of a traditional modeling process, ensures calculation efficiency and calculation accuracy of a model, and increases physical interpretation of calculation results.
Claims (4)
1. A modeling method of electromagnetic field during electromagnetic wave propagation in a marine multilayer medium is characterized in that: when the sea water depth D is greater than the skin depth delta, i.eWherein: the working frequency f, the sea water conductivity constant ζ and the sea water permeability constant μ are modeled as follows:
step 1, splitting an air-seawater-submarine three-layer medium into two-layer medium models:
1. constructing an electromagnetic wave propagation model by using two layers of semi-infinite media of air and seawater, and generating vector potential F in the seawater 1 ′ z The method comprises the following steps:
wherein ε is 1 Is the dielectric constant of seawater, I m Magnetic dipole moment of dl magnetic dipole, gamma 1 Is propagation constant in sea water, gamma 2 Is propagation constant in air, z is distance from receiving antenna to sea surface, d is distance from transmitting antenna to sea surface, lambda is integral variable, ρ is horizontal distance, J 0 Is a zero-order Bessel function;
2. constructing an electromagnetic wave propagation model by using two layers of semi-infinite media of sea water and seabed to obtain vector potential F' generated in sea water 1z The method comprises the following steps:
wherein D is sea water depth, gamma -1 Is a propagation constant in the sea floor;
step 2: superposing the two-layer medium model to obtain the result of the three-layer medium, and obtaining the vector potential F generated by the vertical magnetic dipole in the sea water in the air-sea water-submarine three-layer medium 1z The method comprises the following steps:
step 3: using the relationship between the vector potential and the electromagnetic field, deriving the expression of the electric field and the magnetic field:
wherein F is a vector potential, E is an electric field, H is a magnetic field, ω is an angular frequency, and v is a rotation operator.
2. The modeling method of electromagnetic field when electromagnetic wave propagates in marine multi-layer medium according to claim 1, characterized in that: when the radiation source is a horizontal magnetic dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when the three-layer medium is obtained, and a vector potential generated by the horizontal magnetic dipole in the sea water in the air-sea water-submarine three-layer medium is obtained; when the radiation source is a horizontal magnetic dipole, the vector potential has a z-direction component F 1z In addition, there is also an x-direction component F 1x ：
Wherein the method comprises the steps of J is the included angle between the field point and ρ 1 Is a first order Bessel function;
will vector potential F 1z And F 1x And (3) carrying out the step (3) to obtain the expression of the electric field and the magnetic field.
3. The modeling method of electromagnetic field when electromagnetic wave propagates in marine multi-layer medium according to claim 1, characterized in that: when the radiation source is a vertical electric dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when the three-layer medium is obtained, and the vertical electric dipole in the sea water when the air-sea water-submarine three-layer medium is obtained is in the sea waterVector magnetic bit A generated in (2) 1z ：
Wherein mu 1 Is the magnetic permeability of sea water, idl is the electric dipole moment of the electric dipole;
will vector magnetic potential A 1z The following expression is taken to obtain the expressions of electric field and magnetic field:
wherein A is vector magnetic potential, E represents electric field, H represents magnetic field, and V is rotation operator.
4. The modeling method of electromagnetic field when electromagnetic wave propagates in marine multi-layer medium according to claim 1, characterized in that: when the radiation source is a horizontal electric dipole, in the step 2, the two-layer medium model is overlapped to obtain a result when three-layer medium is obtained, and a vector magnetic level generated by the horizontal electric dipole in the sea water in the air-sea water-submarine three-layer medium is obtained; when the radiation source is a horizontal electric dipole, the vector magnetic potential has a z direction component A 1z In addition, there is also an x-direction component A 1x ：
Will vector magnetic potential A 1z And A 1x The expression of the electric field and the magnetic field is obtained by bringing the vector magnetic potential and the electromagnetic field into the relation of the claim 3.
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