A FDTD method for analyzing the electric field scattered by a large-scale target in a seawater dispersive medium

Abstract

The present invention discloses an FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium, belonging to the field of computational electromagnetics technology. The method converts the constitutive equation established in the frequency domain in the seawater model to the time domain, obtains the time-domain discrete relationship between the underwater electric field and the underwater electric displacement, and combines the FDTD method to calculate the underwater propagation and scattering of electromagnetic waves. The electric field distribution when there is no underwater detection target in the seawater model is the incident electric field. The electric field distribution calculated after constructing a function model of the underwater detection target in the seawater model is the total field. The difference between the incident electric field and the total field is the scattered electric field of the detection target. The method provided by the present invention can control parameters such as the incident electromagnetic wave waveform, electromagnetic wave frequency, underwater target shape and size to analyze the influencing factors and distribution characteristics of the scattered electric field, which has important reference significance for research in the fields of underwater submarine detection, seabed minerals, and underwater long-distance communication.

Description

Technical Field

[0001] The invention relates to an FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersion medium, and belongs to the technical field of computational electromagnetics. Background Art

[0002] With the advancement of underwater electromagnetic wave communications and ocean exploration technologies, electromagnetic detection of underwater targets has gradually become a key area of ​​underwater electromagnetic field research. Currently, analytical methods and finite element methods are commonly used in electromagnetic wave propagation and scattering technology. The analytical method numerically discretizes Maxwell's equations, but the approximate numerical solutions it obtains for low-frequency electromagnetic waves do not meet the requirements of high-precision underwater detection. Furthermore, due to the propagation characteristics of low-frequency electromagnetic waves, underwater electromagnetic detection calculations require a large simulated space, and analytical methods have significant limitations when calculating the long-distance propagation of electromagnetic waves in large spaces. While the finite element method can calculate the scattering of complex models and handle complex boundary conditions, it is difficult to simulate and is not suitable for calculating the long-distance propagation of electromagnetic waves.

[0003] Due to the high conductivity of seawater, medium- and high-frequency electromagnetic waves experience significant attenuation when propagating in it. Therefore, studying the propagation and scattering of low-frequency electromagnetic waves underwater is increasingly important. To address this issue, this paper aims to construct a finite-difference time-domain electromagnetic computational model in a three-dimensional seawater Debye dispersion medium.

[0004] It should be noted that the above content falls within the technical knowledge of the inventor and does not necessarily constitute prior art. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems existing in the prior art and provide an FDTD method for analyzing the scattered electric field of large-scale targets in seawater dispersive media. The method can control parameters such as the incident electromagnetic wave waveform, electromagnetic wave frequency f, underwater target shape and size to analyze the influencing factors and distribution characteristics of the scattered electric field.

[0006] The present invention achieves the above-mentioned purpose by adopting the following technical solutions:

[0007] An FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium includes the following steps:

[0008] S1. Establish a Debye lossy dissipative medium model for a three-dimensional seawater environment. Use the Debye formula to calculate the frequency-dependent complex dielectric constant of the established seawater model, as shown in formula (1).

[0009]

[0010] Where, ε ∞is the dielectric constant of seawater at infinite frequency, ε s is the zero-frequency relative permittivity, the jω term is the imaginary loss, ω = 2πf, j is the imaginary unit, and τ is the relaxation time, which represents the time taken for seawater to reach the polarization state from the beginning of polarization;

[0011] S2. In the frequency domain, the constitutive equations of electric field intensity and electric displacement are established in the seawater model as shown in formula (2).

[0012]

[0013] Where ε0 is the dielectric constant of vacuum, is the complex dielectric constant of seawater calculated in formula (1), substitute formula (1) into formula (2), and let △ε=ε s -ε ∞ , we get the vector equations of electric field intensity and electric displacement in the frequency domain as formula (3),

[0014]

[0015] S3. Introduce auxiliary variable A, set , substituting into formula (3), we get D(ω)=ε0ε ∞ E(ω)+ε0A(ω), the Z transform method is used to transform the auxiliary variable A, electric displacement vector D and electric field intensity E in the frequency domain into the calculation equations in the Z domain such as formulas (4), (5) and (6).

[0016]

[0017]

[0018]

[0019] S4. Use D n Instead of D(z), A n-1 Instead of z -1 A(z), the calculation formula (4) of the auxiliary variable A in the Z domain and the calculation formula (6) of the electric field intensity E are transferred to the discrete form in the time domain, and the differential equations of the electric field intensity E and the auxiliary variable A in the time domain are obtained as formulas (7) and (8).

[0020]

[0021]

[0022] S5. Divide the calculation area of ​​the seawater model into three-dimensional spatial and temporal differential grids of electric and magnetic field intensities, discretize space and time based on the divided grids, and assume that the conductivity and relative permittivity within each grid are the same; wherein the spatial step size and time step size above the detection target are larger than those below the detection target;

[0023] S6. In the time domain, the Maxwell curl equation is used to perform central difference on the discretized seawater model using the FDTD method to obtain the differential equations of the electric field intensity E and magnetic field intensity H in the x direction of the seawater depth, as shown in formulas (9) and (10).

[0024]

[0025]

[0026] Δt is the time discrete interval, △x is the space discrete interval, the superscript n represents the time step of the calculation, the calculation time t = n·△t; k represents the space step of the calculation, the spatial distance calculated in the depth x direction is x = k·△x, the electric field E z In integer steps of space and time, the magnetic field H y Scaling in half-integer steps of space and time,

[0027] S7. Add the initial condition, i.e. the incident electromagnetic wave source D, to the calculation area of ​​the seawater model. z n (k) simulating underwater electromagnetic detection, setting absorption boundary conditions, iteratively calculating the grid divided in step S6 based on the differential equations obtained in steps S4 and S5, updating the electric field, and obtaining the underwater electric field distribution in the entire space and at all times;

[0028] S8. When there is no underwater detection target in the calculation area of ​​the seawater model, the electric field distribution calculated by steps S1-S7 is the incident electric field;

[0029] S9. Constructing a function model of the detection target using a function within the calculation region of the seawater model. The detection target is set as a lossy dispersive medium. The electric field distribution after adding the detection target is calculated as the total field.

[0030] S10, the difference between the total field and the incident electric field is the scattered electric field of the detection target.

[0031] Optionally, in step S9, the total field calculation method after adding the detection target includes the following steps:

[0032] S9.1. Calculate the complex dielectric constant of the detection target related to frequency. The calculation equation is as follows:

[0033]

[0034] Where σ target is the dielectric conductivity of the detection target, ε0 is the vacuum dielectric constant, is the relative dielectric constant of the detected target, and the jω term is the imaginary loss;

[0035] S9.2. Substituting formula (11) into formula (2), we can obtain the relationship between the electric field intensity and electric displacement vector of the scattering target in the frequency domain as formula (12).

[0036]

[0037] S9.3. Use Fourier integral transform to convert the electric displacement vector formula (12) in the frequency domain into the integral with respect to time t in the time domain as shown in formula (13);

[0038]

[0039] S9.4. Perform discrete difference on formula (13) in the time domain, approximate the integral in formula (13) to the sum of the time step △t, and obtain the differential equation of the electric displacement vector D and the electric field intensity E as shown in formula (14).

[0040]

[0041] S9.5. Within the function model of the detection target, iterative calculations are performed based on the differential equation obtained from formula (14) and formulas (9) and (10); for the seawater area outside the function model of the detection target, iterative calculations are performed based on the differential equation obtained from steps S4 and S5 and formulas (9) and (10), so as to update the electric field and obtain the electric field distribution after the detection target is added.

[0042] Optionally, in step S6, when dividing the differential grid, the differential grid above the detection target is selected with a spatial step of δ = 0.1 m and a time step of dt = δ / 2c0 = 1 / 6 × 10 -9 s; the differential grid below the detection target is selected with a spatial step of δ = 1m and a time step of dt = δ / 2c0 = 1 / 6×10 -8 s, where c0 is the speed of light in vacuum.

[0043] Optionally, step S7 specifically includes:

[0044] Starting from the initial condition electromagnetic wave source, the calculation is done step by step. At the time step n=0, the electromagnetic wave source introduced is , calculated by formula (7) and (8) Substituting into formula (9) and formula (10), we can get The electric field value of the kth layer space step can be used to calculate the electric field value of the k+1th layer;

[0045] At time step n=1, the electromagnetic wave source introduced is , the electric field intensity in the whole space at the previous time step is Calculated Substituting into formula (9) and (10), we can get

[0046] By repeating the iteration in time, the underwater electric field distribution in the entire space and time period of the calculation area can be obtained.

[0047] Optionally, in step S7, the incident electromagnetic wave source is a sinusoidal point source or a pulse source, and the differential expressions of the sinusoidal point source or the pulse source in the time domain are:

[0048] Sinusoidal point source

[0049] Pulse source

[0050] Where f is the frequency of the sinusoidal electromagnetic wave, t is the total number of time steps of the operation, I is the pulse width of the pulse wave, and t0 is the pulse wave interval time.

[0051] Optionally, in step S7, PML is used as the absorbing boundary condition.

[0052] Optionally, in step S7, the relationship between the conductivity in the PML absorption layer and the length ρ from the inner boundary is:

[0053]

[0054] Where, d is the thickness of the PML absorption layer, δ is the spatial step size, and m is a constant. m is set to 4 to ensure the absorption effect of the PML layer.

[0055] Optionally, in step S8, the function model of the underwater detection target is an ellipsoid function, a spherical function or a ship-shaped function.

[0056] The beneficial effects of the present invention include but are not limited to:

[0057] The present invention provides an FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium. The method converts the constitutive equation established in the frequency domain of the seawater model into the time domain, obtains the time-domain discrete relationship between the underwater electric field and the underwater electric displacement, and combines the FDTD method to calculate the underwater propagation and scattering of electromagnetic waves. The electric field distribution when no underwater detection target is added to the seawater model is the incident electric field. The electric field distribution calculated after constructing a function model of the underwater detection target in the seawater model is the total field. The difference between the incident electric field and the total field is the scattered electric field of the detection target. In this way, the scattered electric field distribution diagram of the underwater detection target in the entire space and time period is obtained. The present invention can control parameters such as the incident electromagnetic wave waveform, electromagnetic wave frequency, and the shape and size of the underwater detection target to analyze the influencing factors and distribution characteristics of the scattered electric field. It has important reference significance for research in the fields of underwater submarine detection, seabed mineral detection, and underwater remote communication.

[0058] During calculation, a method combining coarse and fine grids is used to handle large underwater detection targets and large calculation space, which improves calculation efficiency.

[0059] The adopted FDTD method has the advantages of rapidity in calculating the scattered electric field distribution of large-scale targets in the entire space and at all times, as well as the ability to simulate large-scale spatial conditions using perfectly matched layer (PML) boundary conditions and solve the full-frequency domain scattering results through Fourier transform. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0061] Figure 1 Schematic diagram of the calculation area and absorption boundary of the seawater model, where x is the seawater depth direction, and y and z are the sea level directions;

[0062] Figure 2 The spatial and temporal difference grids used to divide the seawater calculation area along the x-direction of the coastal water depth;

[0063] Figure 3 is the electric field amplitude distribution without underwater detection target under different incident electromagnetic wave frequencies;

[0064] Figure 4 is the total field amplitude distribution of underwater detection targets at the incident sinusoidal electromagnetic wave frequency f = 10 Hz;

[0065] Figure 5 is the total field amplitude distribution of underwater detection targets at the incident sinusoidal electromagnetic wave frequency f = 20 Hz;

[0066] Figure 6is the total field amplitude distribution at the axis (y = 300m) in the calculation area when there is an underwater detection target at different incident electromagnetic wave frequencies;

[0067] Figure 7 The distribution of scattered electric field amplitude at the axis (y = 300m) in the calculation area when there is an underwater detection target at different incident electromagnetic wave frequencies;

[0068] Figure 8 To detect the scattered electric field amplitude distribution at the axis (y = 300m) in the calculation area when the incident sinusoidal electromagnetic wave frequency f = 20Hz under different conductivity of the target;

[0069] Figure 9 The FDTD calculation results and logarithmic fitting curve of the scattered electric field amplitude of underwater detection targets with different electrical conductivities at 75m above the target (the position where the scattered electric field amplitude is maximum) under the incident electromagnetic wave frequency of 20Hz. DETAILED DESCRIPTION

[0070] The present invention will be described in further detail below. However, it should be noted that the following specific embodiments are merely illustrative examples of the specific operation of the present invention, and the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention is limited solely by the claims. It will be apparent to those skilled in the art that various other improvements and substitutions can be made to the embodiments of the present invention within the scope of protection defined by the claims of the present invention, and that the same technical effects can still be achieved, thereby achieving the ultimate technical purpose of the present invention.

[0071] The FDTD method for analyzing the scattered electric field of a large-sized target in a seawater dispersive medium provided by the present invention will be described in detail below with specific implementation methods.

[0072] The FDTD method provided in this embodiment for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium includes the following steps:

[0073] Step S1: Establish a Debye lossy dissipative medium model for a three-dimensional seawater environment, and use the Debye formula to calculate the frequency-dependent complex dielectric constant of the established seawater model, as shown in formula (1).

[0074]

[0075] Where, ε ∞ is the dielectric constant of seawater at infinite frequency, usually taken as ε ∞ =4.9,ε s is the zero-frequency relative permittivity, jω is the imaginary loss, ω = 2πf, j is the imaginary unit, and τ is the relaxation time, which represents the time it takes for seawater to reach the polarization state from the beginning of polarization; Figure 1 As shown in , the established seawater model is an area with a length and width of 600m×300m;

[0076] Among them, the empirical expressions of relaxation time, static dielectric constant of seawater and conductivity of seawater with temperature and salinity are:

[0077] τ(S,T)=(1.768×10 -11 -6.086×10 -13 T+1.104×10 -14 T 2 -8.111×10 -17 T 3 )(1+12.282×10 -5 TS-7.638×10 -4 S-7.760×10 -6 S 2 +1.105×10 -8 S 3 )

[0078] ε1(S,T)=(87.134-0.1949T-0.0127T 2 +0.0002491T 3 )(1+1.613×10 -5 TS-0.003656S+3.21×10 -5 S 2 -4.232×10 -7 S 3 )

[0079] σ(S,T)=S(0.182521-0.00146192S+2.09324×10 -5 S 2 -1.28205×10 -7 S 3 )×exp((T-25)(0.02033+0.0001266(25-T+2.464×10 -6 (25-T) 2 -S(1.849×10 -5 -2.551×10 -7 (25-T)+2.551×10 -8 (25-T) 2 )))

[0080] Where S is the salinity of seawater and T is the temperature of seawater;

[0081] In the Debye lossy dissipative medium model, the empirical formula is used to calculate seawater, which has higher authenticity and can analyze the influence of seawater temperature and salinity on the scattered electric field.

[0082] Step S2: Establish the constitutive equations of electric field intensity and electric displacement in the seawater model in the frequency domain as shown in formula (2).

[0083]

[0084] Where ε0 is the dielectric constant of vacuum, is the complex dielectric constant of seawater calculated in formula (1), substitute formula (1) into formula (2), and let △ε=ε s -ε ∞ , we get the vector equations of electric field intensity and electric displacement in the frequency domain as formula (3),

[0085]

[0086] Step S3: Introduce auxiliary variable A, set Substituting into formula (3), we get D(ω)=ε0ε ∞ E(ω)+ε0A(ω), the Z transform method is used to transform the auxiliary variable A, electric displacement vector D and electric field intensity E in the frequency domain into the calculation equations in the Z domain such as formulas (4), (5) and (6).

[0087]

[0088]

[0089]

[0090] Step S4: Use D n Instead of D(z), A n-1 Instead of z -1 A(z), the calculation formula (4) of the auxiliary variable A in the Z domain and the calculation formula (6) of the electric field intensity E are transferred to the discrete form in the time domain, and the differential equations of the electric field intensity E and the auxiliary variable A in the time domain are obtained as formulas (7) and (8).

[0091]

[0092]

[0093] Step S5: Divide the calculation area of ​​the seawater model into three-dimensional spatial and temporal differential grids of electric field intensity and magnetic field intensity, and discretize space and time based on the divided grids. Figure 2As shown, it is assumed that the conductivity and relative permittivity within each grid are the same; the boundary above and below the detection target is located at a horizontal plane passing through the center of the detection target and parallel to the sea level, and the spatial step and time step above the detection target are larger than those below;

[0094] In this embodiment, the differential grid above the detection target is selected with a spatial step of δ = 0.1 m and a time step of dt = δ / 2c0 = 1 / 6 × 10 -9 s; the differential grid below the detection target is selected with a spatial step of δ = 1m and a time step of dt = δ / 2c0 = 1 / 6×10 -8 s, where c0 is the speed of light in vacuum;

[0095] Step S6: In the time domain, the discretized seawater model is centrally differenciated using the Maxwell curl equation and the FDTD method to obtain the differential equations of the electric field intensity E and the magnetic field intensity H in the x-direction of the seawater depth, as shown in formulas (9) and (10).

[0096]

[0097]

[0098] Δt is the time discrete interval, △x is the space discrete interval, the superscript n represents the time step of the calculation, the calculation time t = n·△t; n+1 represents running forward one time step, n+1 / 2 represents running forward half a time step; k represents the space step of the calculation, the spatial distance calculated in the depth x direction x = k·△x, k+1 represents running one space step, k+1 / 2 represents running half a space step; the electric field E z In integer steps of space and time, the magnetic field H y Scaling in half-integer steps of space and time,

[0099] Step S7: Add the initial condition, i.e. the incident electromagnetic wave source, to the calculation area of ​​the seawater model To simulate underwater electromagnetic detection, a PML (perfectly matched layer) is set as the absorption boundary condition. Based on the differential equations obtained in steps S4 and S6, the seawater model grid divided in step S5 is iteratively calculated to update the electric field and obtain the electric field distribution when no underwater detection target is added.

[0100] like Figure 1 As shown, a sinusoidal point source is used as the incident electromagnetic wave source, and the incident electromagnetic wave source is placed underwater at a distance of 30m from the sea level.

[0101] Among them, the incident electromagnetic wave source added is a sinusoidal point source or a pulse source, and the differential expressions of the sinusoidal point source or the pulse source in the time domain are:

[0102] Sinusoidal point source

[0103] Pulse source

[0104] Where f is the frequency of the sinusoidal electromagnetic wave, t is the total number of time steps of the operation, I is the pulse width of the pulse wave, and t0 is the pulse wave interval time;

[0105] The specific process of iterative calculation is:

[0106] Starting from the initial condition electromagnetic wave source, the calculation is done step by step. At the time step n=0, the electromagnetic wave source introduced is , calculated by formula (7) and (8) Substituting into formula (9) and formula (10), we can get The electric field value of the kth layer space step can be used to calculate the electric field value of the k+1th layer;

[0107] At time step n=1, the electromagnetic wave source introduced is The electric field intensity in the entire space at the previous time step is , calculated Substituting into formula (9) and (10), we can get

[0108] By repeating the iteration in time, the underwater electric field distribution in the entire space and time period of the calculation area can be obtained.

[0109] For further reference, Figure 1 The basic principle of the PML absorption layer is to set a dielectric layer that completely matches the medium of the calculation area at the boundary of the calculation area, so that the electromagnetic wave will not be reflected and will be completely attenuated after entering the PML absorption layer. In order to prevent the electromagnetic wave from being reflected in the PML absorption layer, Γ should be kept constant at the boundary of the PML absorption layer, that is, Where η1 and η2 are the impedances of seawater and PML absorption layer respectively, and the calculation formula is: It is related to the magnetic permeability and relative dielectric constant of the medium. Therefore, the PML absorption layer needs to set the magnetic permeability and relative dielectric constant parameters to meet the impedance matching conditions as follows: In actual calculations, the relative dielectric constant and relative permeability must take into account the loss, that is, there is an imaginary part.

[0110] The relationship between the conductivity in the PML absorption layer and the distance ρ from the inner boundary is:

[0111]

[0112] Where, d is the thickness of the PML absorption layer, δ is the spatial step size, and m is a constant. m is set to 4 to ensure the absorption effect of the PML layer.

[0113] Step S8: When there is no underwater detection target in the calculation area, the electric field distribution calculated by steps S1-S7 is the incident electric field;

[0114] Step S9: Use COMSOL software to construct a function model of the underwater detection target in the calculation area, such as an ellipsoid function, a spherical function, or a ship-shaped function, and use the center of the function model as the center point of the calculation area; the detection target is set as a steel medium, which is a dispersive medium, and the electric field distribution after adding the detection target is calculated as the total field. The function model is equivalent to defining a spatial range. Within the defined spatial range, ε r , σ are the parameters of the detection target, which are different from the surrounding seawater medium.

[0115] The specific calculation method of the electric field distribution after adding the detection target is:

[0116] S9.1. Calculate the complex dielectric constant of the detection target related to frequency. The calculation equation is as follows:

[0117]

[0118] By changing the formula (11) σ target The complex dielectric constant of the target dielectric material under a certain frequency can be obtained.

[0119] Where σ target is the dielectric conductivity of the detection target, ε0 is the vacuum dielectric constant, is the target relative dielectric constant, and the jω term is the imaginary loss. In this embodiment, the detection target σ=5×10 6 S / m.

[0120] S9.2. Substituting formula (11) into formula (2), we can obtain the relationship between the electric field intensity and electric displacement vector of the scattering target in the frequency domain as formula (12).

[0121]

[0122] S9.3. Use Fourier integral transform to convert the electric displacement vector formula (12) in the frequency domain into the integral with respect to time t in the time domain as shown in formula (13);

[0123]

[0124] S9.4. Perform discrete difference on formula (13) in the time domain, approximate the integral in formula (13) to the sum of the time step △t, and obtain the differential equation of the electric displacement vector D and the electric field intensity E as shown in formula (14).

[0125]

[0126] S9.5. Within the function model of the detection target, iterative calculations are performed based on the differential equation obtained from formula (14) and formulas (9) and (10); for the seawater area outside the function model of the detection target, iterative calculations are performed based on the differential equation obtained from steps S4 and S5 and formulas (9) and (10), so as to update the electric field and obtain the electric field distribution after the detection target is added.

[0127] Figure 3 The electric field amplitude distribution diagram without underwater target when a sinusoidal point source is used as the incident electromagnetic wave source and the frequency of the incident electromagnetic wave source is 5, 20, and 100 Hz;

[0128] When the frequency is 10 Hz and 20 Hz, the total field amplitude distribution calculated after adding an ellipsoidal underwater detection target with a length of 120 m and a width of 20 m is as follows: Figure 4 、 Figure 5 As shown in .

[0129] Figure 6 This is the distribution diagram of the total field amplitude at the axis (y=300m) in the calculation area when there is an underwater detection target at the incident electromagnetic wave frequencies of 10, 20, and 30 Hz.

[0130] Step S10: Calculate the difference between the total field and the incident electric field to obtain the scattered electric field of the detection target. Figure 7 As shown in , it is the distribution diagram of the scattered electric field amplitude of the underwater detection target when the incident electromagnetic wave source is a sinusoidal point source and the frequency is 10, 20, and 30 Hz.

[0131] Depend on Figure 4 、 Figure 5 and Figure 7 It can be seen that due to the influence of the detection target, the total field and scattered electric field amplitudes at different depths are significantly different.

[0132] In the depth range of 30 to 100 m, that is, above the detection target, the amplitude of the underwater total field decays exponentially, and the spatial distribution of the scattered electric field of the detection target first increases and then decreases and approaches 0. The reason is that the induced electric field and the scattered electric field generated by the underwater detection target cancel each other out at 100 m, and the scattered electric field plays a dominant role in the range above the detection target.

[0133] In the depth range of 100-140m, due to the large conductivity of the ellipsoidal detection target, the detection target affects the propagation of underwater electromagnetic waves, the scattered electric field increases rapidly, and cancels out the incident electric field, which leads to a rapid attenuation of the total field amplitude.

[0134] At a depth of 140-160m, that is, inside the underwater detection target, the electromagnetic waves are absorbed at the surface of the detection target and can hardly enter the interior of the detection target, and the electric field is approximately 0. This is because the electromagnetic waves incident on the surface of the detection target have a skin effect. The electromagnetic waves cannot propagate in the detection target and can only propagate on its surface, generating an induced current on the surface of the metal shell, and then generating a scattered electric field at the lower end of the underwater detection target, which guides the propagation of the electromagnetic waves.

[0135] When the depth is greater than 160m, that is, the area below the detection target, the total field amplitude gradually decays due to the blocking of electromagnetic waves by the detection target. The scattered electric field generated by the induced current plays a dominant role, and the scattered electric field decreases rapidly with increasing depth and gradually approaches 0.

[0136] In addition, Figure 7 It can be seen that the scattered electric field on the upper side of the detection target is stronger than that on the lower side. The main reason is that the low-frequency field source is closer to the upper side of the underwater detection target, and the electromagnetic wave target has a blocking effect on the low-frequency electromagnetic waves. The scattered electric field is mainly distributed on the upper side of the detection target, and the scattered field generated at the lower end of the underwater detection target comes from the induced current, and its magnitude is smaller than that of the upper side of the detection target.

[0137] Depend on Figure 6 It can be seen that the amplitude of the total field at the axis in the calculation area is related to the frequency of the incident sinusoidal point source. The lower the frequency of the incident electromagnetic wave, the larger the overall amplitude of the total field, and the overall amplitude of the underwater total field is proportional to

[0138] Figure 7 The distribution of underwater scattered electric fields of electromagnetic waves of different frequencies on the axis of the calculation area is given. It can be found that with the increase of depth, the amplitude of the scattered electric field in the range above the detection target shows a trend of first increasing and then decreasing. The height of the ellipsoid is set as a unit length, and the extreme position of the scattered electric field can be reached at 3-4 unit lengths above the detection target. The scattered electric field below the detection target decays rapidly to 0 with depth in an e exponential relationship. The frequency affects the distribution characteristics of the scattered electric field as follows: (1) The lower the frequency, the larger the overall scattered electric field amplitude in the seawater, and the easier it is to detect the detection target position. (2) The lower the frequency, the farther the extreme distribution of the scattered electric field above the detection target is from the submarine, which means that the scattered electric field changes can be detected at a farther distance, and thus the detection target position at a deeper depth can be detected.

[0139] analyze Figure 7 and Figure 8Frequency affects the total and scattered electric fields for two main reasons: First, the attenuation of electromagnetic waves underwater is frequency-dependent; lower frequencies weaken the attenuation. Second, the induced current generated on metal surfaces is frequency-dependent: lower frequencies increase the induced current, resulting in stronger scattered electric fields above and below the target, and the farther the extreme values ​​of the scattered electric fields are from the target. Therefore, in practical underwater electromagnetic detection, it is best to select incident electromagnetic waves with low frequencies.

[0140] From the above, we can conclude that the lower the frequency of the incident electromagnetic wave, the greater the overall amplitude of the total electric field and scattered electric field of the underwater detection target. The farther the scattered electric field extremes are from the submarine, the better the electromagnetic detection effect. Therefore, in actual underwater detection, electromagnetic waves with lower frequencies should be selected.

[0141] Figure 8 The scattered electric field distribution for underwater targets with different conductivity values ​​at the axis (y = 300 m) of the calculation region is presented. It can be seen that as the conductivity of the target increases, the overall amplitude of the scattered electric field also increases, while the extreme distribution points of the scattered electric field remain unchanged. In other words, changes in the target conductivity only affect the amplitude of the scattered electric field, not its distribution. This is because the target conductivity is only related to the electric field amplitude. The lower the conductivity of the target material, the weaker its absorption of electromagnetic waves, and the smaller the scattered electric field generated by the surface induced current.

[0142] Figure 9 The FDTD calculated amplitudes of the scattered electric field at 75 m above the target (maximum amplitude of the scattered electric field) for underwater targets of varying conductivities at a 20 Hz incident electromagnetic wave frequency are presented, along with their logarithmic fitting curves. It can be seen that the scattered electric field amplitude at this location increases significantly within the conductivity range of 0 to 2000 S / m, increasing logarithmically with conductivity. The scattered electric field amplitude and conductivity at this location are fitted using the following formula: Amp = a·ln(bσ). The parameters in the fitting curves are: a = 2.31×10 - 4 V / m, b=1.21×10 3 (S / m) -1 . Figure 9 The logarithmic fitting results are shown in the figure, which agree well with the FDTD calculation results of the scattered electric field amplitude, indicating that the scattered electric field extreme value is proportional to lnσ. As shown in the figure, when the detection conductivity exceeds 2000 S / m, the increase in the scattered electric field amplitude gradually decreases until it stabilizes. This is because when the conductivity of the detection target is very high, due to the skin effect, electromagnetic waves can no longer penetrate into the metal. Underwater targets of various conductivities have the same impact on electromagnetic wave propagation, and the induced current generated on the detection target surface is basically the same. The scattered electric field generated by the induced current tends to stabilize, which in turn leads to the stable scattered electric field of underwater detection targets under different conductivities.

[0143] From the above, we can conclude that the greater the conductivity of an underwater target, the greater the overall amplitude of the scattered electric field underwater, making it easier for electromagnetic detectors to accurately detect it. When the conductivity exceeds 2000 S / m, the amplitude gradually stabilizes, indicating that changes in conductivity do not affect the detection of the target's scattered electric field.

[0144] Both seawater and underwater detection targets are lossy dispersive media. The incident electromagnetic wave frequency f and the target's conductivity significantly impact practical underwater detection. The present invention utilizes the FDTD method to differentiate the Maxwell curl equations in the time domain, obtaining a time-space coupled discrete differential equation satisfying the electric and magnetic field intensities. This equation is then iteratively solved to calculate the full-space electromagnetic field distribution. Because the FDTD method can solve transient electromagnetic problems in dispersive media in the time domain, it offers advantages in addressing electromagnetic attenuation in dispersive media and calculating the full-space instantaneous scattered electromagnetic field distribution of underwater targets.

[0145] The above specific implementation manner cannot be used as a limitation on the protection scope of the present invention. For those skilled in the art, any replacement, improvement or transformation made to the implementation manner of the present invention falls within the protection scope of the present invention.

[0146] Any matters not described in detail in the present invention are well-known technologies to those skilled in the art.

Claims

1. An FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium, characterized by: The steps include: S1. Establish a Debye lossy dissipative medium model for a three-dimensional seawater environment. Use the Debye formula to calculate the frequency-dependent complex dielectric constant of the established seawater model, as shown in formula (1). Where, ε ∞ is the dielectric constant of seawater at infinite frequency, ε s is the zero-frequency relative permittivity, the jω term is the imaginary loss, ω = 2πf, j is the imaginary unit, and τ is the relaxation time, which represents the time taken for seawater to reach the polarization state from the beginning of polarization; S2. In the frequency domain, the constitutive equations of electric field intensity and electric displacement are established in the seawater model as shown in formula (2). Where ε0 is the dielectric constant of vacuum, is the complex dielectric constant of seawater calculated in formula (1), substitute formula (1) into formula (2), and let △ε=ε s -ε ∞ , we get the vector equations of electric field intensity and electric displacement in the frequency domain as formula (3), S3. Introduce auxiliary variable A, set Substituting into formula (3), we get D(ω)=ε0ε ∞ E(ω)+ε0A(ω), the Z transform method is used to transform the auxiliary variable A, electric displacement vector D and electric field intensity E in the frequency domain into the calculation equations in the Z domain such as formulas (4), (5) and (6). but S4. Use D n Instead of D(z), A n-1 Instead of z -1 A(z), the calculation formula (4) of the auxiliary variable A in the Z domain and the calculation formula (6) of the electric field intensity E are transferred to the discrete form in the time domain, and the differential equations of the electric field intensity E and the auxiliary variable A in the time domain are obtained as formulas (7) and (8). S5. Divide the calculation area of ​​the seawater model into three-dimensional spatial and temporal differential grids of electric and magnetic field intensities, discretize space and time based on the divided grids, and assume that the conductivity and relative permittivity within each grid are the same; wherein the spatial step size and time step size above the detection target are larger than those below the detection target; S6. In the time domain, the Maxwell curl equation is used to perform central difference on the discretized seawater model using the FDTD method to obtain the differential equations of the electric field intensity E and magnetic field intensity H in the x direction of the seawater depth, as shown in formulas (9) and (10). Δt is the time discrete interval, △x is the space discrete interval, the superscript n represents the time step of the calculation, the calculation time t = n·△t; k represents the space step of the calculation, the spatial distance calculated in the depth x direction is x = k·△x, the electric field E z In integer steps of space and time, the magnetic field H y Scaling in half-integer steps of space and time, S7. Add the initial condition, i.e. the incident electromagnetic wave source D, to the calculation area of ​​the seawater model. z n (k) simulating underwater electromagnetic detection, setting absorption boundary conditions, iteratively calculating the grid divided in step S6 based on the differential equations obtained in steps S4 and S5, updating the electric field, and obtaining the underwater electric field distribution in the entire space and at all times; S8. When there is no underwater detection target in the calculation area of ​​the seawater model, the electric field distribution calculated by steps S1-S7 is the incident electric field; S9. Constructing a function model of the detection target using a function within the calculation region of the seawater model. The detection target is set as a lossy dispersive medium. The electric field distribution after adding the detection target is calculated as the total field. S10, the difference between the total field and the incident electric field is the scattered electric field of the detection target.

2. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1 is characterized in that: In step S9, the total field calculation method after adding the detection target includes the following steps: S9.

1. Calculate the complex dielectric constant of the detection target related to frequency. The calculation equation is as follows: Where, σ target is the dielectric conductivity of the detection target, ε0 is the vacuum dielectric constant, ε r target is the relative dielectric constant of the detected target, and the jω term is the imaginary loss; S9.

2. Substituting formula (11) into formula (2), we can obtain the relationship between the electric field intensity and electric displacement vector of the scattering target in the frequency domain as formula (12). S9.

3. Use Fourier integral transform to convert the electric displacement vector formula (12) in the frequency domain into the integral with respect to time t in the time domain as shown in formula (13); S9.

4. Perform discrete difference on formula (13) in the time domain, approximate the integral in formula (13) to the sum of the time step △t, and obtain the differential equation of the electric displacement vector D and the electric field intensity E as shown in formula (14). S9.

5. Within the function model of the detection target, iterative calculations are performed based on the differential equation obtained from formula (14) and formulas (9) and (10); for the seawater area outside the function model of the detection target, iterative calculations are performed based on the differential equation obtained from steps S4 and S5 and formulas (9) and (10), so as to update the electric field and obtain the electric field distribution after the detection target is added.

3. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1 is characterized in that: Step S6: When dividing the differential grid, the differential grid above the detection target is selected with a spatial step of δ = 0.1m and a time step of dt = δ / 2c0 = 1 / 6×10 -9 s; the differential grid below the detection target is selected with a spatial step of δ = 1m and a time step of dt = δ / 2c0 = 1 / 6×10 -8 s, where c0 is the speed of light in vacuum.

4. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1, characterized in that: Step S7 is specifically as follows: Starting from the initial condition electromagnetic wave source, the calculation is done step by step. At the time step n=0, the electromagnetic wave source introduced is Calculated by formulas (7) and (8) Substituting into formula (9) and formula (10), we can get The electric field value of the kth layer space step can be used to calculate the electric field value of the k+1th layer; At time step n=1, the electromagnetic wave source introduced is The electric field intensity in the entire space at the previous time step is Calculated Substituting into formula (9) and (10), we can get By repeating the iteration in time, the underwater electric field distribution in the entire space and time period of the calculation area can be obtained.

5. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1, characterized in that: In step S7, the incident electromagnetic wave source is a sinusoidal point source or a pulse source, and the differential expressions of the sinusoidal point source or the pulse source in the time domain are: Sinusoidal point source Pulse source Where f is the frequency of the sinusoidal electromagnetic wave, t is the total number of time steps of the operation, I is the pulse width of the pulse wave, and t0 is the pulse wave interval time.

6. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1, characterized in that: In step S7, PML is used as the absorbing boundary condition.

7. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 5, characterized in that: In step S7, the relationship between the conductivity in the PML absorption layer and the distance ρ from the inner boundary is: Where, d is the thickness of the PML absorption layer, δ is the spatial step size, and m is a constant. m is set to 4 to ensure the absorption effect of the PML layer.

8. The FDTD method for analyzing the scattered electric field of a large-scale target in a seawater dispersive medium according to claim 1, characterized in that: In step S8, the function model of the underwater detection target is an ellipsoid function, a spherical function or a ship-shaped function.

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