Simulation method of electric field induced by bounded sinusoidal ocean current based on real seawater resistivity

Abstract

The present invention discloses a method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity, including: setting parameters: calculating or observing seawater conductivity and environmental parameters; determining ocean current mode: establishing a Cartesian rectangular coordinate system, and according to the convolution theory, performing Fourier transformation on the ocean current velocity to obtain Fourier coefficients; solving scalar potential: deriving the control equation and boundary conditions of the induced electric field scalar potential in the horizontal ocean current layer, the still seawater layer, and the seabed sediment layer medium, and solving to obtain the scalar potential of the induced electric field of bounded sinusoidal ocean current; solving the electric field: finding the gradient of the scalar potential, obtaining the horizontal component and the vertical component of the ocean current induced electric field in the ocean current layer, the still seawater layer, and the seabed sediment layer, and analyzing the spatial distribution characteristics of the induced electric field of the ocean current model. The present invention realizes the simulation of bounded sinusoidal ocean current induced electric field that is closer to the real ocean model, and can analyze the induced electric field under the conductivity model with longitudinal variation.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic simulation, in particular to a method for simulating bounded sinusoidal ocean current induced electric fields based on real seawater resistivity. Background Art

[0002] According to Faraday's electromagnetic induction principle, the moving seawater will generate induced electromagnetic signals in the ocean due to cutting the geomagnetic field. On the one hand, in the marine electromagnetic detection of the seabed geological structure, the electromagnetic noise induced by the movement of seawater is the main interference affecting the quality of the measured data. On the other hand, there are periodic electromagnetic signals in the ocean electromagnetic field. Generally speaking, they are mainly generated by the regular movement of seawater, which contains rich information about the movement of the ocean. By deeply analyzing and studying the electromagnetic observation data induced by the movement of seawater in a certain sea area, the characteristics of the seawater movement in that sea area can be learned.

[0003] Generally, the spatial scale of ocean currents is large, with a width of 10-1000km and a depth of 0.1-10km. The currents are highly consistent within a certain area, and their paths, speeds and directions remain stable for a long time. The speed of ocean currents varies in different sea areas, ranging from 1m / s to 1cm / s. If seawater is regarded as an incompressible irrotational fluid, then the ocean currents can be simplified as uniform ocean currents with constant speed in the direction of flow. The seawater is divided into layers in the vertical direction, generally into ocean current layers and stationary seawater layers. The most simplified model is a steady flow, that is, the speed does not change in the horizontal direction perpendicular to the direction of seawater flow, and is always a constant value. This ocean current model is currently the most widely studied. In order to be closer to the actual ocean current, it is usually assumed that the ocean current speed in the horizontal direction perpendicular to the direction of seawater flow is a sine (cosine) variation. Chen Biao et al. (2001) assumed that the ocean current speed extends infinitely and uniformly in the horizontal direction, and divided the seawater into an ocean current layer and a stationary seawater layer. The ocean current model used by Lin Chunsheng and Ren Dekui (2003) is that the velocity in the horizontal direction perpendicular to the flow direction of seawater is a constant value, and in the vertical direction, the velocity of the upper current layer decreases with depth. However, in reality, the ocean current does not extend infinitely, its width is limited, and the change of seawater conductivity is often ignored in the calculation of the ocean current induced electric field. It is assumed that the conductivity is constant in a certain area. In fact, the conductivity of the ocean current changes with the spatial position and directly affects the intensity of the induced electric field. It is necessary to take the change of seawater conductivity into account and make accurate calculations. Therefore, how to provide a bounded sinusoidal ocean current induced electric field simulation method based on the real seawater resistivity has become a technical problem that technicians in this field need to solve urgently. Summary of the invention

[0004] In order to overcome the above-mentioned deficiencies of the prior art, the present invention proposes a bounded sinusoidal current induced electric field simulation method based on real seawater resistivity, which realizes a bounded sinusoidal current induced electric field simulation that is closer to the real ocean model and can analyze the induced electric field under the longitudinally varying conductivity model.

[0005] A method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity comprises the following steps:

[0006] Step S1, setting parameters: calculating or observing seawater conductivity and environmental parameters;

[0007] Step S2, determining the ocean current pattern: establishing a Cartesian rectangular coordinate system, and performing Fourier transformation on the ocean current velocity to obtain Fourier coefficients according to the convolution theory;

[0008] Step S3, solving the scalar potential: deriving the control equations and boundary conditions satisfied by the induced scalar potential of the bounded sinusoidal current in the horizontal ocean current layer, the still seawater layer, and the seafloor sediment layer, and solving to obtain the expression thereof;

[0009] Step S4, solving the electric field: finding the gradient of the scalar potential, obtaining the horizontal and vertical components of the current induced electric field in the current layer, the still seawater layer and the seabed sediment layer, and analyzing the spatial distribution characteristics of the current model induced electric field.

[0010] Furthermore, in step S1, the ocean current physical model is a data set of a multi-layer structure; one layer of structure corresponds to one layer of ocean current layer, and the environmental parameters of each layer of structure include the horizontal flow velocity, salinity, temperature, thickness of the seawater of the corresponding ocean current layer and the intensity of each component of the geomagnetic field at the location.

[0011] Furthermore, in step S2, the method for establishing a Cartesian rectangular coordinate system is as follows:

[0012] Assume that the coordinate origin is on the sea surface, the z-axis is vertically upward, the x-axis points to the east, and the y-axis points to the north; set the classic ocean current velocity model - the sinusoidal ocean current model; the north component of the ocean current velocity The velocity along the y-axis is constant, and only changes along the x-axis. In the actual ocean, the current has boundaries, so a rectangular function is set. , only set the current of L width; current speed Expressed as the product of a rectangular function, a cosine function, and a constant:

[0013] (1),

[0014] in, is the ocean current velocity amplitude, L is the width of the current, is the circumference of a circle, xis the east-west coordinate in the Cartesian coordinate system.

[0015] Furthermore, in step S2, according to the convolution theory, the method of performing Fourier transform on the ocean current velocity to obtain the Fourier coefficient is:

[0016] According to the convolution theory, the ocean current velocity Perform Fourier transform to get , use * to represent convolution, that is:

[0017] (2),

[0018] In the formula Indicates the functional form of the expressions in brackets after Fourier transformation; the rectangular function , cosine function and constant Substituting the Fourier transform of The Fourier coefficients of the ocean current induced electric field are obtained from the expression The expression is:

[0019] (3),

[0020] in, , represents pi, N is the total number of terms in the Fourier expansion, The number representing the number of terms in the Fourier expansion; M is a dimensionless integer greater than 1 that determines the wave number resolution (1< M < N ),Pick:

[0021] ,

[0022] in, ceil represents the rounding function, H is the seawater depth, is the depth of the seafloor sediment layer, L is the width of the current, represent the average electrical conductivity of seawater and seafloor sediments, respectively; Represents a pulse function, which means that only when the wave number is When , and the rest of the values ​​are 0.

[0023] Furthermore, in step S3, the method for deriving the induced electric field expression in the horizontal ocean current layer, the still seawater layer, and the seabed sediment layer medium is as follows:

[0024] Based on Maxwell's equations and generalized Ohm's law, the induced scalar potential partial differential equation of the active velocity field is derived:

[0025] (4),

[0026] In the formula, is the Laplace operator, which is a second-order differential operator. is the curl operator, and the curl of velocity is expressed as , They are the electric field scalar potentials in the ocean current layer, the still seawater layer, and the seafloor sediment layer, and they satisfy the velocity-induced electric field The relationship of are the velocity induced electric fields in the east, north and vertical upward components respectively, is the Earth's magnetic field, are the geomagnetic field in the east, north and vertical upward components respectively, is the velocity field vector, Represent the velocity field in the east, north and vertical upward components respectively.

[0027] Furthermore, in step S3, by deriving the control equations and boundary conditions satisfied by the bounded sinusoidal ocean current scalar potential, the method for solving the expression is as follows:

[0028] Scalar potential The boundary conditions satisfied are as follows: (a) on the sea surface, the normal component of the conduction current density is zero; (b) at the interface between the ocean current layer and the still seawater layer, the normal components of the scalar potential and the conduction current density are both continuous; (c) at the interface between different resistivities of seawater, the normal components of the scalar potential and the conduction current density are both continuous; (d) on the seafloor interface, the normal components of the scalar potential and the conduction current density are both continuous; (e) at the bottom interface of the sediment layer, the normal component of the conduction current density is zero; that is,

[0029] (5),

[0030] in, is the conductivity of the upper medium, is the conductivity of the underlying medium, are the scalar potential of the upper layer in the multilayer structure of the ocean current layer and the still seawater layer, It is the scalar potential of the lower layer in the multilayer structure of the current layer and the still seawater layer;

[0031] Combined scalar potential Solving the above formula 4 at the boundary conditions at infinity and at the interface between different media), we can obtain the total scalar potential in the current layer, the still seawater layer, and the seafloor sediment layer: The expression is:

[0032] (6),

[0033] in, , The ocean current layer scalar potential The vertical component of the Earth's magnetic field and the horizontal component The general solution coefficient is The seawater layer scalar potential and seafloor sedimentation scalar potential The coefficient of the product layer is expressed as

[0034] (7),

[0035] Where z is the vertical coordinate in the Cartesian coordinate system, are the depths of ocean currents, seawater, and sediment bottom, respectively. It represents the ratio of the conductivity of the lower medium to that of the upper medium, that is, the relative conductivity of the lower medium. It is a dimensionless parameter. Indicates the absolute thickness of the seafloor sediment layer. scrcs and ccrss are custom expressions for simplifying the formula. For different expressions C, C is expressed as Format, scrcs, ccrs are always expressed in the following format:

[0036] ,

[0037] Substituting the Fourier coefficients into the above In expression (6), the scalar potential of the induced electric field of the bounded sinusoidal ocean current is obtained:

[0038] ,

[0039] in, As shown in formula (7), the subscripts 1, 2, and 3 represent the current layer, the static seawater layer, and the seafloor sediment layer, respectively. As shown in expression (3).

[0040] Further, in step S4, Finding the Gradient , and obtain the horizontal component of the current-induced electric field in the ocean current layer, the still seawater layer, and the seafloor sediment layer and the vertical component expression:

[0041] (8)

[0042] (9).

[0043] The beneficial effects of the present invention are:

[0044] The present invention provides a bounded sinusoidal ocean current induced electric field simulation method based on real seawater resistivity, which realizes a bounded sinusoidal ocean current induced electric field simulation that is closer to the real ocean model. The method can analyze the induced electric field under the longitudinally varying conductivity model, and the ocean current pattern is sinusoidally varying and bounded. Compared with the prior art, the present invention is more in line with the actual ocean environment and ocean current pattern. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 Schematic diagram of the resistivity model for determining the layers (every 30 m) in the seawater resistivity observed by ADCP;

[0047] Figure 3 Schematic diagram of bounded sinusoidal current model;

[0048] Figure 4 is the Fourier coefficient The value of Change diagram of , M=8;

[0049] Figure 5 is the ocean current velocity profile;

[0050] Figure 6 This is the layered profile of seawater conductivity;

[0051] Figure 7 is the conduction current density J in seawater i The direction indicated by the arrow represents the flow direction of the induced current density, and the length represents the conduction current density J i The amplitude of

[0052] Figure 8 is the induced electric field E between seawater and seabed sediment x The profile distribution diagram of

[0053] Fig. 9 is the induced electric field E between seawater and seabed sediment z The cross-sectional distribution diagram. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] The present invention discusses the bounded cosine current induced electric field in a multi-layer ocean physical model based on the real ocean resistivity. That is, a model is established with reference to the ocean resistivity that varies with depth. The velocity in the horizontal direction perpendicular to the seawater flow direction is set to a cosine variation of half a cycle, and the ocean current velocity in other areas is zero. The induced electric field under the model is solved, and the synthetic induced electric field data is used to analyze its characteristics.

[0056] refer to Figure 1 The present invention provides a method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity, comprising the following steps:

[0057] Step S1, setting parameters: calculating or observing seawater conductivity and environmental parameters;

[0058] The ocean current physical model is a data set with a multi-layer structure; one layer of structure corresponds to one ocean current layer, and the environmental parameters of each layer of structure include the horizontal flow velocity, salinity, temperature, thickness of the seawater in the corresponding ocean current layer and the intensity of each component of the geomagnetic field at the location.

[0059] Seawater conductivity can indicate the ability of dissolved salts in seawater to conduct electric current. It is one of the important parameters for evaluating ocean salinity, salinity and seawater quality. The conductivity of seawater is not only related to the salt components dissolved in the water, but also closely related to factors such as water temperature, salinity and pressure. When setting up a multi-layer ocean current physical model, you can refer to the data observed by ADCP (Acoustic Doppler Current Profiler) in nearby waters, or you can use different empirical formulas and correction factors to estimate and extrapolate the conductivity according to specific application scenarios and experimental requirements, thereby providing support for research.

[0060] Based on the estimated or observed conductivity, the seawater is stratified vertically to set conductivity layers of different depths that vary with depth.

[0061] Step S2, determining the ocean current pattern: establishing a Cartesian rectangular coordinate system, and performing Fourier transformation on the ocean current velocity to obtain Fourier coefficients according to the convolution theory;

[0062] The method to establish a Cartesian rectangular coordinate system is as follows:

[0063] Assume that the coordinate origin is on the sea surface, the z-axis is vertically upward, the x-axis points to the east, and the y-axis points to the north; set the classic ocean current velocity model - the sinusoidal ocean current model; the north component of the ocean current velocity The velocity along the y-axis is constant, and only changes along the x-axis; however, in the actual ocean, the current has boundaries, so a rectangular function is set. , only set the current of L width; in summary, the current speed Expressed as the product of a rectangular function, a cosine function, and a constant:

[0064] (1),

[0065] in, is the ocean current velocity amplitude, L is the width of the current, is the circumference of a circle, x is the east-west coordinate in the Cartesian coordinate system.

[0066] According to the convolution theory, the method of Fourier transforming the ocean current velocity to obtain the Fourier coefficient is:

[0067] According to the convolution theory, the ocean current velocity Perform Fourier transform to get , use * to represent convolution, that is:

[0068] (2),

[0069] In the formula Indicates the functional form of the expressions in brackets after Fourier transformation; the rectangular function , cosine function and constant Substituting the Fourier transform of The Fourier coefficients of the ocean current induced electric field are obtained from the expression The expression is:

[0070] (3),

[0071] in, , represents pi, N is the total number of terms in the Fourier expansion, The number representing the number of terms in the Fourier expansion; M is a dimensionless integer greater than 1 that determines the wave number resolution (1< M < N ), generally take:

[0072] ,

[0073] in, ceil represents the rounding function, H is the seawater depth, is the depth of the seafloor sediment layer, L is the width of the current, Represent the average conductivity of seawater and seabed sediment respectively; N is usually a sufficiently large positive integer, and the value of N determines the Fourier coefficient The number of summation terms; when N is large enough, the error caused by discrete Fourier expansion will be very small; in the examples, the value of N is generally taken as 1000 times the value of M. Represents a pulse function, which means that only when the wave number is When .

[0074] Step S3, solving the scalar potential: deriving the control equations and boundary conditions satisfied by the induced scalar potential of the bounded sinusoidal current in the horizontal ocean current layer, the still seawater layer, and the seafloor sediment layer, and solving to obtain the expression thereof;

[0075] The method for deriving the expression of the scalar potential of the induced electric field in the horizontal ocean current layer, the still seawater layer, and the seafloor sediment layer is as follows:

[0076] Based on Maxwell's equations and generalized Ohm's law, the induced scalar potential partial differential equation of the active velocity field is derived:

[0077] (4),

[0078] In the formula, is the Laplace operator, which is a second-order differential operator. is the curl operator, and the curl of velocity is expressed as , They are the electric field scalar potentials in the ocean current layer, the still seawater layer, and the seafloor sediment layer, and they satisfy the velocity-induced electric field The relationship of are the velocity induced electric fields in the east, north and vertical upward components respectively, is the geomagnetic field (refer to the specific scenario and experimental requirements), are the geomagnetic field in the east, north and vertical upward components respectively, is the velocity field vector, Represent the velocity field in the east, north and vertical upward components respectively.

[0079] By deriving the governing equations and boundary conditions satisfied by the bounded sinusoidal current scalar potential, the method for solving its expression is as follows:

[0080] Scalar potential The boundary conditions satisfied are as follows: (a) on the sea surface, the normal component of the conduction current density is zero; (b) at the interface between the ocean current layer and the still seawater layer, the normal components of the scalar potential and the conduction current density are both continuous; (c) at the interface between different resistivities of seawater, the normal components of the scalar potential and the conduction current density are both continuous; (d) on the seafloor interface, the normal components of the scalar potential and the conduction current density are both continuous; (e) at the bottom interface of the sediment layer, the normal component of the conduction current density is zero; that is,

[0081] (5),

[0082] in, is the conductivity of the upper medium, is the conductivity of the underlying medium, are the scalar potential of the upper layer in the multilayer structure of the ocean current layer and the still seawater layer, It is the scalar potential of the lower layer in the multi-layer structure of the ocean current layer and the still sea water layer.

[0083] Combined scalar potential Solving the above formula (4) at the boundary conditions at infinity and at the interface between different media, we can obtain the expression of the total scalar potential in the ocean current layer, the still seawater layer and the seafloor sediment layer:

[0084] (6),

[0085] in, , The ocean current layer scalar potential The vertical component of the Earth's magnetic field and the horizontal component The general solution coefficient is The seawater layer scalar potential and seafloor sedimentation scalar potential The coefficient of the product layer is expressed as:

[0086] (7),

[0087] Where z is the vertical coordinate in the Cartesian coordinate system, are the depths of ocean currents, seawater, and sediment bottom, respectively. It represents the ratio of the conductivity of the lower medium to that of the upper medium, that is, the relative conductivity of the lower medium. It is a dimensionless parameter. Indicates the absolute thickness of the seafloor sediment layer. scrcs and ccrss are custom expressions for simplifying the formula. For different expressions C (C is represented by etc.), scrcs and ccrss are always expressed in the following form:

[0088] ,

[0089] Substituting the Fourier coefficients into the above In expression (6), the scalar potential of the induced electric field of the bounded sinusoidal ocean current is obtained:

[0090] ,

[0091] in, As shown in formula (7), the subscripts 1, 2, and 3 represent the current layer, the static seawater layer, and the seafloor sediment layer, respectively. As shown in expression (3).

[0092] Step S4, solving the electric field: finding the gradient of the scalar potential, obtaining the horizontal and vertical components of the current induced electric field in the current layer, the still seawater layer and the seabed sediment layer, and analyzing the spatial distribution characteristics of the current model induced electric field.

[0093] right Finding the Gradient , and obtain the horizontal component of the current-induced electric field in the ocean current layer, the still seawater layer, and the seafloor sediment layer and the vertical component expression:

[0094] (8)

[0095] (9).

[0096] The present invention provides a method for simulating bounded sinusoidal ocean current induced electric field based on real ocean resistivity. The method discusses bounded cosine ocean current induced electric field based on real ocean resistivity, that is, a model is established with reference to ocean resistivity that varies with depth, and the velocity in the horizontal direction perpendicular to the flow direction of seawater is set to be a cosine variation of half a cycle, and the ocean current velocity in other areas is zero. The bounded ocean current induced electric field formula is derived by using the wave number domain Maxwell equations and the generalized Ohm's law, and the induced electric field is simulated under the model, so that the calculation result is accurate and reliable, and the characteristics of the induced electric field of the ocean current model can be analyzed, so as to provide a reference basis for the design of electromagnetic field detection equipment and the correction of magnetotelluric measurement. Example

[0097] 1. If Figure 2 As shown, the seawater conductivity actually observed by ADCP is layered, and the average value is taken every 30m as the conductivity of the layer. Based on this, the conductivity of the seawater layer that changes with depth is set.

[0098] 2. If Figure 3 As shown in the figure, the geoelectric model is set up, and the conductivity of the reference seabed sediment layer is The depth of seawater is , where the depth of the ocean current layer is The direction of the current is parallel to the y-axis, and the maximum speed of the current is , the width is The depth of the bottom interface of the seafloor sediment layer is .

[0099] 3. Refer to the Fourier transform correspondence table in Table 1 to transform the set sinusoidal speed mode into a discrete Fourier coefficient form, and determine the values ​​of M and N according to the set model parameters to determine the Fourier coefficients In this example, M is set to 8 and N is 1000 times of that, and we can get With the normalized wave frequency The change curve of Figure 4 shown.

[0100] Table 1 is the Fourier transform correspondence table:

[0101]

[0102] 4. The international geomagnetic field model WMM2024 is used to calculate the amplitudes of the components of the geomagnetic field at (30°N, 120°E). The north component is 33814.4nT, the east component is -3516.5nT, and the vertical component is 34970.8nT.

[0103] 5. Substituting the solved Fourier coefficients into the solution of the partial differential equation system, we can get the expression of the scalar potential, and taking the negative gradient we can get Electric field at any location E x According to the generalized Ohm's law, the expression of conduction current density can be calculated:

[0104]

[0105] 6. Figure 5 , Figure 6 Set the geoelectric model and ocean current model, and input the model parameters respectively.

[0106] 7. Figure 7 is the induced conduction current density J in seawater i The direction indicated by the arrow represents the flow direction of the current density, and the length represents the conduction current density J i From the amplitude of the velocity, it can be found that the conduction current density induced by the velocity in the ocean current layer flows back to the ocean current layer through the static seawater layer below, forming a closed loop.

[0107] 8. Figure 8 The induced electric field in seawater and seabed sediments E x The cross-sectional distribution diagram of the induced electric field E x It is not only distributed in the ocean current layer, but also has amplitude in the static seawater layer and the seabed sediment layer, and the magnitude is Such electric field magnitudes do have an impact on the design of electromagnetic field detection equipment and magnetotelluric measurements. Fig. 9 The induced electric field in seawater and seabed sediments E z The cross-sectional distribution diagram of the induced electric field E z The energy is only concentrated in the ocean current layer, and is very small in the static seawater layer and the seabed sediment layer. It can be ignored in the design of electromagnetic field detection equipment and magnetotelluric measurement.E z impact.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for simulating bounded sinusoidal current induced electric field based on real seawater resistivity, characterized in that: The steps include: Step S1, setting parameters: calculating or observing seawater conductivity and environmental parameters; Step S2, determining the ocean current pattern: establishing a Cartesian rectangular coordinate system, and performing Fourier transformation on the ocean current velocity to obtain Fourier coefficients according to the convolution theory; Step S3, solving the scalar potential: deriving the control equations and boundary conditions satisfied by the induced scalar potential of the bounded sinusoidal current in the horizontal ocean current layer, the still seawater layer, and the seafloor sediment layer, and solving to obtain the expression thereof; Step S4, solving the electric field: finding the gradient of the scalar potential, obtaining the horizontal and vertical components of the current induced electric field in the current layer, the still seawater layer and the seabed sediment layer, and analyzing the spatial distribution characteristics of the current model induced electric field.

2. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 1 is characterized in that: In step S1, the ocean current physical model is a data set of a multi-layer structure; one layer of structure corresponds to one layer of ocean current layer, and the environmental parameters of each layer of structure include the horizontal flow velocity, salinity, temperature, thickness of the seawater of the corresponding ocean current layer and the intensity of each component of the geomagnetic field at the location.

3. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 2 is characterized in that: In step S2, the method of establishing a Cartesian rectangular coordinate system is as follows: Assume that the coordinate origin is on the sea surface, the z-axis is vertically upward, the x-axis points to the east, and the y-axis points to the north; set the classic ocean current velocity model - the sinusoidal ocean current model; the north component of the ocean current velocity The velocity along the y-axis is constant, and only changes along the x-axis. In the actual ocean, the current has boundaries, so a rectangular function is set. , only set the current of L width; current speed Expressed as the product of a rectangular function, a cosine function, and a constant: (1）， in, is the ocean current velocity amplitude, L is the width of the current, is the circumference of a circle, x is the east-west coordinate in the Cartesian coordinate system.

4. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 3 is characterized in that: In step S2, according to the convolution theory, the method of performing Fourier transform on the ocean current velocity to obtain the Fourier coefficient is: According to the convolution theory, the ocean current velocity Perform Fourier transform to get , * is used to represent convolution, that is: （2）， In the formula Indicates the functional form of the expressions in brackets after Fourier transformation; the rectangular function , cosine function and constant Substituting the Fourier transform of The Fourier coefficients of the ocean current induced electric field are obtained from the expression The expression is: （3）， in, , represents pi, N is the total number of terms in the Fourier expansion, The number representing the number of terms in the Fourier expansion; M is a dimensionless integer greater than 1 that determines the wave number resolution (1< M < N ),Pick: ， in, ceil Indicates a round-up function, the return value is an integer greater than or equal to the function parameter and closest to it; H is the seawater depth, is the depth of the seafloor sediment layer, L is the width of the current, represent the average electrical conductivity of seawater and seafloor sediments, respectively; Represents a pulse function, which means that only when the wave number is When , and the rest of the values ​​are 0.

5. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 4 is characterized in that: In step S3, the method for deriving the induced electric field expression in the horizontal ocean current layer, the still seawater layer, and the seafloor sediment layer medium is as follows: Based on Maxwell's equations and generalized Ohm's law, the induced scalar potential partial differential equation of the active velocity field is derived: （4）， In the formula, is the Laplace operator, which is a second-order differential operator. is the curl operator, and the curl of velocity is expressed as , They are the electric field scalar potentials in the ocean current layer, the still seawater layer, and the seafloor sediment layer, and they satisfy the velocity-induced electric field The relationship of are the velocity induced electric fields in the east, north and vertical upward components respectively, is the Earth's magnetic field, are the geomagnetic field in the east, north and vertical upward components respectively, is the velocity field vector, Represent the velocity field in the east, north and vertical upward components respectively.

6. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 5 is characterized in that: In step S3, by deriving the control equations and boundary conditions satisfied by the bounded sinusoidal ocean current scalar potential, the method for solving the expression is as follows: Scalar potential The boundary conditions satisfied are as follows: (a) on the sea surface, the normal component of the conduction current density is zero; (b) at the interface between the ocean current layer and the static seawater layer, the normal components of the scalar potential and the conduction current density are both continuous; (c) at the interface between different resistivities of seawater, the normal components of the scalar potential and the conduction current density are both continuous; (d) on the seafloor interface, the normal components of the scalar potential and the conduction current density are both continuous; (e) on the bottom interface of the sediment layer, the normal component of the conduction current density is zero; that is: （5）， in, is the conductivity of the upper medium, is the conductivity of the underlying medium, are the scalar potential of the upper layer in the multilayer structure of the ocean current layer and the still seawater layer, It is the scalar potential of the lower layer in the multilayer structure of the current layer and the still seawater layer; Combined scalar potential Solving the above formula (4) at the boundary conditions at infinity and at the interface between different media, we can obtain the total scalar potential in the current layer, the still seawater layer and the seafloor sediment layer: The expression is: （6）， in, , The ocean current layer scalar potential The vertical component of the Earth's magnetic field and the horizontal component The general solution coefficient is The seawater layer scalar potential and the scalar potential of the seafloor sediments The coefficient of is expressed as: （7）， Where z is the vertical coordinate in the Cartesian coordinate system, are the depths of ocean currents, seawater, and sediment bottom, respectively. It represents the ratio of the conductivity of the lower medium to that of the upper medium, that is, the relative conductivity of the lower medium. It is a dimensionless parameter. Indicates the absolute thickness of the seafloor sediment layer. scrcs and ccrss are custom expressions for simplifying the formula. For different expressions C, C is expressed as Format, scrcs, ccrs are always expressed in the following format: ， Substituting the Fourier coefficients into the above In expression (6), the scalar potential of the induced electric field of the bounded sinusoidal ocean current is obtained: ， in, As shown in formula (7), the subscripts 1, 2, and 3 represent the current layer, the static seawater layer, and the seafloor sediment layer, respectively. As shown in expression (3).

7. The method for simulating bounded sinusoidal ocean current induced electric field based on real seawater resistivity according to claim 6 is characterized in that: In step S4, Finding the Gradient , and obtain the horizontal component of the current-induced electric field in the ocean current layer, the still seawater layer, and the seafloor sediment layer and the vertical component expression: （8）， （9）。

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