Internal wave electromagnetic response numerical simulation method based on layered ocean model

Abstract

The invention discloses an internal wave electromagnetic response numerical simulation method based on a layered ocean model. The method comprises the following steps: acquiring geomagnetic field parameters; calculating distribution characteristics of seawater conductivity along with depth, and dispersing the distribution characteristics into a layered ocean conductivity model; an internal wave mechanical model is constructed, internal wave velocity field distribution is established through characteristic parameters of internal waves, and dynamic input is provided for electromagnetic field response calculation; substituting the internal wave velocity field and the geomagnetic field into a Maxwell equation set, and constructing an internal wave induction electromagnetic field control equation; and applying tangential electric field continuity and normal current continuity conditions on a layered interface, and performing discrete and iterative solution on an equation by adopting a finite difference method to obtain distribution characteristics of the electric field and the magnetic field at different depths and frequencies. According to the method, the problem of insufficient precision caused by a uniform conductivity hypothesis is solved, and application limitation caused by an ideal geomagnetic field hypothesis is avoided, so that accurate simulation of internal wave induction electromagnetic response under a complex ocean condition can be realized.

Description

Technical Field

[0001] This invention relates to the field of marine electromagnetic technology, and in particular to a numerical simulation method for internal wave electromagnetic response based on a layered ocean model. Background Technology

[0002] Against the backdrop of the increasing strategic value of marine resources and the growing national demand for marine observation and monitoring, marine electromagnetic detection technology has gradually become an important means of understanding and utilizing the ocean. Internal waves, as a typical stratified dynamic phenomenon in the ocean, play a crucial role in energy transport, mass mixing, and environmental regulation. During propagation, internal waves generate disturbances in seawater and interact with the Earth's magnetic field to form induced electromagnetic field signals. These electromagnetic signals, on the one hand, constitute background interference for marine electromagnetic detection, and on the other hand, provide potential observational pathways for the inversion and monitoring of marine dynamic processes. Therefore, establishing an accurate model of the induced electromagnetic field of internal waves and conducting simulation studies based on this model is an important prerequisite for improving the accuracy of marine electromagnetic detection and expanding its application value.

[0003] However, existing technologies still have the following two limitations in the simulation study of internal wave induced electromagnetic fields:

[0004] 1. The conductivity assumption is overly simplistic.

[0005] Most existing studies employ a uniform seawater conductivity model, assuming a constant vertical conductivity across the entire water body. While this assumption significantly reduces the complexity of mathematical modeling and calculation, it deviates considerably from the real marine environment. In reality, seawater conductivity is controlled by temperature, salinity, and pressure, exhibiting a distinct stratification characteristic in the vertical direction. For example, in a typical ocean profile, the conductivity differences between the surface, hydrome, and deep layers are significant, and this stratified structure has a crucial impact on the amplitude and spatial distribution of the internal wave-induced electromagnetic field. Ignoring conductivity stratification not only leads to discrepancies between simulation results and measured data but may also obscure certain key characteristics of the internal wave electromagnetic signal, limiting the reliability and generalizability of the model in engineering applications.

[0006] 2. Failure to incorporate actual geomagnetic field parameters

[0007] Most studies simulating internal wave-induced electromagnetic fields use only an idealized, constant background magnetic field or simplified magnetic field conditions with fixed direction and intensity, failing to incorporate the spatial variations and regional differences of the real geomagnetic field. In reality, the geomagnetic field exhibits differences in intensity, dip, and declination across different sea areas and latitudes; these parameters directly determine the geomagnetic field's behavior. The direction and amplitude of the induced source term. If the model fails to incorporate the actual geomagnetic field characteristics of the study area, the simulation results will not match the observation data, thus limiting the model's interpretability and application value in actual marine environments.

[0008] In summary, existing technologies for simulating internal wave-induced electromagnetic fields generally suffer from insufficient consideration of conductivity stratification effects and failure to incorporate actual geomagnetic field parameters. These shortcomings lead to discrepancies between simulation results and the real marine environment, making it difficult to accurately reflect the amplitude and spatial distribution characteristics of the internal wave electromagnetic response. Consequently, these limitations restrict their reliability and widespread application in observational data interpretation, parameter inversion, and engineering applications.

[0009] Therefore, how to provide a numerical simulation method for the electromagnetic response of internal waves based on a layered ocean model has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In view of this, the purpose of this invention is to provide a numerical simulation method for internal wave electromagnetic response based on a layered ocean model, which not only overcomes the problem of insufficient accuracy caused by the assumption of uniform conductivity, but also avoids the application limitations caused by the assumption of idealized geomagnetic field, thereby enabling accurate simulation of internal wave induced electromagnetic response under complex ocean conditions.

[0011] The present invention solves the technical problem by adopting the following technical solution:

[0012] A numerical simulation method for internal wave electromagnetic response based on a layered ocean model includes the following steps:

[0013] Step S10: Obtain geomagnetic field parameters;

[0014] Step S20: Establish a layered ocean conductivity model. Combine measured or reanalysis data of temperature, salinity and pressure in the study area to calculate the distribution characteristics of seawater conductivity with depth and discretize it into a layered ocean conductivity model.

[0015] Step S30: Construct an internal wave dynamic model and establish the internal wave velocity field distribution through the characteristic parameters of the internal wave to provide dynamic input for electromagnetic field response calculation;

[0016] Step S40: Solve the electromagnetic field response based on the finite difference method. Under the combined conditions of the layered ocean conductivity model, actual geomagnetic field parameters, and internal wave dynamics model, substitute the internal wave velocity field and geomagnetic field into Maxwell's equations to construct the control equations for the internal wave-induced electromagnetic field. Apply the conditions of continuous tangential electric field and continuous normal current at the layered interface, and use the finite difference method to discretize and iteratively solve the equations to obtain the distribution characteristics of electric and magnetic fields at different depths and frequencies.

[0017] Furthermore, prior to step S10, step S00 is included, which establishes a target conductivity model by combining regional hydrological and geophysical data, as follows:

[0018] Based on existing temperature, salinity, and pressure profiles of the sea area, as well as geophysical survey data, a background conductivity structure and target conductivity model for the region were established. The target conductivity model is divided into three layers: the upper layer is the air layer, with approximately zero conductivity; the middle layer is the seawater layer, with a conductivity of... The density varies with depth z and exhibits significant stratification near the thermocline, along with distinct density stratification. The densities of the upper and lower layers are respectively... , The lower part is a seabed sedimentary layer or bedrock, with an electrical conductivity set to [value missing]. .

[0019] Furthermore, in step S10, the method for obtaining the geomagnetic field parameters is as follows:

[0020] Based on the latitude and longitude of the study area and the observation time, the three elements of the geomagnetic field in the region are obtained using the International Geomagnetic Reference Field or the World Geomagnetic Field Model, including magnetic declination, magnetic inclination, and total field intensity. The three elements of the geomagnetic field are transformed into geomagnetic vectors in a rectangular coordinate system through coordinate transformation, which serve as the background field input in the subsequent electromagnetic response calculation.

[0021] Furthermore, in step S30, based on the water depth conditions and density stratification of the study area, the depth of the inner wave interface and the density difference between the upper and lower layers are determined, and the characteristic parameters of the inner wave, including wave height and period parameters, are set.

[0022] Furthermore, the governing equations for the internal wave-induced electromagnetic field are:

[0023]

[0024] in, For spatial gradient operators, For the Laplace operator, The vector of the induced magnetic field. The internal wave frequency, The electrical conductivity of seawater, The background geomagnetic field vector. For internal wave velocity field, is the electric field intensity vector.

[0025] The present invention discloses a numerical simulation method for internal wave electromagnetic response based on a layered ocean model, which has the following advantages:

[0026] This invention overcomes the shortcomings of existing technologies, such as insufficient accuracy due to the assumption of uniform conductivity and limited applicability caused by idealized magnetic field conditions, by systematically introducing the vertical stratification of seawater conductivity into electromagnetic field simulation and combining it with actual geomagnetic field parameters of the study area. The finite difference method is used to numerically solve the governing equations, maintaining the stability and accuracy of the calculations under stratified boundary conditions. This allows the simulation results of internal wave-induced electromagnetic fields to more realistically reflect the electromagnetic response characteristics in complex marine environments. By simultaneously considering stratified conductivity and actual geomagnetic field parameters, the simulation results obtained by this invention better match real-world observations and can be directly applied to electromagnetic noise identification, observation data interpretation, and internal wave parameter inversion, thereby significantly improving the realism, reliability, and engineering application value of internal wave electromagnetic field simulations. Attached Figure Description

[0027] Figure 1 This is a flowchart of the method of the present invention.

[0028] Figure 2 This is a layered model of how the electrical conductivity of seawater varies with depth in a three-layer structure of air-seawater-sediment layer.

[0029] Figure 3 This is a roadmap for finite-difference numerical simulation of internal wave-induced electromagnetic fields based on a layered ocean model.

[0030] Figure 4 This is a profile of temperature, salinity, pressure, and seawater conductivity in a certain area of ​​the South China Sea.

[0031] Figure 5 The results show the comparison of the internal wave induced electromagnetic field components (Bx, Ey, Bz) under the conditions of the layered conductivity model and the uniform conductivity model. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] The purpose of this invention is to provide a numerical simulation method for internal wave electromagnetic response based on a layered ocean model, in order to address the shortcomings of existing technologies in simulating internal wave induced electromagnetic fields: First, the commonly used assumption of uniform seawater conductivity fails to reflect the layered conductivity characteristics of seawater with depth, resulting in a significant discrepancy between the calculated results and the actual marine environment; Second, existing studies often use idealized or simplified background magnetic field conditions, failing to incorporate actual geomagnetic field parameters, which limits the realism of the simulation results and their engineering application value.

[0034] To overcome the aforementioned shortcomings, this invention systematically introduces a stratified seawater conductivity model during the numerical simulation process. Combined with the actual geomagnetic field parameters of the study area, the finite difference method is used to solve the governing equations, enabling the simulation results to more closely approximate the real marine environment. Compared with existing technologies, this invention not only overcomes the accuracy limitations caused by the uniform conductivity assumption but also avoids the application limitations brought about by the idealized geomagnetic field assumption, thus achieving accurate simulation of the internal wave-induced electromagnetic response under complex marine conditions.

[0035] This invention effectively improves the realism and reliability of internal wave electromagnetic field simulation, providing more scientific and powerful technical support for the interpretation of marine electromagnetic observation data, the study of internal wave dynamic processes, and related engineering applications.

[0036] To overcome the shortcomings of existing technologies that commonly employ uniform seawater conductivity models, fail to consider conductivity stratification effects, and do not incorporate actual geomagnetic field conditions, this invention provides a numerical simulation method for internal wave electromagnetic response based on a stratified ocean model. This method systematically introduces the vertical stratification structure of seawater conductivity into the electromagnetic field simulation and incorporates the actual geomagnetic field parameters of the study area as the background field. The finite difference method is then used to solve the electromagnetic field governing equations, thereby significantly improving the realism and applicability of the simulation results.

[0037] refer to Figure 1 A numerical simulation method for the electromagnetic response of internal waves based on a layered ocean model includes the following steps:

[0038] Step S00: Establish the target conductivity model by combining regional hydrological and geophysical data, as follows:

[0039] Based on existing temperature, salinity, and pressure profiles of the sea area, as well as geophysical survey data, a background conductivity structure and target conductivity model for the region were established. The target conductivity model is divided into three layers: the upper layer is the air layer, with approximately zero conductivity; the middle layer is the seawater layer, with a conductivity of... The density varies with depth z and exhibits significant stratification near the lattice layer, along with distinct density stratification. The densities of the upper and lower layers are respectively... , The lower part is a seabed sedimentary layer or bedrock, with an electrical conductivity set to [value missing]. This layered structure can accurately reflect the vertical variation of seawater conductivity, effectively avoiding the systematic bias caused by the traditional assumption of uniform conductivity.

[0040] Step S10: Obtain geomagnetic field parameters. Based on the latitude and longitude of the study area and the observation time, use the International Geomagnetic Reference Field (IGRF) or the World Geomagnetic Model (WMM) to obtain the three elements of the geomagnetic field in the region: magnetic declination, magnetic inclination, and total field intensity. Transform these three elements into geomagnetic vectors in a rectangular coordinate system, which will then serve as the background field input for subsequent electromagnetic response calculations. This step ensures that the geomagnetic conditions used in the simulation are consistent with the actual marine environment, providing a basis for driving the induced electromagnetic field.

[0041] Step S20: Establish a layered ocean conductivity model. Combine measured or reanalytical data on temperature, salinity, and pressure in the study area to calculate the distribution characteristics of seawater conductivity with depth and discretize it into a layered ocean conductivity model. This step can avoid the systematic bias caused by the traditional uniform conductivity assumption and more realistically reflect the vertical electrical structure of the marine environment.

[0042] Step S30 involves constructing an internal wave dynamic model. Based on the water depth conditions and density stratification of the study area, the depth of the internal wave interface and the density difference between the upper and lower layers are determined, and characteristic parameters of the internal waves, including wave height and period (or frequency), are set. These parameters are used to establish the internal wave velocity field distribution, providing dynamic input for electromagnetic field response calculations. The purpose of this step is to introduce the physical characteristics of internal waves into the numerical model, enabling the simulation results to reflect the electromagnetic effects of different types of internal waves in a stratified ocean.

[0043] Step S40 involves solving for the electromagnetic field response using the finite difference method. Under the combined conditions of the layered ocean conductivity model, actual geomagnetic field parameters, and internal wave dynamics model, the internal wave velocity field and geomagnetic field are substituted into Maxwell's equations to construct the governing equations for the internal wave-induced electromagnetic field. Conditions of tangential electric field continuity and normal current continuity are applied at the layered interfaces. The finite difference method is then used to discretize and iteratively solve the equations, obtaining the distribution characteristics of the electric and magnetic fields at different depths and frequencies. This step ensures the stability and reliability of the calculation process, enabling physically reasonable simulation results to be obtained in complex layered environments.

[0044] The governing equations for the internal wave-induced electromagnetic field are:

[0045]

[0046] in, For spatial gradient operators, For the Laplace operator, The vector of the induced magnetic field. The internal wave frequency, The electrical conductivity of seawater, The background geomagnetic field vector. For internal wave velocity field, The electric field intensity vector, denoted as ρ, where ρ is the permeability of the medium.

[0047] Through the above steps, this invention achieves high-precision simulation of internal wave-induced electromagnetic fields in a stratified marine environment. It not only overcomes the shortcomings of existing technologies caused by neglecting conductivity stratification and idealized magnetic field conditions, but also fully considers the influence of internal wave interfaces, density differences between upper and lower layers, and internal wave parameters on electromagnetic response, thereby significantly improving the realism, reliability, and engineering application value of the simulation results.

[0048] Example

[0049] To verify the effectiveness of this invention and further illustrate its application in complex marine environments, this embodiment proposes and implements a numerical simulation method for internal wave electromagnetic response based on a layered ocean model. Specifically, it includes the following steps:

[0050] S1: Establish a target conductivity model by combining regional hydrological and geophysical data.

[0051] Before conducting numerical simulations, it is necessary to first clarify the hydrological environment and electrical structure characteristics of the study area. This embodiment selects a sea area in the South China Sea as the research object, and combines existing temperature, salinity, and pressure profile data with geophysical survey data to establish a background conductivity structure and target conductivity model for the region. This model uses a three-layer division: the upper layer is the air layer, with approximately zero conductivity; the middle layer is the seawater layer, with a conductivity of... The density varies with depth z and exhibits significant stratification near the lattice layer, along with distinct density stratification. The densities of the upper and lower layers are respectively... , The lower part is a seabed sedimentary layer or bedrock, with an electrical conductivity set to [value missing]. This layered structure accurately reflects the vertical variation of seawater conductivity, effectively avoiding the systematic biases introduced by the traditional assumption of uniform conductivity. The target conductivity model is as follows: Figure 2 As shown, this provides physical boundary conditions for subsequent numerical simulations. Figure 2 The upper and middle sections consist of an air layer, while the middle section is composed of layered seawater (divided into upper and lower layers with different densities). , The conductivity varies with depth. The bottom is the seabed medium (conductivity) ).

[0052] S2: Obtain regional geomagnetic field parameters and internal wave parameters

[0053] In addition to establishing the conductivity structure, it is also necessary to introduce actual geomagnetic field parameters and internal wave motion characteristics.

[0054] First, using the International Geomagnetic Reference Field (IGRF) model or the World Geomagnetic Magnetic Model (WMM), based on the latitude and longitude of the study area and the observation time, the three elements of the geomagnetic field are obtained: magnetic declination D, magnetic inclination I, and total field intensity F0. Then, through coordinate transformation, the background magnetic field vector F in the rectangular coordinate system is obtained as follows:

[0055]

[0056] The background magnetic field vector is used as the background condition input to the numerical model to drive the internal wave-induced electromagnetic field. Secondly, by combining existing internal wave observations and statistical results in the region, parameters such as wave height and dominant frequency of the internal waves are determined to make the internal wave input conditions closely approximate real sea conditions. Finally, measured hydrological profile data are substituted into empirical formulas to obtain the seawater conductivity curve varying with depth. Through the above steps, this embodiment establishes a complete regional environmental model, including the conductivity layering structure, geomagnetic field background, and internal wave motion conditions, laying the foundation for subsequent calculations. The technical route of this step is as follows: Figure 3 As shown.

[0057] S3: Establishing a Seawater Conductivity Model Based on Empirical Formulas After determining the regional environmental parameters, this embodiment establishes a seawater conductivity model based on hydrological profile data (temperature T(z), salinity S(z), and pressure P(z)) using empirical formulas. The seawater conductivity variation curve with depth was calculated. This method incorporates the combined effects of decreasing temperature, abrupt salinity changes, and increasing pressure on conductivity into the model, thus obtaining a vertical conductivity distribution that conforms to the characteristics of actual sea areas. By segmenting the curve, a layered conductivity model can be established in numerical simulations, more realistically reflecting the vertical electrical structure of the marine medium. This step effectively overcomes the bias caused by the traditional assumption of uniform conductivity, providing reasonable input conditions for subsequent finite difference numerical calculations. The seawater conductivity profile model obtained based on temperature, salinity, and pressure data from a certain sea area in the South China Sea is shown below. Figure 4 As shown.

[0058] S4: Simulation and Result Comparison of Internal Wave Electromagnetic Response Based on Layered Ocean Model

[0059] After obtaining the above environmental conditions, the layered conductivity model, internal wave velocity field, and background geomagnetic field were substituted into Maxwell's equations. The governing equations were discretized and iteratively solved using the finite difference method to obtain the distribution characteristics of the electric and magnetic fields at different depths, frequencies, and directions. The governing equations are as follows: The simulation results are as follows: Figure 5As shown, the components of the internal wave-induced electromagnetic field (Bx, Ey, Bz) are compared under the conditions of the layered conductivity model and the uniform conductivity model. The results show that under the uniform conductivity condition, the electromagnetic field response amplitude is low and the variation is simple, making it difficult to reflect the detailed characteristics of the internal wave-induced electromagnetic field; while under the layered conductivity condition, the response amplitude is higher and the fluctuation is more complex, which is closer to the actual observation results, and significantly improves the realism and applicability of the simulation.

[0060] As can be seen from this embodiment, by introducing a layered seawater conductivity model, combining regional geomagnetic field parameters, and using the finite difference method for solution, the present invention effectively overcomes the problem of insufficient accuracy caused by the assumption of uniform conductivity in the prior art. It can achieve accurate simulation of the internal wave induced electromagnetic field in the real marine environment, and provide scientific support for the interpretation of marine electromagnetic observation data, noise identification, and internal wave parameter inversion.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A numerical simulation method for the electromagnetic response of internal waves based on a layered ocean model, characterized in that, Includes the following steps: Step S10: Obtain geomagnetic field parameters; Step S20: Establish a layered ocean conductivity model. Combine measured or reanalysis data of temperature, salinity and pressure in the study area to calculate the distribution characteristics of seawater conductivity with depth and discretize it into a layered ocean conductivity model. Step S30: Construct an internal wave dynamic model and establish the internal wave velocity field distribution through the characteristic parameters of the internal wave to provide dynamic input for electromagnetic field response calculation; Step S40: Solve the electromagnetic field response based on the finite difference method. Under the combined conditions of the layered ocean conductivity model, actual geomagnetic field parameters, and internal wave dynamics model, substitute the internal wave velocity field and geomagnetic field into Maxwell's equations to construct the control equations for the internal wave-induced electromagnetic field. Apply the conditions of continuous tangential electric field and continuous normal current at the layered interface, and use the finite difference method to discretize and iteratively solve the equations to obtain the distribution characteristics of electric and magnetic fields at different depths and frequencies.

2. The numerical simulation method for internal wave electromagnetic response based on a layered ocean model according to claim 1, characterized in that, Before step S10, there is also step S00, which establishes a target conductivity model by combining regional hydrological and geophysical data, as follows: Based on existing temperature, salinity, and pressure profiles of the sea area, as well as geophysical survey data, a background conductivity structure and target conductivity model for the region were established. The target conductivity model is divided into three layers: the upper layer is the air layer, with approximately zero conductivity; the middle layer is the seawater layer, with a conductivity of... The density varies with depth z and exhibits significant stratification near the lattice layer, along with distinct density stratification. The densities of the upper and lower layers are respectively... , The lower part is a seabed sedimentary layer or bedrock, with an electrical conductivity set to [value missing]. .

3. The numerical simulation method for internal wave electromagnetic response based on a layered ocean model according to claim 2, characterized in that, In step S10, the method for obtaining geomagnetic field parameters is as follows: Based on the latitude and longitude of the study area and the observation time, the three elements of the geomagnetic field in the region are obtained using the International Geomagnetic Reference Field or the World Geomagnetic Field Model, including magnetic declination, magnetic inclination, and total field intensity. The three elements of the geomagnetic field are transformed into geomagnetic vectors in a rectangular coordinate system through coordinate transformation, which serve as the background field input in the subsequent electromagnetic response calculation.

4. The numerical simulation method for internal wave electromagnetic response based on a layered ocean model according to claim 3, characterized in that, In step S30, based on the water depth conditions and density stratification of the study area, the depth of the inner wave interface and the density difference between the upper and lower layers are determined, and the characteristic parameters of the inner wave, including wave height and period, are set.

5. The numerical simulation method for internal wave electromagnetic response based on a layered ocean model according to claim 4, characterized in that, The governing equations for the internal wave-induced electromagnetic field are: in, For spatial gradient operators, For the Laplace operator, The vector of the induced magnetic field. The internal wave frequency, The electrical conductivity of seawater, The background geomagnetic field vector. For internal wave velocity field, is the electric field intensity vector.

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