Method and device for forward modeling by simulating rugged topography

Abstract

The invention discloses a method and equipment for simulating rugged topography to carry out forward modeling, and the method comprises the steps: building a curved coordinate system according to the form of a target rugged topography, and obtaining the number of curved coordinate systems of each calculation node under the curved coordinate system; electromagnetic parameters required by forward modeling simulation are set, and a radar wave fluctuation equation under the curved coordinate system is split to obtain a plurality of split equations which can be independently calculated; according to the number of the curved coordinate systems and the structure of the splitting equation, the deployment positions of the electric field intensity and the magnetic field intensity in the staggered grids are optimized, so that the staggered grids are matched with the spatial characteristics of the curved coordinate systems and the number of the curved coordinate systems; staggered grid calculation is carried out on the splitting equations, calculation results of the splitting equations are recombined and added, the calculation results are stored in grid units according to a staggered rule, and high-precision forward modeling of the rugged topography is achieved. According to the method, the problems of stepped angular points and derived frequency dispersion and scattering generated when the rugged topography is simulated by a conventional regular grid can be effectively avoided, and the wave field simulation precision is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of earth exploration technology, and in particular to a method and apparatus for simulating undulating terrain in forward modeling. Background Technology

[0002] Ground-penetrating radar (GPR) is a geophysical exploration method that relies on differences in electromagnetic media for shallow exploration. It is characterized by its simple operation, lightweight instruments, and high resolution, and is widely used in shallow geological identification and prediction, quality inspection, engineering inspection, environmental protection, and geological disaster monitoring. With the increasing demand for high-precision wavefield simulation of GPR, the influence of surface undulations on radar wave propagation needs to be incorporated into the simulation process.

[0003] Existing simulations of undulating terrain mostly use regular grids, which artificially introduce stepped corner points, causing dispersion in the wave field simulation and seriously affecting the simulation accuracy. Although curved grids can better fit the real surface undulations and avoid the introduction of corner points, the staggered grid calculation format, which has better stability, cannot be adapted in conventional forward wave field simulations due to the introduction of new parameters by the curved coordinate system.

[0004] Therefore, how to use staggered grids in curved coordinates to realize radar wave forward modeling simulation, overcome the corner scattering and dispersion problems of regular grids, and improve the simulation accuracy of undulating terrain wave fields is a technical problem that urgently needs to be solved.

[0005] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method and apparatus for simulating undulating terrain in forward modeling. By establishing a curved coordinate system that fits the target undulating terrain and a radar wave equation under a split curved coordinate system, the deployment positions of electric field strength and magnetic field strength in the staggered grid are optimized and the results are recombined after calculation. This solves the technical problems of wave field dispersion and low simulation accuracy caused by the introduction of stepped corner points when simulating undulating terrain with regular grids, and the inability of conventional staggered grids to adapt to curved coordinate systems.

[0007] To achieve the above objectives, the present invention provides a method for simulating undulating terrain through forward modeling, the method comprising:

[0008] Establish a curved coordinate system based on the target undulating terrain morphology, and obtain the curved coordinate coefficients of each calculation node under the curved coordinate system;

[0009] Set the electromagnetic parameters required for forward modeling and split the radar wave equation in the curved coordinate system to obtain multiple independently computable split equations;

[0010] Based on the curvilinear coordinate coefficients and the structure of the splitting equation, the deployment positions of the electric field strength and magnetic field strength in the staggered grid are optimized so that the staggered grid adapts to the spatial characteristics of the curvilinear coordinate system and the curvilinear coordinate coefficients.

[0011] Each split equation is calculated using staggered grids. The calculation results of each split equation are then recombined and added together, and stored in grid cells according to the staggered rules to achieve high-precision forward modeling of undulating terrain.

[0012] In one embodiment of the present invention, the specific method for establishing a curved coordinate system based on the target undulating terrain morphology is as follows:

[0013] Based on the surface contour features of the target undulating terrain, a curved coordinate system is constructed using a body-fitting coordinate transformation method, so that the boundary of the curved coordinate system fits the surface contour of the target undulating terrain.

[0014] In one embodiment of the present invention, the specific method for obtaining the curvilinear coordinate coefficients of each calculation node in the curvilinear coordinate system is as follows:

[0015] By solving a set of equations that satisfy the preset boundary conditions, the curvature coordinate coefficients of each computation node are obtained. These curvature coordinate coefficients reflect the degree of mesh curvature and coordinate transformation relationship of the corresponding node.

[0016] In one embodiment of the present invention, the specific method for setting the electromagnetic parameters required for forward modeling is as follows:

[0017] The electromagnetic parameters include the dielectric constant, conductivity, and magnetic permeability of the medium, and the values ​​of each parameter are determined with reference to the measured data of the physical properties of the actual medium corresponding to the target terrain.

[0018] In one embodiment of the present invention, the specific method for setting the electromagnetic parameters required for forward modeling is as follows:

[0019] When setting electromagnetic parameters, the parameter values ​​should be checked for rationality in accordance with the accuracy requirements of forward modeling, and abnormal values ​​that exceed the range of physical characteristics should be eliminated.

[0020] In one embodiment of the present invention, the specific method for splitting the radar wave equation in the curved coordinate system is as follows:

[0021] The split equation follows the physical laws of wave field propagation, splitting the original wave equation into two independently solvable split equation structures without losing the spatial characteristic information of the curved coordinate system.

[0022] In one embodiment of the present invention, the specific method for optimizing the deployment positions of electric field strength and magnetic field strength in the staggered grid based on the curved coordinate coefficients and the structure of the splitting equation is as follows:

[0023] The electric field strength is deployed at 1 / 4 nodes of the grid, and the magnetic field strength is deployed at the whole nodes of the interlaced grid, with the deployment positions matching the curvilinear coordinate coefficient characteristics of the corresponding nodes one by one.

[0024] In one embodiment of the present invention, the specific method for performing staggered grid calculations on each splitting equation is as follows:

[0025] The calculation uses the curved coordinate coefficients as a reference and employs second-order precision differential calculation logic to reduce the calculation error caused by mesh curvature.

[0026] In one embodiment of the present invention, the specific method for recombining and adding the calculation results of each split equation and storing them in the grid cells according to the interleaving rule is as follows:

[0027] During reorganization, the results of each split equation are summarized according to the physical quantity type of electric field strength and magnetic field strength. When storing, the results are kept consistent with the optimized deployment location, and a data call interface is reserved for subsequent iterative calculations.

[0028] Secondly, the present invention provides an apparatus for simulating undulating terrain in forward modeling, characterized in that the apparatus comprises:

[0029] One or more processors;

[0030] A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method for forward modeling undulating terrain as described in the first aspect.

[0031] Compared with the prior art, the method and apparatus for forward modeling undulating terrain according to the present invention have significant technical advantages:

[0032] The present invention provides a method and apparatus for forward modeling undulating terrain, which can effectively avoid the stepped corner points and the resulting dispersion and scattering problems generated when simulating undulating terrain using conventional regular grids, thus significantly improving the accuracy of wave field simulation. It achieves the adaptation of the staggered grid calculation format to the curved coordinate system, giving full play to the stability advantage of the staggered grid, and the curved grid can accurately fit the real surface undulation, making the wave field propagation simulation more in line with the actual scene. The calculation logic is concise and efficient, controlling the amount of calculation while ensuring high accuracy. The wave field propagation process is stable, and there is no obvious reflection interference at the boundary, meeting the high accuracy requirements of radar wave forward modeling under undulating terrain. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of a method for simulating undulating terrain using forward modeling, provided in Embodiment 1.

[0034] Figure 2a is a diagram showing the mapping relationship between the curved mesh conforming to the undulating terrain in the Cartesian coordinate system (xz) and the body coordinate system (qr) provided in this embodiment.

[0035] Figure 2 b is a diagram showing the regular computational mesh in the body-fitted coordinate system (qr) provided in this embodiment;

[0036] Figure 3 This is a schematic diagram of the conventional staggered grid difference calculation of the transverse electric wave (TE wave) equation provided in this embodiment 2;

[0037] Figure 4 This is a schematic diagram showing the calculation positions of each field component and auxiliary parameter of the radar wave equation (Equation 16) in the curved coordinate system provided in this embodiment 2;

[0038] Figure 5 This is a schematic diagram of the optimized staggered mesh difference structure in curved coordinates provided in Embodiment 2.

[0039] Figure 6 This is a simulation model of the undulating terrain based on curved mesh construction provided in Embodiment 2;

[0040] Figure 7 a is the transverse electric wave of the peak model at time 60 ns provided in this embodiment two. Figure showing the results of the forward modeling simulation of the wavefield (components);

[0041] Figure 7 b is the transverse electric wave of the peak model at 100 ns, as provided in this embodiment two. Figure showing the results of the forward modeling simulation of the wavefield (components);

[0042] Figure 7 c is the transverse electric wave of the peak model at time 140 ns provided in this embodiment two. Figure showing the results of the forward modeling simulation of the wavefield (components);

[0043] Figure 8 This is a schematic diagram of a device for simulating undulating terrain and performing forward modeling, provided in Embodiment 3. Detailed Implementation

[0044] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0045] Unless otherwise expressly stated, throughout the specification and claims, the term "comprising" or its variations such as "including" or "comprises" shall be understood to include the stated elements or components without excluding other elements or other components.

[0046] Existing regular grids introduce stepped corner points when simulating undulating terrain, resulting in wave field dispersion and low simulation accuracy. Furthermore, conventional staggered grids are not suitable for curved coordinate systems.

[0047] Example 1:

[0048] This embodiment provides a method for forward modeling undulating terrain, such as... Figure 1 As shown, the method includes the following steps:

[0049] S101: Establish a curved coordinate system based on the target undulating terrain morphology, and obtain the curved coordinate coefficients of each calculation node under the curved coordinate system.

[0050] Before constructing the curved coordinate system, the surface contour features of the target undulating terrain must first be clearly defined, such as the undulation height and contour curve shape. In this first embodiment, the boundary of the simulation area is set to satisfy the Dirichlet boundary condition. Through body-fit coordinate transformation, the actual surface contour of the target undulating terrain is directly used as the boundary coordinate axis of the curved coordinate system. For a two-dimensional undulating surface, orthogonal and non-orthogonal curves are drawn along the surface undulation shape, such as... Figure 2 (a) Make these curves correspond to the coordinate axes q=constant and r=constant in the body-fitted coordinate system, such as... Figure 2 (b) This allows the boundary of the curved coordinate system to be directly associated with the boundary of the real terrain. The boundary lines of the real physical domain form the coordinate axes of the body-fitted coordinate system, which can accurately obtain the correspondence between the internal parameters of the irregular physical region and the grid nodes of the body-fitted coordinate system, thereby improving the calculation accuracy of subsequent electromagnetic wave field simulations.

[0051] By solving the partial differential equations that satisfy the Dirichlet boundary conditions, this embodiment can optimize the mesh density by combining the Poisson equations, determine the distribution of computation nodes inside the curved coordinate system, ensure that the arrangement logic of the internal nodes is consistent with the surface undulation trend, and ultimately achieve the effect that the coordinate system boundary and the terrain outline are completely aligned and the internal nodes are aligned with the terrain trend.

[0052] S102: Set the electromagnetic parameters required for forward modeling and split the radar wave equation in the curved coordinate system to obtain multiple independently computable split equations.

[0053] Specific types of electromagnetic parameters include dielectric constant. Electrical conductivity magnetic permeability In this first embodiment, the relative permittivity is set to 5, the permeability is set to the vacuum permeability, and the conductivity is set to 0.001 S / m.

[0054] The purpose of the splitting equation is to adapt the new parameters of the curved coordinate system, namely the curved coordinate coefficients, to solve the problem that conventional staggered meshes cannot be applied.

[0055] S103: Based on the curved coordinate coefficients and the structure of the splitting equation, optimize the deployment positions of the electric field strength and magnetic field strength in the staggered grid, so that the staggered grid adapts to the spatial characteristics of the curved coordinate system and the curved coordinate coefficients.

[0056] In this first embodiment, after splitting the equations, the parameters in the x and z directions are swapped when calculating the spatial difference. The parameter deployment positions of conventional staggered meshes, such as the fixed distribution of electric and magnetic fields at the half-nodes, cannot accommodate this swapping, leading to calculation errors. Curved coordinate coefficients are core parameters reflecting the relationship between the curvature of the curved mesh and coordinate transformation; their positions must conform to the mesh's curvature characteristics during optimized deployment.

[0057] After optimization, the electric field strength ( , Deployed at 1 / 4 nodes, magnetic field strength ( Deployed at the entire node, this staggered distribution is perfectly adapted to the spatial characteristics of the curved coordinate system boundary conforming to the terrain and the internal nodes bending with the undulations. This deployment can avoid scattering at the corners of the regular grid and eliminate wave field dispersion.

[0058] S104: Perform staggered grid calculations on each split equation, recombine and add the calculation results of each split equation, and store them in grid cells according to the staggered rules to achieve high-precision forward modeling of undulating terrain.

[0059] The decomposition does not lose the spatial characteristic information of the curved coordinate system, and can restore the complete physical quantities of the wave field. Relevant parameters are calculated separately at each node of the entire mesh, and then summed after calculation to obtain the magnetic field strength. ); Calculate the electric field intensity after splitting at the staggered grid nodes respectively. , The relevant components are added together to obtain the final electric field strength.

[0060] If the curved coordinate system does not closely match the actual undulating terrain, leading to deviations in the subsequent simulation, a preferred implementation scheme exists in conjunction with the embodiments of the present invention. Specifically, the method for establishing a curved coordinate system based on the target undulating terrain morphology is as follows:

[0061] Based on the surface contour features of the target undulating terrain, a curved coordinate system is constructed using a body-fitting coordinate transformation method, so that the boundary of the curved coordinate system fits the surface contour of the target undulating terrain.

[0062] If the process of obtaining the curvilinear coordinate coefficients is not rigorous or has low accuracy, it cannot provide reliable data support for subsequent calculations. In conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, the method for obtaining the curvilinear coordinate coefficients of each calculation node in the curvilinear coordinate system is as follows:

[0063] By solving a set of equations that satisfy the preset boundary conditions, the curvature coordinate coefficients of each computation node are obtained. These curvature coordinate coefficients reflect the degree of mesh curvature and coordinate transformation relationship of the corresponding node.

[0064] If the electromagnetic parameters are set arbitrarily and do not match the actual terrain and medium characteristics, leading to distorted simulation results, then, in conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, the method for setting the electromagnetic parameters required for forward modeling is as follows:

[0065] The electromagnetic parameters include the dielectric constant, conductivity, and magnetic permeability of the medium, and the values ​​of each parameter are determined with reference to the measured data of the physical properties of the actual medium corresponding to the target terrain.

[0066] If abnormal values ​​exist in the electromagnetic parameters, leading to logical contradictions and unreliable results in the wave field simulation, a preferred implementation scheme exists in conjunction with the embodiments of the present invention. Specifically, the method for setting the electromagnetic parameters required for forward modeling is as follows:

[0067] When setting electromagnetic parameters, the parameter values ​​should be checked for rationality in accordance with the accuracy requirements of forward modeling, and abnormal values ​​that exceed the range of physical characteristics should be eliminated.

[0068] If, after splitting the wave equation, the split equation has poor compatibility with the curved coordinate system, or if key features are lost leading to calculation errors, then, in conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, the method for splitting the radar wave equation in the curved coordinate system is as follows:

[0069] The split equation follows the physical laws of wave field propagation, splitting the original wave equation into two independently solvable split equation structures without losing the spatial characteristic information of the curved coordinate system.

[0070] If the deployment positions of the electric and magnetic field intensities are unclear, leading to an imbalance in adaptation with the curved mesh features, in conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, based on the curved coordinate coefficients and the structure of the splitting equation, the specific method for optimizing the deployment positions of the electric and magnetic field intensities in the staggered mesh is as follows:

[0071] The electric field strength is deployed at 1 / 4 nodes of the grid, and the magnetic field strength is deployed at the whole nodes of the interlaced grid, with the deployment positions matching the curvilinear coordinate coefficient characteristics of the corresponding nodes one by one.

[0072] If the calculation accuracy of the staggered mesh is insufficient, it cannot offset the error caused by the curvature of the curved mesh, affecting the accuracy of the simulation results. In conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, the method for performing staggered mesh calculation on each split equation is as follows: when calculating, the curved coordinate coefficients are used as a reference, and second-order precision differential calculation logic is adopted to reduce the calculation error caused by the curvature of the mesh.

[0073] If the result reorganization logic is chaotic and the storage location is inconsistent with the deployment location, resulting in the inability to efficiently call data in subsequent iterative calculations, in conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. Specifically, the method of reorganizing and adding the calculation results of each split equation and storing them in the grid cell according to the staggered rule is as follows: when reorganizing, the results of each split equation are summarized according to the physical quantity type of electric field strength and magnetic field strength, and the storage is kept consistent with the optimized deployment location, reserving a data call interface for subsequent iterative calculations.

[0074] Example 2:

[0075] This second embodiment uses a two-dimensional model as an example to introduce the specific method for generating a body-fitted mesh by solving partial differential equations:

[0076] Two-dimensional physical region Its boundary is , , Let q and r represent the coordinates of the real physical region in the Cartesian coordinate system, and q and r represent the coordinates in the body-fitted coordinate system obtained through body-fitted coordinate transformation. When the boundary of the irregular physical region satisfies the Dirichlet boundary condition, the following relationship exists:

[0077] (1)

[0078] Further solving the Poisson equations yields the following expression:

[0079] (2)

[0080] in, Represents the Laplace operator. and These are called adjustment factors, also source terms, and they have the function of adjusting the density of the mesh curve in the physical region. and When all values ​​are set to 0, it means the equation being solved is the Laplace equation, meaning the real physical domain has a regular rectangular shape. Currently, for... and To obtain the value of the grid line, many scholars have conducted research and proposed various expressions, such as Thompson's method of adjusting the grid line to approach a target point. Middlecoff and Thomas, Steger and Sorenson, Hilgenstock, and others have proposed methods to infer the values ​​of internal nodes by controlling orthogonal boundaries. and Expression evaluation. It also includes providing special expressions based on the target object.

[0081] The inverse transformation of the Poisson equation yields the following differential equation:

[0082] (3)

[0083] Further solution , We can obtain:

[0084] (4)

[0085] in, Represented as a Jacobian determinant, its expression is as follows: .

[0086] In the computational domain, and The following relationship must be satisfied:

[0087] (5)

[0088] By comparing the above formulas, we can obtain , and , The partial derivative relationship between the two coordinate systems:

[0089] (6)

[0090] right , By taking the partial derivative using the chain rule, we get:

[0091] (7)

[0092] By using formulas (6) and (7) and differentiating the composite function, we can obtain the inverse transformation equation of formula (2), the specific expression of which is:

[0093] (8)

[0094] in:

[0095] , , (9)

[0096] By rearranging formulas (8) and (9), and... , Discretize it to obtain its discrete format as follows:

[0097] (10)

[0098] Through a series of operations from formula (3) to formula (10), the inverse transformation equation set (11) for the Dirichlet boundary condition (1) can be obtained. The acquisition of this equation set can serve the derivation of the electromagnetic wave equation in the subsequent curved coordinate system.

[0099] (11)

[0100] The expressions for Maxwell's electromagnetic equations are as follows:

[0101] (12)

[0102] Where H is the magnetic field strength, D is the electric flux density, J is the current density, E is the electric field strength, B is the magnetic flux density, and J is the electric field strength. m denoted as magnetic flux density.

[0103] For isotropic media, equation (13) is satisfied:

[0104] (13)

[0105] in, Indicates the dielectric constant of the medium. Indicates electrical conductivity. Represents the permeability coefficient. Indicates permeability in vacuum. , , , .

[0106] The finite difference calculation model is simple and provides high accuracy in simulating wave field propagation. Therefore, this patent employs the finite difference method for forward modeling in curved coordinates. The innovation of the patent is also based on this, and equation 14 can be obtained by performing finite difference processing on Maxwell's equations:

[0107] (14a)

[0108] (14b)

[0109] For two-dimensional profiles, set The TE wave and TM wave can be obtained respectively, as shown in equations (15a) and (15b).

[0110] (15a)

[0111] (15b)

[0112] The following descriptions will all use the TE equation as an example, whose staggered grid form is as follows: Figure 3 As shown.

[0113] Substituting equation (3) into equation (15b), we obtain the TE wave field equation in curved coordinates:

[0114] (16)

[0115] in, Indicates the dielectric constant of the medium. Indicates electrical conductivity. Indicates permeability, , , , The characteristic coefficients at each point in the curved coordinate system represent the degree of curvature of the curved mesh. , Represents the electric field intensity in the x and y directions. This represents the magnetic field strength in the z-direction.

[0116] Applying an interleaved grid difference scheme for wavefield simulation demonstrates better stability and accuracy compared to a full-grid node strategy. Based on this, this embodiment two proposes a curved grid-based interleaved grid difference calculation mode, with the specific steps as follows:

[0117] Step 1: Split equation (16) to obtain two equations, the results of which are as follows:

[0118] (17a)

[0119] (17b)

[0120] in, , , , , , , The curvilinear coordinate coefficients of the nodes within each grid are calculated.

[0121] Step 2: Perform conventional staggered mesh calculations on equations (17a) and (17b) respectively, but the parameter positions are different from the conventional method.

[0122] As can be seen from equation (17), when calculating the spatial difference, and There is a positional interchange. Therefore, this patent presents a novel grid difference calculation format that only requires spatially staggered calculations without introducing any other operations. It can be easily combined with existing finite difference methods to ensure accuracy without introducing any additional calculations. The placement of the parameters involved in the difference calculation is as follows: Figure 4 .

[0123] Step 3: After the calculation of equation (17) is completed, the corresponding parameters are added together and stored alternately in the computational grid cells for the next calculation.

[0124] As can be seen from the parameter placement, calculations are performed on each node of the entire grid. , The parameters are then summed after the calculation to obtain the result. And still stored on the whole node, on the staggered mesh nodes, the split results are calculated separately. , , , The components are summed after the calculation to obtain the result. , It is stored in the staggered position of 1 / 4 of the nodes. Figure 5 Provide a specific difference structure.

[0125] from Figure 5 As can be seen from this, the 1 / 4 node can be used. , Components, calculated separately by difference , The sum of their results They are still stored in the same location, as shown by the blue line in the diagram. Integer nodes are used. Calculate the difference separately , , , The components are summed and stored at node 1 / 4, with identical parameters added together. Here, we use... For example, a difference expression with second-order precision is given, where Set it to 0.

[0126]

[0127] (18a)

[0128]

[0129] (18b)

[0130] (18c)

[0131] The calculation methods for the remaining parameters are exactly the same as those for equation (18), and can be derived by analogy. They will not be shown here.

[0132] To verify the reliability of the method, this second embodiment uses a uniform medium model to verify the model, and the boundary adopts a convolutional perfect matching layer to absorb the boundary conditions.

[0133] In this second embodiment, a peak model is set using a Gaussian function. The model is 5m high, 15m deep, and 40m wide. The model is as follows: Figure 6 As shown. Figure 6 This is a simulation model of undulating terrain based on a curved mesh. The horizontal axis corresponds to distance, and the vertical axis to depth. The model shows a peak outline that bulges upwards at a distance of approximately 20m, extending to a depth of about -15m. The entire model uses a curved mesh structure that conforms to the undulating terrain, with irregular, stepped corner points. This not only visually demonstrates the precise adaptation of the curved mesh to the undulating terrain outline but also serves as a basis for subsequent simulations. Figure 7 Target terrain carrier in medium-wave forward modeling.

[0134] The region was set as a homogeneous medium for TE wavefield forward modeling, where... , The vacuum dielectric constant is The relative permittivity is set to 5, and the permeability is taken as the free permeability. electrical conductivity Taken as 0.001 S / m, permeability Set to 0. A Ricker wavelet was used as the seismic source (dominant frequency 10⁻⁸ Hz) and applied to the ground surface at a horizontal distance of 9 meters. Figure 5 The differential grid structure shown is used for forward modeling of the radar TE wavefield, and the wavefield slices are as follows: Figure 7 As shown.

[0135] Figure 7 This demonstrates the transverse radio wave (TE wave) under a peak-shaped terrain model. Forward modeling results of component wavefields at different times, including wavefield distributions for three time slices: 60 ns, 100 ns, and 140 ns:

[0136] At 60 ns, the wavefield propagates near the surface of the terrain with a clear, arc-shaped wavefront, its outline precisely conforming to the undulating shape of the peak. As time progresses to 100 ns and 140 ns, the wavefield gradually extends deeper, with the wavefront maintaining a continuous and concentrated shape without any diffusion or blurring. These wavefield distributions directly demonstrate the technical effectiveness of the method of this invention: the curved mesh can adapt to undulating terrain to avoid corner scattering, while the wavefield propagation is stable and there is no obvious reflection interference at the boundaries.

[0137] Figure 7 The mid-wave forward modeling simulation employed a perfectly matched layer absorbing boundary condition (roller type), resulting in strong wave field attenuation and no significant reflection at the boundary. Figure 7 As can be seen from the above, the forward modeling simulation of the grid difference calculation format in this embodiment shows that as the propagation time increases, the waveform propagation distance gradually increases, and no dispersion phenomenon occurs before and after the waveform. At the same time, the propagation process is stable in the undulating terrain, avoiding the corner scattering phenomenon caused by regular grid modeling. This indicates that the curved grid calculation format is suitable for radar wave field simulation of undulating terrain in curved coordinate system.

[0138] The method for forward modeling undulating terrain provided in this embodiment can effectively avoid the stepped corner points and the resulting dispersion and scattering problems generated when simulating undulating terrain using conventional regular grids, thus significantly improving the accuracy of wavefield simulation. It achieves the adaptation of the staggered grid calculation format to the curved coordinate system, giving full play to the stability advantage of the staggered grid. Moreover, the curved grid can accurately fit the real surface undulation, making the wavefield propagation simulation more in line with the actual scene. The calculation logic is concise and efficient, controlling the amount of computation while ensuring high accuracy. The wavefield propagation process is stable, and there is no obvious reflection interference at the boundary, meeting the high-precision requirements of radar wave forward modeling under undulating terrain.

[0139] Example 3:

[0140] This third embodiment provides a device for simulating undulating terrain for forward modeling, used to execute the method for simulating undulating terrain for forward modeling provided in embodiment one, such as... Figure 8 As shown, the device includes:

[0141] One or more processors;

[0142] A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to implement the method for forward modeling undulating terrain as described in Embodiments 1 and 2.

[0143] Figure 8 This is a schematic diagram of the device for performing forward modeling of undulating terrain as provided in Embodiment 3 of the present invention. Figure 8 The device shown for simulating undulating terrain in forward modeling is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0144] like Figure 8 As shown, the device for simulating undulating terrain in forward modeling is represented in the form of a general-purpose device. The components of the device for simulating undulating terrain in forward modeling may include, but are not limited to: one or more processors or processing units, memory, and buses connecting different system components (including memory and processing units).

[0145] A bus refers to one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. Examples of these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0146] Devices used for forward modeling undulating terrain typically include a variety of computer-readable media. These media can be any available media accessible to the device simulating undulating terrain, including volatile and non-volatile media, and portable and non-portable media.

[0147] The memory may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The apparatus for simulating undulating terrain in forward modeling may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system may be used to read and write non-removable, non-volatile magnetic media (…). Figure 8 Not shown; usually referred to as a "hard drive"). Although Figure 8 As not shown, disk drives for reading and writing to removable non-volatile disks (e.g., "floppy disks") and optical disc drives for reading and writing to removable non-volatile optical discs (e.g., CD-ROMs, DVD-ROMs, or other optical media) may be provided. In these cases, each drive may be connected to a bus via one or more data media interfaces. The memory may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of the present invention.

[0148] A program / utility having a set (at least one) of program modules can be stored, for example, in memory. Such program modules include, but are not limited to, an operating system, one or more applications, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The program modules typically perform the functions and / or methods described in the embodiments of this invention.

[0149] The device simulating undulating terrain for forward modeling can also communicate with one or more external devices (e.g., keyboard, pointing device, monitor, etc.), one or more devices that enable users to interact with the device simulating undulating terrain, and / or any device that enables the device simulating undulating terrain for forward modeling to communicate with one or more other devices (e.g., network interface card, modem, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the device simulating undulating terrain for forward modeling can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via a network adapter. Figure 8 As shown, the network adapter communicates with other modules of the device that performs forward modeling of undulating terrain via a bus. It should be understood that, although not shown in the figure, the device that can perform forward modeling in conjunction with undulating terrain uses other hardware and / or software modules, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0150] The processing unit executes various functional applications and data processing by running programs stored in the memory, such as implementing the method for forward modeling of undulating terrain provided in any embodiment of the present invention.

[0151] It is worth noting that the information interaction and execution process between the modules and units in the above-mentioned device and system are based on the same concept as the processing method embodiment of the present invention. For details, please refer to the description in the method embodiment of the present invention, and will not be repeated here.

[0152] Those skilled in the art will understand that all or part of the steps in the various methods of the embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for forward modeling undulating terrain, characterized in that, The method includes: Establish a curved coordinate system based on the target undulating terrain morphology, and obtain the curved coordinate coefficients of each calculation node under the curved coordinate system; Set the electromagnetic parameters required for forward modeling and split the radar wave equation in the curved coordinate system to obtain multiple independently computable split equations; Based on the curvilinear coordinate coefficients and the structure of the splitting equation, the deployment positions of the electric field strength and magnetic field strength in the staggered grid are optimized so that the staggered grid adapts to the spatial characteristics of the curvilinear coordinate system and the curvilinear coordinate coefficients. Each split equation is calculated using staggered grids. The calculation results of each split equation are then recombined and added together, and stored in grid cells according to the staggered rules to achieve high-precision forward modeling of undulating terrain.

2. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for establishing a curved coordinate system based on the target's undulating terrain morphology is as follows: Based on the surface contour features of the target undulating terrain, a curved coordinate system is constructed using a body-fitting coordinate transformation method, so that the boundary of the curved coordinate system fits the surface contour of the target undulating terrain.

3. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for obtaining the curvilinear coordinate coefficients of each calculation node in the curvilinear coordinate system is as follows: By solving a set of equations that satisfy the preset boundary conditions, the curvature coordinate coefficients of each computation node are obtained. These curvature coordinate coefficients reflect the degree of mesh curvature and coordinate transformation relationship of the corresponding node.

4. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for setting the electromagnetic parameters required for forward modeling is as follows: The electromagnetic parameters include the dielectric constant, conductivity, and magnetic permeability of the medium, and the values ​​of each parameter are determined with reference to the measured data of the physical properties of the actual medium corresponding to the target terrain.

5. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for setting the electromagnetic parameters required for forward modeling is as follows: When setting electromagnetic parameters, the parameter values ​​should be checked for rationality in accordance with the accuracy requirements of forward modeling, and abnormal values ​​that exceed the range of physical characteristics should be eliminated.

6. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for splitting the radar wave equation in the curved coordinate system is as follows: The split equation follows the physical laws of wave field propagation, splitting the original wave equation into two independently solvable split equation structures without losing the spatial characteristic information of the curved coordinate system.

7. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for optimizing the deployment positions of electric and magnetic field strengths in the staggered grid based on the curved coordinate coefficients and the structure of the splitting equation is as follows: The electric field strength is deployed at 1 / 4 nodes of the grid, and the magnetic field strength is deployed at the whole nodes of the interlaced grid, with the deployment positions matching the curvilinear coordinate coefficient characteristics of the corresponding nodes one by one.

8. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for performing staggered grid calculations on each splitting equation is as follows: The calculation uses the curved coordinate coefficients as a reference and employs second-order precision differential calculation logic to reduce the calculation error caused by mesh curvature.

9. The method for forward modeling undulating terrain according to claim 1, characterized in that, The specific method for recombining and adding the calculation results of each split equation and storing them in the grid cells according to the staggered rule is as follows: During reorganization, the results of each split equation are summarized according to the physical quantity type of electric field strength and magnetic field strength. When storing, the results are kept consistent with the optimized deployment location, and a data call interface is reserved for subsequent iterative calculations.

10. A device for simulating undulating terrain in forward modeling, characterized in that the device... include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method for forward modeling of undulating terrain as described in any one of claims 1 to 9.

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