49 results about "Green's function" patented technology

The invention provides a DCIM-based method for rapidly calculating a green function of a uniaxial anisotropic layered medium and an electromagnetic simulation system. The method comprises the following steps: modeling a uniaxial anisotropic layered medium to be simulated; determining a uniaxial anisotropic dielectric material of each layer, and assigning transverse parameters and longitudinal parameters; determining longitudinal coordinates of field point and source point distribution required to be solved, fitting a uniaxial anisotropic medium Green function spectral domain expression under the field source distribution by using a DCIM method, and solving an analytical expression in a spatial domain by using Somerfeld identical equation properties; solving the size of the electromagnetic field on the plane according to the fitted analytical expression; compared with a direct numerical integration method or a finite element method numerical solution using the Green function, the method has the advantages that the airspace analytical expression corresponding to the field source distributed on the plane is directly fitted, so that the solution of the airspace Green function is greatly accelerated, and the calculation efficiency and the calculation precision are both good in an actual example.

The invention belongs to the technical field related to tunnel anti-seismic analysis, and discloses a green function analytical method and equipment for rayleigh wave dynamic coupling response of an interval tunnel in an inclined field. The method comprises the steps that S1, soil deformation and displacement in the x direction and the y direction caused by Rayleigh wave propagation are converted into tunnel equivalent seismic loads in the x direction and the y direction through a viscoelastic geobasic structure model; s2, a Timoshenko beam model on a viscoelastic Pasternak foundation is adopted to establish a partial differential equation set for controlling axial and transverse dynamic displacement responses of longitudinal discrete units of the interval tunnel; s3, deducing four Green functions representing the bidirectional dynamic coupling response of the tunnel in combination with a Green function method and an artificial spring boundary; and S4, performing integral operation on the Green function by using a superposition principle, and introducing an exponential function term containing time t to obtain axial displacement and transverse displacement of the tunnel and corresponding axial and transverse dynamic coupling response coefficients. According to the invention, the solving efficiency is improved.

The invention relates to the technical field of radar target characteristic analysis, in particular to a radar near-field target polarization characteristic analysis method based on a vector Green function. Firstly, a target three-dimensional scattering point model is constructed, a coordinate-based scattering coefficient is defined, a full-polarization observation mode is designed, a near-field measurement matrix is calculated based on a vector Green function, and an observation model is constructed. Secondly, designing a fusion far-field constraint orthogonal matching pursuit (OMP) algorithm, realizing high-precision inversion of scattering coefficients, calculating a target far-field single-station RCS (HH / HV / VV mode) through dynamic polarization-based projection and phase compensation, and establishing a near-far field scattering characteristic mapping model; according to the method, near-field three-dimensional imaging and far-field polarization characteristic analysis are fused, the problem of insufficient cross polarization component recovery in a traditional method is solved, and the method has the advantages of high-resolution imaging, multi-physical field collaborative optimization, adaptive noise suppression and the like, and can be applied to the fields of stealth target recognition, radar cross section testing, unmanned aerial vehicle navigation and the like.

According to the main shock and aftershock time sequence rapid construction method and device provided by the invention, the influence of similar source generation mechanisms of main shock and aftershock, similar propagation paths, the same field effect and the like is fully considered, and the main shock and aftershock time sequence is rapidly and accurately constructed. The method comprises the steps that 1, the most dangerous fault plane and the spatial position and size of the fault plane are determined according to seismic fault data, sub-events with different circle center positions are generated randomly, and the size of each sub-event is represented by a radius; 2, determining the magnitude of the aftershock according to the set main shock magnitude and the main and aftershock power law relationship; step 3, according to the magnitude of the main earthquake and the aftershock, using rectangles consistent with the size of a main earthquake source and aftershock source to perform frame selection on the fault plane, and using sub-events contained in the rectangles to form an earthquake source model so as to obtain an earthquake source finite fault model of the main earthquake and the aftershock; 4, a deterministic Green function is obtained through decoupling; and step 5, carrying out convolution on the seismic source finite fault model and the deterministic Green function to obtain a final main shock and aftershock sequence.

The invention discloses a bridge bearing capacity dynamic evaluation method based on multi-source monitoring data driving, and aims to solve the problem that the bearing evaluation precision is difficult to guarantee under a sparse sensing coverage condition. According to the method, through cross-modal attention alignment guided by event anchor points, mask codes influencing line and propagation time delay constraints and geometric position coding, Green function kernels and time-varying boundary flexibility latent variables are introduced into a physical constraint neural operator model, symplectic integral propulsion is adopted, and block shape-preserving interval estimation and order-preserving calibration weighted according to working conditions are adopted. According to the method, the full-bridge space-time response and the bearing utilization coefficient are calculated, the risk level and the load limiting suggestion are output, and the technical effects of reliability improvement, physical consistency and long-time energy stability evaluation under the complex working conditions and the low signal-to-noise ratio are achieved.

The invention discloses an earthquake risk evaluation method and system, and relates to the technical field of earthquake numerical simulation, and the method comprises the steps: receiving a three-dimensional geometric model of a grid fault, and setting an initial condition; constructing a simulation operation equation to solve a shear stress loading rate, a normal stress loading rate and a state variable, and constructing an ordinary differential equation system; based on the three-dimensional geometric model and the initial conditions, accelerated simulation operation of the shear stress loading rate, the normal stress loading rate and the state variables is achieved through the ordinary differential equation system, and the accelerated simulation operation method comprises the steps that accelerated simulation operation is achieved through the method of combining an H-matrix and MPI, comprising the steps that a layered matrix is obtained based on a Green function under the half-space condition in combination with an adaptive cross-approximation algorithm, the layered matrix comprises a normal stiffness H-matrix and a shear stiffness H-matrix, and MPI parallel operation matrix-vector multiplication is adopted. According to the invention, the hierarchical matrix is introduced and the MPI parallel computing framework is fused, so that the simulation period is greatly shortened.

The invention relates to an interconnection line parameter extraction method based on a layered medium Green function improved moment method and a program product, and the method comprises the following steps: setting a sweep frequency parameter and a layered medium structure parameter, constructing a layered medium Green function, and carrying out the calculation to obtain an approximate solution of the layered medium Green function; establishing an electric field integral equation under the layered medium, and performing discretization processing to obtain a corresponding matrix equation; and performing iterative solution on the matrix equation to obtain the overall current distribution of the model, calculating the current value and impedance / admittance value of a port, performing electromagnetic calculation in a frequency sweep mode to obtain different port parameter values, and finally obtaining a parameter-frequency curve to complete the extraction of the port parameters. Compared with the prior art, the stratified medium Green function is fused into the frame of the enhanced electric field integral equation, electromagnetic simulation calculation of the full wave band from 0 frequency to 20 GHz can be achieved, and the method has the advantage of being high in calculation and solving efficiency.

The invention relates to the technical field of seismic exploration data processing methods, and particularly discloses a bidirectional phase and amplitude method and device for improving the quality of an empirical Green function, and the method comprises the steps: calculating the root mean square and the signal-to-noise ratio of a short-time cross function based on a seismic signal containing noise; updating a root mean square by using a root mean square ratio selection superposition method; performing iterative calculation by using a phase signal-to-noise ratio formula, and updating the signal-to-noise ratio; and utilizing the updated root mean square and the signal-to-noise ratio to recover the Green function, and calculating an effective seismic signal. According to the method, joint evaluation of the amplitude and the phase signal-to-noise ratio is introduced, so that the algorithm can be adaptively converged to an optimal set of short-time cross functions showing the highest signal consistency, test results of synthetic data and field data show that the method effectively eliminates interference of a non-static phase source, and the method has the advantages of being simple in structure and convenient to operate. And the capability of extracting a high-quality empirical Green function from more complex environmental noise is enhanced.

The application discloses a seismic risk evaluation method and system, relates to the technical field of seismic numerical simulation, and receives a three-dimensional geometric model of a gridded fault and sets initial conditions; a simulation operation equation is constructed to solve a shear stress loading rate, a normal stress loading rate and a state variable, and a common differential equation system is constructed; based on the three-dimensional geometric model and the initial conditions, the common differential equation system is used to realize accelerated simulation operation of the shear stress loading rate, the normal stress loading rate and the state variable, wherein the method of the accelerated simulation operation comprises: using a method combining an H-matrix and MPI to accelerate simulation operation, comprising obtaining a layered matrix based on a Green function under a half-space condition in combination with an adaptive cross approximation algorithm, comprising a normal stiffness H-matrix and a shear stiffness H-matrix, and using MPI parallel operation matrix-vector multiplication. The application introduces a hierarchical matrix and fuses an MPI parallel computing framework, so that the simulation period is greatly shortened.

According to one embodiment, a near-field data is used to determine a taper length that can isolate the source signature at the top of near-field data with minimum interaction with the Green's function. In some embodiments, a range of taper lengths is selected and for each length after tapering the near-filed data, converting each filtered near-field data to its minimum-phase equivalents. Summing pairwise cross-correlation of all of the minimum-phase equivalent wavelets at the zero-lag provides an attribute that shows how much the tapered portions of the near-field data look alike. An acceptable taper size will be the one that has the highest summation value. Finally, the average of the minimum-phase equivalents of tapered near-field data with the selected taper size is the estimated source signature.

The invention belongs to the field of earthquake and stress distribution calculation, and particularly relates to an earthquake deformation and stress distribution calculation method and system based on a Green function. The method comprises the following steps: acquiring a triangular mesh and a to-be-measured point of a fault; constructing an earth fixed coordinate system, a triangular dislocation coordinate system and an angular dislocation coordinate system based on the triangular mesh of the fault; determining a transformation matrix to obtain a coordinate system; calculating interior angles of three vertexes of the triangular mesh in the coordinate system and corresponding supplementary angles, selecting equivalent configuration based on the supplementary angles, calculating barycentric coordinates of orthogonal projection of the to-be-measured point on the triangular dislocation plane, and selecting configuration based on a partition inequality of the barycentric coordinates; according to configuration, a Burgers function is obtained through calculation by using a solid angle formula, incomplete displacement contributions of all angular dislocations are superposed, and a complete displacement field containing slip continuity correction is obtained; a stress field is calculated based on a complete displacement field or through a Green function of strain. And the seismic deformation and stress distribution calculation performance is obviously improved.

This invention relates to the field of numerical simulation and computational technology for seismic wave propagation, and discloses a method and apparatus for generating seismic ground motions based on target spectra and Green's functions. It aims to address the difficulty in achieving a balance between physical consistency, computational efficiency, and spectral compatibility in existing methods. The scheme mainly includes: preprocessing environmental noise records and extracting empirical Green's functions through unsupervised clustering; constructing a spatially continuous propagation tensor by performing depth correction and gradient interpolation based on surface wave eigenfunctions; discretizing the kinematically finite fault model into sub-source units and generating long-period seismic ground motions including path effects using propagation tensor convolution; optimizing source parameters through Bayesian inversion using the GMPE target spectrum as a constraint; and finally generating high-frequency components and fusing them with the long-period waveform to obtain a broadband seismic ground motion time history. This invention achieves a unification of physical propagation mechanisms and statistical spectral constraints, significantly improving computational efficiency while ensuring spectral compatibility, and is particularly suitable for basin areas.

The application belongs to the technical field of electromagnetic modeling of targets in layered media, and specifically provides a plane multilayer medium electromagnetic scattering modeling method based on layered medium Green function, which is used to solve the problems of large number of unknown quantities and low calculation efficiency when analyzing the electromagnetic scattering characteristics of targets in layered media; first, the medium target in the plane multilayer medium is meshed; then, the layered medium Green function is calculated based on the space list and interpolation method, and the matrix equation of the target current and magnetic current is constructed by solving the surface integral equation of the target by using the method of moments; finally, the improved stacked non-diagonal low-rank matrix is used to solve the matrix equation to calculate the target scattering field. The application adopts a direct solving calculation method, effectively solves the problem of ill-conditioned matrix difficult to converge in the conventional iterative method, especially for the multi-port excitation problem, without the need for repeated calculation, improving the solving efficiency of large-scale problems and reducing the consumption of calculation resources.

The present invention discloses a method for solving three-dimensional water wave energy band structure based on high-order boundary elements, which belongs to the field of water wave control and includes the following steps: S1. Based on the linear potential flow theory, a model of an infinite periodic array of three-dimensional fixed structures is established, the fluid is divided into a number of identical units, and the control equations and boundary conditions satisfied by the velocity potential of the fluid domain are obtained; S2. The high-order boundary element method is used to solve the three-dimensional Laplace equation, the boundary conditions are substituted into the boundary integral equation and a simple Green's function is selected. By numerically discretizing into high-order grid units, a linear homogeneous system of equations is established; S3. By arranging the system of equations, the solvable problem of the system of equations is converted into an eigenvalue problem to solve the real Bloch wave number and obtain a water wave energy band structure diagram. The present invention adopts the above-mentioned method for solving three-dimensional water wave energy band structure based on high-order boundary elements to achieve a rapid and accurate solution of the water wave energy band structure of three-dimensional fixed structures of arbitrary shape and underwater terrain.

The present application belongs to the technical field of oil and gas seismic exploration, and particularly relates to a pre-stack depth migration imaging method based on generalized diffraction stacking. The present application uses one-way wave equation to calculate the Green's function required for imaging, thereby avoiding the defects of two-way wave equation, making the imaging result not containing the wave field component useless for imaging, ensuring good imaging effect, and reducing the calculation amount, accelerating the operation speed, and improving the imaging efficiency. Moreover, the Green's function is solved in the frequency domain, and there is no sampling rate dispersion problem in the time domain, so that the calculation mode of one-way wave equation can adapt to larger spatial grid interval. Moreover, the relative positions of the imaging point, the source point and the receiver point are judged through angle calculation, so as to perform regional decomposition on the velocity model, and only the necessary region needs to be recursively calculated when solving the Green's function, without recursively calculating in the whole velocity model space. On the basis of ensuring the recursive effect, the useless calculation region is removed, and the imaging efficiency is further improved.

The invention discloses a characteristic model analysis method based on a periodic Green function and application thereof, and the method is characterized in that a unit structure model of a target unit is obtained, triangular mesh generation is carried out, and an RWG primary function is constructed; acquiring a periodic Green function and splitting the periodic Green function into a spatial domain part and a spectral domain part by using EWALD transformation; constructing an impedance matrix; after the impedance matrix is decomposed, a generalized eigenvalue equation is constructed, and eigenvalues are solved, so that the mode importance of a target unit is obtained, and analysis of a feature mode is completed; the method has the advantages that coupling of a target unit and other units in a periodic structure is directly calculated by adopting a periodic Green function, and a real mode in an infinite period is accurately reflected; according to the method, the periodic Green function is split into the spatial domain part and the spectral domain part by utilizing EWALD transformation, convergence is carried out on the spatial domain part and the spectral domain part respectively, and addition is carried out after convergence, so that the convergence speed is greatly accelerated, the calculation complexity is greatly reduced, and the calculation efficiency is improved.

The invention discloses a method for reducing storage and calculation amount in electromagnetic scattering non-singularity solution of a rotating body, and belongs to the field of electromagnetic engineering. According to the method, on the basis of a moment method (MoM) theoretical framework, an auxiliary function is introduced to eliminate the influence of Green function singularity in a surface integral equation on numerical calculation, and meanwhile, the physical constraint that the electric field divergence of a passive area is zero is further combined, so that effective order reduction of an unknown quantity is achieved; a traditional four-variable integral equation set is simplified into a three-variable coupled wave equation, the order and storage requirements of an impedance matrix are remarkably reduced, and the solving efficiency is greatly improved while the calculation precision is guaranteed. A specific electromagnetic rotating body device model is used for simulation, numerical verification shows that the method has excellent performance in calculation of an electromagnetic scattering field of a typical rotating body structure, and an efficient and reliable technical means is provided for rapid electromagnetic calculation of engineering equipment such as spherical communication satellites and missile nose cones.

The application provides a novel adaptive weighted fusion land water storage anomaly inversion method, and relates to the technical field of earth science, and the method comprises the following steps: acquiring global navigation satellite system (GNSS) monitored surface vertical deformation time series data and gravity field data of GRACE / GRACE-FO satellites, and performing pretreatment; constructing a Green function inversion model according to the pretreated GNSS data, and obtaining initial land water storage anomaly TWSAGNSS. The purpose of the application is to provide a novel adaptive weighted fusion land water storage anomaly inversion method, which improves the precision and reliability of land water storage anomaly inversion by fusing GNSS and GRACE / GRACE-FO data characteristics, adaptive weighting algorithm and high space-time resolution technical means.

The application provides a plate thinning defect shape finding method based on a few-frequency reflected ultrasonic guided wave, and comprises the following steps: S1: mode separation is performed on a total field of a reflected wave to obtain a reflection coefficient of a required guided wave mode; S2: a Green function in a defect-free plate is solved to obtain an approximate solution of a far field; S3: a reconstruction equation of a plate defect is established and preliminary reconstruction is performed; and S4: accurate determination of a plate defect shape is performed. The method is used for rapid quantitative detection of a plate structure thinning defect, and based on reflection data of the ultrasonic guided wave at a few frequency points, the shape of the defect can be found, the defect shape is accurately determined, a better detection effect is realized at a relatively low cost, and thus a convenient and reliable detection technology is provided for engineering detection.

The present application belongs to the field of ship hydrodynamics and motion prediction, and in particular to a device and method for predicting the hydrodynamics and motion of a ship coupled with ice, which first derives a Green function that satisfies the boundary conditions of the ice layer and the free surface, as well as all other conditions except the surface condition of the ship, and through the Green function, the differential equation of the velocity potential is converted into a boundary integral equation on the surface of the ship only, which introduces an extended surface at the waterline of the ship body to eliminate the influence of irregular wave frequencies; an asymptotic solution formula of the Green function is analytically derived, thereby establishing an approximate and effective solution program for the coupled interaction of the ship / wave / ice layer, and numerically calculating the results of the added mass, damping coefficient and wave exciting force of the ship body; through the method, the interaction mechanism of the water wave / ship / ice layer under different parameter characteristics can be deeply understood, and theoretical support is provided for the hydrodynamic problems, motion prediction and rational design of polar ships.

The present invention relates to a method for analyzing the wave diffraction coefficient for an open double jetty. The method comprises the following steps: Step S1, establishing an open double jetty model in a Cartesian coordinate system; Step S2, obtaining the Helmholtz equation for the complex function in the velocity potential function based on the velocity potential function and linearized free surface boundary conditions; using the Schwarz-Christoffel conformal transformation and the Green's function method to perform a boundary value solution on the Helmholtz equation to obtain a wave diffraction coefficient model for the open double jetty; and Step S3, numerically solving the wave diffraction coefficient model using the method to obtain an analytical value of the wave diffraction coefficient. Compared with the prior art, the method of the present invention fills a gap in the theory of wave diffraction for open double jetties and has the advantage of high analytical prediction accuracy.

The present application relates to the technical field of underground structure detection, and discloses a background noise empirical Green function interpolation method based on a conditional diffusion model, which comprises the following steps: collecting empirical Green function signals between station pairs formed by all seismographs in a target area and position coordinates of all seismographs as a training data set; inputting the empirical Green function signal containing noise, position coordinates of two seismographs in a station and a current denoising step number into a denoising neural network; taking the original empirical Green function signal in the training data set as a training target, inputting corresponding position coordinates of any two target points without seismographs into the trained denoising neural network, and generating an interpolated empirical Green function signal between the two target points. The method is more accurate than a traditional empirical Green function signal interpolation algorithm, can replace real observation data to a certain extent in a scenario where the number of seismographs is insufficient, and improves the underground structure detection capability.

Embodiments of a system and methods for utilizing ambient seismic noise to implement a modality based on the geometric phase for sending the effect of environmental conditions on ground properties are disclosed. The geometric phase is a global measure of the geometry of the seismic field which can be reconstructed via seismic interferometry. The change in geometric phase is the defined as the rotation angle of the complex state vector.

The application discloses a Green function reconstruction method combining S transform and dictionary learning. The method is as follows: S transform denoising is performed on a background noise cross-correlation function containing noise to obtain time-frequency spectrum coefficients and extract real coefficient matrix and imaginary coefficient matrix of the time-frequency spectrum coefficients; dictionary learning is performed on the real coefficient matrix and the imaginary coefficient matrix respectively to obtain a real coefficient matrix dictionary and an imaginary coefficient matrix dictionary; real coefficients after dictionary learning and imaginary coefficients after dictionary learning are obtained; reconstructed spectrum coefficients are obtained, and S inverse transform is performed on the reconstructed spectrum coefficients to obtain reconstructed Green functions. The application can eliminate the interference of noise sources with different directions in the seismic background noise cross-correlation function, and good results can also be achieved for background noise cross-correlation data with low signal-to-noise ratio; the application has low complexity, high timeliness and high reconstruction precision.

The invention discloses a time migration method for a three-dimensional pre-stack wave equation in an imaging ray domain, which relates to the technical field of exploration geophysics and comprises the following steps of: deducing a bidirectional acoustic wave equation in an imaging ray coordinate system based on a Riemann wave field extrapolation theory in a three-dimensional semi-orthogonal coordinate system; an equation is directly solved by adopting a finite difference method, extrapolation of a seismic source and a receiving end wave field is achieved, and errors caused by Green function approximation in a traditional migration method are avoided; and generating a pre-stack time migration result by applying a zero-lag cross-correlation imaging condition. Through first-order linear disturbance approximation, an accurate three-dimensional time-depth conversion partial differential equation set is simplified into an optimized layer stripping algorithm, and a corresponding equation suitable for a weak transverse velocity change medium is deduced. According to the invention, the working process of three-dimensional wave equation time migration is realized in an imaging ray coordinate system, and an accurate seismic imaging result is generated; two-dimensional plane hypothesis limitation is avoided, and high-precision imaging technical guarantee is provided for seismic data processing of a complex structure area.

The invention relates to a low-pressure pulsating vane pump design method based on three-source decomposition and source item analysis and a vane pump, and the method comprises the steps that full-flow-field unsteady flow data of the vane pump under a preset working condition is obtained; a three-source decomposition model is established, and the total pressure pulsation under the static coordinate system is decoupled into a non-uniform pulsation component, a flow synchronous pulsation component and a flow non-synchronous pulsation component; constructing a pressure Poisson equation, and quantitatively analyzing the contribution proportion of a hydrodynamic source item by using a Green function integral method; optimization design is executed based on the analysis result, if the non-uniform pulsation component is dominant, the kinematic sweeping effect is judged, and the load distribution or stacking rule of the impeller blades is optimized; and if the flow synchronous pulsation component is dominant, the dynamic instability is judged, and the geometric parameters of the blade tip clearance are optimized or a vortex suppression structure is configured on the wall surface of the rim. Therefore, accurate decoupling of the kinematics effect and the fluid instability in the vane pump is achieved, and therefore accurate design of the low-pulsation vane pump is guided.

The application discloses a kind of based on high-order boundary element's three-dimensional water wave band gap attenuation coefficient solving method, belong to water wave regulation field, including the following steps: S1, based on linear potential flow theory establishes three-dimensional fixed structure infinite periodic array model, fluid is divided into several identical units, and the control equation and boundary condition that fluid domain velocity potential satisfies are obtained;S2, high-order boundary element method is selected to solve three-dimensional Laplace equation, boundary condition is substituted into boundary integral equation and simple Green function is selected, by numerical dispersion into high-order grid unit, and linear homogeneous equation set is established;S3, by organizing equation set, equation set has solution problem is converted into local minimum value problem to solve complex Bloch wave number, and the attenuation coefficient of water wave band in band gap is obtained.The application adopts the above solving method, realizes the fast and accurate solution of three-dimensional fixed structure band gap structure and attenuation coefficient in band gap.

This invention discloses an eigenmode analysis method based on periodic Green's functions and its application. The method is characterized by: obtaining the element structure model of the target element and performing triangular mesh generation; constructing RWG basis functions; obtaining the periodic Green's function and using the EWALD transform to decompose it into spatial and spectral parts; constructing an impedance matrix; decomposing the impedance matrix to construct generalized eigenvalue equations and solving for the eigenvalues, thereby obtaining the mode importance of the target element and completing the eigenmode analysis. The advantages are: by using the periodic Green's function, the coupling between the target element and other elements in the periodic structure is directly calculated, accurately reflecting the true modes under infinite periods; using the EWALD transform to decompose the periodic Green's function into spatial and spectral parts, and then performing convergence in the spatial and spectral parts respectively, followed by summing, greatly accelerates the convergence speed, thereby significantly reducing computational complexity and improving computational efficiency.

The invention discloses a rapid calculation method for the dynamic stiffness of a complex layered foundation, and the method comprises the steps: selecting the number M of discrete circles with minimum discrete wavelengths, and calculating the total number of the circles and the radiuses of the circles on an exposed foundation which fully covers a whole to-be-researched hydraulic structure according to the M; discretizing the clear foundation, and acting unit loads in three directions by taking the center of any circle as an observation point to obtain the displacement of the observation point in a frequency domain-wave number domain; calculating a flexibility coefficient of a frequency domain-space domain representing the relationship between the unit load and the observation point, obtaining a Green function between the two circles through the flexibility coefficient, and calculating the dynamic stiffness of the foundation under M based on the Green function; repeating the steps to obtain the dynamic stiffness under different values of M, and calculating undetermined parameters in a dynamic stiffness fitting formula according to the dynamic stiffness and the radius of the circle corresponding to two discretions; and selecting an empirical value of the M, calculating the radius of a circle bestrewing the whole exposed foundation, and calculating the infinite domain dynamic stiffness of the foundation after convergence according to the radius and a dynamic stiffness fitting formula.

The invention relates to the technical field of electromagnetic full-wave inversion, in particular to a two-dimensional cross-layered efficient electromagnetic full-wave inversion method based on a spectral element boundary integral method.During forward modeling calculation, a scatterer crossing multiple horizontal layers is surrounded by a one-dimensional smooth boundary, and two-dimensional electromagnetic field distribution is solved by adopting a spectral element method in a region; accurately truncating an SEM solving domain on the boundary by using a boundary integral equation; for a transverse electric mode and a transverse magnetic mode, equivalent current / magnetic current is solved by using BIE, and a receiver scattering field is calculated in combination with a layered two-dimensional vector Green function; in the full-wave inversion, in order to reconstruct TE mode isotropic scatterer model parameters and TM mode anisotropic scatterer model parameters respectively, first-order derivatives of a mass matrix and a stiffness matrix relative to the corresponding parameters are calculated respectively, a sensitivity matrix is constructed, and an LM optimization algorithm is adopted to iteratively call an SEBI forward solver to complete inversion; multiple groups of numerical experiments verify the accuracy and high efficiency of the SEBI-LM algorithm in forward modeling and FWI.