A seismic wave field inference method and system suitable for different shape canyon sites

Abstract

The application discloses a kind of suitable for different shape canyon site seismic wave field reasoning method and system, belong to the field of earthquake engineering and intelligent computing. Obtain canyon boundary spectral coefficient, medium parameter and seismic wave incidence working condition, according to boundary curvature and shortest calculation wavelength Normalized calculation coordinate is constructed, form non-uniform boundary matching point in physical arc length coordinate, and construct the virtual source boundary coupled with canyon boundary. Based on boundary integral equation, numerical sample is established, the local geometric characteristics of virtual source point are constituted into double-branch input with spectral coefficient, medium parameter and incidence working condition, cross attention fusion and neural operator reasoning discrete virtual wave source density coefficient, combined with free surface traction constraint and displacement response reconstruction loss training model, to reconstruct the frequency domain and time domain seismic wave field of target canyon site. The application solves the problem that existing method is difficult to use the same model to train and quickly reason different canyon shapes, which limits its engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of earthquake engineering and intelligent computing technology, specifically relating to a seismic wavefield reasoning method and system applicable to canyon sites of different shapes. Background Technology

[0002] The scattering of seismic waves by canyon topography produces ground motion focusing and local amplification effects, resulting in significant temporal and spatial heterogeneity of ground motion parameters. Existing research has shown that factors such as canyon geometry and incident wave angle have a significant impact on canyon site effects. Therefore, achieving rapid and accurate seismic wavefield analysis for different canyon shapes and incident conditions is of great significance for site ground motion assessment, structural seismic resistance analysis, and pre-earthquake decision-making.

[0003] Currently, existing methods for analyzing seismic waves in canyon sites mainly include numerical simulation methods and intelligent computing methods. In terms of numerical simulation methods, domain discretization methods such as the finite difference method and the spectral element method typically require the overall discretization of the site's computational domain when constructing the seismic wavefield. They also need to handle the infinite-domain radiation problem using absorbing boundaries, artificial boundaries, or truncated boundaries. This process is not only computationally intensive, but the accuracy of the boundary treatment directly affects the reliability of the results. While the boundary integral equation method can automatically satisfy the infinite-domain radiation condition, it still requires repeatedly establishing and solving the boundary integral equation for different canyon geometric parameters, incident wave angles, and frequency combinations, resulting in high overall computational costs and making it difficult to meet the needs of rapid assessment under multiple conditions.

[0004] In terms of intelligent computing methods, one type focuses on establishing a point-to-point mapping from parameters to responses, which typically can only predict the responses of a small number of feature points and is difficult to directly obtain the seismic wave field distribution of the entire site. Another type of method, such as physical information neural networks, can achieve physical constraint solutions by introducing governing equations and boundary conditions, but the model still needs to be retrained when the geometry changes. Especially in geometrically variable computational domain problems such as canyons, existing methods lack a unified, low-dimensional representation of boundary geometry, making it difficult to use the same model for unified training and rapid inference for different canyon shapes, thus limiting their engineering applicability. Summary of the Invention

[0005] The purpose of this invention is to provide a seismic wavefield inference method and system applicable to canyon sites of different shapes. It achieves a unified low-dimensional representation of different canyon geometries through boundary function spectral coefficient encoding, and unifies the non-uniform discretization of physical boundaries with the fixed-length input of neural operators through normalized computational coordinates. Combining the dimensionality reduction advantages of the boundary integral equation method and the rapid inference capability of the neural operator model, it enables rapid inference and reconstruction of the frequency-domain and time-domain seismic wavefields of canyon sites under multiple geometries, frequencies, and incident angles. Furthermore, by introducing inference losses based on discrete virtual source density coefficients, physical constraint losses based on traction forces, and reconstruction losses based on frequency-domain displacement response, the accuracy and physical consistency of the seismic wavefield inference results are improved.

[0006] In a first aspect, the present invention provides a seismic wavefield inference method applicable to canyon sites of different shapes, comprising the following steps: The geometric features, medium parameters, and seismic wave incident conditions of the canyon site are obtained. The geometric features are used to characterize the spatial morphology of the canyon's free surface. Based on the geometric feature information, the free surface undulation boundary function of the canyon is recovered, and the geometric feature field of the canyon boundary, including the boundary curvature field, is generated. The local discrete spacing of the canyon boundary is determined based on the shortest computational wavelength corresponding to the boundary curvature field and the incident frequency of the seismic wave. Normalized computational coordinates are constructed based on these local discrete spacings, and uniform sampling with a fixed number of points is performed within these coordinates to form non-uniform boundary points in the physical arc length coordinates. A virtual source boundary coupled with the shape of the canyon boundary is constructed based on the non-uniformly discrete canyon boundary, and multiple virtual source points are set on the virtual source boundary. The canyon site is solved in the frequency domain using the boundary integral equation method to establish a numerical computation sample set. A geometric feature sequence is constructed based on the local geometric characteristics of each virtual source point, and a parameter labeling sequence is constructed based on the geometric feature information, medium parameters, and seismic wave incident conditions. The geometric feature sequence and parameter labeling sequence form a dual-branch input, and the numerical computation sample set is organized into the corresponding output sequence to form a training dataset. The dual-branch input is fed into the neural operator model to fuse the geometric feature sequence and the parameter label sequence, forming a geometric-working condition fused feature sequence arranged along the normalized computation coordinates. Based on the geometric-working condition fused feature sequence, the inferred discrete virtual wave source density coefficient is obtained. Based on the inferred discrete virtual wave source density coefficient, the frequency domain displacement response of the canyon site is reconstructed. According to the inferred discrete virtual wave source density coefficient, the frequency domain displacement response, and the free surface boundary condition constraints, a joint loss function is constructed and the neural operator model is trained to obtain the operator inference model. The geometric features, medium parameters, and seismic wave incident conditions of the target canyon site are input into the operator inference model to obtain the discrete virtual source density coefficients of the inference, and the seismic wave field of the target canyon site is reconstructed based on the discrete virtual source density coefficients of the inference.

[0007] As an alternative implementation, the geometric feature information is a spectral coefficient encoding vector. The spectral coefficient encoding vector consists of the expansion coefficients obtained by expanding the free surface undulation boundary function of the canyon on a preset basis function system. It is used to uniformly map different canyon geometries to a low-dimensional boundary representation of the same dimension. The preset basis function system is any one of the Fourier basis function system, Chebyshev basis function system, Legendre basis function system, or wavelet basis function system.

[0008] As an alternative implementation, the geometric feature field includes the canyon boundary coordinate field, the boundary normal vector field, the boundary curvature field, and the boundary arc length increment field; p Local geometric feature vectors of virtual source points g p The geometric feature sequence is composed of the normalized calculated coordinates of the virtual source point, the physical arc length parameter and coordinates, the boundary normal vector, boundary curvature, and boundary arc length increment corresponding to the virtual source point. All local geometric feature vectors are stacked row by row to form a geometric feature sequence. G 0; Each expansion coefficient, medium parameter component, and seismic wave incident condition component in the spectral coefficient encoding vector is encoded as a parameter label vector, and arranged according to the parameter components to form a parameter label sequence. Z Geometric feature sequence G 0 contains N s Each local geometric feature vector corresponds to a virtual source point, and the parameter label sequence is... Z It contains M parameter label vectors, each corresponding to a global parameter component; geometric feature sequence. G 0 and parameter marker sequence Z The two-branch input that constitutes the neural operator model X =( G 0, Z Geometric feature sequence G 0 is mapped to the parameter tag sequence via the virtual source point geometric encoder. Z The same characteristic dimension is required, but the same sequence length is not required; the medium parameters include one or more of shear wave velocity, density and Poisson's ratio, and the seismic wave incident conditions include one or more of incident wave type, incident angle and angular frequency.

[0009] As an alternative implementation, the neural operator model includes a virtual source-point geometric encoder, a parameter label encoder, a multi-head cross-attention fusion module, and a neural operator layer; the virtual source-point geometric encoder processes the geometric feature sequence. G 0 is encoded as a geometrically encoded feature sequence G and by geometrically encoded feature sequences G Generate the query matrix; the parameter tag encoder encodes each global parameter component into a parameter tag vector, forming a parameter tag sequence.Z And the sequence is labeled by parameters. Z The key matrix and value matrix are generated through corresponding linear mapping; the multi-head cross-attention fusion module calculates the attention weights of each virtual source point to different parameter label vectors based on the correlation between the query matrix and the key matrix, and then combines the weighted value matrix with the geometrically encoded feature sequence. G Residual fusion is performed to obtain a geometry-condition fusion feature sequence with a sequence length equal to the number of virtual source points. H ; fuse geometry-working condition feature sequences H The neural operator layer inputs the normalized computation coordinates in a uniform order and outputs the real and imaginary parts of the discrete virtual source density coefficients corresponding to each virtual source point.

[0010] As an alternative implementation method, the canyon site is solved in the frequency domain based on the boundary integral equation method to establish a numerical calculation sample set, specifically including: The local boundary discrete spacing is determined based on the absolute value of the curvature of the canyon boundary and the shortest computational wavelength corresponding to the highest computational angular frequency. The boundary sampling density is set to the reciprocal of the local boundary discrete spacing. Normalized computational coordinates with values ​​ranging from 0 to 1 are constructed based on the cumulative integral of the boundary sampling density along the physical arc length direction. A fixed number of values ​​are selected from the normalized computational coordinates. N b We find a uniform node and inversely calculate the physical arc length position corresponding to each uniform node, so as to set up boundary points densely in the high curvature region and sparsely in the low curvature region. Number of virtual source points N s Number of boundary points N b When the coordinates are equal, virtual source boundaries are constructed and virtual source points are set on the preset normal side of the canyon boundary according to the normalized calculation coordinates that correspond one-to-one with each boundary point. The offset distance of each virtual source point relative to the corresponding canyon boundary point is determined according to the local boundary discrete spacing and the local radius of curvature, and is limited to the preset minimum offset distance and the preset maximum offset distance. The boundary discrete equation of the free surface zero traction condition is established using the Green's function that satisfies the infinite domain radiation condition, and the discrete virtual wave source density coefficient corresponding to each virtual source point is obtained by numerical calculation. c p And the frequency domain displacement response of the canyon site; among which, c p For the virtual source density in the first... p The value at each virtual source point is the product of the corresponding discrete weight; the boundary collocation points and the virtual source points are two sets of points with different spatial locations and physical effects. The boundary collocation points and the virtual source points correspond one-to-one with the same normalized calculation coordinates, and the virtual source boundary does not intersect with the physical solution domain where the target field point is located.

[0011] As an alternative implementation method, the joint loss function includes: Discrete virtual source density coefficient inference loss term, used to constrain the prediction accuracy of discrete virtual source density coefficients in the source domain; The traction force physical constraint loss term based on free surface boundary conditions is used to constrain the degree of satisfaction of the zero traction boundary conditions on the free surface in the boundary condition domain. The frequency domain displacement response reconstruction loss term is used to constrain the difference between the frequency domain displacement response reconstructed from the inference results and the numerical calculation results in the response domain. The above loss terms are weighted and summed to form a joint loss function, which is used to train the neural operator model.

[0012] As an alternative implementation method, reconstructing the seismic wave field of the target canyon site specifically includes: The discrete virtual wave source density coefficients obtained by reasoning are multiplied by the Green's functions of displacement from each virtual source point to the target field point and then superimposed to obtain the discrete radio frequency domain displacement. The frequency domain displacement is superimposed with the free field frequency domain displacement to obtain the frequency domain displacement response; By combining the incident seismic wave spectrum and inverse Fourier transform, the time-domain seismic wave field of the canyon site under the action of a specific incident seismic wave is obtained; The time-domain seismic wavefield includes the spatial distribution of ground motion displacement, velocity, and acceleration at any time in the canyon site, as well as the spatial distribution of peak ground motion displacement, velocity, and acceleration at the site.

[0013] Secondly, the present invention provides a seismic wavefield inference system suitable for canyon sites of different shapes, comprising: The data acquisition module is configured to acquire geometric feature information, medium parameters and seismic wave incident conditions of the canyon site. The geometric feature information is used to characterize the spatial morphology of the canyon's free surface. The geometric feature field generation module is configured to: recover the undulating boundary function of the canyon's free surface based on the geometric feature information, and generate the canyon boundary geometric feature field, including the boundary curvature field. The training dataset generation module is configured to: determine the local discrete spacing of the canyon boundary based on the shortest computational wavelength corresponding to the boundary curvature field and the incident frequency of the seismic wave; construct normalized computational coordinates based on the local discrete spacing; and perform uniform sampling of a fixed number of points in the normalized computational coordinates to form non-uniform boundary points in the physical arc length coordinates; construct a virtual source boundary coupled with the shape of the canyon boundary based on the non-uniformly discretized canyon boundary, and set multiple virtual source points on the virtual source boundary; perform frequency domain solution of the canyon site based on the boundary integral equation method to establish a numerical computation sample set; construct a geometric feature sequence based on the local geometric features of each virtual source point; construct a parameter label sequence based on the geometric feature information, medium parameters, and seismic wave incident conditions; use the geometric feature sequence and parameter label sequence as a dual-branch input; and organize the numerical computation sample set into the corresponding output sequence to form the training dataset. The model training module is configured to: feed the dual-branch input into the neural operator model, perform feature fusion on the geometric feature sequence and parameter label sequence to form a geometric-working condition fusion feature sequence arranged along the normalized computation coordinates, obtain the inferred discrete virtual wave source density coefficient based on the geometric-working condition fusion feature sequence, reconstruct the frequency domain displacement response of the canyon site based on the inferred discrete virtual wave source density coefficient, construct a joint loss function based on the inferred discrete virtual wave source density coefficient, frequency domain displacement response and free surface boundary condition constraints, and train the neural operator model to obtain the operator inference model; The output module is configured to input the geometric features, medium parameters, and seismic wave incident conditions of the target canyon site into the operator inference model to obtain the discrete virtual source density coefficients of the inference, and reconstruct the seismic wave field of the target canyon site based on the discrete virtual source density coefficients of the inference.

[0014] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0015] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a seismic wavefield inference method and system applicable to canyon sites of different shapes. By utilizing the boundary integral equation method, the wave problem within the computational domain of the canyon site is transformed into a response inference problem on the computational boundary, significantly reducing the dimensionality of input and output data. Boundary function spectral coefficient encoding is used to achieve a unified low-dimensional representation of different canyon geometries. Normalized computational coordinates are used to simultaneously achieve curvature adaptive non-uniform point distribution in physical arc length coordinates and fixed-length, uniform indexing of the neural operator input sequence. A virtual source point arrangement coupled with local point spacing and curvature radius is adopted to improve the adaptability of the boundary and virtual source to different canyon shapes. Geometric feature sequences and parameter label sequences are used as independent input branches, and spatially related parameter weights can be learned through geometry-condition multi-head cross-attention. The frequency and time domain seismic wavefields are reconstructed by combining boundary integral equations and inverse Fourier transform, improving the physical consistency, computational accuracy, and engineering applicability of the model.

[0017] Furthermore, normalized computation coordinates transform the curvature-adaptive non-uniform distribution of points in the physical arc length coordinates into a model sequence with a fixed length and uniform index. This ensures the geometric resolution of the high-frequency wave field and local turning points while enabling the Fourier neural operator to perform spectral convolution along the uniform computation coordinates. The arrangement of virtual source points coupled with local point spacing and curvature radius improves the geometric adaptability of the virtual source boundary. Cross-attention, using geometric feature sequences as queries and parameter label sequences as keys and values, enables different virtual source points to obtain spatially relevant parameter weights. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of a seismic wavefield inference method applicable to canyon sites of different shapes, as disclosed in an embodiment of the present invention. Figure 2 This is a schematic diagram of canyon boundary spectral coefficient encoding, curvature-wavelength constrained non-uniform discretization under normalized calculation coordinates, dual-branch input, and geometry-working condition cross-attention fusion disclosed in the embodiments of the present invention. Figure 3 This is a schematic diagram of the joint loss function disclosed in an embodiment of the present invention; Figure 4 This is a comparison diagram of the discrete virtual wave source density coefficients calculated by numerical calculation and the discrete virtual wave source density coefficients inferred by operator inference disclosed in the embodiments of the present invention; Figure 5 This is a comparison diagram of the frequency domain displacement response of the canyon site calculated by numerical calculation and the frequency domain displacement response of the canyon site calculated by operator inference, as disclosed in the embodiments of the present invention. Figure 6 This is a comparison chart of the time history of ground motion acceleration at typical observation points in a canyon site calculated by numerical calculation and the ground motion acceleration at typical observation points reconstructed after operator inference, as disclosed in the embodiments of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0020] The technical solutions disclosed in the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0021] Example 1 like Figure 1 As shown, the overall process of seismic wavefield inference applicable to canyon sites of different shapes in this scheme includes canyon site parameter acquisition, geometric feature field generation, boundary adaptive discretization and virtual source point arrangement, numerical sample generation, bi-branch input construction, geometric-condition feature fusion, neural operator training, and target seismic wavefield inference and reconstruction. The following steps S1-S11 provide a detailed explanation of the above overall process.

[0022] The canyon sites of different shapes referred to in this invention are those whose free surface boundaries, within a preset design parameter range, can be expanded by a preset basis function system or by parametric curves. r ( s The function represents a canyon section that is piecewise continuous of second order and does not self-intersect, including symmetrical or asymmetrical canyons, combinations of different valley depths and slopes, and canyons with piecewise smooth local transitions. This does not apply to canyons that cannot be represented as single-valued functions. z = h ( x The boundary of ) is determined using parametric curves. r ( s ) and its arc length parameter to calculate normal vector and curvature.

[0023] The geometric features, medium parameters, and seismic wave incident conditions of the canyon site are obtained. The geometric features are used to characterize the spatial morphology of the canyon's free surface. Based on the geometric feature information, the free surface undulation boundary function of the canyon is recovered, and the geometric feature field of the canyon boundary, including the boundary curvature field, is generated. The local discrete spacing of the canyon boundary is determined based on the shortest computational wavelength corresponding to the boundary curvature field and the incident frequency of the seismic wave. Normalized computational coordinates are constructed based on these local discrete spacings, and uniform sampling with a fixed number of points is performed within these coordinates to form non-uniform boundary points in the physical arc length coordinates. A virtual source boundary coupled with the shape of the canyon boundary is constructed based on the non-uniformly discrete canyon boundary, and multiple virtual source points are set on the virtual source boundary. The canyon site is solved in the frequency domain using the boundary integral equation method to establish a numerical computation sample set. A geometric feature sequence is constructed based on the local geometric characteristics of each virtual source point, and a parameter labeling sequence is constructed based on the geometric feature information, medium parameters, and seismic wave incident conditions. The geometric feature sequence and parameter labeling sequence form a dual-branch input, and the numerical computation sample set is organized into the corresponding output sequence to form a training dataset. The dual-branch input is fed into the neural operator model to fuse the geometric feature sequence and the parameter label sequence, forming a geometric-working condition fused feature sequence arranged along the normalized computation coordinates. Based on the geometric-working condition fused feature sequence, the inferred discrete virtual wave source density coefficient is obtained. Based on the inferred discrete virtual wave source density coefficient, the frequency domain displacement response of the canyon site is reconstructed. According to the inferred discrete virtual wave source density coefficient, the frequency domain displacement response, and the free surface boundary condition constraints, a joint loss function is constructed and the neural operator model is trained to obtain the operator inference model. The geometric features, medium parameters, and seismic wave incident conditions of the target canyon site are input into the operator inference model to obtain the discrete virtual source density coefficients of the inference, and the seismic wave field of the target canyon site is reconstructed based on the discrete virtual source density coefficients of the inference.

[0024] The specific steps of this invention are as follows: S1. Obtain the spectral coefficient encoding vector used to characterize the boundary function of the canyon's free surface undulations. a Medium parameter vector m and the incident vector of seismic waves q .

[0025] In this embodiment, the canyon site contains locally undulating terrain, and the canyon free surface undulation boundary function is used to describe the spatial morphology of the canyon free surface. The canyon free surface undulation boundary function is represented as a low-dimensional boundary representation formed by a linear combination of a baseline boundary function and multiple preset basis functions according to their corresponding expansion coefficients, specifically as follows: ; in, x The horizontal position of the undulating terrain of the canyon site. h ( x ) represents the boundary function for the free surface undulation of the canyon. h 0( x ) is the baseline boundary function. fk ( x ) is the first k One preset basis function a k For the corresponding expansion coefficients, N a This represents the number of expanded terms. The spectral coefficient encoding vector, composed of individual spectral coefficients, can be represented as... .

[0026] The preset basis function system is preferably any one of the following: Fourier basis function system, Chebyshev basis function system, Legendre basis function system, and wavelet basis function system. By using a fixed-length spectral coefficient encoding vector, different canyon geometries can be uniformly mapped to a low-dimensional boundary representation of the same dimension, thereby enabling the same neural operator model to be uniformly trained and rapidly inferred under different canyon geometric conditions.

[0027] In one specific implementation, the canyon site is a two-dimensional isotropic elastic half-space. For the plane wave problem, the medium parameter vector... m =[ c s , r , n ],in c s For shear wave velocity, r For density, n Poisson's ratio; seismic wave incident vector q =[ b , α , oh ],in b For incident wave type identification, α For the angle of incidence, oh The incident wave angular frequency is given; different waveforms employ the displacement Green's function and traction Green's function corresponding to their governing equations, and can be identified by waveform marking. b The same model can be trained, or corresponding models can be trained separately. Preferably, the spectral coefficient encoding vector, medium parameter vector, and seismic wave incident vector are respectively processed to be dimensionless.

[0028] S2. Recover the free surface undulation boundary function of the canyon based on the spectral coefficient encoding vector, and generate the geometric feature field for boundary discretization. The geometric feature field includes the canyon boundary coordinate field, the boundary normal vector field, the boundary curvature field, and the boundary arc length increment field.

[0029] In this embodiment, as Figure 2 As shown, the boundary function of the canyon's free surface undulation is recovered based on the spectral coefficient encoding vector obtained in step S1. h ( x ), and according to the physical arc length parameter s Calculate boundary curvature k( s The highest angular frequency within the design frequency range is... oh max The minimum wave velocity of the medium is c s,min Then the shortest calculated wavelength l min =2π c s,min / oh max The discrete spacing of local targets can be expressed as Δ. s b ( s )=min{ l min / n λ , h max / [1+ c κ | k ( s )|]}, where, n λ The minimum number of preset boundary points within each shortest wavelength. h max The maximum allowable discrete spacing for low curvature regions. c κ Let be the curvature adjustment coefficient. Let the boundary sampling density... r b ( s )=1 / Δ s b ( s The total arc length of the canyon boundary is... L b The boundary sampling density is set from 0 to... s The cumulative points divided by its range from 0 to L b The cumulative integral is defined, and the normalized calculation coordinates ζ( s ), where ζ(0)=0, ζ( L b =1. Let the number of boundary points be... N b Then the coordinates ζ are normalized. i =( i -1) / ( N b -1), i =1,…, N b , through ζ( s The physical arc length position is obtained by using the inverse function of ). s iThis results in a uniform and fixed number of nodes in the computational coordinates, while the boundary points in the physical arc length coordinates are denser in high curvature regions and sparser in low curvature regions.

[0030] For each boundary point, record the normalized calculated coordinates ζ. i and physical arc length parameters s i Extract the boundary coordinate field x ( s i ), z ( s i ), calculate the normal vector field n x ( s i )and n z ( s i ), boundary curvature field k ( s i and the arc length increment Δ between adjacent collocation points s ( s i The normalized computation coordinates are used to form a fixed-length, uniformly indexed neural operator input sequence, and the physical arc length parameter and local geometric features are used for non-uniform boundary discretization, virtual source point arrangement, sample generation, boundary integral solving, and response reconstruction.

[0031] S3. Construct a virtual source boundary based on the non-uniformly discretized canyon boundary, and solve the canyon site in the frequency domain based on the boundary integral equation method to establish a numerical calculation sample set. The numerical calculation sample set includes a discrete virtual wave source density coefficient sample set and a canyon site frequency domain response sample set.

[0032] Set on the actual canyon boundary N b A boundary point is selected. In a preferred embodiment, the boundary point is selected. N s = N b And calculate the coordinates ζ according to the same normalization as the collocation points of each boundary. p Construct one-to-one correspondence on the pre-defined normal side of the canyon boundary. N s One virtual source point. p A virtual source point can be represented as x p = r b ( s p )+ s nd p × n ( s p ),in, s p For the first p The physical arc length parameter of the canyon boundary position corresponding to each virtual source point is used to inherit and normalize the coordinates ζ of the virtual source points through this correspondence. p ; r b ( s p ) represents the corresponding point on the canyon boundary. n ( s p () is the unit normal vector at that point. s n Set to 1 or -1 to select the side that does not intersect with the physical solution domain where the target field point is located; let v p =min{ m Δ s ( s p ), c r / [| k ( s p )|+ k 0]}, offset distance d p =clip( v p , d min , d max )=min{ d max ,max[ d min , v p ]}.in, m This is the local point distance control coefficient. c r This is the radius of curvature control coefficient. k 0 is a regularization parameter to prevent the denominator from being zero when the absolute value of curvature is zero; d min and d max These represent the minimum and maximum allowed offset distances, respectively. `clip` restricts candidate values ​​to a given interval. After constructing candidate virtual source boundaries, it checks whether adjacent virtual source segments intersect and whether the virtual source boundary enters the physical solution domain; if the conditions are not met, the offset is reduced. d maxAnd recalculate until the conditions of non-self-intersection and not entering the physical solution domain are met. N b Greater than N s In the overdetermined solution method, uniform boundary calculation coordinate sequences and virtual source calculation coordinate sequences are set respectively. Local geometric features are interpolated based on the calculation coordinates, and the discrete virtual wave source density coefficients are solved by the least squares method.

[0033] The scattered wave field is constructed using the Green's function that satisfies the infinite domain radiation condition, and the boundary discrete equations satisfying the zero traction condition of the free surface are established based on the Green's function of traction force. The discrete virtual wave source density coefficients corresponding to each virtual source point are obtained by numerical calculation. c p And the frequency domain displacement response samples of the canyon site. Let the density of continuous virtual wave sources be... f ( x ), No. p The discrete weights corresponding to the virtual source points are: w p ,but c p = w p f ( x p Subsequent neural operator direct inference has absorbed discrete weights. c p .

[0034] In one embodiment, the first l Target sites x l Frequency domain displacement response and the first i The traction force at each boundary point can be expressed as: ; ; in, x l For the first l One target site, For the first i A boundary point, x p For the first p A virtual source point, c p For the first p Discrete virtual wave source density coefficients corresponding to each virtual source point; u f ( x l () represents the free-field frequency domain displacement of the target field point. tf ( The free field traction force is the point where the boundary is collocation. U ( x l , x p ) is the displacement Green's function. T ( , x p The traction force Green's function is used to establish and solve the boundary equations of the free surface. c p The displacement Green's function is used in c p The frequency domain displacement response of the target field point is reconstructed after the information is known.

[0035] By solving multiple combinations of different canyon geometries, media parameters, and incident conditions in the frequency domain, discrete virtual source density coefficient sample sets and canyon site frequency response sample sets can be established in batches.

[0036] S4. Construct a geometric feature sequence based on the normalized coordinates and local geometric features of the virtual source point. G 0. Encode each expansion coefficient, medium parameter component, and seismic wave incident condition component in the spectral coefficient encoding vector into a parameter label vector, and arrange them according to the parameter components to form a parameter label sequence. Z , with geometric feature sequence G 0 and parameter marker sequence Z Combining two-branch input X= ( G 0, Z The real and imaginary parts of the discrete virtual source density coefficients obtained by numerical calculation are used to construct the corresponding multi-channel output sequences, thus obtaining the training dataset.

[0037] like Figure 2 As shown, the geometric branch carries local geometric information that varies with the virtual source point, including the normalized calculated coordinates, physical arc length parameters, and coordinates of the virtual source point, as well as the boundary normal vector, boundary curvature, and boundary arc length increment corresponding to the virtual source point; the parameter branch carries global information, including the spectral coefficient encoding vector. a Medium parameter vector m and the incident vector of seismic waves q .

[0038] In a preferred embodiment, the first p The local geometric feature vectors, geometric feature sequences, and parameter label sequences of each virtual source point are represented as follows: ; ; in, x p,x and x p,z These are the horizontal and vertical coordinate components of the virtual source point location; n x ( s p )and n z ( s p ) represents the component of the unit normal vector corresponding to the true boundary.

[0039] Let the set of scalars consist of all spectral coefficient components, medium parameter components, and incident condition components. P ={ v 1, v 2, ..., v M},in, M The total number of spectral coefficient components, medium parameter components, and seismic wave incident condition components, the first... j The parameter label vector is z j = E val ( v j )+ E type ( t j )+ E index ( j ), j =1,2,…, M ,in E val , E type , E index These represent parameter numerical encoding, parameter type embedding, and parameter sequence number embedding, respectively. v j Indicates the first j The values ​​of each global parameter component t j This indicates the identifier of the parameter type it belongs to. j This indicates the index of the component in the preset parameter sequence; parameter tag sequence ,in d The dimension of the parameter label is encoded; geometric feature sequence. G The sequence length of 0 is equal to the number of virtual source points. N s Parameter tag sequence Z The sequence length is equal to the number of parameter tags. MThe two do not need to have the same sequence length. The bi-branch input of the neural operator model is represented as... X =( G 0, Z ).thus, G 0. Preserve the spatial order between virtual source points. Z Preserve the type and index information of each global parameter component. The output corresponding to each virtual source point is the discrete virtual source density coefficient. c p The real and imaginary parts. Preferably, the multi-channel output sequence can be represented as: ; in, y p =[Re( c p ),Im( c p Re and Im represent the real and imaginary parts of the discrete virtual source density coefficients, respectively. Y Sequence length and number of virtual source points N s Consistent.

[0040] S5, Input the dual branches X =( G 0, Z The data is fed into the neural operator model; using geometric feature sequences. G 0. Generate query information, using parameter-labeled sequences. Z Generate key and value information, and perform feature fusion through geometry-condition multi-head cross attention to obtain a geometry-condition fused feature sequence arranged along normalized computational coordinates. H ; fuse geometry-working condition feature sequences H Input the neural operator layer to obtain the discrete virtual wave source density coefficients for inference.

[0041] In this embodiment, the neural operator model includes a virtual source point geometric encoder, a parameter label encoder, a multi-head cross-attention fusion module, a neural operator layer, and an output projection layer. The virtual source point geometric encoder processes local geometric features arranged along uniformly normalized computational coordinates; the parameter label encoder encodes each expansion coefficient, each medium parameter, and each incident condition parameter of the spectral coefficient encoding vector into a parameter label vector with parameter type and sequence number embedding. When using multi-head cross-attention, the virtual source point geometric features are used as queries, and the parameter label vectors are used as keys and values, allowing different virtual source points to assign different weights to the spectral components, medium parameters, and condition parameters that affect their discrete virtual source density coefficients. The outputs of each attention head are concatenated and mapped, and then combined with the geometrically encoded feature sequence. G The matrix representations are summed to obtain the geometry-condition fusion feature sequence.H Then, the neural operator layer is input, enabling the model to adaptively select geometric spectral components, medium parameters, and operating parameters that have a significant impact on the local discrete virtual wave source density coefficient for virtual source points with different curvatures, normals, and positions.

[0042] The neural operator model is preferably any one of the Fourier neural operator, the factorized Fourier neural operator, or an improved model thereof, and the neural operator model can be expressed as: ; Where Θ is the set of parameters of the model to be trained. N Θ This represents the corresponding neural operator model. These are the real and imaginary parts of the discrete virtual wave source density coefficients obtained from model inference.

[0043] Obtaining the geometric feature sequence of the virtual source point G 0 and parameter marker sequence Z Then, the geometric feature sequence G 0-input virtual source point geometry encoder E g Mapping to a preset feature dimension yields a virtual source point geometrically encoded feature sequence. G=E g ( G 0), where, , , , N s The number of virtual source nodes. d g The original geometric dimension, d To achieve a unified feature encoding dimension, M This represents the total number of parameter labels corresponding to the spectral coefficient components, medium parameter components, and seismic wave incident condition components. Parameter label sequence. Z In the matrix representation, each row corresponds to a parameter label vector. Geometrically encoded feature sequence. G and parameter tag sequence Z Having the same feature dimension d However, each has N s and M A sequence of elements. Virtual source point geometry encoder. E g It may include one or more fully connected layers and non-linear activation layers.

[0044] Geometric encoding feature sequences of virtual source points G and parameter tag sequence Z Perform multi-head cross-attention processing. For the first... rEach attention head uses a virtual source point to geometrically encode the feature sequence. G As a source of query information, the sequence is labeled with parameters. Z As the source of key and value information, the query matrix is ​​obtained respectively. Q (r) = GW Q (r) Key matrix K (r) = ZW K (r) Sum matrix V (r) = ZW V (r) ,in, W Q (r) , W K (r) and W V (r) The first r A trainable linear mapping matrix for each attention head.

[0045] Based on the query matrix Q (r) Bond matrix K (r) The correlation between them is calculated. r Attention weight matrix for each attention head A (r) : ; in, d r For the first r The feature dimensions of the query vector, key vector, and value vector in each attention head; softmax Z This indicates normalization along the parameter label dimension. For any virtual source point, the sum of the attention weights of the parameter labels corresponding to the spectral coefficient components, medium parameters, and operating condition parameters is 1.

[0046] No. r The output of each attention head O (r) = A (r) V (r) Therefore, each virtual source point can determine the attention weights corresponding to different spectral coefficient components, medium parameters, and operating condition parameters based on its geometric characteristics, and perform weighted combination of the value vectors labeled with the corresponding parameters. The outputs of each attention head are concatenated and mapped through the output mapping matrix.W O Mapped to the geometrically encoded feature sequence of the virtual source point G With the same feature dimension, and then geometrically encoded feature sequences from virtual source points. G By summing the residuals, we obtain the geometry-working-condition fusion feature sequence. H : ; in, R For the total number of attention heads, .sequence H The p The row corresponds to the first p A virtual source point is obtained, and its local geometric information, as well as its related global geometric spectrum components, medium parameter information, and operating condition parameter information are fused together.

[0047] Calculate coordinates according to normalization g p In ascending order, the geometric-working-condition fusion feature sequence H The rows are arranged accordingly. Since the virtual source points are uniformly distributed on the normalized calculation coordinates, the resulting geometric-condition fusion feature sequence... H The feature sequence is constructed along the uniformly normalized computation coordinate direction and then input into the neural operator layer.

[0048] The neural operator layer may include multiple sequentially connected Fourier operator layers. Each Fourier operator layer includes spectral convolution along the normalized computational coordinate direction, local linear mapping acting on the channel dimension, residual connections, and nonlinear activation. For the input features, a Fourier transform is first performed along the normalized computational coordinate direction, preserving a preset number of Fourier modes in the frequency domain, and a trainable linear transform is performed on the preserved Fourier modes; then an inverse Fourier transform is performed, and the resulting spectral convolution result is combined with the local linear mapping result, followed by residual connections and nonlinear activation to obtain the output of the corresponding Fourier operator layer.

[0049] After processing through multiple Fourier operator layers, the hidden features are mapped to discrete virtual source density coefficients corresponding to each virtual source point using the output projection layer. c p The real and imaginary parts of the discrete virtual wave source density coefficient are output by the output projection layer when the discrete virtual wave source density coefficient includes multiple components.

[0050] Although each virtual source point is in physical arc length coordinates s p The spacing on the surface can be non-uniform, but the physical arc length position... s p Local arc length increment Δ s ( sp Both the boundary normal vector and the boundary curvature are preserved in the geometric feature sequence. G In step 0, the data is processed by a virtual source point geometric encoder and multi-head cross-attention, and then passed to the geometry-condition fusion feature sequence. H Therefore, neural operators can utilize the non-uniform distribution information of virtual source points in physical space, and can also perform spectral operations on uniformly normalized computational coordinates.

[0051] In one specific implementation, the geometric encoding dimension and parameter tag encoding dimension of the virtual source point are both set to 64, that is... d =64; The total number of attention heads for multi-head cross-attention is set to 4, that is... R =4, the feature dimension of each attention head is set to 16, that is d r =16. The neural operator layer consists of four Fourier operator layers, each retaining 16 low-order Fourier modes and employing the GELU activation function. During training, the Adam optimizer is used, with an initial learning rate of 0.001 and a batch size of 32. Training stops when the validation set loss does not decrease for 50 consecutive training epochs. The above network structure parameters and training parameters are only an example and can be adjusted according to the training sample size, the number of virtual source points, the input wave frequency range, and the target accuracy.

[0052] S6. Substitute the inferred discrete virtual wave source density coefficients into the field point displacement reconstruction expression based on the displacement Green's function to obtain the inferred canyon site frequency domain displacement response.

[0053] The discrete virtual source density coefficients corresponding to each virtual source point obtained by inference are multiplied by the Green's function of the displacement from each virtual source point to the target field point and then superimposed to obtain the inferred divergent frequency domain displacement. The divergent frequency domain displacement is then superimposed with the free field frequency domain displacement to obtain the inferred total frequency domain displacement response of the canyon site. The frequency domain displacement response includes the real part, imaginary part, and amplitude of the frequency domain surface reset displacement of the canyon site.

[0054] S7. Based on the inference of discrete virtual wave source density coefficients, inference of canyon site frequency domain displacement response, and traction residuals of free surface boundary conditions, a joint loss function is constructed.

[0055] like Figure 3 As shown, the joint loss function includes the discrete virtual source density coefficient inference loss term. L φ Traction force physical constraint loss term based on free surface boundary conditions L τ Frequency domain displacement response reconstruction loss term L rec .

[0056] Among them, the inference loss term for discrete virtual source density coefficients L φ The prediction accuracy for constraining the discrete virtual wave source density coefficients in the source domain can be written as: ; in, N s The number of virtual source nodes. and These are the real and imaginary parts of the discrete virtual source density coefficients for inference, respectively. and These are the real and imaginary parts of the discrete virtual wave source density coefficients calculated numerically.

[0057] Traction physical constraint loss term L τ This is used to determine the degree to which the zero-traction boundary condition of the free surface is satisfied in the constraint boundary condition domain. The boundary collocation points used to calculate this loss are the same as those used in establishing the boundary discretization equations in step S3. N b If the boundary points are all from the same set of points, it can be written as: ; in, Indicates the first i The total traction force residual at each boundary collocation point is formed by the superposition of the free field traction force and the scattered traction force obtained by the inferred discrete virtual wave source density coefficient through the traction force Green's function; the same boundary collocation points and discrete weights as those used in the numerical sample generation are adopted to ensure that the physical constraints of the traction force are consistent with the boundary integral discrete equation.

[0058] Frequency domain displacement response reconstruction loss term L rec The difference between the frequency domain displacement response reconstructed from the inference results and the numerical calculation results in the constrained response domain can be written as: ; in, N f The total number of target sites The first is the result of reconstructing the discrete virtual source density coefficients obtained from the inference. l Frequency domain displacement response of a target field point The first numerical calculation of boundary integral equations l Frequency domain displacement response of a target field point.

[0059] S8. Train the neural operator model using the joint loss function to obtain the operator inference model.

[0060] like Figure 3 As shown, the weighted sum of the above multiple loss terms forms a joint loss function, which can be written as: ; in, or φ ,or τ and or u These are the non-negative weight coefficients for the discrete virtual wave source density coefficient inference loss, the traction force physical constraint loss, and the frequency domain displacement response reconstruction loss, respectively. Preferably, the Adam optimizer is used to minimize the joint loss function, and the neural operator model parameters are iteratively updated until the loss converges, thus obtaining the trained operator inference model.

[0061] S9. Input the spectral coefficient encoding vector of the target canyon site, medium parameters and seismic wave incident conditions into the operator inference model to obtain the discrete virtual wave source density coefficients for inference.

[0062] The spectral coefficient encoding vector of the target canyon site, medium parameters, and seismic wave incident conditions are input into the trained neural operator model to obtain the inferred discrete virtual source density coefficients. For example... Figure 4 As shown, the inference results are compared with the numerical calculation results of the boundary integral equation method, and the inference accuracy of the real and imaginary parts of the discrete virtual wave source density coefficients is evaluated by relative L2 error and maximum relative error.

[0063] S10. Substitute the inferred discrete virtual wave source density coefficients into the field point displacement reconstruction expression based on the displacement Green's function to reconstruct the frequency domain seismic wave field of the canyon site.

[0064] Substituting the discrete virtual source density coefficients obtained in step S9 into the field point displacement reconstruction expression based on the displacement Green's function, the frequency domain seismic wavefield of the target canyon site is reconstructed. The frequency domain seismic wavefield of the canyon site includes the real and imaginary parts and amplitudes of the canyon site reset displacement, complex velocity, and complex acceleration. Preferably, at the incident angular frequency of... oh Next, the l The velocity and acceleration of each target point can be respectively derived from... well ( x l )=j oh ( x l )and acc ( x l )=- oh ² û ( x l ) is obtained, where j is the imaginary unit.

[0065] like Figure 5As shown, the reconstructed frequency domain displacement amplitude of the canyon site is compared with the numerical calculation results of the boundary integral equation method, and the relative L2 error and the maximum relative error are used to evaluate the reconstruction accuracy of the frequency domain seismic wave field.

[0066] S11. By combining the incident seismic wave spectrum and inverse Fourier transform, the time-domain seismic wave field of the canyon site under the action of a specific incident seismic wave is obtained.

[0067] The frequency domain responses of the canyon site obtained at multiple discrete frequencies are combined with the spectrum of a given incident seismic wave, and an inverse Fourier transform is performed to obtain the corresponding time-domain ground motion displacement, velocity, and acceleration time histories. This yields the time-domain seismic wavefield of the target canyon site under the action of a given incident seismic wave. The time-domain seismic wavefield of the canyon site includes the spatial distribution of ground motion displacement, velocity, and acceleration at any given time, as well as the spatial distribution of peak ground motion displacement, velocity, and acceleration.

[0068] like Figure 6 As shown, the reconstructed ground motion acceleration time histories of typical observation points are compared with the numerical calculation results, and the reconstruction accuracy of the time-domain seismic wavefield is evaluated by relative L2 error and maximum relative error.

[0069] In other embodiments of the present invention, the basis function system described in step S1 can also be replaced with other types of orthogonal function systems, such as Haar wavelet bases or Daubechies wavelet bases, to adapt to canyon boundaries with local mutation features; the neural operator layer can also be replaced with factorized Fourier neural operators or DeepONet. The geometry-condition fusion module can employ multi-layer cross-attention or alternately execute virtual source point self-attention and parameter cross-attention, but both maintain the principle of determining the query based on the local geometric features of the virtual source point, and determining the key and value based on the parameter labels corresponding to the spectral coefficients, medium parameters, and incident condition parameters. The weight coefficients of the joint loss function... or τ ,or φ and or u It can be adjusted based on the validation set error.

[0070] The method provided by this invention can be applied to fields such as seismic wavefield calculation, spatiotemporal distribution characteristic analysis, or earthquake early warning auxiliary decision-making in canyon sites.

[0071] Example 2 This embodiment provides a seismic wavefield inference system suitable for canyon sites of different shapes, including: The data acquisition module is configured to acquire geometric feature information, medium parameters and seismic wave incident conditions of the canyon site. The geometric feature information is used to characterize the spatial morphology of the canyon's free surface. The geometric feature field generation module is configured to: recover the undulating boundary function of the canyon's free surface based on the geometric feature information, and generate the canyon boundary geometric feature field, including the boundary curvature field. The training dataset generation module is configured to: determine the local discrete spacing of the canyon boundary based on the shortest computational wavelength corresponding to the boundary curvature field and the incident frequency of the seismic wave; construct normalized computational coordinates based on the local discrete spacing; and perform uniform sampling of a fixed number of points in the normalized computational coordinates to form non-uniform boundary points in the physical arc length coordinates; construct a virtual source boundary coupled with the shape of the canyon boundary based on the non-uniformly discretized canyon boundary, and set multiple virtual source points on the virtual source boundary; perform frequency domain solution of the canyon site based on the boundary integral equation method to establish a numerical computation sample set; construct a geometric feature sequence based on the local geometric features of each virtual source point; construct a parameter label sequence based on the geometric feature information, medium parameters, and seismic wave incident conditions; use the geometric feature sequence and parameter label sequence as a dual-branch input; and organize the numerical computation sample set into the corresponding output sequence to form the training dataset. The model training module is configured to: feed the dual-branch input into the neural operator model, perform feature fusion on the geometric feature sequence and parameter label sequence to form a geometric-working condition fusion feature sequence arranged along the normalized computation coordinates, obtain the inferred discrete virtual wave source density coefficient based on the geometric-working condition fusion feature sequence, reconstruct the frequency domain displacement response of the canyon site based on the inferred discrete virtual wave source density coefficient, construct a joint loss function based on the inferred discrete virtual wave source density coefficient, frequency domain displacement response and free surface boundary condition constraints, and train the neural operator model to obtain the operator inference model; The output module is configured to input the geometric features, medium parameters, and seismic wave incident conditions of the target canyon site into the operator inference model to obtain the discrete virtual source density coefficients of the inference, and reconstruct the seismic wave field of the target canyon site based on the discrete virtual source density coefficients of the inference.

[0072] It should be noted that the above modules correspond to the steps in Embodiment 1, and the examples and application scenarios implemented by the above modules and their corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1. It should also be noted that the above modules can be executed in a computer system as part of the system.

[0073] In further embodiments, the following is also provided: An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0074] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0075] A computer-readable storage medium for storing computer instructions that, when executed by a processor, perform the method of Embodiment 1.

[0076] The method in Example 1 can be directly executed by a hardware processor, or it can be executed by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0077] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A seismic wavefield inference method applicable to canyon sites of different shapes, characterized in that, Includes the following steps: The geometric features, medium parameters, and seismic wave incident conditions of the canyon site are obtained. The geometric features are used to characterize the spatial morphology of the canyon's free surface. Based on the geometric feature information, the free surface undulation boundary function of the canyon is recovered, and the geometric feature field of the canyon boundary, including the boundary curvature field, is generated. The local discrete spacing of the canyon boundary is determined based on the boundary curvature field and the shortest computational wavelength corresponding to the seismic wave incident frequency. Normalized computational coordinates are constructed based on these local discrete spacings, and a fixed number of points are uniformly sampled within these normalized coordinates to form non-uniform boundary points in the physical arc length coordinates. A virtual source boundary coupled to the shape of the canyon boundary is constructed based on the non-uniformly discrete canyon boundary, and multiple virtual source points are set on the virtual source boundary. The canyon site is solved in the frequency domain using the boundary integral equation method to establish a numerical computation sample set. A geometric feature sequence is constructed based on the local geometric features of each virtual source point. A parameter labeling sequence is constructed based on the geometric feature information, medium parameters, and seismic wave incident conditions. The geometric feature sequence and the parameter labeling sequence form a dual-branch input, and the numerical computation sample set is organized into a corresponding output sequence to form a training dataset. The dual-branch input is fed into the neural operator model, and the geometric feature sequence and the parameter label sequence are fused to form a geometric-condition fused feature sequence arranged along the normalized calculation coordinates. Based on the geometric-condition fused feature sequence, the inferred discrete virtual wave source density coefficient is obtained. Based on the inferred discrete virtual wave source density coefficient, the frequency domain displacement response of the canyon site is reconstructed. According to the inferred discrete virtual wave source density coefficient, the frequency domain displacement response, and the free surface boundary condition constraints, a joint loss function is constructed, and the neural operator model is trained to obtain the operator inference model. The geometric features, medium parameters, and seismic wave incident conditions of the target canyon site are input into the operator inference model to obtain the inferred discrete virtual source density coefficients, and the seismic wave field of the target canyon site is reconstructed based on the inferred discrete virtual source density coefficients.

2. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 1, characterized in that, The geometric feature information is a spectral coefficient encoding vector, which is composed of the expansion coefficients obtained by expanding the free surface undulation boundary function of the canyon on a preset basis function system. It is used to uniformly map different canyon geometries to a low-dimensional boundary representation of the same dimension. The preset basis function system is any one of the Fourier basis function system, Chebyshev basis function system, Legendre basis function system or wavelet basis function system.

3. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 2, characterized in that, The geometric feature field includes the canyon boundary coordinate field, the boundary normal vector field, the boundary curvature field, and the boundary arc length increment field; the first p Local geometric feature vectors of virtual source points g p The geometric feature sequence is composed of the normalized calculated coordinates of the virtual source point, the physical arc length parameter and coordinates, the boundary normal vector, boundary curvature, and boundary arc length increment corresponding to the virtual source point. All local geometric feature vectors are stacked row by row to form a geometric feature sequence. G 0; Each expansion coefficient, medium parameter component, and seismic wave incident condition component in the spectral coefficient encoding vector is encoded as a parameter marker vector, and arranged according to the parameter components to form a parameter marker sequence. Z The geometric feature sequence G 0 contains N s Each of the local geometric feature vectors corresponding to the virtual source point, the parameter label sequence Z It contains M parameter label vectors, each corresponding to a global parameter component; the geometric feature sequence G 0 and the parameter tag sequence Z The two-branch input that constitutes the neural operator model X =( G 0, Z Geometric feature sequence G 0 is mapped to the parameter tag sequence via the virtual source point geometric encoder. Z The same feature dimension is required, but the same sequence length is not required; the medium parameters include one or more of shear wave velocity, density and Poisson's ratio, and the seismic wave incident conditions include one or more of incident wave type, incident angle and angular frequency.

4. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 3, characterized in that, The neural operator model includes a virtual source-point geometric encoder, a parameter label encoder, a multi-head cross-attention fusion module, and a neural operator layer; the virtual source-point geometric encoder processes the geometric feature sequence. G 0 is encoded as a geometrically encoded feature sequence G and by the geometrically encoded feature sequence G Generate a query matrix; the parameter tag encoder encodes each global parameter component into a parameter tag vector, forming a parameter tag sequence. Z， And the sequence is labeled by the parameters. Z A key matrix and a value matrix are generated through a corresponding linear mapping; the multi-head cross-attention fusion module calculates the attention weights of each virtual source point to different parameter label vectors based on the correlation between the query matrix and the key matrix, and then combines the weighted value matrix with the geometrically encoded feature sequence. G Residual fusion is performed to obtain a geometry-condition fusion feature sequence with a sequence length equal to the number of virtual source points. H The geometry-condition fusion feature sequence H The neural operator layer inputs the normalized computation coordinates in a uniform order and outputs the real and imaginary parts of the discrete virtual source density coefficients corresponding to each virtual source point.

5. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 1, characterized in that, The frequency domain solution of the canyon site based on the boundary integral equation method, and the establishment of a numerical calculation sample set, specifically include: The local boundary discrete spacing is determined based on the absolute value of the curvature of the canyon boundary and the shortest computational wavelength corresponding to the highest computational angular frequency. The boundary sampling density is set to the reciprocal of the local boundary discrete spacing. Normalized computational coordinates with values ​​ranging from 0 to 1 are constructed based on the cumulative integral of the boundary sampling density along the physical arc length direction. A fixed number of these normalized computational coordinates are selected. N b We find a uniform node and inversely calculate the physical arc length position corresponding to each uniform node, so as to set up boundary points densely in the high curvature region and sparsely in the low curvature region. Number of virtual source points N s Number of boundary points N b When the coordinates are equal, virtual source boundaries are constructed and virtual source points are set on the preset normal side of the canyon boundary according to the normalized calculation coordinates that correspond one-to-one with each boundary point. The offset distance of each virtual source point relative to the corresponding canyon boundary point is determined according to the local boundary discrete spacing and the local radius of curvature, and is limited to between the preset minimum offset distance and the preset maximum offset distance. The boundary discrete equation for the zero traction condition of the free surface is established using the Green's function that satisfies the infinite domain radiation condition, and the discrete virtual wave source density coefficient corresponding to each virtual source point is obtained by numerical calculation. c p And the frequency domain displacement response of the canyon site; among which, c p For the virtual source density in the first... p The value at each virtual source point is the product of the corresponding discrete weight; the boundary points and the virtual source points are two sets of points with different spatial locations and physical effects. The boundary points and the virtual source points correspond one-to-one with the same normalized calculation coordinates, and the virtual source boundary does not intersect with the physical solution domain where the target field point is located.

6. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 1, characterized in that, The joint loss function includes: Discrete virtual source density coefficient inference loss term, used to constrain the prediction accuracy of discrete virtual source density coefficients in the source domain; The traction force physical constraint loss term based on free surface boundary conditions is used to constrain the degree of satisfaction of the zero traction boundary conditions on the free surface in the boundary condition domain. The frequency domain displacement response reconstruction loss term is used to constrain the difference between the frequency domain displacement response reconstructed from the inference results and the numerical calculation results in the response domain. The above loss terms are weighted and summed to form a joint loss function, which is used to train the neural operator model.

7. The seismic wavefield inference method applicable to canyon sites of different shapes as described in claim 1, characterized in that, The reconstructed seismic wave field of the target canyon site specifically includes: The discrete virtual wave source density coefficients obtained by reasoning are multiplied by the Green's functions of displacement from each virtual source point to the target field point and then superimposed to obtain the discrete radio frequency domain displacement. The frequency domain displacement is superimposed with the free field frequency domain displacement to obtain the frequency domain displacement response; By combining the incident seismic wave spectrum and inverse Fourier transform, the time-domain seismic wave field of the canyon site under the action of a specific incident seismic wave is obtained; The time-domain seismic wavefield includes the spatial distribution of ground motion displacement, velocity, and acceleration at any time in the canyon site, as well as the spatial distribution of peak ground motion displacement, velocity, and acceleration at the site.

8. A seismic wavefield inference system applicable to canyon sites of different shapes, characterized in that, include: The data acquisition module is configured to acquire geometric feature information, medium parameters and seismic wave incident conditions of the canyon site, wherein the geometric feature information is used to characterize the spatial morphology of the free surface of the canyon. The geometric feature field generation module is configured to: recover the free surface undulation boundary function of the canyon based on the geometric feature information, and generate a canyon boundary geometric feature field including the boundary curvature field; The training dataset generation module is configured to: determine the local discrete spacing of the canyon boundary based on the shortest computational wavelength corresponding to the boundary curvature field and the incident frequency of the seismic wave; construct normalized computational coordinates based on the local discrete spacing; perform uniform sampling of a fixed number of points in the normalized computational coordinates to form non-uniform boundary points in the physical arc length coordinates; construct a virtual source boundary coupled with the shape of the canyon boundary based on the non-uniformly discrete canyon boundary; set multiple virtual source points on the virtual source boundary; perform frequency domain solution on the canyon site based on the boundary integral equation method to establish a numerical computation sample set; construct a geometric feature sequence based on the local geometric features of each virtual source point; construct a parameter label sequence based on the geometric feature information, medium parameters, and seismic wave incident conditions; use the geometric feature sequence and the parameter label sequence to form a dual-branch input; and organize the numerical computation sample set into a corresponding output sequence to form a training dataset. The model training module is configured to: feed the dual-branch input into the neural operator model, perform feature fusion on the geometric feature sequence and the parameter label sequence to form a geometric-condition fusion feature sequence arranged along the normalized calculation coordinates, obtain the inferred discrete virtual wave source density coefficients based on the geometric-condition fusion feature sequence, reconstruct the frequency domain displacement response of the canyon site based on the inferred discrete virtual wave source density coefficients, construct a joint loss function based on the inferred discrete virtual wave source density coefficients, the frequency domain displacement response and the free surface boundary condition constraints, and train the neural operator model to obtain the operator inference model; The output module is configured to input the geometric features, medium parameters, and seismic wave incident conditions of the target canyon site into the operator inference model to obtain the inferred discrete virtual source density coefficients, and reconstruct the seismic wave field of the target canyon site based on the inferred discrete virtual source density coefficients.

9. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-7.

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