VSP uplink and downlink wave field separation method based on signal knowledge representation

Abstract

The invention discloses a VSP uplink and downlink wave field separation method based on signal knowledge representation, which comprises the following steps: firstly, extracting knowledge representation from original VSP data to guide a separation process, namely physical knowledge representation, morphological knowledge representation and propagation direction knowledge representation; and then, constructing a dual-convolution auto-encoder network architecture KGCAE based on signal knowledge representation guidance by utilizing knowledge representation of uplink and downlink waves, inputting the knowledge representation for training, carrying out uplink and downlink wave separation problem modeling, realizing end-to-end learning from original VSP records to a separation wave field, outputting a predicted uplink wave field and a predicted downlink wave field, and completing VSP uplink and downlink wave separation. According to the method, a complete signal knowledge representation system is established, wave field features are extracted from multiple dimensions, comprehensive priori knowledge guidance is provided for uplink and downlink wave separation, the separation accuracy and reliability are remarkably improved, an additional training data set is not needed, and high-quality wave field separation can be achieved under unsupervised and complex geological conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic data processing, and particularly relates to a method for separating up - and - down - going wave fields of VSP based on signal knowledge representation. Background Art

[0002] Vertical Seismic Profile (VSP) technology is an important method for seismic data acquisition. Compared with surface seismic exploration, it has a higher signal - to - noise ratio and resolution. At the same time, VSP can more accurately measure formation velocity parameters, amplitude information, and lithology parameters, greatly enhancing the ability of seismic data in interpreting structures, strata, and lithology. In VSP data processing, the separation of up - and - down - going waves is crucial for seismic migration imaging. The up - going wave usually contains useful information from underground reflectors, while the down - going wave is mainly composed of direct waves and multiple waves. Accurately separating up - and - down - going waves can not only improve the signal quality but also provide important bases for velocity model building and formation identification. However, under complex geological conditions, the obtained original signal often has the situation of up - and - down - going wave overlap and noise, which poses challenges to existing up - and - down - going wave separation methods.

[0003] Existing wave - field separation methods are mainly divided into two categories. The first category is time - depth separation methods, including Singular Value Decomposition (SVD) and median filtering. The SVD method realizes separation by using the difference in the lateral coherence of seismic waves. However, due to the non - orthogonality of the up - and - down - going wave fields, its effect is not good when processing VSP wave fields. The median filtering method is based on the characteristic that up - and - down - going waves have different dips in the time - depth domain and realizes separation by performing statistical filtering within an inclined time window. However, it has high requirements for the accuracy of first - arrival wave picking and may cause frequency distortion when processing high - frequency signals. The other category of methods is called transform - domain filtering methods, which currently mainly include f - k filtering and Radon transform. Their main idea is to convert the time - depth domain to a specific parameter domain to achieve wave - field separation. F - K filtering separates waves by using the characteristic that up - and - down - going waves have different slopes in the frequency - wavenumber domain. The Radon transform maps the data to the τ - p domain and uses the dip angle for wave - field separation, avoiding manual picking operations. However, the separation results of both methods are affected by truncation effects and spatial aliasing, and manual window setting is required, which may lead to signal loss and thus affect the accuracy of VSP wave - field separation. Generally speaking, existing wave - field separation methods have poor effects when processing VSP data under complex geological conditions and are difficult to balance both computational efficiency and separation accuracy.

[0004] In recent years, deep learning has received extensive attention in solving complex non-linear optimization problems. In the field of seismic data processing, deep learning has been successfully applied to seismic inversion, seismic data denoising, etc. In VSP wavefield separation, the up- and down-going wave separation method based on deep learning can overcome the problems of existing methods to a certain extent. The wavefield separation based on data-driven convolutional neural network (CNN) and generative adversarial network (GAN) can effectively capture the weak wavefield features in VSP signals, alleviate the influence of the amplitude difference between up- and down-going waves on network update, and improve the separation accuracy of up- and down-going waves. However, the effect of wavefield separation using deep learning depends to a large extent on the quality of the training dataset, which requires the training dataset to have accurate up- and down-going waves and generalization. The literature "Tao B, Yang Y, Zhou H, et al. Deep learning-based upgoing and downgoing wavefield separation for vertical seismic profile data. Geophysics, 2023, 88(6):

[0005] D339-D355" creates a training set by simulating a large number of wavefields with different slopes and amplitudes, while "Margrave GF. Stratigraphic filtering and Q estimation. 2015." considers physical characteristics to generate a synthetic training set. The above methods for constructing training sets are challenging in practical applications due to the lack of real samples. Summary of the Invention

[0006] To solve the above technical problems, the present invention proposes a method for separating up- and down-going wavefields of VSP based on signal knowledge representation, which can achieve high-quality wavefield separation without additional training datasets under unsupervised and complex geological conditions.

[0007] The technical solution adopted by the present invention is as follows: A method for separating up- and down-going wavefields of VSP based on signal knowledge representation, and the specific steps are as follows:

[0008] S1. Construct a multi-dimensional knowledge representation system, and extract knowledge representations from the original VSP data to guide the separation process;

[0009] The multi-dimensional knowledge representation system includes: physical knowledge representation, morphological knowledge representation, and propagation direction difference knowledge representation.

[0010] S2. Based on step S1, construct a dual convolutional autoencoder network architecture KGCAE guided by signal knowledge representation using the knowledge representations of up- and down-going waves;

[0011] The double convolutional autoencoder network architecture KGCAE adopts an encoder-decoder structure, including two independent branches, Net-U and Net-D, which respectively predict the up-going wavefield and the down-going wavefield, and at the same time convert three kinds of knowledge representations into loss functions. The input is the original VSP record, and the output is the predicted up- and down-going wavefields with the same shape as the original record.

[0012] The overall structure of KGCAE is an encoder and a decoder. The encoder consists of convolutional layers and max-pooling layers, and is used for feature extraction and compression of VSP data. The decoder consists of convolutional layers and upsampling layers, and is used for feature reconstruction and restoration of data.

[0013] The specific architectures of Net-U and Net-D include: 1) convolutional layers, 2) max-pooling layers, 3) upsampling layers, and 4) activation functions.

[0014] Among them, the activation functions include: ReLU and Tanh. KGCAE extracts features through convolutional layers, compresses data through pooling layers, and reconstructs the wavefield through upsampling layers.

[0015] S3. Based on the KGCAE constructed in step S2, the knowledge representations obtained in step S1 are input for training, that is, the up- and down-going wave separation problem is modeled, and end-to-end learning from the original VSP record to the separated wavefield is realized. The predicted up-going wavefield and down-going wavefield are output to complete the up- and down-going wave separation of VSP.

[0016] Furthermore, the specific steps of step S1 are as follows:

[0017] S11. Extract the physical knowledge representations of up- and down-going waves based on physical knowledge. First, an accurate underground velocity model is obtained through full waveform inversion (FWI), then the elastic wave equation forward modeling is performed using this model, and finally the physical knowledge representations of up- and down-going waves are extracted based on the Poynting vector.

[0018] The two-dimensional elastic wave equation is used to simulate the propagation behavior of the wavefield in the depth-offset dimension. In 2D space, the density of the medium is set as ρ, and the displacement field vector is u = (u x , u z ). The expression of the elastic wave equation is as follows:

[0019]

[0020] Among them, u x , u z respectively represent the displacements in the horizontal and vertical directions, t represents time, and λ and μ respectively represent the Lame coefficients; λ + 2μ corresponds to the bulk modulus. The operator represents the gradient operator, represents the divergence operator, represents the Laplace operator.

[0021] The elastic wave equation of Equation (1) can be expressed by the longitudinal wave velocity c p and the shear wave velocity c s as follows:

[0022]

[0023] where the dilatation scalar θ is defined as

[0024] Then, by introducing the energy flux density vector to describe the energy transfer rate per unit time through a unit area, reflecting the flow direction and intensity of energy, Equation (2) can be expressed as follows:

[0025]

[0026] where the rotation vector ω is defined as In two dimensions, ω has only one non-zero component, i.e., the component perpendicular to the propagation plane. And the dilatation scalar field is an irrotational field, i.e., while the rotation vector is also a solenoidal field, i.e., Then the wave field can be decomposed into a longitudinal wave field and a shear wave field.

[0027] Next, simplify the equation and transform Equation (3) into a system of first-order differential equations. By introducing the particle vibration velocity the expression of the system of first-order differential equations is obtained as follows:

[0028]

[0029] where v is composed of the longitudinal wave particle vibration velocity v p and the shear wave particle vibration velocity v s , i.e., v = v p + v s .

[0030] Based on Equation (4), the specific expression of the energy flux density vector in the two-dimensional elastic wave field is derived as follows:

[0031]

[0032] where e p =(e px , e pz ) represents the energy flux density vector of the longitudinal wave, and e s =(e sx , e sz ) represents the energy flux density vector of the shear wave. Then the expression of the overall energy flux density vector e is as follows:

[0033] e = e p + es (6)

[0034] The full waveform inversion method based on the physically embedded recurrent neural network PIRNN is used to obtain geological model parameters, which include: P-wave velocity and S-wave velocity. By solving the elastic wave equation in Equation (3), the mapping relationship from geological model parameters to the VSP wave field is established.

[0035] The P-wave velocity and S-wave velocity in the geological model are respectively denoted as c p ∈R N×M and c s ∈R N×M , and the forward process expression is as follows:

[0036]

[0037] where N represents the number of longitudinal sampling points, M represents the number of transverse sampling points, and R represents the complex domain. denotes the VSP wave field obtained by forward modeling, T represents the number of time sampling points, F(·) represents the forward process, and is implemented using the physically embedded recurrent neural network PIRNN method.

[0038] Then, the geological model parameters c p and c s are inverted. Taking the observed VSP wave field X as the label, the inversion problem of geological model parameters is transformed into a constrained optimization problem, and the expression is as follows:

[0039]

[0040] Furthermore, by solving the optimization problem in Equation (8), the optimal solutions of the geological model parameters and are obtained, and an approximate solution of the seismic wave field is obtained through the forward process

[0041] During the process of obtaining the approximate solution of the seismic wave field , the energy flux density vector e is used to extract the knowledge representation of the up-going and down-going wave fields. First, the energy flux density vectors of P-waves and S-waves are calculated respectively according to Equation (5) to obtain e p and e s . Then, for P-waves, according to the sign of the vertical component e pz of the energy flux density vector, the wave propagation direction is determined, and the expression is as follows:

[0042]

[0043] where U rp represents the knowledge representation of the up-going P-wave, D rp represents the knowledge representation of the down-going P-wave, and z rIndicates the depth position of the geophone underground. Indicates the approximate solution of the longitudinal wave field in time t and the vertical direction z. r e. pz Indicates the longitudinal wave energy flux density vector e. p The component in the vertical direction.

[0044] Similarly, the shear wave separation process can be obtained. According to the sign of the horizontal component e of the energy flux density vector, the wave propagation direction is determined, and the expression is as follows: sx The wave propagation direction is determined according to the sign of the horizontal component e of the energy flux density vector, and the expression is as follows:

[0045]

[0046] Where, U rs Represents the knowledge representation of the up-going shear wave, D rs Represents the knowledge representation of the down-going shear wave, x r Indicates the depth position of the geophone underground. Indicates the approximate solution of the shear wave field in time t and the horizontal direction x. r e. sx Indicates the shear wave energy flux density vector e. s The component in the horizontal direction.

[0047] S12. Extract the morphological knowledge representation. First, manually pick up the axial dip angle sets of the up-going and down-going waves according to the original VSP data, then construct a modified Sobel operator according to the dip angle sets, and finally use the corresponding modified Sobel operators to extract the axial gradient information of the predicted up-going and down-going wave fields, that is, extract the axial gradient information of the up-going and down-going waves in the depth-time domain.

[0048] The up-going wave field forms an inverse proportional pattern with a negative slope in the depth-time domain, while the down-going wave field forms a direct proportional pattern with a positive slope, and a set of axial dip angle sets α = {α i |1 ≤ i ≤ p, α i ∈ R}, β = {β i |1 ≤ i ≤ q, β i ∈ R} between the up-going wave and the down-going wave and the horizontal interface are obtained.

[0049] Where, p and q respectively represent the number of elements in the sets α and β.

[0050] Then construct a modified Sobel operator according to the dip angle sets. The expression for rotating the Sobel operator is as follows:

[0051]

[0052] Where, α i Represents the rotation angle, and A and B respectively represent the horizontal and vertical Sobel operators. Indicates the rotated gradient operator.

[0053] Then set the prediction result of the network for the up - going wave as The prediction result for the down - going wave is The predicted up - and down - going wave fields and Use the corresponding modified Sobel operator to extract the axial gradient information respectively. Then the calculation expressions for the gradients of the up - and down - going waves along their axes are as follows:

[0054]

[0055] where, * represents the convolution operation, and min represents the element - by - element minimum operation. and represent the modified Sobel operators constructed according to the axial dip angle sets of the up - and down - going waves respectively. and represent the calculated gradient information matrix. Based on this matrix, the morphological knowledge representation can be obtained.

[0056] S13. Extract the propagation direction difference knowledge representation, that is, calculate the cosine similarity between the prediction results of the up - and down - going waves;

[0057] The difference between the up - going wave and the down - going wave is represented by the included angle between them, and the mean value of the wave fields is close to 0. Then the cosine similarity is introduced to extract the propagation direction difference knowledge representation. The cosine similarity is defined as the cosine of two vectors, and its value range is [-1, 1]. When the two vectors are orthogonal, the cosine similarity is 0. When the two vectors are the same or opposite, the value is 1 or -1.

[0058] Remap the cosine similarity to the interval [0, 1] through a single absolute - value operation. Let the up - going predicted wave field be The down - going predicted wave field is Then the definition expression of the cosine similarity is as follows:

[0059]

[0060] where, represents the dot product of the two wave fields. and represent the L2 norms of the two wave fields respectively. In the propagation direction difference knowledge representation, the absolute value L of the cosine similarity direction is used as the measure of the direction difference, and the expression is as follows:

[0061]

[0062] Furthermore, in the step S2, the loss function of the KGCAE is specifically as follows:

[0063] Model the knowledge representation as a loss function \(L\), including: reconstruction loss, representation loss, gradient loss, and cosine loss. The definition expression of the loss function \(L\) is as follows:

[0064] \(L = L\) rec +\(\lambda\) 1 \(L\) rep +\(\lambda\) 2 \(L\) grad +\(\lambda\) 3 \(L\) cos (15)

[0065] Among them, \(L\) rec represents the reconstruction loss, measuring the difference between the original wave field and the reconstructed wave field. \(L\) rep represents the representation loss, measuring the difference between the predicted wave field and the wave field of physical knowledge representation. \(L\) grad represents the gradient loss obtained from the morphological knowledge representation, emphasizing the continuity of the wave field. \(L\) cos represents the cosine loss obtained from the knowledge representation of the propagation direction difference, used to reduce the aliasing phenomenon in wave field separation.

[0066] The specific losses are as follows:

[0067] 1) Reconstruction loss;

[0068] The reconstruction loss \(L\) rec is used to measure the difference between the sum of the up-going wave field and the down-going wave field predicted by the double convolutional autoencoder and the original VSP record \(X\). The definition expression is as follows:

[0069]

[0070] Among them, \(\|\cdot\|\) h represents the error metric based on the Huber function, and the definition expression is as follows:

[0071]

[0072] Among them, \(s\) represents the independent variable of the Huber function, and \(d\) represents the threshold.

[0073] 2) Gradient loss;

[0074] The gradient loss \(L\) grad is obtained from the morphological knowledge representation and is used to measure the axial continuity of the up and down wave fields predicted by the network. The definition expression is as follows:

[0075]

[0076] 3) Representation loss;

[0077] The representation loss \(L\) repObtained from the physical knowledge representation, used to measure the predicted up-going wavefield of the model and the down-going wavefield and the difference between the knowledge representation wavefields U rp and D rp extracted based on the energy flux density vector. The definition expression is as follows:

[0078]

[0079] 4) Cosine loss;

[0080] Cosine loss L cos Obtained from the knowledge representation of the propagation direction difference, used to optimize the direction difference of the up- and down-going wavefields. The calculation expression of the cosine loss is as follows:

[0081]

[0082] where N r represents the number of receivers, u i and d i respectively represent the values of the up-going wavefield and the down-going wavefield predicted by the autoencoder at the i-th receiver, ||·|| 2 represents the two-norm of the vector.

[0083] Furthermore, the specific steps of step S3 are as follows:

[0084] The goal of signal separation is to recover the unknown up-going wavefield U ∈ R T×N from the observed VSP record X ∈ R T×N and the down-going wavefield D ∈ R T×N . The U-Net network architecture is adopted, and the up-going wavefield and the down-going wavefield are predicted by two independent networks respectively, and the physical knowledge representations U rp and D rp , the morphological knowledge representation, and the knowledge representation of the wavefield direction difference are explicitly introduced as constraints during the solution process.

[0085] Then the modeling expression for the up- and down-going wave separation problem is as follows:

[0086]

[0087] where, in the first term, X represents the original VSP record, represents the predicted reconstructed wavefield, and the remaining terms are the constraint terms introduced from the knowledge representation construction, namely the physical knowledge constraint, the morphological constraint, and the propagation direction difference constraint. ||·||:

[0088] R T×N →R +The operator for measuring error is denoted as, and the element-wise product is denoted as ⊙. R T×N →R T×N Denote two branch network mapping functions for predicting the up- and down-going wavefields, which are recovered from the original wavefield X and θ u , θ d denote the parameters of, ||·|| h denotes the Huber function, ||·|| F denotes the Frobenius norm, λ 1 , λ 2 , λ 3 , λ 4 denote the regularization parameters, which are used to adjust the weights of each loss in the overall objective function.

[0089] Advantages of the present invention: The method of the present invention first extracts knowledge representations from the original VSP data to guide the separation process, namely physical knowledge representation, morphological knowledge representation, and propagation direction knowledge representation. Then, a dual convolutional autoencoder network architecture KGCAE based on signal knowledge representation guidance is constructed using the knowledge representations of the up- and down-going waves, and the input knowledge representations are trained to model the up- and down-going wave separation problem, realizing end-to-end learning from the original VSP record to the separated wavefield, outputting the predicted up-going wavefield and down-going wavefield, and completing the separation of the up- and down-going waves in VSP. The method of the present invention establishes a complete signal knowledge representation system, extracts wavefield features from multiple dimensions, provides comprehensive prior knowledge guidance for the separation of up- and down-going waves, significantly improves the accuracy and reliability of the separation, and adopts an unsupervised learning method without the need for an additional training dataset. The wavefield separation is realized by converting the knowledge representation into a loss function constraint term, effectively avoiding the dependence on large-scale labeled samples in existing data-driven methods, reducing the application cost of the method, and being able to achieve high-quality wavefield separation under unsupervised and complex geological conditions. Description of the Drawings

[0090] Figure 1 is a flowchart of a method for separating the up- and down-going wavefields in VSP based on signal knowledge representation according to the present invention.

[0091] Figure 2 is an architecture diagram of KGCAE in an embodiment of the present invention.

[0092] Figure 3 is a schematic flow diagram of extracting physical knowledge representation in an embodiment of the present invention.

[0093] Figure 4 is a schematic flow diagram of extracting morphological knowledge representation in an embodiment of the present invention.

[0094] Figure 5 This is a schematic flow chart for extracting the propagation direction knowledge representation in the embodiments of the present invention.

[0095] Figure 6 This is the Marmousi model parameters, forward VSP data, and frequency-wavenumber diagram in the embodiments of the present invention.

[0096] Figure 7 This is a schematic diagram of the separation experiment results of the Marmousi model data in the embodiments of the present invention.

[0097] Figure 8 This is a schematic diagram of the change curve of the reconstruction loss of the Marmousi model under the method of the present invention in the embodiments of the present invention. Detailed implementation manners

[0098] The method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0099] As Figure 1 shown, the flow chart of a VSP up-down wavefield separation method based on signal knowledge representation of the present invention is as follows:

[0100] S1. Construct a multi-dimensional knowledge representation system, and extract knowledge representations from the original VSP data to guide the separation process;

[0101] The multi-dimensional knowledge representation system includes: physical knowledge representation, morphological knowledge representation, and propagation direction difference knowledge representation.

[0102] S2. Based on step S1, use the knowledge representations of the up and down waves to construct a dual convolutional autoencoder network architecture KGCAE (Knowledge-Guided Convolution Autoencoder) guided by signal knowledge representation;

[0103] As Figure 2 shown, the dual convolutional autoencoder network architecture KGCAE adopts an encoder-decoder structure, including two independent branches, Net-U and Net-D, to predict the up wavefield and down wavefield respectively, and at the same time convert the three knowledge representations into loss functions. The input is the original VSP record, and the output is the predicted up and down wavefields with the same shape as the original record.

[0104] In this embodiment, the specific structure and parameters of Net-U are shown in Table 1 (the structure and parameters of each layer of Net-U in the convolutional autoencoder). It is set that the shape of the input original VSP record in this embodiment is (1600, 100, 1), representing 1600 time points, 100 geophones, and 1 channel number. The overall structure of KGCAE is composed of an encoder and a decoder. The encoder is composed of convolutional layers and max-pooling layers, and is used for feature extraction and compression of VSP data. The decoder is composed of convolutional layers and upsampling layers, and is used for feature reconstruction and recovery of the data.

[0105] Table 1

[0106]

[0107] The network structure of Net-D is the same as that of Net-U. The specific architectures of Net-U and Net-D include:

[0108] 1) Convolutional layers: used to extract local features in the input VSP record, and capture fluctuation features at different scales and directions through multiple convolutional kernels;

[0109] 2) Max-pooling layers: used for downsampling, reducing the size of the feature map, retaining the most significant features, and improving the computational efficiency;

[0110] 3) Upsampling layers: used for upsampling, restoring the spatial resolution of the feature map, and realizing the reconstruction of the wave field;

[0111] 4) Activation functions:

[0112] ReLU: The ReLU activation function is used in the intermediate layer to introduce non-linear features and improve the expression ability of the model;

[0113] Tanh: The Tanh activation function is used in the output layer to limit the output wave field within the range of [-1, 1], ensuring the physical rationality of the output.

[0114] Among them, the activation functions include: ReLU, Tanh. KGCAE extracts features through convolutional layers, compresses data through pooling layers, and reconstructs the wave field through upsampling layers.

[0115] S3. Based on the KGCAE constructed in step S2, the knowledge representation obtained in step S1 is input for training, that is, the up and down wave separation problem is modeled, and end-to-end learning from the original VSP record to the separated wave field is realized, and the predicted up wave field and down wave field are output to complete the VSP up and down wave separation.

[0116] In this embodiment, the specific steps of step S1 are as follows:

[0117] S11. Extract the up - and - down wave knowledge representation based on physical knowledge. First, obtain an accurate underground velocity model through full - waveform inversion (FWI). Then, use this model for forward modeling of the elastic wave equation. Finally, extract the physical knowledge representation of the up - and - down waves based on the Poynting vector;

[0118] Use the two - dimensional elastic wave equation to simulate the propagation behavior of the wave field in the depth - offset dimension. In 2D space, set the density of the medium as ρ, and the displacement field vector as u=(u x ,u z ). The expression of the elastic wave equation is as follows:

[0119]

[0120] Among them, u x , u z represent the displacements in the horizontal and vertical directions respectively, t represents time, λ and μ represent the Lame coefficients respectively, which describe the elastic properties of the medium. And μ is called the shear modulus, reflecting the resistance ability of the material when subjected to shear force; λ + 2μ corresponds to the bulk modulus, describing the resistance ability of the medium to volume deformation. The operator represents the gradient operator, represents the divergence operator, represents the Laplace operator, which are used to describe the gradient, divergence, and Laplace operations of the displacement field in space respectively.

[0121] The elastic wave equation of Equation (1) can be expressed by the longitudinal wave velocity c p and the transverse wave velocity c s , and the expression is as follows:

[0122]

[0123] Among them, the dilation scalar θ is defined as It describes the volume change rate of the displacement field. This form of the wave equation describes the propagation mechanisms of longitudinal and transverse waves in the medium, corresponding to the waves caused by volume deformation and shear deformation respectively.

[0124] The elastic wave equation provides a mathematical basis for describing the dynamic process of medium vibration in the wave field. To further understand the propagation direction and distribution of energy in the wave field for guiding the subsequent wave - field separation task, it is necessary to introduce the energy - flux density vector to describe the energy transfer rate per unit time through a unit area, reflecting the flow direction and intensity of energy. Then, Equation (2) can be expressed as follows:

[0125]

[0126] Among them, the rotation vector ω is defined as In two dimensions, ω has only one non-zero component, i.e., the component perpendicular to the propagation plane. And the dilatation scalar field is an irrotational field, that is while the rotation vector is also a solenoidal field, that is Then the wave field can be decomposed into a longitudinal wave field and a transverse wave field. This decomposition not only simplifies the solution process of the wave equation but also facilitates the analysis of the energy propagation direction.

[0127] Then simplify the equation, transform Equation (3) into a system of first-order differential equations, and introduce the particle vibration velocity The expression of the system of first-order differential equations is as follows:[[]]END

[0128]

[0129] where v is composed of the longitudinal wave particle vibration velocity v p and the transverse wave particle vibration velocity v s , that is, v = v p + v s .

[0130] Equation (4) clarifies the mutual relationship between the longitudinal wave and the transverse wave during the propagation process over time, and how they are coupled with the dilatation scalar and the rotation vector. Then, based on Equation (4), the specific expression of the energy flux density vector in the two-dimensional elastic wave field can be derived as follows:[[]]END

[0131]

[0132] where e p =(e px , e pz ) represents the energy flux density vector of the longitudinal wave, and e s =(e sx , e sz ) represents the energy flux density vector of the transverse wave. The expression of the overall energy flux density vector e is as follows:[[]]END

[0133] e = e p + e s (6)

[0134] The energy flux density vector e not only describes the propagation direction and intensity of energy but also provides a basis for distinguishing between upward waves and downward waves. As can be seen from Equation (5), the longitudinal wave part e p is related to the dilatation scalar and the longitudinal wave particle vibration velocity field v p , while the transverse wave part e s is related to the rotation vector ω of the shear wave. In this embodiment, by comprehensively analyzing these two parts, the energy distribution in the wave field can be preliminarily depicted.

[0135] To obtain accurate geological model parameters, a full-waveform inversion method based on a physically embedded recurrent neural network (PIRNN) is adopted. Geological model parameters include the P-wave velocity and the S-wave velocity, which are key parameters describing the elastic properties of the underground medium. By solving the elastic wave equation in Equation (3), a mapping relationship from geological model parameters to the VSP wavefield is established.

[0136] Let the P-wave velocity and the S-wave velocity in the geological model be denoted as c p ∈R N×M and c s ∈R N×M , and the forward process expression is as follows:

[0137]

[0138] where N represents the number of longitudinal sampling points, M represents the number of transverse sampling points, and R represents the complex domain. represents the VSP wavefield obtained through forward modeling, T represents the number of time sampling points, F(·) represents the forward process, and is implemented using the physically embedded recurrent neural network PIRNN method.

[0139] Then, invert the geological model parameters c p and c s . Taking the observed VSP wavefield X as the label, the inversion problem of geological model parameters is transformed into a constrained optimization problem, and the expression is as follows:

[0140]

[0141] Then, by solving the optimization problem in Equation (8), the optimal solutions of the geological model parameters and are obtained, and an approximate solution of the seismic wavefield is obtained through the forward process The PIRNN network incorporates the physical constraints of the wave equation into the neural network and uses the time-stepping mechanism of the RNN for forward modeling, thereby realizing the simulation of the VSP wavefield. Through the backpropagation algorithm, PIRNN can invert the geological model parameters from the observed VSP wavefield, and these parameters provide a basis for subsequent up- and down-going wave knowledge representation.

[0142] In the process of obtaining the approximate solution of the seismic wavefield, the energy flux density vector e is used to extract the knowledge representation of the up- and down-going wavefields. First, the energy flux density vectors of the P-wave and the S-wave are calculated according to Equation (5) respectively to obtain e p and e s . Then, for the P-wave, the propagation direction of the wave is determined according to the sign of the vertical component e pz of the energy flux density vector, and the expression is as follows:

[0143]

[0144] Among them, U rp represents the knowledge representation of the up-going longitudinal wave, D rp represents the knowledge representation of the down-going longitudinal wave, z r represents the depth position of the geophone underground, represents the approximate solution of the longitudinal wave field in the time t and the vertical direction z r e. pz represents the component of the longitudinal wave energy flux density vector e p in the vertical direction.

[0145] Similarly, the shear wave separation process can be obtained. According to the sign of the horizontal component E sx of the energy flux density vector, the wave propagation direction is determined. The expression is as follows:

[0146]

[0147] Among them, u rs represents the knowledge representation of the up-going shear wave, d rs represents the knowledge representation of the down-going shear wave, x r represents the depth position of the geophone underground, represents the approximate solution of the shear wave field in the time t and the horizontal direction x r e. sx represents the component of the shear wave energy flux density vector e s in the horizontal direction.

[0148] The process of extracting the physical knowledge representation in this embodiment is as Figure 3 shown, where Figure 3 (a) and (b) respectively represent the parts of the longitudinal wave energy flux density vector e pz >0 and e pz <0 obtained through the above forward modeling process. From this, the distribution of the up and down waves can be seen, and it is applied to Figure 3 (c) the approximate solution X * of the seismic wave field, and then Figure 3 (d) and (e) the physical knowledge representations of the up and down waves can be obtained. This knowledge representation is directly derived from the physical model, has a clear physical meaning, can reflect the propagation direction of the wave field, and can provide important physical constraint information for the subsequent separation of the up and down waves.

[0149] S12. Extract the morphological knowledge representation. First, manually pick up the set of axial dips of the up and down waves from the original VSP data, then construct a modified Sobel operator according to the dip set, and finally use the corresponding modified Sobel operator to extract the axial gradient information of the predicted up and down wave fields, that is, extract the axial gradient information of the up and down waves in the depth-time domain;

[0150] The process of extracting morphological knowledge representation in this embodiment is as follows Figure 4 shown. In near-offset vertical seismic profile (VSP) data, the propagation direction of odd-order reflected waves (downward waves) is usually downward, while the propagation direction of even-order reflected waves (upward waves) is usually upward. This difference in propagation direction results in different apparent velocity and slope characteristics of the up and down waves in the depth-time domain. That is, the upward wave field forms an inverse proportional pattern with a negative slope in the depth-time domain, while the downward wave field forms a direct proportional pattern with a positive slope. Figure 4 (a) shows a near-offset VSP record of a simple flat layer model, from which it can be seen that the upward and downward waves have a set of axial dip angles α = {α i |1 ≤ i ≤ p, α i ∈ R}, β = {β i |1 ≤ i ≤ q, β i ∈ R} with the horizontal interface. To utilize these morphological features to constrain the up and down wave fields, this embodiment introduces a knowledge representation based on morphological prior, which aims to emphasize the axial continuity and slope difference of the up and down wave fields, thereby improving the accuracy of wave field separation.

[0151] Among them, p and q respectively represent the number of elements in sets α and β.

[0152] To extract this knowledge representation, this embodiment uses a modified Sobel operator to calculate the gradient along the axis. The Sobel operator is a commonly used discrete differential operator for calculating the approximate gradient of an image or signal. It detects edges and direction changes in an image through convolution operations. To adapt to the slope characteristics of the up and down wave fields, the Sobel operator should be modified to enable it to capture gradient information in different directions. That is, a modified Sobel operator is constructed according to the dip angle set, and the expression for rotating the Sobel operator is as follows:

[0153]

[0154] where α i represents the rotation angle, A and B respectively represent the horizontal and vertical Sobel operators, represents the rotated gradient operator. When α i = 45°, the rotated Sobel operator can effectively capture the axial gradient information of the downward wave with a 45° dip angle between the downward wave field and the horizontal plane.

[0155] In summary, a gradient knowledge representation based on morphological prior is proposed. Let the predicted result of the network for the upward wave be and the predicted result for the downward wave be The predicted up and down wave fields and Extract the gradient information in the axial direction using the corresponding modified Sobel operators respectively. The gradient calculation expressions for the up and down traveling waves along their axial directions are as follows:

[0156]

[0157] where * represents the convolution operation, and min represents the element-wise minimum operation. and represent the modified Sobel operators constructed according to the axial inclination angle sets of the up and down traveling waves respectively. and represent the calculated gradient information matrices. Based on this matrix, the morphological knowledge representation can be obtained. Since the up and down traveling waves have characteristics such as axial slope differences and axial continuity, and the up and down traveling wave fields should be smooth along their axial directions, that is, the changes in the up and down traveling wave fields in their axial directions are small. Using this knowledge representation, a loss function can be constructed according to and to guide the network to optimize the axial continuity during training, thereby realizing the morphological constraint on the up and down traveling waves. The process of extracting the morphological prior knowledge representation is as shown in Figure 4 (b), (c). First, manually pick the axial inclination angle sets α and β of the up and down traveling waves from the original VSP data, then construct the modified Sobel operators according to the inclination angle sets, and finally use the corresponding modified Sobel operators to extract the gradient information in the axial direction for the predicted up and down traveling wave fields and respectively.

[0158] S13. Extract the knowledge representation of the propagation direction difference, that is, calculate the cosine similarity between the prediction results of the up and down traveling waves;

[0159] In the VSP record, the up and down traveling waves have significant differences in the propagation direction, and due to the zero-mean characteristic of the VSP wave field, as shown in the schematic diagram of the process of extracting the propagation direction knowledge representation in Figure 5 , where α 1 , α 2 , α 3 , α 4 represent the included angles between the up and down traveling waves. It can be seen that there are obvious differences between the up and down traveling waves. The difference between the up and down traveling waves is represented by the included angle between the two, and the mean value of the wave field is close to 0. Then, the cosine similarity is introduced to extract the knowledge representation of the propagation direction difference. The cosine similarity is defined as the cosine of two vectors, and its value range is [-1, 1]. When the two vectors are orthogonal, the cosine similarity is 0. When the two vectors are the same or opposite, the value is 1 or -1.

[0160] However, if the problem scenario of VSP traveling wave separation contains negative value signals, in this embodiment, the cosine similarity is remapped to the interval [0, 1] through another absolute value operation. Let the up-going predicted wavefield be and the down-going predicted wavefield be Then the defined expression of the cosine similarity is as follows:

[0161]

[0162] where represents the dot product of the two wavefields, and respectively represent the L2 norms of the two wavefields. In the knowledge representation of the propagation direction difference, the absolute value L direction of the cosine similarity is used as the measure of the direction difference, and the expression is as follows:

[0163]

[0164] Under the guidance of the knowledge representation of the wavefield direction difference, the model can learn the difference in direction between the up-going wave and the down-going wave, and can better restore the zero-mean characteristic of the VSP wavefield, so as to better perform wavefield separation.

[0165] In this embodiment, in the step S2, the loss function of the KGCAE is specifically as follows:

[0166] In order to use the knowledge representation to guide the traveling wave separation, the knowledge representation is modeled as a loss function L, including: reconstruction loss, representation loss, gradient loss, and cosine loss. Then the defined expression of the loss function L is as follows:

[0167] L = L rec + λ 1 L rep + λ 2 L grad + λ 3 L cos (15)

[0168] where L rec represents the reconstruction loss, measuring the difference between the original wavefield and the reconstructed wavefield. L rep represents the representation loss, measuring the difference between the predicted wavefield and the physically knowledge-represented wavefield. L grad represents the gradient loss obtained from the morphological knowledge representation, emphasizing the continuity of the wavefield. L cos represents the cosine loss obtained from the knowledge representation of the propagation direction difference, used to reduce the aliasing phenomenon in wavefield separation. The specific losses are as follows:

[0169] (1) Reconstruction loss;

[0170] The reconstruction loss Lrec Used to measure the predicted upgoing wavefield of the double convolutional autoencoder and the downgoing wavefield The difference between the sum of them and the original VSP record X. The defined expression is as follows:

[0171]

[0172] where, ||·|| h represents the error metric based on the Huber function, and the defined expression is as follows:

[0173]

[0174] where, s represents the dependent variable of the Huber function, d represents the threshold, and in this embodiment, d = 1. The Huber function adopts the squared loss for small errors and the linear loss for large errors, thus taking into account the advantages of both the mean squared error and the absolute error, and effectively reducing the sensitivity to outliers.

[0175] The introduction of the reconstruction loss ensures that when the model predicts the up- and downgoing wavefields, the overall wavefield can accurately reconstruct the original observed data. This loss term prompts the model to maintain the overall consistency and physical rationality of the wavefield during the process of separating the up- and downgoing waves.

[0176] (2) Gradient loss;

[0177] The gradient loss L grad is obtained from the morphological knowledge representation and is used to measure the axial continuity of the up- and downgoing wavefields predicted by the network. The defined expression is as follows:

[0178]

[0179] (3) Representation loss;

[0180] The representation loss L rep is obtained from the physical knowledge representation and aims to enhance the accuracy and stability of the up- and downgoing wavefield separation by introducing physical rules. The representation loss is used to measure the upgoing wavefield predicted by the model and the downgoing wavefield and the knowledge representation wavefields U rp and D rp extracted based on the energy flux density vector. The difference between them. The defined expression is as follows:

[0181]

[0182] By introducing the representation loss, the model not only focuses on the reconstruction of the overall wave field but also emphasizes the consistency between the predicted wave field and the knowledge representation of the up- and down-going wave fields extracted by physical methods. This loss ensures that during the separation of up- and down-going waves, the model can accurately capture the physical characteristics and propagation directions of the wave field, improving the separation accuracy. Moreover, under complex geological structures, the representation loss can provide additional constraints to prevent unreasonable wave field reconstruction during wave field separation, enhancing the stability of the separation process.

[0183] (4) Cosine loss;

[0184] Cosine loss L cos It is obtained from the knowledge representation of the propagation direction difference and is used to further optimize the direction difference between the up- and down-going wave fields. The calculation expression of the cosine loss is as follows:

[0185]

[0186] where N r represents the number of receivers, u i and d i respectively represent the values of the up-going wave field and the down-going wave field predicted by the autoencoder at the i-th receiver, and ||·|| 2 represents the two-norm of the vector.

[0187] The introduction of the cosine loss is to make the up- and down-going wave fields have obvious differences, reduce the aliasing phenomenon in wave field separation, and make the separated wave field more in line with the actual physical laws.

[0188] In this embodiment, the specific steps of step S3 are as follows:

[0189] The goal of signal separation is to recover the unknown up-going wave field U ∈ R T×N and the down-going wave field D ∈ R T×N from the observed VSP record X ∈ R T×N . This embodiment adopts the U-Net network architecture, predicts the up-going wave field and the down-going wave field through two independent networks respectively, and explicitly introduces the physical knowledge representation U rp and D rp , the morphological knowledge representation, and the knowledge representation of the wave field direction difference as constraints, thereby enhancing the physical consistency and accuracy of wave field separation.

[0190] Then the modeling expression for the up- and down-going wave separation problem is as follows:

[0191]

[0192] where, in the first term, X represents the original VSP record, denotes the predicted reconstructed wavefield, and the remaining terms are constraint terms introduced in the construction of knowledge representation, namely physical knowledge constraint, morphological constraint, and propagation direction difference constraint. ||·||:

[0193] R T×N →R + denotes the operator used to measure the error, and ⊙ denotes the element-wise product. R T×N →R T×N denotes the two-branch network mapping functions for predicting the up- and down-going wavefields, which recover from the original wavefield X and θ u , θ d denotes the parameter of h denotes the Huber function, ||·|| F denotes the Frobenius norm, λ 1 、λ 2 、λ 3 、λ 4 denote the regularization parameters, which are used to adjust the weights of each loss in the overall objective function.

[0194] The modeling process shown in Equation (21) not only needs to measure the reconstruction error between the observed record X and the reconstructed wavefield but also needs to measure the error between the predicted wavefield and and its knowledge representation, so as to constrain the continuity and direction consistency of the wavefield and ensure the physical rationality of wavefield separation.

[0195] This embodiment further conducts experimental verification to evaluate the performance and stability of the method of the present invention under complex geological structures, and selects the Marmousi model widely used in seismic wave propagation and inversion algorithm testing. The Marmousi model, with its complex two-dimensional geological structure including features such as reverse faults, can truly simulate the propagation and reflection behavior of seismic waves in complex media and becomes an ideal test object for verifying the effectiveness of wavefield separation methods.

[0196] The Marmousi geological model adopted in this embodiment is as Figure 6 shown. Among them Figure 6 (a), (b), and (c) respectively represent the density, longitudinal wave velocity (P-wave), and shear wave velocity (S-wave) of the Marmousi model. The observation system is configured at Figure 6In the identification in (a), the seismic source emission point is located 40 m offset from the surface. The geophones are distributed within the range of 0 m to 500 m underground, with an interval of 5 m. A Ricker wavelet with a dominant frequency of 30 Hz is used as the seismic source signal, and VSP data is generated through elastic wave forward modeling. The specific forward modeling parameters are shown in Table 2. The VSP data obtained through forward modeling of the Marmousi geological model is as shown in Figure 6 (d), and its corresponding f-k diagram (frequency-wavenumber diagram) is as shown in Figure 6 (e). It can be clearly seen from the f-k diagram that there is obvious up- and down-going wave energy in the original VSP record, and the energy is concentrated around 30 Hz.

[0197] Table 2

[0198]

[0199] To evaluate the method of the present invention, Figure 7 shows the separation results and their frequency-wavenumber spectra on the Marmousi model. Among them, Figure 7 (a) and (c) are the knowledge representations of the up- and down-going waves generated based on physical rules, showing the wave field distribution extracted based on the energy flux density vector. Figure 7 (e) and (g) are the predictions of the up- and down-going wave fields using KGCAE, Figure 7 (b) and (d) are Figure 7 the dispersion spectra corresponding to the up- and down-going waves in Figure 7 (a) and (c), Figure 7 (f) and (h) are Figure 8 the dispersion spectra corresponding to the up- and down-going waves in rec (e) and (g). It can be seen from the results that KGCAE can effectively utilize the axial and numerical distribution information of the wave field in the knowledge representation, making the axial direction of the separated up- and down-going wave fields clearer, the zero-mean characteristic more completely retained, and the high-frequency noise pollution effectively eliminated, thus restoring the frequency characteristics of the original signal. This shows that when dealing with complex wave fields, KGCAE can maintain physical consistency and the true characteristics of the signal. In addition,

[0200] In summary, the double convolutional autoencoder architecture of the method of the present invention can directly act on the original VSP data without domain transformation, can automatically handle the problem of frequency-domain aliasing, and exhibits good separation effect, fast convergence speed and stable training process under complex geological conditions. The verification experiments on the flat layer model and the Marmousi model show that it has a better separation effect and stronger generalization ability than the prior art, and can effectively solve the problem of separating the up-going and down-going waves of VSP data under complex geological conditions.

[0201] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A VSP uplink and downlink wave field separation method based on signal knowledge characterization, the specific steps are as follows: S1. Construct a multi-dimensional knowledge representation system to extract knowledge representation from the original VSP data to guide the separation process; The multi-dimensional knowledge representation system includes: Physical knowledge representation, morphological knowledge representation and propagation direction difference knowledge representation; S2. Based on step S1, the knowledge representation of uplink and downlink waves is used to construct a dual convolutional autoencoder network architecture KGCAE guided by signal knowledge representation; The dual convolutional autoencoder network architecture KGCAE adopts an encoder-decoder structure, including two independent branches, Net-U and Net-D, to predict the uplink wavefield and the downlink wavefield respectively, and convert the three knowledge representations into a loss function; the input is the original VSP record, and the output is the predicted uplink and downlink wavefields with the same shape as the original record; The overall structure of KGCAE consists of an encoder and a decoder. The encoder consists of a convolutional layer and a maximum pooling layer, which is used to extract and compress VSP data features; The decoder consists of convolutional layers and upsampling layers, which are used to reconstruct and restore the features of the data; The specific architecture of Net-U and Net-D includes: 1) convolution layer, 2) max pooling layer, 3) upsampling layer, 4) activation function; Among them, the activation functions include: ReLU, Tanh; KGCAE extracts features through the convolution layer, compresses data through the pooling layer, and reconstructs the wave field through the upsampling layer; S3. Based on the KGCAE constructed in step S2, the knowledge representation obtained in step S1 is input for training, that is, the uplink and downlink wave separation problem is modeled, end-to-end learning from the original VSP record to the separated wave field is realized, and the predicted uplink and downlink wave fields are output to complete the VSP uplink and downlink wave separation.

2. According to the method for separating VSP uplink and downlink wave fields based on signal knowledge characterization according to claim 1, it is characterized in that: The step S1 is specifically as follows: S11, extracting the knowledge representation of up and down waves based on physical knowledge, firstly obtaining an accurate underground velocity model through full waveform inversion FWI, then using the model to perform elastic wave equation forward modeling, and finally extracting the physical knowledge representation of up and down waves based on Poynting vector; The two-dimensional elastic wave equation is used to simulate the propagation behavior of the wave field in the depth-offset dimension. In the 2D space, the density of the medium is set to ρ and the displacement field vector is set to u = (u x ,u z ), the elastic wave equation is expressed as follows: Among them, u x ,u z Respectively represent the horizontal and vertical displacements, t represents time, λ and μ represent the Lame coefficients, respectively; λ+2μ corresponds to the bulk modulus; the operator represents the gradient operator, represents the divergence operator, Then it represents the Laplace operator; The elastic wave equation of formula (1) can be expressed by the longitudinal wave velocity c p and the shear wave velocity c s To express it, the expression is as follows: Here, the expansion scalar θ is defined as The energy flux density vector is introduced to describe the energy transfer rate per unit area per unit time, reflecting the flow direction and intensity of energy. Then equation (2) can be expressed as follows: The rotation vector ω is defined as In the two-dimensional case, ω has only one non-zero component, which is perpendicular to the plane of propagation; and the expansion scalar field is an irrotational field, that is The rotation vector There is no end, that is Then the wave field can be decomposed into longitudinal wave field and transverse wave field; Then simplify the equation and transform equation (3) into a first-order differential equation system, introducing the particle vibration velocity The expression of the first-order differential equation system is as follows: Where v is the velocity v of the longitudinal wave particle vibration p and the shear wave particle vibration velocity v s composition, that is, v = v p +v s ; Based on formula (4), the specific expression of the energy flux density vector in the two-dimensional elastic wave field is derived as follows: Among them, e p =(e px ,e pz ) represents the energy flux density vector of the longitudinal wave, e s =(e sx ,e sz ) represents the energy flux density vector of the shear wave; then the overall energy flux density vector e is expressed as follows: and=and p +e s (6) The full waveform inversion method based on physical embedded recurrent neural network (PIRNN) is used to obtain geological model parameters, including P-wave velocity and S-wave velocity. The mapping relationship from geological model parameters to VSP wave field is established by solving the elastic wave equation in equation (3). The P-wave velocity and S-wave velocity in the geological model are assumed to be c p ∈R N×M and c s ∈R N×M , the forward modeling process expression is as follows: Where N represents the number of longitudinal sampling points, M represents the number of transverse sampling points, and R represents the complex domain; represents the VSP wave field obtained by forward modeling, T represents the number of time sampling points, and F(·) represents the forward modeling process, which is implemented by the physical embedding recurrent neural network PIRNN method; Then the geological model parameter c is inverted p and c s , taking the observed VSP wave field X as the label, the inversion problem of geological model parameters is transformed into a constrained optimization problem, which is expressed as follows: Then, by solving the optimization problem (8), the optimal solution of the geological model parameters is obtained. and The approximate solution of the seismic wave field is obtained through the forward modeling process. In the approximate solution of the seismic wave field In the process of extracting the knowledge representation of the uplink and downlink wave fields, the energy flux density vector e is used. First, the energy flux density vectors of the longitudinal wave and the transverse wave are calculated according to formula (5) to obtain e p and e s , then, for longitudinal waves, according to the vertical component of the energy flux density vector e pz The sign of is used to determine the propagation direction of the wave, and the expression is as follows: Among them, U rp represents the knowledge representation of the upward longitudinal wave, D rp represents the knowledge representation of the downward longitudinal wave, z r Indicates the depth of the detector underground. represents the longitudinal wave field at time t and vertical direction z r The approximate solution on pz represents the longitudinal wave energy flux density vector e p Component in the vertical direction; Similarly, the shear wave separation process can be obtained according to the horizontal component e of the energy flux density vector sx The sign of is used to determine the propagation direction of the wave, and the expression is as follows: Among them, U rs represents the knowledge representation of the upward shear wave, D rs represents the knowledge representation of the downward shear wave, x r Indicates the depth of the detector underground. represents the shear wave field at time t and horizontal direction x r The approximate solution on sx represents the shear wave energy flux density vector e s Component in the horizontal direction; S12, extracting morphological knowledge representation, first manually picking up the axial dip angle set of the up and down waves according to the original VSP data, then constructing a modified Sobel operator according to the dip angle set, and finally extracting the axial gradient information of the predicted up and down wave fields using the corresponding modified Sobel operator, that is, extracting the axial gradient information of the up and down waves in the depth-time domain; The upgoing wave field forms an inversely proportional pattern with a negative slope in the depth-time domain, while the downgoing wave field forms a positively proportional pattern with a positive slope, thus obtaining a set of axial inclination angles α={α i |1≤i≤p,α i ∈R},β={β i |1≤i≤q,β i ∈R}; Where p and q represent the number of elements in sets α and β respectively; Then, the modified Sobel operator is constructed according to the inclination set. The expression of the rotation Sobel operator is as follows: Among them, α i represents the rotation angle, A and B represent the horizontal and vertical Sobel operators respectively, represents the rotated gradient operator; Then set the network's prediction result for the uplink wave to The prediction result for the downtrend wave is The predicted up and down wave fields and The corresponding modified Sobel operators are used to extract the axial gradient information, and the gradient calculation expressions of the uplink and downlink waves along their axial directions are as follows: Among them, * represents the convolution operation, min represents the element-by-element minimum operation, and They represent the modified Sobel operator constructed according to the axial inclination set of the uplink and downlink waves, and represents the calculated gradient information matrix, from which the morphological knowledge representation can be obtained; S13, extracting knowledge representation of propagation direction differences, that is, calculating the cosine similarity between the uplink and downlink prediction results; The difference between the upgoing wave and the downgoing wave is represented by the angle between them, and the wave field mean is close to 0, so the cosine similarity is introduced to extract the knowledge representation of the difference in propagation direction; the cosine similarity is defined as the cosine of two vectors, and the value range is [-1,1]. When the two vectors are orthogonal, the cosine similarity is 0, and when the two vectors are the same or opposite, the value is 1 or -1; The cosine similarity is remapped to the interval [0,1] by taking the absolute value operation once; let the uplink prediction wave field be The downside prediction wave field is The cosine similarity definition expression is as follows: in, represents the dot product of two wave fields, and Represent the L2 norm of the two wave fields respectively; in the knowledge representation of propagation direction difference, the absolute value of cosine similarity L direction As a measure of directional difference, the expression is as follows:

3. According to the method of VSP uplink and downlink wave field separation based on signal knowledge characterization in claim 1, it is characterized in that: In step S2, the loss function of the KGCAE is as follows: The knowledge representation is modeled as a loss function L, including reconstruction loss, representation loss, gradient loss, and cosine loss; the loss function L is defined as follows: L=L rec +λ1L rep +λ2L grad +λ3L cos (15) Among them, L rec represents the reconstruction loss, which measures the difference between the original wavefield and the reconstructed wavefield; L rep represents the representation loss, which measures the difference between the predicted wavefield and the wavefield represented by physical knowledge; L grad represents the gradient loss obtained by characterizing morphological knowledge, emphasizing the continuity of the wave field; L cos The cosine loss obtained by characterizing the knowledge of propagation direction differences is used to reduce the aliasing phenomenon in wave field separation; The losses are as follows: 1) Reconstruction loss; Reconstruction loss L rec Upstream wave field for measuring predictions of dual convolutional autoencoders and downlink wave field The difference between the sum and the original VSP record X; the definition expression is as follows: Among them, ||·|| h Represents the error metric based on the Huber function, and the definition expression is as follows: Among them, s represents the dependent variable of the huber function, and d represents the threshold; 2) Gradient loss; Gradient loss L grad It is obtained by characterizing morphological knowledge and is used to measure the axial continuity of the uplink and downlink wave fields predicted by the network. The definition expression is as follows: 3) Characterization loss; Representation loss L rep It is characterized by physical knowledge and used to measure the upgoing wave field predicted by the model. and downlink wave field The knowledge representation of wave field U based on energy flux density vector extraction rp and D rp The difference between; the definition expression is as follows: 4) Cosine loss; Cosine loss L cos It is obtained by characterizing the knowledge of propagation direction differences and is used to optimize the directional differences of uplink and downlink wave fields. The calculation expression of cosine loss is as follows: Among them, N r represents the number of receivers, u i and d i They represent the uplink wave field predicted by the autoencoder. and downlink wave field The value at the i-th receiver, ||·||2 represents the two-norm of the vector.

4. According to the method for separating VSP uplink and downlink wave fields based on signal knowledge characterization according to claim 1, it is characterized in that: The step S3 is specifically as follows: The goal of signal separation is to separate the observed VSP records X∈R T×N Recover the unknown upgoing wave field U∈R T×N and the downlink wave field D∈R T×N ; The U-Net network architecture is used to predict the uplink wave field and the downlink wave field through two independent networks, and physical knowledge is explicitly introduced to represent the U in the solution process. rp and D rp , morphological knowledge representation and wave field direction difference knowledge representation as constraints; The modeling expression for the uplink and downlink wave separation problem is as follows: Among them, X in the first item represents the original VSP record, represents the predicted reconstructed wave field, and the remaining items are constraints introduced from the knowledge representation construction, namely physical knowledge constraints, morphology constraints, and propagation direction difference constraints; ||·||: R T×N →R + represents the operator used to measure the error, ⊙ represents the element-wise product; R T×N →R T×N represents the two branch network mapping functions used to predict the uplink and downlink wavefields, which are recovered from the original wavefield X and θ u ,θ d express The parameters of ||·|| h represents the Huber function, ||·|| F represents the Frobenius norm, λ1, λ2, λ3, and λ4 represent regularization parameters, which are used to adjust the weights of each loss in the overall objective function.

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