Transverse wave velocity prediction method, apparatus and device, and readable storage medium

Abstract

The invention discloses a shear wave velocity prediction method, device and equipment and a readable storage medium, and is applied to the technical field of geophysics, and the method comprises the steps: constructing a shear wave velocity prediction model in advance based on a KAN network and a sequence displacer; an activation function of the shear wave velocity prediction model is a B-spline primary function; obtaining logging data of the target area; and inputting the logging data into the shear wave velocity prediction model to obtain a prediction result. The shear wave velocity prediction model based on the KAN network has robustness and accuracy, the model is combined with a sequence displacer architecture to be fused with the KAN network to perform feature extraction, efficient modeling of logging data is realized through a dynamic weight fusion mechanism and a learnable B-spline basis function, and the prediction accuracy is improved. The model can be used in various large oil fields in a large scale, deals with various complex geological conditions and accurately predicts the shear wave velocity, so that the exploration and development risk is reduced, and the benefit development of each large oil field is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of geophysical technology, and in particular to a shear wave velocity prediction method, device, equipment and readable storage medium. Background Art

[0002] Shear wave prediction plays an irreplaceable role in petroleum geology. Its core lies in inverting the P / S wave velocity ratio (Vs / Vp) and elastic parameters, providing a key basis for reservoir lithology identification, fracture detection, and fluid property identification. Currently, algorithms for shear wave velocity prediction are unable to accurately predict shear wave velocities in complex geological conditions. Traditional methods, such as empirical geophysical models, rely on specific physical equations tailored for different reservoir types, making their application time-consuming and labor-intensive.

[0003] Therefore, how to provide a method for accurate shear wave velocity prediction in various complex geological conditions is a technical problem that urgently needs to be solved. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a shear wave velocity prediction method, device, equipment and readable storage medium, which solve the problems of accurate formation and poor adaptability of shear wave velocity prediction in the prior art.

[0005] To solve the above technical problems, the present invention provides a shear wave velocity prediction method, comprising:

[0006] A shear wave velocity prediction model is pre-built based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function;

[0007] Obtain well logging data for the target area;

[0008] The logging data is input into the shear wave velocity prediction model to obtain a prediction result.

[0009] Optionally, inputting the logging data into the shear wave velocity prediction model to obtain a prediction result includes:

[0010] Inputting the logging data into the embedding layer of the shear wave velocity prediction model to obtain a mapping result;

[0011] Inputting the mapping result into the feature interaction layer of the shear wave velocity prediction model to obtain a feature vector; the feature interaction layer is constructed based on the KAN network and combined with the sequence permutator;

[0012] The feature vector is input into the classification layer of the shear wave velocity prediction model to obtain the prediction result.

[0013] Optionally, the logging data is input into the embedding layer of the shear wave velocity prediction model to obtain a mapping result, including:

[0014] The convolution layer of the shear wave velocity prediction model performs a one-dimensional convolution operation on the local features of the logging data to extract the initial internal input feature variables, and maps the dimensions of the internal input feature variables of the data to the internal channel dimension D of the shear wave velocity prediction model to obtain the mapping result. ;

[0015] The formula expression of the embedding layer is:

[0016] ;

[0017] in, is the parameter of the convolution kernel at position r and channel d; R is the kernel size; bd is the bias; L is the depth of data sampling; Well logging data.

[0018] Optionally, the mapping result is input into the feature interaction layer of the shear wave velocity prediction model to obtain a feature vector, including:

[0019] Inputting the mapping result into a plurality of consecutive feature interaction layers of the shear wave velocity prediction model to obtain the feature vector; each feature interaction layer includes a sequence permutator structure feature extraction module and a fully connected layer;

[0020] The formula expression of the feature interaction layer is:

[0021] ;

[0022] in, is the output of the current feature interaction layer; is the feature interaction layer; is the input of the current feature interaction layer; K is the total number of feature interaction layers; PKAN is the sequence permutator structure feature extraction module; LP is the fully connected layer.

[0023] Optionally, the sequence permutator structural feature extraction module includes:

[0024] Channel permutation KAN and depth permutation KAN;

[0025] Correspondingly, the formula expression of the sequence permutator structural feature extraction module PKAN is:

[0026] ;

[0027] ;

[0028] ;

[0029] Correspondingly, the formula expression of the feature interaction layer is for:

[0030] = (α +β ) ;

[0031] ;

[0032] in, Permutate KAN for the channel; is the deep permutation KAN; is the output result of channel permutation KAN; is the output result of deep permutation KAN; and are the dynamic weights of channel and depth respectively; is the normalization function; is the average value.

[0033] Optionally, before inputting the feature vector into the classification layer of the shear wave velocity prediction model to obtain the prediction result, the method further includes:

[0034] The feature vector is input into the fully connected layer and normalized layer of the shear wave velocity prediction model and mapped into the regressor; the formula is: ;

[0035] in, ∈R D×1 is the regressor weight; is the output of the regressor; is the normalization layer; is a fully connected layer; is the final output of the feature interaction layer.

[0036] Optionally, the well logging data includes:

[0037] Density data, photoelectric index data, deep lateral resistivity data, shallow lateral resistivity data, natural gamma ray data and compensated neutron data.

[0038] The present invention also provides a shear wave velocity prediction device, comprising:

[0039] A model building module is used to pre-build a shear wave velocity prediction model based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function;

[0040] Well logging data acquisition module, used to obtain well logging data of the target area;

[0041] The prediction module is used to input the logging data into the shear wave velocity prediction model to obtain a prediction result.

[0042] The present invention also provides a shear wave velocity prediction device, comprising:

[0043] memory for storing computer programs;

[0044] A processor is used to implement the above-mentioned shear wave velocity prediction method when executing the computer program.

[0045] The present invention also provides a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are loaded and executed by a processor, the shear wave velocity prediction method as described above is implemented.

[0046] It can be seen that the present invention pre-constructs a shear wave velocity prediction model based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function; well logging data of the target area is obtained; and the well logging data is input into the shear wave velocity prediction model to obtain a prediction result. The shear wave velocity prediction model based on the KAN network of the present invention is robust and accurate. The model is combined with a sequence permutator architecture to fuse it with the KAN network for feature extraction. Through a dynamic weight fusion mechanism and a learnable B-spline basis function, efficient modeling of well logging data is achieved. The model can be used on a large scale in major oil fields to cope with various complex geological conditions, accurately predict shear wave velocity, thereby reducing exploration and development risks and ensuring the efficient development of major oil fields.

[0047] In addition, the present invention also provides a shear wave velocity prediction device, equipment and computer-readable storage medium, which also have the above-mentioned beneficial effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0049] Figure 1 A flow chart of a shear wave velocity prediction method provided by an embodiment of the present invention;

[0050] Figure 2 An example flow chart of a shear wave velocity prediction model provided by an embodiment of the present invention;

[0051] Figure 3 A comparison chart of shear wave velocity prediction results of a clastic rock single well at different depths provided by an embodiment of the present invention;

[0052] Figure 4 A comparison chart of shear wave velocity prediction results of a carbonate well at different learning depths provided by an embodiment of the present invention;

[0053] Figure 5 A comparison chart of shear wave velocity prediction results of a volcanic rock single well at different depths provided by an embodiment of the present invention;

[0054] Figure 6 A schematic structural diagram of a shear wave velocity prediction device provided by an embodiment of the present invention;

[0055] Figure 7 A schematic structural diagram of a shear wave velocity prediction device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0057] Shear wave (S-wave) prediction plays an irreplaceable role in petroleum geology. Its core lies in providing key insights for reservoir lithology identification, fracture detection, fluid property discrimination, and sweet spot prediction through the inversion of the P-wave velocity ratio (Vs / Vp) and elastic parameters. First, S-wave velocity is more sensitive to the rock skeleton and can effectively distinguish complex lithologies, such as the ratio of dolomite to mudstone in carbonate rocks or the sandstone to mudstone ratio in clastic rocks. Second, S-wave splitting (fast and slow S-waves) is a crucial tool for fracture detection. The fast wave (S1) propagates along the fracture plane, while the slow wave (S2) is perpendicular to the fracture plane. The difference in amplitude between the two can quantify fracture density and direction, providing a basis for horizontal well trajectory design and significantly improving drilling success rates. Furthermore, a comprehensive analysis of the S-wave and P-wave amplitude ratio can determine whether a "bright spot" is a gas reservoir. For example, an increase in P-wave amplitude while no significant change in S-wave amplitude often indicates a gas-bearing reservoir. This method is particularly important in natural gas exploration. At the same time, shear wave velocity prediction combined with parameters such as porosity and brittleness index can optimize fracturing plans and improve the development efficiency of tight reservoirs.

[0058] However, current S-wave velocity prediction faces the following two challenges: First, measured S-wave data are scarce and of varying quality, especially in deep or complex formations. S-wave logging is costly and technically difficult, leading to reliance on empirical formulas (such as the Greenberg-Castagna model, which is a S-wave velocity prediction method established using statistical methods based on P-wave and S-wave velocity measurement data of rock samples and logging data) or theoretical models (such as the Xu-White model) for prediction. However, these models are of limited applicability in areas with strong heterogeneity and complex mineral compositions (such as carbonate rocks containing mud or analcime), and need to be modified based on regional geological characteristics. Secondly, the problem of multi-solution is prominent, especially in areas with developed fractures or fluid mixed phases. The shear wave response is easily affected by pore structure, pressure changes and fluid saturation. For example, the dynamic changes in reservoir elastic parameters after CO2 (carbon dioxide) injection require the joint modeling of Hertz-Mindlin (a contact model used to describe particle contact) and Gassmann equation (this equation establishes the relationship between rock bulk modulus, porosity, pore fluid bulk modulus and rock skeleton bulk modulus). However, the uncertainty of key parameters such as the coordination number increases the difficulty of prediction.

[0059] The inherent complexity of oil and gas reservoirs currently makes it difficult to develop high-precision, comprehensive models for various fields. Currently, algorithms for shear wave velocity prediction are unable to accurately predict shear wave velocities under complex geological conditions. Traditional methods, such as empirical geophysical models, rely on specific physical equations tailored for different reservoir types, which is both time-consuming and labor-intensive.

[0060] Therefore, the present invention proposes a shear wave velocity prediction model based on KAN (Kolmogorov-Arnold Networks, a new neural network architecture) network and sequence permutation period, which is called the SuperKAN model. This model, combined with the architecture of the sequence permutator, can be used on a large scale in major oil fields to cope with various complex geological conditions, accurately predict shear wave velocity, thereby reducing exploration and development risks and ensuring the efficient development of major oil fields.

[0061] Please refer to Figure 1 , Figure 1 A flow chart of a shear wave velocity prediction method provided by an embodiment of the present invention. The method may include:

[0062] S101: Preliminarily construct a shear wave velocity prediction model based on the KAN network and the sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function.

[0063] The execution subject of this embodiment is a terminal. This embodiment does not limit the type of terminal, as long as it can complete the operation of the shear wave velocity prediction method.

[0064] The core function of the sequence permutator is the structured reorganization and interpretable processing of sequence data. Its essence lies in the modular reorganization of the input sequence by dynamically adjusting the order of neuron connections, thereby revealing the dependencies between variables. The KAN network is an adaptive activation network designed based on the Kolmogorov-Arnold theorem. It realizes nonlinear mapping and feature expression of input data through learnable B-spline basis functions and dynamic grid adjustment mechanism. Define the input data X∈ N ×Cin×Din , N is the number of input samples, C in is the first feature dimension of the input data X, D in is the second feature dimension of the input data X. The final output of the KAN network is determined by the basis function expansion result and the linear transformation:

[0065] .

[0066] Among them, Y is the output target of the current layer; is the learnable weight; B∈ N×Din×(T×P) is the basis function tensor, T is the spline order, P is the number of segments; W spline are the spline coefficients.

[0067] The adaptive activation calculation process in the KAN network first calculates the basis function tensor through the initial grid tensor, and then obtains the spline coefficients as the network weights. After that, G is updated during the backpropagation process, and the basis function tensor is updated at the same time to achieve the adaptive effect. The specific process can be referred to as follows:

[0068] (1) The basis function tensor is obtained by expanding the basis function through the B-spline basis function. The basis function tensor is constructed based on a uniform distribution in the preset grid range (G=[a,b]), and then expanded recursively:

[0069] .

[0070] Among them, G∈ Din×(K×S) is the initial grid tensor.

[0071] (2) KAN fits the spline coefficient W by the least squares method spline :

[0072] ;

[0073] Where W is the coefficient vector defined on each grid interval, which is used to combine the B-spline basis functions to form the final spline function.

[0074] (3) To achieve self-adaptation to the distribution of input data X, the KAN network will dynamically adjust the grid position G during the training process. adaptive , during backpropagation, the grid is expanded at both ends to support the recursive computation:

[0075] ;

[0076] .

[0077] in, is the mixing coefficient; G adaptive The grid position is dynamically adjusted; X sorted It is the result of sorting the input data from large to small; I T is the index vector; The new position of the grid after dynamic adjustment.

[0078] As can be seen, the KAN network achieves a more refined and transparent representation of the inherent laws of the data through its dynamically learnable activation functions and hierarchical function combination mechanism. The KAN network parameterizes each connecting edge as a differentiable spline function, allowing the model to adaptively adjust the nonlinear form of each feature interaction during training. This allows the model to directly capture the fundamental mathematical relationship between input and output with fewer parameters in shallow networks. This hierarchical feature construction transforms the feature learning process from the fuzzy mapping of traditional neural networks to a traceable and actionable symbolic reasoning path.

[0079] Furthermore, based on the KAN network, a sequence permutator is integrated to establish a feature interaction layer. Then, through the dynamic weight fusion mechanism and the learnable B-spline basis function, the logging data can be efficiently modeled to obtain a shear wave velocity prediction model. The model consists of three parts: the embedding layer, the feature interaction layer, and the classification layer. For details, please refer to Figure 2 , Figure 2 This is an example flow chart of a shear wave velocity prediction model provided by an embodiment of the present invention.

[0080] S102: Acquire well logging data of the target area.

[0081] In well logging prediction, data selection and collection are key to ensuring model accuracy and reliability. Appropriate selection of logging parameters can enhance the model's geological relevance and avoid redundant interference. Furthermore, high-quality logging data must be collected to avoid the influence of equipment and human factors. Such logging data can truly reflect formation characteristics and reduce noise and errors. Systematic data collection must cover multi-dimensional information of the target horizon to ensure the representativeness and completeness of the sample, thereby improving model evaluation accuracy. This example selects six logging data items related to the physical properties and lithologic characteristics of the rock: density (DEN), photoelectric index (PE), deep lateral resistivity (LLD), shallow lateral resistivity (LLS), natural gamma ray (GR), and compensated neutron (CNL).

[0082] S103: Input the logging data into the shear wave velocity prediction model to obtain a prediction result.

[0083] The shear wave velocity prediction model used in this step is the same as the one constructed in step S101. This model consists of three components: an embedding layer, a feature interaction layer, and a classification layer. This model incorporates a sequence permutator architecture, integrating it with a KAN network for feature extraction. Through a dynamic weight fusion mechanism and learnable B-spline basis functions, it achieves efficient modeling of well logging data.

[0084] Furthermore, the above-mentioned input of the logging data into the shear wave velocity prediction model to obtain the prediction results may specifically include:

[0085] Step 11: Input the logging data into the embedding layer of the shear wave velocity prediction model to obtain the mapping results.

[0086] It should be noted that the embedding layer in this embodiment is a one-dimensional convolution layer. The convolution layer of the shear wave velocity prediction model is used to embed the well logging data. ∈ N×C×L The local features of the 1D convolution operation are performed to extract the initial internal input feature variable X 0 ∈ N×D×L And the dimension of the internal input characteristic variable of the data is mapped to the internal channel dimension D of the shear wave velocity prediction model to obtain the mapping result ; The formula expression of the embedding layer is:

[0087] ;

[0088] in, is the parameter of the convolution kernel at position r and channel d; R is the kernel size; bd is the bias, specifically the bias term of the dth channel of the output feature map, and the bias bd is a learnable parameter; L is the depth of data sampling; Well logging data.

[0089] Step 12: Input the mapping results into the feature interaction layer of the shear wave velocity prediction model to obtain the feature vector.

[0090] It should be noted that the feature interaction layer in this embodiment is constructed based on the KAN network and combined with the sequence permutator. This embodiment uses a stack of K layers of feature interaction layers to achieve multi-scale feature interaction. Specifically, the mapping results are input into multiple consecutive feature interaction layers of the shear wave velocity prediction model to obtain feature vectors; each feature interaction layer includes a sequence permutator structural feature extraction module and a fully connected layer; the formula expression of the feature interaction layer is:

[0091] ;

[0092] in, is the output of the current feature interaction layer; is the feature interaction layer; is the input of the current feature interaction layer; K is the total number of feature interaction layers; PKAN is the sequence permutator structure feature extraction module; LP is the fully connected layer.

[0093] like Figure 2 As shown, the Sequence Permutator structural feature extraction module in this embodiment consists of two parallel feature extraction branches: the channel permutation KAN and the depth permutation KAN. The Sequence Permutator is a dynamic feature interaction module designed for lithologic data. By integrating a channel-space dual-branch architecture with KAN basis functions, it enables adaptive modeling of nonlinear coupling relationships between logging parameters.

[0094] Correspondingly, the formula expression of the sequence permutator structural feature extraction module PKAN is:

[0095] ;

[0096] ;

[0097] ;

[0098] Correspondingly, the formula expression of the feature interaction layer is for:

[0099] = (α +β ) ;

[0100] ;

[0101] in, Permutate KAN for the channel; is the deep permutation KAN; is the output result of channel permutation KAN; is the output result of deep permutation KAN; and are the dynamic weights of channel and depth respectively; is the normalization function; is the average value.

[0102] It can be seen that for each layer of input data, it is obtained by passing it through the channel branch and the spatial branch in parallel. and In order to enable the depth branch to obtain the depth features of the logging data, the features are first transposed and reconstructed, and then restored to the original dimension of the input data after feature extraction by the KAN layer. Subsequently, the dynamic weights of the two branches are calculated. and Finally, the sequence permutator multiplies the structures of the two branches by the channel-depth weights, calculates the dynamic eigenvalues, and adds them to the original data to get the output The sequence permutator realizes the feature extraction of logging data in both the channel and depth directions, and realizes the adaptive allocation of channel and depth by combining the feature contribution.

[0103] Step 13: Input the feature vector into the classification layer of the shear wave velocity prediction model to obtain the prediction result.

[0104] In this embodiment, the classification layer is used to output the prediction result. Further, before inputting the feature vector into the classification layer of the shear wave velocity prediction model to obtain the prediction result, the following steps may also be included:

[0105] The feature vector is input into the fully connected layer and normalized layer of the shear wave velocity prediction model and mapped into the regressor; the formula is: ;

[0106] in, ∈R D×1 is the regressor weight; is the output of the regressor; is the normalization layer; is a fully connected layer; is the final output of the feature interaction layer.

[0107] The shear wave velocity prediction method provided by an embodiment of the present invention pre-constructs a shear wave velocity prediction model based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function; well logging data of the target area is obtained; and the well logging data is input into the shear wave velocity prediction model to obtain a prediction result. The shear wave velocity prediction model based on the KAN network of the present invention is robust and accurate. Furthermore, the model combines the sequence permutator architecture, enabling fusion with the KAN network for feature extraction. Through a dynamic weight fusion mechanism and learnable B-spline basis functions, efficient modeling of well logging data is achieved. This model can be widely used in major oil fields to accurately predict shear wave velocities in response to various complex geological conditions, thereby reducing exploration and development risks and ensuring the efficient development of major oil fields. Furthermore, the shear wave velocity prediction model established by fusing the sequence permutator with the KAN network combines the channel-space separation interaction mechanism of the sequence permutator with the nonlinear expression capability and interpretability of the KAN network, enhancing the feature extraction effect of the shear wave velocity prediction model on well logging data.

[0108] To verify the feasibility of the method, volcanic and clastic reservoirs were selected as research objects. Both tectonic blocks have complex geological structures, providing excellent validation of the model's feasibility. This dataset records six well logging data items related to rock physical properties and lithologic characteristics: density (DEN), photoelectric index (PE), deep lateral resistivity (LLD), shallow lateral resistivity (LLS), natural gamma ray (GR), and compensated neutron (CNL). Four evaluation criteria were used for analysis: mean absolute percentage error (MAPE), mean absolute error (MAE), root mean squared error (RMSE), and correlation coefficient (R²). Details are as follows:

[0109] MAPE is a statistical indicator used to measure the error between predicted and actual values. It is an average of percentage errors and is often used to evaluate the forecast accuracy of regression models. Its characteristic is that it expresses the error as a percentage, treats positive and negative errors equally, and reflects the average deviation between the predicted and actual values. The formula for MAPE is as follows:

[0110] .

[0111] Where s is the total number of samples and yi is the true value of the i-th sample. is the predicted value of the i-th sample.

[0112] MAE is also a regression analysis metric that measures the average difference between predicted values ​​and true values. It reflects the accuracy of the model's predictions by calculating the average absolute error between the predicted values ​​and the true values ​​for all sample points. The smaller the value, the better the prediction effect. The MAE formula is as follows:

[0113] .

[0114] RMSE is a commonly used error metric in regression analysis, used to measure the average deviation between the predicted value and the true value. It is calculated by taking the square root of the mean square error (MSE) and essentially reflects the difference in standard deviation between the predicted value and the true value. A smaller value indicates a higher prediction accuracy. The formula is as follows:

[0115] .

[0116] R² (R-Squared) is a core metric used in regression analysis to measure model fit. It reflects the similarity between the measured and predicted results, and its value range in practical applications is [0, 1]. The closer R² is to 1, the better the model fits the data, and the higher the accuracy of the established model. The formula for R² is as follows:

[0117] .

[0118] SST (Total Sum of Squares) refers to the sum of squares of the error between the true value and the mean. The formula for SST is as follows:

[0119] .

[0120] in, is the mean of the true values. SSE (Sum of Squared Errors) refers to the sum of squared errors between the true value and the predicted value. The formula for SSE is as follows:

[0121] .

[0122] SSR (Sum of Squared Regression) refers to the sum of squared errors between the predicted value and the mean. The formula for SSR is as follows:

[0123] .

[0124] To verify the model's effectiveness in shear wave velocity prediction, we selected eleven mainstream comparison models (CNN (convolutional neural network), TCN (temporal convolutional network), LSTM (long short-term memory network), GRU (gated recurrent network), N-BEATS (a neural network-based time series prediction model), ViT (a visual model based on the Transformer architecture), Informer (a Transformer model designed specifically for long time series prediction), MLP-Mixer (multi-layer perceptron), TSMixer (a model based on multi-layer perceptron), PatchMixer (a new CNN-based model for long time series prediction), and MSD-Mixer (a multi-granularity patch partitioning time series model)). A systematic comparative experiment was conducted, and the prediction performance of each model was comprehensively evaluated using multiple metrics such as MAPE, MAE, RMSE, and R². As shown in Table 1, SuPerKAN (the shear wave velocity prediction model of the present invention) achieved the best results in all four metrics. Specifically, SuPerKAN achieved a MAPE of only 1.88%, approximately 9% lower than the second-best TSMixer (2.07%), demonstrating its lowest relative error across different amplitude data. SuPerKAN significantly outperformed TSMixer in MAE, achieving a 5.02 reduction compared to the next-best TSMixer. SuPerKAN also achieved the best RMSE, reaching 66.29, demonstrating its strongest ability to suppress extreme deviations. SuPerKAN achieved an R² of 0.9470, indicating that the model explained approximately 94.7% of the observed variance. This was higher than the next-best Informer (0.9418) and TSMixer (0.9404), demonstrating its robust fitting accuracy for shear wave velocity prediction. In contrast, the R² of traditional CNN, TCN, LSTM, and GRU models were mostly concentrated in the 0.89–0.92 range, reflecting the inability of single convolutional or recurrent structures to capture complex geological time series. Architectures such as MLP-Mixer, TSMixer, PatchMixer, and MSD-Mixer generally outperform traditional networks. Informer, which incorporates a temporal attention mechanism, and TSMixer and MSD-Mixer, which utilize multi-scale information processing, improve R2 to 0.91–0.94. SuPerKAN, through the synergistic effect of multi-scale complementary feature fusion and self-attention, effectively balances global dependencies with local details, providing enhanced modeling capabilities for non-stationary changes commonly found in geological sequences, such as sudden enrichment and cyclical fluctuations.In summary, among the twelve deep learning architectures compared, SuPerKAN achieved the best effect in shear wave velocity prediction with the lowest MAPE, MAE, RMSE, and the highest R2. It has significant application potential and promotion value, and also demonstrates the algorithmic superiority of SuPerKAN.

[0125] Table 1. Shear wave velocity (Vs) prediction results for clastic rock dataset using various deep learning methods (the best results are shown in bold)

[0126]

[0127] Figure 3 A comparison chart of shear wave velocity prediction results of different depths of a clastic rock single well provided by the embodiment of the present invention. In the single well verification, Figure 3The middle blue line represents the measured results, while the red lines represent well logging results using various deep learning methods for shear velocity prediction. The left column contains key well logging curves such as density (DEN), photoelectric index (PE), deep lateral resistivity (LLD), and shallow lateral resistivity (LLS). These curves reflect the physical and lithologic characteristics of clastic rocks and serve as important model input parameters. In the right columns, the blue curves represent the actual Vs values, while the red curves represent the corresponding model predictions. Comparing the goodness of fit between the red and blue curves provides an intuitive assessment of the Vs prediction capabilities of each model. Clastic rock data is highly heterogeneous, and Vs is sensitive to lithology, porosity, and fluid properties. Deep learning models achieve Vs prediction by capturing the complex nonlinear relationships between well logging data. Due to structural differences, different deep learning models have varying strengths and weaknesses in predicting Vs157 in clastic rocks. Comparing the goodness of fit between the red and blue curves in the figure clearly analyzes the adaptability of each model to the characteristics of clastic rock data (heterogeneity, sequence dependence, and multi-parameter correlation). SuperKAN performs well overall. Its predicted curve closely tracks the fluctuations of the actual values, particularly in key depth ranges (e.g., around 2300 meters). The curve morphology closely matches the fluctuations of the actual values, demonstrating that SuperKAN effectively captures the variability of Vs. Compared to neighboring models (e.g., MSD-Mixer and PatchMixer), SuperKAN's blue curve deviates less from the actual red curve and closely matches the actual values ​​in most areas. This demonstrates its strong ability to capture data characteristics when predicting Vs, adapting well to the complexity of clastic rock data and providing reliable results for Vs prediction. The CNN's red and blue curves agree well with the local fluctuations (3265-3275 meters), demonstrating its ability to effectively extract local features. However, this approach may be limited in capturing depth trends over long time series due to local processing characteristics. The TCN curves also fit the depth series well, demonstrating its strong ability to process the sequential characteristics of clastic rocks that gradually change with sedimentary environment and its ability to capture the evolution of Vs with depth. Compared with the LSTM and GRU models, the GRU model has a smoother curve, indicating that it retains long-term information while reducing computational burden, achieving both efficiency and effectiveness in processing clastic rock data. The LSTM model has a high degree of fit in areas with dramatic depth variations (e.g., 3295-3315 m), demonstrating its ability to adapt to the complex sequential dependencies of clastic rocks. The MSD-Mixer model's overall curve fluctuations closely match the actual values, demonstrating its strong ability to model inter-channel dependencies. However, the model exhibits instability in some areas (3345-3365 m).

[0128] Carbonate reservoirs are highly heterogeneous and have complex pore structures, resulting in shear wave Vs predictions being affected by multiple factors, including porosity, fractures, and mineral composition. Table 2 shows the Vs prediction performance of various deep learning methods. SuPerKAN achieves a MAPE of 0.88%, significantly outperforming other methods, demonstrating its ability to best control relative error. Most other methods range from around 1.0% to 1.5%, with recurrent neural networks such as LSTM and GRU performing slightly higher. SuPerKAN achieves the best MAE of 41.48. Among the other methods, TSMixer also performs exceptionally well, achieving a MAE of 51.91, while traditional GRU and CNN methods achieve errors exceeding 65%. SuPerKAN achieves the lowest RMSE of 30.12, a 6.61% reduction from the next-best method, MSD-Mixer, demonstrating its best ability to suppress large prediction errors. SuPerKAN achieves an R² of 0.9811, demonstrating the best fit. Leveraging the strong nonlinear mapping capabilities of KANs, SuPerKAN accurately captures local features such as pore structure. SuPermutator enhances the capture of global information across reservoirs through adaptive sequence rearrangement. The complementary feature aggregation of the two is synergistically integrated at multiple scales, both vertically and horizontally, effectively suppressing the adverse effects of logging noise on Vs prediction and significantly improving the robustness of the model. Traditional time series networks (CNN, LSTM, GRU) focus on local convolution or short-term recursive dependencies, making it difficult to capture long-distance correlations across scales and layers; error indicators are generally high, indicating that their ability to describe the response of heterogeneous carbonate rocks is limited. MSD-Mixer enhances global dependency modeling through the design of multi-scale receptive fields and dual-channel mixing. It is second only to SuPerKAN in RMSE and R2, and is suitable for processing logging data with long sequences and high noise.

[0129] Table 2. Shear wave velocity (Vs) prediction results for carbonate rock datasets using various deep learning methods (the best results are shown in bold)

[0130]

[0131] Figure 4A comparison chart of the shear wave velocity prediction results of a single carbonate well learned at different depths provided in an embodiment of the present invention. SuPerKAN shows the best fitting accuracy and robustness in Vs prediction of carbonate rocks, and the study interval is about 3720-3700m in depth. The prediction curves of the SuPerKAN model in multiple complex layers are close to the measured data, showing higher fitting accuracy and change response ability, especially in sections with dense fractures or strong reservoir heterogeneity, and can effectively capture small nonlinear changes in shear wave velocity. In layers with obvious velocity mutations (such as 3450-3550m), most models (such as CNN, LSTM, N-BEATS, etc.) have fitting lags or prediction offsets in the interval of steep velocity changes, indicating that they have certain limitations in dealing with carbonate rocks with sudden lithology mutations and strong fracture influences. Some models based on attention mechanisms or hybrid structures (such as ViT, MLP-Mixer, TSMixer, etc.) perform well in relatively stable formations, but still suffer from overfitting or under-prediction in areas with rapidly changing velocity. A comprehensive comparison shows that SuPerKAN's prediction curve is smoother and has stronger trend tracking capabilities, maintaining good consistency and detail recovery capabilities at velocity mutation points, highlighting its advantages in integrating feature selection, adaptive structure modeling, and collaborative modeling of high-dimensional data.

[0132] Volcanic rocks often have complex structures, such as pores and fractures, and significant lithologic variation. These factors affect Vs, presenting a significant challenge in oilfield exploration and development. Vs is also crucial in volcanic rocks, as varying lithologies and structures can lead to varying velocities. The results, as shown in Table 3, show that the SuPerKAN model achieved optimal performance across all evaluation metrics, with a MAPE of 1.33%, a MAE of 41.57, an RMSE of 67.44, and an R² of 0.9748. This demonstrates its significant advantage in characterizing the nonlinear variations and spatial heterogeneity of Vs. Furthermore, hybrid structural models such as TSMixer, MSD-Mixer, and MLP-Mixer also performed well, demonstrating their strong ability to model the complex temporal dependencies and structural characteristics of seismic sequences. In contrast, traditional convolutional models (such as CNNs) exhibited lower prediction accuracy, reflecting their inability to model long-range dependencies.

[0133] Table 3 Comparison of shear wave velocity (Vs) prediction results for volcanic rock datasets using various deep learning methods (the best results are shown in bold)

[0134]

[0135] Different deep learning models performed differently when predicting Vs in volcanic rocks at different depths (approximately 3970–4080 m). Some models (such as those with high curve fit) more accurately captured the characteristics of volcanic rock data, demonstrating the potential of deep learning technology for Vs prediction in complex reservoirs such as volcanic rocks. Figure 5 This is a comparison chart of the shear wave velocity prediction results of a volcanic rock single well at different depths provided by the embodiment of the present invention. Figure 5 As can be seen, SuperKAN's predicted curves closely match the actual curves at certain depths. This is particularly true in areas where volcanic rock lithology varies regularly or where pore structure influences are relatively stable. SuperKAN's predictions are able to capture the Vs trend well, demonstrating its strong learning and fitting capabilities for the nonlinear relationships commonly found in volcanic rock data. This allows for effective exploration of the complex relationships between logging parameters (such as CNL, DEN, and Vp) and Vs, demonstrating the model's advantages in processing complex geological data such as volcanic rock. In regions of strong nonlinear distribution in volcanic rock (e.g., depths around 3980–4000 m), most traditional models (such as CNN, LSTM, and GRU) exhibit significant deviations in their predictions, failing to accurately fit the actual velocity trends and demonstrating their limited ability to model complex geological responses. Transformer architectures (such as Informer and ViT) and MLP-Mixer models perform reasonably well in certain continuous sections (3960–3980 m), but exhibit significant lag or overfitting at locations with abrupt velocity changes. The prediction curve of the SuPerKAN model has the highest fit with the measured data, especially in multiple velocity mutation interfaces and nonlinear perturbation intervals. The prediction results can accurately capture the jump changes in shear wave velocity, indicating that it has excellent feature extraction and expression capabilities in dealing with the heterogeneous structure of volcanic rocks, fracture systems and formation interface characteristics.

[0136] In the above-mentioned predictions of shear wave velocity for three different complex lithologies, it is intuitively clear that, regardless of geological conditions or lithology, SuPerKAN outperforms other deep learning models in terms of adaptability and accuracy in shear wave velocity prediction. Therefore, the SuPerKAN model was chosen for this project as a safer and more reliable choice than other models. The SuPerKAN model demonstrated excellent results in predicting shear wave velocity across a wide range of oilfield reservoir types. It is robust to unbalanced datasets and can handle complex geological environments, accurately predicting shear wave Vs for various lithologies and reducing exploration and development risks.

[0137] The following is an introduction to a shear wave velocity prediction device provided by an embodiment of the present invention. The shear wave velocity prediction device described below and the shear wave velocity prediction method described above can be referenced to each other.

[0138] Please refer to Figure 6 , Figure 6 A schematic structural diagram of a shear wave velocity prediction device provided in an embodiment of the present invention may include:

[0139] The model construction module 100 is used to construct a shear wave velocity prediction model based on the KAN network and the sequence permutator in advance; the activation function of the shear wave velocity prediction model is a B-spline basis function;

[0140] The well logging data acquisition module 200 is used to acquire well logging data of the target area;

[0141] The prediction module 300 is used to input the logging data into the shear wave velocity prediction model to obtain a prediction result.

[0142] Based on the above embodiment, the prediction module 300 may include:

[0143] an embedding unit, configured to input the logging data into an embedding layer of the shear wave velocity prediction model to obtain a mapping result;

[0144] A feature interaction unit is used to input the mapping result into the feature interaction layer of the shear wave velocity prediction model to obtain a feature vector; the feature interaction layer is constructed based on the KAN network and in combination with a sequence permutator;

[0145] A classification unit is used to input the feature vector into the classification layer of the shear wave velocity prediction model to obtain the prediction result.

[0146] Based on the above embodiment, the embedding unit may include:

[0147] The embedding subunit is used to perform a one-dimensional convolution operation on the local features of the logging data through the convolution layer of the shear wave velocity prediction model to extract the initial internal input feature variables, and map the dimensions of the internal input feature variables of the data to the internal channel dimension D of the shear wave velocity prediction model to obtain the mapping result. ;

[0148] The formula expression of the embedding layer is:

[0149] ;

[0150] in, is the parameter of the convolution kernel at position r and channel d; R is the kernel size; bd is the bias; L is the depth of data sampling; Well logging data.

[0151] Based on the above embodiment, the feature interaction unit may include:

[0152] A feature interaction subunit is configured to input the mapping result into a plurality of consecutive feature interaction layers of the shear wave velocity prediction model to obtain the feature vector; each feature interaction layer includes a sequence permutator structure feature extraction module and a fully connected layer;

[0153] The formula expression of the feature interaction layer is:

[0154] ;

[0155] in, is the output of the current feature interaction layer; is the feature interaction layer; is the input of the current feature interaction layer; K is the total number of feature interaction layers; PKAN is the sequence permutator structure feature extraction module; LP is the fully connected layer.

[0156] Based on the above embodiment, the sequence permutator structural feature extraction module may include:

[0157] Channel permutation KAN and depth permutation KAN;

[0158] Correspondingly, the formula expression of the sequence permutator structural feature extraction module PKAN is:

[0159] ;

[0160] ;

[0161] ;

[0162] Correspondingly, the formula expression of the feature interaction layer is for:

[0163] = (α +β ) ;

[0164] ;

[0165] in, Permutate KAN for the channel; is the deep permutation KAN; is the output result of channel permutation KAN; is the output result of deep permutation KAN; and are the dynamic weights of channel and depth respectively; is the normalization function; is the average value.

[0166] Based on the above embodiment, the shear wave velocity prediction device may further include:

[0167] The regression module is used to input the feature vector into the fully connected layer and normalization layer of the shear wave velocity prediction model and map it to the regressor; the formula is: ;

[0168] in, ∈R D×1 is the regressor weight; is the output of the regressor; is the normalization layer; is a fully connected layer; is the final output of the feature interaction layer.

[0169] Based on the above embodiment, the well logging data acquisition module may include:

[0170] The data acquisition unit is used for density data, photoelectric index data, deep lateral resistivity data, shallow lateral resistivity data, natural gamma ray data and compensated neutron data.

[0171] It should be noted that the order of the modules and units in the above-mentioned shear wave velocity prediction device can be changed without affecting the logic.

[0172] The shear wave velocity prediction device provided by the embodiment of the present invention uses a model construction module 100 to pre-construct a shear wave velocity prediction model based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function; a well logging data acquisition module 200 is used to acquire well logging data from a target area; and a prediction module 300 is used to input the well logging data into the shear wave velocity prediction model to obtain a prediction result. The shear wave velocity prediction model based on the KAN network in this device is robust and accurate. The model is combined with a sequence permutator architecture to fuse it with the KAN network for feature extraction. Through a dynamic weight fusion mechanism and a learnable B-spline basis function, efficient modeling of well logging data is achieved. This model can be used on a large scale in major oil fields to cope with various complex geological conditions, accurately predict shear wave velocity, thereby reducing exploration and development risks and ensuring the efficient development of major oil fields.

[0173] The following is an introduction to a shear wave velocity prediction device provided by an embodiment of the present invention. The shear wave velocity prediction device described below and the shear wave velocity prediction method described above can be referenced to each other.

[0174] Please refer to Figure 7 , Figure 7 A schematic structural diagram of a shear wave velocity prediction device provided in an embodiment of the present invention may include:

[0175] Memory 10, for storing computer programs;

[0176] The processor 20 is configured to execute a computer program to implement the above-mentioned shear wave velocity prediction method.

[0177] The memory 10 , the processor 20 , and the communication interface 31 all communicate with each other via the communication bus 32 .

[0178] In the embodiment of the present invention, the memory 10 is used to store one or more programs. The program may include program code, and the program code includes computer operation instructions. In the embodiment of the present invention, the memory 10 may store programs for implementing the following functions:

[0179] A shear wave velocity prediction model is constructed in advance based on the KAN network and the sequence permutator; the activation function of the shear wave velocity prediction model is the B-spline basis function;

[0180] Obtain well logging data for the target area;

[0181] The logging data are input into the shear wave velocity prediction model to obtain the prediction results.

[0182] In one possible implementation, the memory 10 may include a program storage area and a data storage area, wherein the program storage area may store an operating system and applications required for at least one function, etc.; the data storage area may store data created during use.

[0183] In addition, the memory 10 may include a read-only memory and a random access memory, and provides instructions and data to the processor. A portion of the memory may also include NVRAM. The memory stores an operating system and operating instructions, executable modules or data structures, or a subset or an extended set thereof. The operating instructions may include various operating instructions for implementing various operations. The operating system may include various system programs for implementing various basic tasks and processing hardware-based tasks.

[0184] The processor 20 may be a central processing unit (CPU), an application-specific integrated circuit, a digital signal processor, a field programmable gate array, or other programmable logic device. The processor 20 may be a microprocessor or any conventional processor. The processor 20 may call a program stored in the memory 10 .

[0185] The communication interface 31 may be an interface of a communication module, used for connecting to other devices or systems.

[0186] Of course, it needs to be explained that Figure 7The structure shown does not constitute a limitation on the shear wave velocity prediction device in the embodiment of the present invention. In actual applications, the shear wave velocity prediction device may include Figure 7 More or fewer components than shown, or combinations of certain components.

[0187] The computer-readable storage medium provided by an embodiment of the present invention is introduced below. The computer-readable storage medium described below and the shear wave velocity prediction method described above can be referenced to each other.

[0188] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned shear wave velocity prediction method are implemented.

[0189] The computer-readable storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., which can store program codes.

[0190] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. Reference can be made to the descriptions of the identical or similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and the relevant parts can be referred to the descriptions of the methods.

[0191] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0192] Finally, it should be noted that, in this document, relationships such as first and second, etc., are used solely to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0193] The above is a detailed introduction to the shear wave velocity prediction method, device, equipment and computer-readable storage medium provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for predicting shear wave velocity, characterized in that: include: A shear wave velocity prediction model is pre-built based on a KAN network and a sequence permutator; an activation function of the shear wave velocity prediction model is a B-spline basis function; Obtain well logging data for the target area; The logging data is input into the shear wave velocity prediction model to obtain a prediction result.

2. The shear wave velocity prediction method according to claim 1, characterized in that: Inputting the logging data into the shear wave velocity prediction model to obtain prediction results includes: Inputting the logging data into the embedding layer of the shear wave velocity prediction model to obtain a mapping result; Inputting the mapping result into the feature interaction layer of the shear wave velocity prediction model to obtain a feature vector; the feature interaction layer is constructed based on the KAN network and combined with a sequence permutator; The feature vector is input into the classification layer of the shear wave velocity prediction model to obtain the prediction result.

3. The shear wave velocity prediction method according to claim 2, characterized in that: Inputting the logging data into the embedding layer of the shear wave velocity prediction model to obtain a mapping result includes: The convolution layer of the shear wave velocity prediction model performs a one-dimensional convolution operation on the local features of the logging data to extract the initial internal input feature variables, and maps the dimensions of the internal input feature variables of the data to the internal channel dimension D of the shear wave velocity prediction model to obtain the mapping result. ; The formula expression of the embedding layer is: ； in, is the parameter of the convolution kernel at position r and channel d; R is the kernel size; bd is the bias; L is the depth of data sampling; Well logging data.

4. The shear wave velocity prediction method according to claim 2, characterized in that: The mapping result is input into the feature interaction layer of the shear wave velocity prediction model to obtain a feature vector, including: Inputting the mapping result into a plurality of consecutive feature interaction layers of the shear wave velocity prediction model to obtain the feature vector; each feature interaction layer includes a sequence permutator structure feature extraction module and a fully connected layer; The formula expression of the feature interaction layer is: ； in, is the output of the current feature interaction layer; is the feature interaction layer; is the input of the current feature interaction layer; K is the total number of feature interaction layers; PKAN is the sequence permutator structure feature extraction module; LP is the fully connected layer.

5. The shear wave velocity prediction method according to claim 4, characterized in that: Sequence permutator structural feature extraction module, including: Channel permutation KAN and depth permutation KAN; Correspondingly, the formula expression of the sequence permutator structural feature extraction module PKAN is: ； ； ； Correspondingly, the formula expression of the feature interaction layer is for: = （α +β ） ； ； in, Permutate KAN for the channel; is the deep permutation KAN; is the output result of channel permutation KAN; is the output result of deep permutation KAN; and are the dynamic weights of channel and depth respectively; is the normalization function; is the average value.

6. The shear wave velocity prediction method according to claim 2, characterized in that: Before inputting the feature vector into the classification layer of the shear wave velocity prediction model to obtain the prediction result, the method further includes: The feature vector is input into the fully connected layer and normalized layer of the shear wave velocity prediction model and mapped into the regressor; the formula is: ; in, ∈R D×1 is the regressor weight; is the output of the regressor; is the normalization layer; is a fully connected layer; is the final output of the feature interaction layer.

7. The shear wave velocity prediction method according to claim 1, characterized in that: The well logging data includes: Density data, photoelectric index data, deep lateral resistivity data, shallow lateral resistivity data, natural gamma ray data and compensated neutron data.

8. A shear wave velocity prediction device, characterized in that: include: A model building module is used to pre-build a shear wave velocity prediction model based on a KAN network and a sequence permutator; the activation function of the shear wave velocity prediction model is a B-spline basis function; Well logging data acquisition module, used to obtain well logging data of the target area; The prediction module is used to input the logging data into the shear wave velocity prediction model to obtain a prediction result.

9. A shear wave velocity prediction device, characterized in that: include: memory for storing computer programs; A processor, configured to implement the shear wave velocity prediction method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are loaded and executed by the processor, the shear wave velocity prediction method according to any one of claims 1 to 7 is implemented.

Images