A coordinate-based five-dimensional seismic data interpolation method and system

Abstract

The application discloses a five-dimensional seismic data interpolation method and system based on coordinates, constructs a point-by-point seismic data interpolation model based on a NeRF theory, modifies an MLP framework by combining an additional convolution layer on the basis of the point-by-point interpolation model, constructs a profile-by-profile seismic data interpolation model, introduces kernel norm regularization to construct an objective function, reads original five-dimensional seismic data D obs and inputs the five-dimensional seismic data with missing traces into the network to realize reconstruction of the five-dimensional seismic data. The application eliminates the need for additional labeled data, utilizes unique characteristics of seismic data, enables a convolution network decoder to output data profile by profile, can significantly improve data processing efficiency by 40 times, and increases kernel norm regularization in the objective function, so that the noise resistance and robustness of the model can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of seismic signal processing technology, specifically relating to a coordinate-based five-dimensional seismic data interpolation method and system. Background Technology

[0002] In exploration seismology, fully sampled seismic data lays a solid foundation for subsequent tasks, such as deconvolution, synchrotron source separation, and fault detection. However, in actual seismic data acquisition, due to physical or economic constraints, missing traces often exist in the observation data. These missing traces carry valuable geological information and can adversely affect subsequent data processing and interpretation. Therefore, the reconstruction of seismic data has attracted widespread attention from both academia and industry.

[0003] Currently, deep learning technology has demonstrated significant potential in various fields, and seismic data interpolation is no exception. Compared to traditional methods, deep learning methods reduce the need for extensive manual parameter adjustments. Furthermore, because deep learning utilizes nonlinear activation functions, neural network models can more effectively capture nonlinear features in the data, thereby enhancing information extraction and representation capabilities.

[0004] Various types of neural networks have been applied to seismic data interpolation, including autoencoder-based methods, generative adversarial networks, deep internal networks, and model-driven networks. However, existing work mainly focuses on low-dimensional data, such as 2D or 3D seismic data. Compared to these, 5D seismic data can better represent the directionality of geological features and the changes in seismic response under different offsets and azimuths, thus providing a more comprehensive understanding of subsurface properties. However, using deep learning to characterize complex geological environments in 5D data faces unique challenges because 5D convolution requires more computational resources than 3D convolution. Existing methods utilize the characteristics of 3D convolution operations to construct 5D convolutional neural networks. This method uses synthetic 5D seismic data as labels to train the network, enabling it to perform data interpolation. However, further improvements in computational efficiency are necessary for wider application of this method.

[0005] In recent years, the field of computer vision has shown great interest in coordinate-based neural representations, leading to the Neural Radiation Field (NeRF) method. This method requires constructing a model that includes a Fourier Feature Map (FFM) module and a Multilayer Perceptron (MLP), enabling the wavefield to be encoded in a point-like manner. The FFM module converts spatial coordinates into Fourier domain codes, while the MLP maps the Fourier codes to pixel values, such as color, density, or occupancy. By training the model using observed data points, complete and continuous wavefield information is encoded in the weight parameters of the MLP. Therefore, lost data can be reconstructed by querying the values ​​corresponding to each coordinate.

[0006] There is a coordinate-based seismic shot point interpolation method that uses an MLP network to encode the seismic wavefield and queries the network at the locations of unobserved shot points to recover the missing shot point set. However, this method still has shortcomings. It mainly solves the problem of incomplete shot-receiver sets, but does not address the challenge of missing irregular trajectories in high-dimensional data. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a coordinate-based five-dimensional seismic data interpolation method and system to address the shortcomings of the prior art, thereby solving the technical problem that the existing methods require additional labeled data.

[0008] The present invention adopts the following technical solution:

[0009] A coordinate-based five-dimensional seismic data interpolation method includes the following steps:

[0010] S1. Constructing a point-by-point interpolation model for unsupervised seismic data based on NeRF theory;

[0011] S2. Modify the MLP framework by combining additional convolutional layers to construct a profile-by-profile interpolation model based on the constructed unsupervised seismic data point-by-point interpolation model.

[0012] S3. Introduce nuclear norm regularization to construct the objective function of the profile interpolation model;

[0013] S4. Read the raw five-dimensional seismic data D obs The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

[0014] Preferably, the objective function of the unsupervised point-by-point interpolation model for seismic data is:

[0015]

[0016] Where v1, v2, v3, v4, and v5 are the five-dimensional coordinates of the seismic data, and D... obs Let θ be the five-dimensional seismic data to be solved, and M be the parameter weights of the MLP. θ This is the function used by the MLP to map coordinates to complete seismic data. The mean square error of the matrix is ​​represented.

[0017] Preferably, five-dimensional seismic data D obs for:

[0018]

[0019] in, Here, is the Hadamard product, P is the sampling matrix, and Z is the complete seismic data.

[0020] Preferably, the elements in the sampling matrix P satisfy the following conditions:

[0021]

[0022] Where, d v1,v2,v3,v4,v5 For five-dimensional seismic data D obs The elements with indices v1, v2, v3, v4, v5.

[0023] 5. The coordinate-based five-dimensional seismic data interpolation method according to claim 1, characterized in that the profile-by-profile interpolation model includes an encoder and a decoder, the encoder including a predefined single FFM layer γ(v) and an encoder based on an MLP, the encoder converting coordinate v into corresponding latent variables. Subsequently, the decoder based on the convolutional network extracts variables. Reconstruct the complete seismic profile using N τ This represents the combination of an encoder and a decoder.

[0024] Preferably, a single FFM layer γ(v) specifically comprises:

[0025] γ K (v)=[cos(w1v1),sin(w1v1),cos(w1v2),sin(w1v2),…,cos(w K v n ),sin(w K v n )] T

[0026] Where K represents the total number of components, and the i-th frequency component is obtained through linear sampling w. i =π2 i Let v represent any coordinate normalized in [0, 1].

[0027] Preferably, for seismic data that has not undergone conventional time-difference correction, the objective function is defined as follows:

[0028]

[0029] Among them, S x and S y R represents the total length of the coupling within the seismic source and the cross-axis, respectively. x r is the total length of the inner coupling of the receiver. x Let P be the index of the receiver on the inner axis, and P be the sampling matrix;

[0030] For common midpoint seismic data using NMO technology, the objective function is defined as:

[0031]

[0032] Among them, M x and M y Here, represents the maximum length of the inner axis and the cross axis, respectively, and U represents the tensor expansion method. The corresponding learning objective, M θ This is a function in MLP that maps coordinates to complete seismic data.

[0033] Preferably, the objective function of the profile-by-profile interpolation model is:

[0034]

[0035] Where λ is a hyperparameter used to balance the fidelity and regularization terms in the objective function, ||| * M is the nuclear norm. x and M y M represents the maximum length of the inner coupling and the cross coupling, respectively. θ MLP is the function that maps coordinates to complete seismic data, U is the tensor expansion method, (P:,m x ,m y ,:,:) represents a specific portion selected from the sampling matrix. The corresponding learning objective is F, where F is the Frobenius norm.

[0036] Preferably, the nuclear norm ||X|| * as follows:

[0037]

[0038] Where, σ i Let be the i-th singular value of X, and k be the total number of singular values. Secondly, embodiments of the present invention provide a coordinate-based five-dimensional seismic data interpolation system, comprising:

[0039] The module is built based on NeRF theory to construct a point-by-point interpolation model for unsupervised seismic data;

[0040] The interpolation module, combined with additional convolutional layers, modifies the MLP framework to construct a profile-by-profile interpolation model based on the constructed unsupervised seismic data point-by-point interpolation model.

[0041] The function module introduces nuclear norm regularization to construct the objective function of the profile interpolation model.

[0042] Reconstruction module, reads raw five-dimensional seismic data D obs The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

[0043] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the coordinate-based five-dimensional seismic data interpolation method described above.

[0044] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described coordinate-based five-dimensional seismic data interpolation method.

[0045] Compared with the prior art, the present invention has at least the following beneficial effects:

[0046] A coordinate-based five-dimensional seismic data interpolation method is proposed. This unsupervised learning approach eliminates the need for additional labeled data. Building upon the original point-by-point method of NeRF, this method leverages the unique characteristics of seismic data to improve the convolutional network decoder, enabling it to output data per profile. Compared to the point-by-point method, this technique significantly improves data processing efficiency by 40 times, thus enabling faster and more accurate reconstruction of five-dimensional seismic data. Kernel norm regularization is added to the objective function, effectively enhancing the model's noise resistance and robustness.

[0047] Furthermore, to supplement missing seismic traces and obtain a complete data set Z, the recovered data Z should be as close as possible to the observed data. Based on these conditions, an unsupervised point-by-point interpolation model for seismic data is constructed, minimizing the difference between the observed data D and the actual data. obs With model prediction data M θ The mean square error of (v) enables the model to accurately reconstruct earthquake data, ensuring that the difference between the model output and the actual observation data is as small as possible.

[0048] Furthermore, to reduce the computational resource consumption of the point-by-point interpolation model, we introduce a novel profile-by-profile interpolation model consisting of an encoder and a decoder. The encoder utilizes an FFM layer and an MLP structure to transform the high-dimensional input coordinates v into low-dimensional latent variables. The aim is to reduce the dimensionality of the data and extract important features from the input data, providing a concise and information-rich representation for subsequent decoding. The decoder uses convolution operations to extract features from the latent variables. Feature information is extracted and fused to reconstruct high-quality seismic profiles. The combination of encoder and decoder N τ This constitutes an end-to-end learning model. By optimizing the parameters of the entire model, an efficient mapping from input coordinates to seismic profiles is achieved, ensuring that the difference between the model output and the actual observation data is minimized.

[0049] Furthermore, different objective functions are used for different seismic data. For seismic data that does not use conventional time-of-flight correction, in order to accurately locate specific data points in the seismic data, s is selected. x ,s y ,r x Develop objective functions for the indexes. These indexes effectively handle gaps and discontinuities in the data, ensuring that the model can perform efficient interpolation and reconstruction on incomplete datasets.

[0050] Furthermore, for public midpoint seismic data using NMO technology, the application of NMO correction significantly enhances the event continuity of specific gathers, helping our network effectively capture their correlations. Therefore, an intuitive strategy is to fix m in the 5D seismic dataset. x ,m y Extract 3D tensors Construct the objective function. This tensor includes multiple traces at the same common midpoint, assigning similar characteristics to different traces, thereby enhancing the continuity and relevance of the data and ensuring that the model can perform effective interpolation and reconstruction on incomplete datasets.

[0051] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0052] In summary, this invention, based on the original point-by-point method of NeRF, improves the convolutional network decoder by leveraging the unique characteristics of seismic data, enabling it to output data per profile. Compared to the point-by-point method, this technique can significantly improve data processing efficiency by 40 times, thus enabling faster and more accurate reconstruction of five-dimensional seismic data. Furthermore, the addition of kernel norm regularization to the objective function effectively enhances the model's noise resistance and robustness.

[0053] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0054] Figure 1 A schematic diagram of the coordinate system used to describe five-dimensional seismic data in three-dimensional seismic exploration.

[0055] Figure 2 A schematic diagram of the MLP network structure for the pointwise interpolation method;

[0056] Figure 3 The diagrams show two different tensor expansion strategies, where (a) is a profile generated by a common offset azimuth gather, and (b) is a profile generated by a common azimuth gather.

[0057] Figure 4The diagram shows actual data examples for two different deployment strategies, where (a) is a profile generated by a common offset azimuth gather, and (b) is a profile generated by an azimuth segment gather.

[0058] Figure 5 This is a schematic diagram of the network architecture of the interpolation method proposed in this invention, wherein (a) is a method that uses position indices as input and MLP+ConvNets to extract data from a compact latent space. (a) Outputs the entire image of a specified dimension, and (b) shows the architecture of the NeRSI block, which aims to increase the feature map through the S factor.

[0059] Figure 6 The diagram illustrates the results of reconstructing synthetic data using different methods. (a) shows eight actual seismic data gathers, (b) shows seismic data with 80% of the seismic traces irregularly missing, (c) shows the recovery result using the PMF-TR method, (d) shows the reconstruction error using the PMF-TR method, (e) shows the recovery result using the point-by-point method, (f) shows the reconstruction error using the point-by-point method, (g) shows the recovery result using the profile-by-profile method, and (h) shows the reconstruction error using the profile-by-profile method. The dark arrows indicate that the PMF-TR method and the point-by-point method did not fully recover the tilt structure in the complete data, while in the areas marked by the light arrows, both methods exhibit signal leakage.

[0060] Figure 7 The diagram shows the seismic gathers obtained with fixed offset bin=6 and azimuth bin=4, where (a) is the actual data, (b) is the reconstruction result using the PMF-TR method, and (c) is the reconstruction result using the method of this invention.

[0061] Figure 8 The diagram shows the seismic gathers obtained with fixed offset bin=6 and CMP x number=4, where (a) is the actual data, (b) is the reconstruction result using the PMF-TR method, and (c) is the reconstruction result using the method of this invention.

[0062] Figure 9 The diagram shows post-stack seismic data, where (a) is before reconstruction, (b) is after reconstruction using the PMF-TR method, and (c) is after reconstruction using the method of this invention.

[0063] Figure 10 The diagram shows the reconstruction results when the regularization factor takes different values, where (a) is incomplete seismic data, (b) is the reconstruction result without using nuclear norm regularization, and (c) is the reconstruction result with nuclear norm regularization.

[0064] Figure 11 This is a flowchart of the present invention.

[0065] Figure 12 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0066] Figure 13 This is a block diagram of a chip provided according to an embodiment of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0069] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0070] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0071] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0072] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0073] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0074] This invention provides a coordinate-based five-dimensional seismic data interpolation method. Based on NeRF theory, it effectively utilizes the inherent structural characteristics between profiles, enabling the convolutional network decoder to output data profile by profile. Furthermore, it uses kernel norm regularization in the objective function. This is a coordinate-based unsupervised internal learning method that eliminates the need for additional labeled data and effectively increases data processing efficiency and model robustness.

[0075] Please see Figure 11 This invention discloses a coordinate-based five-dimensional seismic data interpolation method. Based on NeRF theory, a profile-by-profile seismic data reconstruction network is constructed, and the objective function is updated, further improving the efficiency of seismic data processing and reconstruction accuracy. The specific implementation steps are as follows:

[0076] S1. Based on NeRF theory, construct an unsupervised point-by-point interpolation model for seismic data;

[0077] Please see Figure 1 Seismic data is structured into a five-dimensional tensor. For source-receiver coordinates, the observation tensor is represented as:

[0078] D obs (t,s x ,s y ,r x ,r y )

[0079] Among them, (s x ,s y ,r x ,r y () represents the coordinates of the earthquake source and receiver locations.

[0080] Using different data sorting methods, the observation tensor is represented as follows:

[0081] D obs (t,m x ,m y ,h x ,h y )

[0082] Where t represents time, and m x and m y h represents the coordinates of the midpoint of the inline and cross lines. x and h y This indicates the offset of inline and cross lines.

[0083] Earthquake data is represented as:

[0084] D obs (t,m x ,m y ,|h|,θ)

[0085] Where |h| represents the offset distance and θ represents the azimuth angle.

[0086] For ease of description, the above coordinate positions are represented as:

[0087] v = [v1, v2, v3, v4, v5]

[0088] Let the observed data D obs Corresponding to complete seismic data Z, five-dimensional seismic data D obs for:

[0089]

[0090] in, Here, is the Hadamard product, P is the sampling matrix, and Z is the complete seismic data.

[0091] The elements in the sampling matrix P satisfy the following condition:

[0092]

[0093] Where, d v1,,,, For five-dimensional seismic data D obs The elements with indices v1, v2, v3, v4, and v5 are represented. Seismic data is conceptualized as a wavefield, which is essentially a function that maps coordinates to corresponding values ​​in the Z-axis.

[0094] z v1v2v3v4v5 =(v)

[0095] This invention uses an MLP to describe this mapping:

[0096] z v1v2v3v4v5 = θ(v)

[0097] Where θ represents the parameter weights of the MLP.

[0098] Considering that complete seismic data cannot be directly observed, this invention utilizes observational data D obs Speculation M θ The objective function is:

[0099]

[0100] Where v1, v2, v3, v4, and v5 represent the five-dimensional coordinates of the seismic data, and D obs Let θ be the seismic data to be solved, and M be the parameter weights of the MLP. θ This is the function used by the MLP to map coordinates to complete seismic data. The mean square error of the matrix is ​​represented.

[0101] Please see Figure 2 The network architecture of the point-by-point interpolation model for seismic data consists of an encoder and a decoder. The encoder consists of 16 fully connected layers, and the decoder consists of 2 fully connected layers.

[0102] S2. Modify the MLP framework by combining additional convolutional layers to construct a profile interpolation model based on the model built in step S1.

[0103] Please see Figure 5 This invention develops an innovative network architecture that modifies the MLP framework by incorporating additional convolutional layers. The network architecture includes an encoder and a decoder; the encoder has two main components: the first is a predefined single FFM layer γ(v) to improve positional encoding capability, and the second is an encoder based on the MLP, which can efficiently transform coordinate v into corresponding latent variables. Subsequently, the decoder based on the convolutional network... Reconstruct the complete seismic profile using N τ Representing the combination of encoder and decoder, the specific model is as follows:

[0104] M θ (v)= τ (γ(v))

[0105] Furthermore, substantial evidence suggests that standard MLPs often face challenges in capturing high-frequency variations. Specifically, directly inputting the raw data location v into an MLP produces over-smoothing results, leading to the loss of high-frequency details in the reconstructed data.

[0106] To address this issue, the input v is expanded to a Fourier spectrum before being fed into the MLP.

[0107] This invention introduces FFM position encoding, which is as follows:

[0108] γ K (v)=[cos(w1v1),sin(w1v1),cos(w1v2),sin(w1v2),

[0109] …,cos(w K v n ),sin(w K v n )] T

[0110] Where K represents the total number of components, and the i-th frequency component is obtained through linear sampling w. i =2 i Let V represent any coordinate normalized in [0, 1].

[0111] While point-by-point methods have demonstrated effectiveness in seismic data reconstruction, their single-point output strategy has significant limitations. This method treats each point in the wavefield as an independent entity, resulting in substantial computational resources required for model training. In real-world data scenarios, especially with low signal-to-noise ratios, this model often overfits to the noise in the data. Therefore, to overcome these challenges, this invention introduces a profile-by-profile interpolation model based on the point-by-point interpolation model. The output of this model is no longer limited to a single pixel but provides a complete seismic profile, thus capturing the characteristics of seismic data more comprehensively.

[0112] Furthermore, since convolution operations are beneficial for extracting observable and regular features, profiles with clear structural information and stable phase axis continuity are very suitable for learning by convolutional neural networks. To ensure good predictability and regularity of the profiles, selecting an appropriate output profile size is crucial, especially considering the five-dimensional characteristics of seismic data.

[0113] Furthermore, this invention explores two different scenarios: seismic data without conventional time difference (NMO) correction and seismic data with a common midpoint (CMP) processed using NMO.

[0114] Different objective functions are used for different types of seismic data.

[0115] For seismic data that has not been corrected using conventional time difference (NMO), this invention fixes s x ,s y and r x The earthquake set D is obtained. obs (:,s x ,s y ,r x,:); By giving V=(s x ,s y ,r x ) T Construct dataset {v,D} obs (:,s x ,s y ,r x ,:)}, the objective function is defined as:

[0116]

[0117] Among them, S x and S y R represents the total length of the coupling axis within the seismic source and the cross axis, respectively. x This indicates the total length of the internal coupling of the receiver.

[0118] For CMP seismic data processed with NMO, the application of NMO correction significantly enhances the continuity of gathers, helping neural networks capture correlations between gathers. Therefore, a common strategy when selecting profile sizes is to fix the m-value of the five-dimensional seismic dataset. x and m y Extracting three-dimensional tensors Due to tensor All trajectories including the same common midpoint will impart similar characteristics to different in-phase axes; therefore, this slicing method helps to enhance... The similarity of the data makes it more suitable for convolutional networks.

[0119] In order to For a more detailed comparison of different cross-sections, this invention employs two different unfolding methods, in which the time dimension remains constant. For example... Figure 3 As shown, tensor Expand into a matrix or Since the amplitude change caused by azimuth anisotropy is usually less significant than the amplitude change caused by offset change, therefore... Figure 4 As shown, with Figure 4 Compared to b, Figure 4 The unfolding method in a can produce more structurally coherent cross-sections.

[0120] This invention adopts Figure 3 The unfolding strategy shown in a (labeled U) creates the dataset for training. Where, v = (m x ,m y ) T It is the input from the network. The corresponding learning objective is defined as follows:

[0121]

[0122] Where M x and M y These represent the maximum lengths of the inner axis and the cross axis, respectively; U is a tensor expansion method; and X is the m value in fixed five-dimensional seismic data. x and m y The extracted three-dimensional tensor is then expanded into a two-dimensional matrix, v = (m x ,m y ) T It is the input from the network.

[0123] S3. Introduce nuclear norm regularization to construct the objective function;

[0124] In seismic exploration, real pre-stack seismic data often contains a large amount of noise, making accurate identification of useful signals quite complex. Since neural networks tend to learn and simulate this noise, the output may be highly noisy. To address this challenge, this invention introduces kernel norm regularization. As a convex relaxation form of low-rank regularization, kernel norm regularization effectively improves the model's generalization ability while effectively controlling its complexity. By introducing kernel norm regularization, this invention aims to better suppress the impact of noise on the model during the learning process, thereby improving the accuracy and robustness of seismic data processing.

[0125] The nuclear norm regularization is introduced into the objective function as follows:

[0126]

[0127] Where λ is a hyperparameter used to balance the fidelity and regularization terms in the objective function, ||| * For nuclear norm,

[0128] The nuclear norm is defined as follows:

[0129]

[0130] Where, σ i It is the i-th singular value of X.

[0131] S4. Read the raw five-dimensional seismic data D obs The five-dimensional seismic data with missing traces is input into the network to achieve five-dimensional seismic data reconstruction.

[0132] After completing model training, process each v = (m x ,m y ) T They obtain their respective profiles for seismic data reconstruction.

[0133] In another embodiment of the present invention, a coordinate-based five-dimensional seismic data interpolation system is provided. This system can be used to implement the above-mentioned coordinate-based five-dimensional seismic data interpolation method. Specifically, the coordinate-based five-dimensional seismic data interpolation system includes a construction module, an interpolation module, a function module, and a reconstruction module.

[0134] Among them, the construction module is based on NeRF theory to build a point-by-point interpolation model for unsupervised seismic data;

[0135] The interpolation module, combined with additional convolutional layers, modifies the MLP framework to construct a profile-by-profile interpolation model based on the constructed unsupervised seismic data point-by-point interpolation model.

[0136] The function module introduces nuclear norm regularization to construct the objective function of the profile interpolation model.

[0137] Reconstruction module, reads raw five-dimensional seismic data D obs The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

[0138] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of a coordinate-based five-dimensional seismic data interpolation method, including:

[0139] A point-by-point interpolation model for unsupervised seismic data is constructed based on NeRF theory. An MLP framework is modified by incorporating additional convolutional layers, and a profile-by-profile interpolation model is built upon this model. Kernel norm regularization is introduced to construct the objective function of the profile-by-profile interpolation model. The original five-dimensional seismic data D is then read. obs The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

[0140] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0141] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the coordinate-based five-dimensional seismic data interpolation method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps:

[0142] A point-by-point interpolation model for unsupervised seismic data is constructed based on NeRF theory. An MLP framework is modified by incorporating additional convolutional layers, and a profile-by-profile interpolation model is built upon this model. Kernel norm regularization is introduced to construct the objective function of the profile-by-profile interpolation model. The original five-dimensional seismic data D is then read. obs The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

[0143] Please see Figure 12 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the fluid composition calculation method in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the fluid composition calculation system in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here.

[0144] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 12This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0145] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, CPUs, graphics processing units (GPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, quantum computing-based data processing logic units, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0146] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0147] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0148] Any references to memory, databases, or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0149] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0150] Please see Figure 13 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the generalizable monocular absolute depth map estimation method described above.

[0151] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0152] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0153] This invention selected an effective traditional PMF-TR method for further comparison, and the results are as follows: Figure 6 As shown. Figure 6 a shows 8 seismic gathers, s x =16, r y =32,s y The range is 1 to 16, r x The range is 1 to 8. As can be seen, the raw data includes both horizontal and tilted phase axes, which poses a challenge for reconstruction. Figure 6 b plotted seismic data with 80% irregular missing traces. The reconstruction results from PMF-TR, point-by-point method, and profile method are as follows: Figure 6 c. Figure 6 e and Figure 6 As shown in g, the corresponding reconstruction error is as follows: Figure 6 d、 Figure 6 B and Figure 6 As shown in h, all three methods are effective in data interpolation. Quantitative calculations show that the SNRs of the PMF-TR method, the pointwise method, and the profile method are 12.37 dB, 16.61 dB, and 18.67 dB, respectively. Both implicit representation methods outperform the PMF-TR method, demonstrating the superior performance of implicit networks. Furthermore, as indicated by the dark arrows, the skewed structure in the complete data was not fully recovered by the PMF-TR method and the pointwise method. In the areas marked by the light arrows, signal leakage is clearly visible in both the PMF-TR method and the pointwise method. In contrast, the profile method proposed in this invention successfully recovered the skewed structure without significant useful signal leakage. This may be attributed to the fact that the convolutional network decoder based on the profile method has a larger receptive field, thus exhibiting stronger feature extraction capabilities in reconstructing data with complex features.

[0154] Compared to synthetic data, real-world data exhibits greater complexity and is significantly affected by noise. To further evaluate the effectiveness of the profile-based reconstruction method proposed in this invention, PMF-TR was selected as the benchmark method, and a land dataset obtained in Canada was used for comparison.

[0155] Figure 7 The image shows a tile plot of the reconstructed data using PMF-TR and the method of this invention. Specifically, Figure 7 a shows the CMP y cross section observed under the condition of fixed CMP x (bin=4) and offset (bin=6). Clearly, the original data segment contains a large number of missing traces and noise, which poses a considerable challenge to reconstruction. Figure 7 b shows the CMP y profile results obtained by PMF-TR, which effectively recovered the... Figure 7 The missing path in 'a'. However, noise interference still exists. Figure 7 c shows the results of the invention, wherein Figure 7 All missing channels in image a were accurately recovered. Compared to the PMF-TR method, the method of this invention achieves a higher signal-to-noise ratio and better performance in recovering the image. These results also demonstrate the effectiveness of the nuclear norm in processing noisy data.

[0156] To further verify the effectiveness of the method of the present invention, the offset bin=6 and the orientation bin=4 were fixed, and the results were observed from different angles. Figure 8 a shows a profile of the original seismic record, compared with Figure 7 Compared to the previous section, these cross-sections show a larger gap. Figure 8 b and Figure 8 c shows the reconstruction results of the PMF-TR method and the method proposed in this invention, respectively. The method of this invention can effectively recover missing tracts, even in locations with significant gaps. Compared with the PMF-TR method, both methods are... Figure 8 The areas indicated by the light-colored boxes all yielded good results, and the method of the present invention demonstrated excellent lateral consistency in the recovery of reflections. On the other hand, significant noise was observed in the results recovered by the PMF-TR method in the areas marked by the dark-colored boxes. In contrast, the method of the present invention was able to handle these areas effectively.

[0157] In order to make a comprehensive comparison, Figure 9 a shows the post-stack seismic data before interpolation. The original post-stack data has a significantly low SNR, and many reflected waves are masked by noise, especially in shallow regions. The reconstructed post-stack cubes obtained using PMF-TR and the method of this invention are shown below. Figure 9 b and Figure 9 As shown in c, with Figure 9Compared to the original post-stack data in a, both effectively eliminated pre-stack noise and significantly enhanced signal energy. However, Figure 9 The profile shown in b still exhibits slight residual noise in the shallow region. Conversely, in Figure 9 The profile shown in c has almost no random noise, thus confirming the effectiveness of the proposed method in recovering seismic data containing noise and irregular sampling.

[0158] To further verify the effect of nuclear norm regularization, another five-dimensional seismic dataset collected in China was selected for comparison. Figure 10 The image shows a set of original CMP gathers, where CMP x = 3 and CMP y = 3. Figure 10 b represents the reconstruction result without nuclear norm regularization (λ = 0). Figure 10 c represents the reconstruction result when λ = 0.0001. Figure 10 b and Figure 10 By comparing with c, it can be observed that when λ changes from 0 to 0.0001, the noise interference in the reconstruction result is significantly reduced. This demonstrates the effectiveness of the nuclear norm regularization constraint. However, when λ exceeds a certain threshold, the reconstruction quality slightly decreases, indicating that a careful balance needs to be struck between data fidelity and regularization.

[0159] In the examples above, the present invention can effectively interpolate five-dimensional seismic data, laying the foundation for subsequent data analysis.

[0160] In summary, this invention presents a coordinate-based five-dimensional seismic data interpolation method and system that eliminates the need for additional labeled data, marking the first attempt at this approach in five-dimensional seismic data processing. Building upon the original point-by-point method of NeRF, this invention leverages the unique characteristics of seismic data to improve the convolutional network decoder, enabling it to output data per profile. Compared to the point-by-point method, this technique significantly improves data processing efficiency by 40 times, thus enabling faster and more accurate reconstruction of five-dimensional seismic data. Furthermore, the addition of kernel norm regularization to the objective function effectively enhances the model's noise resistance and robustness.

[0161] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0162] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0163] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0164] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0165] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0166] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0167] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0168] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0169] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0170] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0171] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A coordinate-based five-dimensional seismic data interpolation method, characterized in that, Includes the following steps: S1. An unsupervised point-by-point interpolation model for seismic data is constructed based on NeRF theory. The objective function of the unsupervised point-by-point interpolation model for seismic data is: in, The five-dimensional coordinates of the seismic data For the five-dimensional seismic data to be solved, For the parameter weights of the MLP, This is the function used by the MLP to map coordinates to complete seismic data. The mean square error of the matrix is ​​represented. S2. Modify the MLP framework by incorporating additional convolutional layers. Based on the constructed unsupervised seismic data point-by-point interpolation model, construct a profile-by-profile interpolation model. The profile-by-profile interpolation model includes an encoder and a decoder. The encoder includes a predefined single FFM layer. And an encoder based on an MLP, the encoder will... Transform into the corresponding latent variables Subsequently, the decoder based on the convolutional network extracts data from the variables. Reconstruct the complete seismic profile, using Represents a combination of encoder and decoder, a single FFM layer. Specifically: in, This represents the total number of components, where the i-th frequency component is obtained through linear sampling. express, Represents any coordinate normalized within [0, 1]; S3. Introducing nuclear norm regularization, we construct the objective function of the profile interpolation model. The objective function of the profile interpolation model is: in, These are hyperparameters used to balance the fidelity and regularization terms in the objective function. For nuclear norm, and These are the maximum lengths of the inner coupling and the cross coupling, respectively. This is the function used by the MLP to map coordinates to complete seismic data. For tensor expansion, For a specific part selected from the sampling matrix, These are the corresponding learning objectives. It is the Frobenius norm; S4. Read raw five-dimensional seismic data The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

2. The coordinate-based five-dimensional seismic data interpolation method according to claim 1, characterized in that, Five-dimensional seismic data for: in, For Hadama product, For the sampling matrix, This is complete earthquake data.

3. The coordinate-based five-dimensional seismic data interpolation method according to claim 2, characterized in that, Sampling matrix The elements in the middle satisfy the following conditions: in, Five-dimensional seismic data The index is Element.

4. The coordinate-based five-dimensional seismic data interpolation method according to claim 1, characterized in that, For seismic data that has not undergone conventional time-of-flight correction, the objective function is defined as follows: in, and These are the total lengths of the coupling shaft within the seismic source and the crossing shaft, respectively. The total length of the receiver's internal coupling. The index of the receiver on the inner axis. The sampling matrix; For common midpoint seismic data using NMO technology, the objective function is defined as: in, and These are the maximum lengths of the inner coupling and the cross coupling, respectively. For tensor expansion, These are the corresponding learning objectives. This is a function in MLP that maps coordinates to complete seismic data.

5. The coordinate-based five-dimensional seismic data interpolation method according to claim 1, characterized in that, nuclear norm as follows: in, for The i-th singular value, This represents the total number of singular values.

6. A coordinate-based five-dimensional seismic data interpolation system, characterized in that, include: The module constructs an unsupervised point-by-point interpolation model for seismic data based on NeRF theory. The objective function of the unsupervised point-by-point interpolation model for seismic data is: in, The five-dimensional coordinates of the seismic data For the five-dimensional seismic data to be solved, For the parameter weights of the MLP, This is the function used by the MLP to map coordinates to complete seismic data. The mean square error of the matrix is ​​represented. The interpolation module, combined with additional convolutional layers, modifies the MLP framework by constructing a profile-by-profile interpolation model based on the existing unsupervised point-by-point interpolation model for seismic data. This profile-by-profile interpolation model includes an encoder and a decoder; the encoder comprises a predefined single FFM layer. And an encoder based on an MLP, the encoder will... Transform into the corresponding latent variables Subsequently, the decoder based on the convolutional network extracts data from the variables. Reconstruct the complete seismic profile, using Represents a combination of encoder and decoder, a single FFM layer. Specifically: in, This represents the total number of components, where the i-th frequency component is obtained through linear sampling. express, Represents any coordinate normalized within [0, 1]; The function module introduces nuclear norm regularization to construct the objective function of the profile interpolation model. The objective function of the profile interpolation model is: in, These are hyperparameters used to balance the fidelity and regularization terms in the objective function. For nuclear norm, and These are the maximum lengths of the inner coupling and the cross coupling, respectively. This is the function used by the MLP to map coordinates to complete seismic data. For tensor expansion, For a specific part selected from the sampling matrix, These are the corresponding learning objectives. It is the Frobenius norm; Reconstruction module reads raw five-dimensional seismic data. The five-dimensional seismic data with missing traces are input into the profile interpolation model to achieve five-dimensional seismic data reconstruction.

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