Triple convex set projection seismic data interpolation method, device and equipment

Abstract

The invention relates to the technical field of seismic data processing, in particular to a triple convex set projection seismic data interpolation method, device and equipment. Obtaining seismic data containing missing channels; obtaining a mask matrix and initial reconstruction data according to the seismic data; projecting the initial reconstruction data to a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result to a preset transverse constraint set to obtain a transverse constraint projection result; projecting the transverse constraint projection result to a preset data constraint set to obtain a data constraint projection result; and taking the data constraint projection result as initial reconstruction data, repeating the three projection steps until a preset convergence condition is met or the maximum number of iterations is reached, and outputting the data constraint projection result obtained by the last iteration as a final interpolation result. The defect that a traditional convex set projection method is insufficient in inter-channel relevance modeling is overcome, and the interpolation precision in a continuous multi-channel missing scene is improved.

Description

Technical Field

[0001] This invention relates to the field of seismic data processing technology, specifically to a method, apparatus, and equipment for interpolating seismic data using triple convex set projection. Background Technology

[0002] Seismic data serves as the core basis for subsurface structural interpretation and hydrocarbon reservoir prediction, and its completeness directly determines the reliability of subsequent processing results. However, in actual acquisition processes, factors such as surface obstacles, limitations of acquisition equipment, and economic cost control often result in missing seismic traces in the observation data. These missing data can produce false structures in migration imaging and introduce errors in reservoir inversion, seriously affecting the accurate characterization of subsurface geological bodies.

[0003] To address the issue of missing seismic data, various interpolation methods have been proposed, primarily categorized into traditional mathematical methods and machine learning methods. Traditional mathematical methods are based on classical mathematical theory and utilize the inherent characteristics of seismic data for interpolation. Among these, predictive filtering methods construct data autocorrelation prediction operators and infer missing information based on the correlation between adjacent traces, but they have poor adaptability to scenarios with multiple consecutive missing traces. Methods based on wave equations follow the physical laws of seismic wave propagation, completing data through wavefield extension, but suffer from high computational complexity and strong dependence on the initial model. Machine learning methods rely on the nonlinear mapping capabilities of deep learning models to learn the mapping relationship between missing patterns and complete data from large amounts of labeled data. However, these methods depend on large-scale, high-quality labeled data, have high model training and inference computational costs, and poor generalization ability to unseen missing patterns, making them difficult to adapt to the complex and ever-changing geological conditions of actual work areas. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, and device for interpolating seismic data with triple convex set projection, which solves the problems in the prior art.

[0005] This invention is achieved through the following technical solution:

[0006] In a first aspect, embodiments of the present invention provide a method for interpolating seismic data with triple convex set projection, comprising:

[0007] Acquire seismic data containing missing traces, the seismic data including multiple time sampling points and multiple seismic traces;

[0008] Based on the seismic data, a mask matrix and initial reconstruction data are obtained. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0, and the corresponding value is known to be 1. The seismic data containing the missing trace is used as the initial reconstruction data.

[0009] The initial reconstructed data is projected onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity.

[0010] The frequency domain sparse projection result is projected onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces.

[0011] The lateral constraint projection result is projected onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix.

[0012] Using the data constraint projection result as the initial reconstructed data, repeat the steps of projecting the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is then output as the final interpolation result.

[0013] Preferably, the step of projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result includes:

[0014] The phase axis curvature features are extracted from the seismic data to generate a normalized curvature matrix of the same dimension as the seismic data. The element values ​​of the normalized curvature matrix are mapped to the interval [0,1], where 0 represents a very gentle phase axis and 1 represents a steep change or break in the phase axis.

[0015] Determine whether the current iteration count has reached the preset base iteration count;

[0016] If the current iteration number does not reach the preset basic iteration number, the frequency domain sparse projection result is projected onto a preset lateral constraint set using fixed basic parameters to obtain the lateral constraint projection result. The fixed basic parameters are the preset lateral constraint basic weight and the inter-channel difference basic threshold.

[0017] If the current iteration number reaches the preset basic iteration number, the basic weight of the lateral constraint and the basic threshold of the inter-path difference are adaptively adjusted based on the normalized curvature matrix to obtain an adaptive lateral constraint set.

[0018] The frequency domain sparse projection result is projected onto the adaptive lateral constraint set to obtain the lateral constraint projection result. The lateral constraint set requires that the sum of the absolute values ​​of the column-direction second-order difference results of the input data does not exceed a preset inter-channel difference threshold. The larger the curvature value of the normalized curvature matrix, the smaller the lateral constraint weight and the larger the inter-channel difference threshold.

[0019] Preferably, the step of extracting the in-phase axis curvature features from the seismic data and generating a normalized curvature matrix of the same dimension as the seismic data includes:

[0020] Calculate the lateral amplitude gradient of the initial reconstructed data in the interchannel direction. and the time amplitude gradient in the time direction ;

[0021] The transverse amplitude gradient is calculated using the Laplace operator. and the time amplitude gradient The second rate of change gives the position. curvature value ,in, For spatial coordinates, For time;

[0022] The curvature value at each position is normalized and mapped to the [0,1] interval to obtain the normalized curvature value;

[0023] The normalized curvature matrix is ​​obtained based on the normalized curvature value at each position.

[0024] Preferably, the adaptive adjustment of the basic weights of the lateral constraints and the basic threshold of the inter-channel difference based on the normalized curvature matrix to obtain the adaptive lateral constraint set includes:

[0025] The basic weights of the lateral constraints are adaptively adjusted based on the normalized curvature matrix to satisfy:

[0026] ;

[0027] in, For earthquake data in Lateral constraint weights for location, The basic weights of the lateral constraints, The curvature sensitivity coefficient, In the normalized curvature matrix The normalized curvature value of the position. This is the minimum weight lower bound;

[0028] The inter-channel difference baseline threshold is adaptively adjusted based on the normalized curvature matrix to satisfy:

[0029] and

[0030] in, For earthquake data in Inter-channel difference threshold at location This is the basic threshold for the inter-channel difference. This is the threshold amplification factor. This represents the upper limit of the inter-channel difference threshold.

[0031] Preferably, the step of projecting the frequency domain sparse projection result onto the adaptive lateral constraint set to obtain the lateral constraint projection result satisfies:

[0032] ;

[0033] ;

[0034] ;

[0035] in, The result is a lateral constraint projection. This refers to the frequency domain sparse projection result. For symbolic functions, It is a second-order difference matrix. This is the transpose of a second-order difference matrix. It is a norm of 1.

[0036] Preferably, the lateral constraint set is:

[0037] ;

[0038] ;

[0039] First Road With the Last Way One-sided second-order difference correction is used. ; ; for Norms are used to enhance the ability to suppress inter-channel mutation signals.

[0040] Preferably, projecting the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result includes:

[0041] ;

[0042] ;

[0043] in, This is the result of sparse projection in the frequency domain. The initial reconstruction data, For sparse transformation, For element-wise multiplication, Dynamic updates are adopted using an exponential decay strategy. As the initial threshold, The minimum threshold, Number of iterations , The maximum number of iterations, As an indicator function, it represents when If the value is 1, then the value is 0; otherwise, the value is 0.

[0044] Preferably, the frequency domain sparse constraint set is:

[0045] ;

[0046] in, To preset sparsity, It is a zero norm.

[0047] Preferably, the step of projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result satisfies:

[0048] ;

[0049] in, To constrain the projection results of the data, This refers to the projection result of the lateral constraint. The sampled mask matrix, For the earthquake data, It is the identity matrix. The number of time sampling points, This represents the number of earthquake traces.

[0050] Preferably, the data constraint set is: .

[0051] Preferably, the convergence condition is: ,in, It is the Frobenius norm. for The data constraint projection results from the previous iteration.

[0052] Thirdly, embodiments of the present invention provide a triple convex set projection seismic data interpolation device, comprising:

[0053] The seismic data module is used to acquire seismic data containing missing traces, the seismic data including multiple time sampling points and multiple seismic traces;

[0054] An initialization module is used to obtain a mask matrix and initial reconstruction data based on the seismic data. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0, and the corresponding value is known to be 1. The seismic data containing the missing trace is used as the initial reconstruction data.

[0055] The first projection module is used to project the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity.

[0056] The second projection module is used to project the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces.

[0057] The third projection module is used to project the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix.

[0058] The iterative module is used to take the data constraint projection result as the initial reconstruction data, repeat the steps of projecting the initial reconstruction data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is output as the final interpolation result.

[0059] Thirdly, embodiments of the present invention provide an electronic device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement the method of the first aspect described above.

[0060] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0061] (1) By combining the inter-trace lateral continuity constraint with the curvature characteristics of the phase axis, a curvature-adaptive lateral constraint parameter adjustment strategy is proposed. While ensuring the inter-trace continuity of gentle strata, key geological features such as faults and steeply dipping structures are effectively preserved, enhancing the interpolation adaptability of seismic data in complex tectonic areas.

[0062] (2) Establish a phased iterative projection mechanism, dividing the basic convergence stage into a curvature adaptive optimization stage. First, fixed constraints are used to achieve fast data convergence and basic continuity correction. Then, curvature adaptive constraints are introduced to carry out fine optimization, thereby improving the stability of the algorithm and the construction fidelity.

[0063] (3) The combination of frequency domain sparse constraints and curvature adaptive transverse constraints can suppress interpolation artifacts and random noise, and can also adapt to changes in different phase axes, so that the interpolation results maintain higher consistency with the original data in the FK domain.

[0064] (4) An incremental curvature update strategy is adopted, which recalculates the curvature only for local areas with missing traces, thereby improving the interpolation adaptability while controlling the computational cost. The method is applicable to the processing of theoretical and measured seismic data under complex geological conditions, is easy to promote in engineering, and can provide high-quality preliminary data for subsequent migration imaging, reservoir inversion and other processes. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0066] Figure 1 This is a flowchart illustrating the triple convex set projection seismic data interpolation method provided by the present invention;

[0067] Figure 2 A comparison chart of interpolation effects when 30% of the pre-stack gather data is missing, provided by this invention;

[0068] Figure 3 This is a schematic diagram illustrating the changing trends of different indicators with the number of iterations when 30% of the pre-stack gather data is missing, as provided by this invention.

[0069] Figure 4 A schematic diagram of FK spectra of different interpolation results when 30% of the data is missing, as provided in this invention;

[0070] Figure 5 A comparison chart of interpolation effects when 50% of the pre-stack gather data is missing, provided by this invention;

[0071] Figure 6 This invention provides a schematic diagram illustrating the changing trends of different indicators with the number of iterations under a 50% data loss condition.

[0072] Figure 7 A schematic diagram of FK spectra of different interpolation results when 50% of the data is missing, as provided in this invention;

[0073] Figure 8 A schematic diagram of the structure of the triple convex set projection seismic data interpolation device provided by the present invention;

[0074] Figure 9 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0076] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0077] It should be noted that all actions involving the acquisition of signals, information, or data in this invention are carried out in compliance with the relevant data protection laws and regulations of the locality and with authorization from the owner of the relevant device.

[0078] Example 1

[0079] Please see Figure 1 This invention provides a method for interpolating seismic data using triple convex set projection, comprising:

[0080] S1. Obtain seismic data containing missing traces, wherein the seismic data includes multiple time sampling points and multiple seismic traces;

[0081] Specifically, seismic data originates from actual acquisitions or theoretical models, and is in the form of a two-dimensional matrix containing several traces (spatial locations) and several time sampling points. Missing traces refer to locations where no valid data was acquired; these locations are represented as invalid or zero values ​​in the data matrix.

[0082] S2. Obtain a mask matrix and initial reconstruction data based on the seismic data. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0. It is known that the corresponding value is 1. Use the seismic data containing the missing trace as the initial reconstruction data.

[0083] Specifically, the mask matrix is ​​used to mark missing data locations. Its dimensions are the same as the seismic data; for example, a 1 in the matrix indicates the presence of actual observation data at that location, while a 0 indicates missing data. By generating the mask matrix and initial reconstruction data, the information areas that need to be protected during the reconstruction process are identified, and initial estimates are provided for iterations, helping to guide the reconstruction direction in subsequent steps.

[0084] S3. Project the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity.

[0085] Specifically, the frequency-domain sparse constraint set is constructed based on the energy concentration characteristic of seismic data in the frequency domain. It defines a data set where, within a specified sparse transform domain, the number of coefficients with amplitudes higher than a dynamic threshold must not exceed a preset sparsity. The process of projecting the initial reconstruction data onto this set typically involves: first, transforming the data to the frequency domain; then, retaining the primary frequency components with higher amplitudes according to the current threshold, discarding secondary components or noise with amplitudes lower than the threshold; and finally, inversely transforming back to the time-space domain. By implementing this projection, artifacts and ineffective signals can be suppressed during reconstruction, improving the rationality of the frequency domain structure of the reconstructed data.

[0086] S4. Project the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces.

[0087] Specifically, the lateral constraint set is constructed based on the similarity and continuity characteristics between seismic traces. When the frequency domain sparse projection results are projected onto this set, optimization algorithms are typically used to adjust the data of each trace to make them as close as possible to the input data while maintaining the smooth changes between adjacent traces. By introducing this constraint, the continuity of the reconstruction results in the lateral direction can be enhanced, especially in regions with smooth phase axes, which helps to improve the geometric consistency of missing trace recovery.

[0088] S5. Project the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix.

[0089] Specifically, the data constraint set is constructed based on the fidelity requirements of the observation data. It defines a set of data whose values ​​at known locations marked by the mask matrix are completely consistent with the original observation data. When projecting the lateral constraint projection results onto this set, the observation values ​​at known locations are usually retained directly, and only the data at missing trace locations are adjusted. This projection ensures that known information is not destroyed during the reconstruction process, and that the iterative process is always based on the actual observation data, avoiding deviation of the reconstruction results from the true observations.

[0090] S6. Using the data constraint projection result as the initial reconstruction data, repeat the steps of projecting the initial reconstruction data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is then output as the final interpolation result.

[0091] Specifically, an alternating projection iterative process is formed by repeatedly executing the aforementioned three projection operations. Each iteration uses the data-constrained projection result from the previous iteration as the new initial reconstruction data, sequentially undergoing frequency-domain sparse projection, lateral-constrained projection, and data-constrained projection. The convergence condition is typically set to the difference between two adjacent iterations being less than a certain threshold, or the number of iterations reaching a preset upper limit. Through iteration, the reconstructed data gradually satisfies the three constraints of frequency-domain sparsity, lateral continuity, and data fidelity, ultimately outputting the interpolated complete seismic data. This process can gradually approach the optimal solution through multiple projections, improving the overall quality of the reconstruction results.

[0092] In some embodiments, S4, projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result, includes:

[0093] S41. Extract the phase axis curvature features from the seismic data and generate a normalized curvature matrix of the same dimension as the seismic data. The element values ​​of the normalized curvature matrix are mapped to the interval [0,1], where 0 represents a very gentle phase axis and 1 represents a steep change or break in the phase axis.

[0094] Specifically, the phase axis curvature feature describes the degree of bending or abrupt change of the phase axis in the lateral direction. Extracting this feature involves calculating a local geometric morphology index for each location in the seismic data. This index quantifies the trend of the phase axis changing from a gentle to abrupt change. The normalized curvature matrix is ​​a matrix with the same dimensions as the original seismic data, where each element corresponds to the curvature feature value at the corresponding location in the original data. These curvature feature values ​​are linearly scaled to a range of 0 to 1 for consistent use in subsequent processing. A value of 0 indicates an extremely gentle change in the phase axis at that location, such as a phase axis reflected from horizontally layered strata; a value of 1 indicates a drastic change or fracture in the phase axis at that location, such as at fault zones, unconformities, or pinch-out points.

[0095] The step of extracting in-phase axis curvature features from the seismic data and generating a normalized curvature matrix of the same dimension as the seismic data includes:

[0096] Calculate the lateral amplitude gradient of the initial reconstructed data in the interchannel direction. and the time amplitude gradient in the time direction ;

[0097] The transverse amplitude gradient is calculated using the Laplace operator. and the time amplitude gradient The second rate of change gives the position. curvature value ;

[0098] The curvature value at each position is normalized and mapped to the [0,1] interval to obtain the normalized curvature value;

[0099] The normalized curvature matrix is ​​obtained based on the normalized curvature value at each position.

[0100] S42. Determine whether the current iteration count has reached the preset base iteration count;

[0101] Specifically, the iteration count is a counter variable that records the number of times the algorithm is repeatedly executed, used to control the algorithm's termination condition. The preset base iteration count is a pre-defined numerical threshold used to delineate different processing strategies during the iteration process. Determining whether the current iteration count has reached the preset base iteration count is done by comparing the currently executed iteration count with the preset threshold, and selecting different subsequent processing paths based on the comparison result.

[0102] S43. If the current iteration number has not reached the preset basic iteration number, the frequency domain sparse projection result is projected onto a preset lateral constraint set using fixed basic parameters to obtain the lateral constraint projection result. The fixed basic parameters are the preset lateral constraint basic weight and the inter-channel difference basic threshold.

[0103] Specifically, the frequency domain sparse projection result is a data matrix obtained after frequency domain sparse constraint processing. The data in this matrix meets the preset sparsity requirements in the sparse transform domain, but inter-trace lateral continuity has not yet been considered. The preset lateral constraint set is a mathematical set that defines the inter-trace continuity conditions that the data should satisfy. This set contains parameters that control the strength of the constraints. Fixed basic parameters are core control quantities that remain unchanged in the early stages of iteration, including the basic weights of the lateral constraints and the basic thresholds for inter-trace differences. The basic weights of the lateral constraints are used to adjust the relative importance of the lateral continuity constraints in the overall optimization; the larger the value, the stronger the requirement for continuity. The basic thresholds for inter-trace differences are used to limit the maximum allowable variation between adjacent seismic traces; the smaller the value, the smaller the allowable inter-trace differences. Projecting the frequency domain sparse projection result onto this set involves adjusting the current data to meet the lateral constraint conditions defined by the fixed parameters through mathematical transformation, while maintaining as close as possible to the original data, thus obtaining the lateral constraint projection result.

[0104] In the initial iteration phase, reliable structural information has not yet been recovered from the missing areas of the seismic data, resulting in low accuracy of the calculated curvature features. Directly using curvature information for adaptive adjustment could lead to parameter settings deviating from the actual geological conditions, thus interfering with the data recovery process. Therefore, fixed basic parameters are used in the initial iteration phase to allow the data to gradually recover missing information under stable constraints. The lateral constraint weights and inter-trace difference thresholds can be constant values ​​pre-set based on the overall characteristics of the data, or initial estimates calculated based on the statistical properties of the data. Under the influence of fixed parameters, each iteration adjusts the data to meet the inter-trace difference constraints while maintaining closeness to the frequency domain sparse projection results, gradually bringing the missing trace data towards a reasonable continuous distribution. This approach ensures the stability of the data recovery process in the initial iteration phase, avoids convergence fluctuations caused by frequent parameter changes, and lays a reliable data foundation for subsequent fine-tuning.

[0105] S44. If the current iteration number reaches the preset basic iteration number, the basic weight of the lateral constraint and the basic threshold of the inter-path difference are adaptively adjusted based on the normalized curvature matrix to obtain an adaptive lateral constraint set.

[0106] Specifically, adaptive adjustment is a process of differentially modifying the basic weights of lateral constraints and the basic thresholds of inter-track differences based on the curvature values ​​at different locations. For gently sloping regions with curvature values ​​close to 0, the geological structure is simple, and the lateral changes of the phase axis are slow, requiring strong continuity constraints. Therefore, the lateral constraint weights are appropriately increased from their basic values, while the inter-track difference thresholds are appropriately decreased. For steeply changing regions with curvature values ​​close to 1, the geological structure is complex, and the phase axis itself exhibits real changes. Therefore, the artificially imposed continuity constraints should be weakened. Consequently, the lateral constraint weights are appropriately decreased from their basic values, while the inter-track difference thresholds are appropriately increased, allowing for greater inter-track differences. After adaptive adjustment, the originally uniform fixed parameters are transformed into spatially location-dependent variable parameters, forming an adaptive lateral constraint set. This set has different constraint strength requirements at different locations.

[0107] After a preset number of iterations, the data has been initially recovered, and the missing areas possess a relatively reliable structural morphology. At this point, the curvature features calculated based on the data can accurately reflect the distribution of the actual geological structures. The lateral constraint parameters are spatially adaptively adjusted based on the normalized curvature matrix to match the constraint strength with the geological complexity. The adjustment method can be achieved using a functional mapping relationship between curvature values ​​and parameters. For example, the curvature value can be set to change negatively with the weight and positively with the threshold, with a reasonable adjustment range. Through this adaptive adjustment, the lateral constraint set maintains strong continuity requirements in gentle regions to suppress random noise and interpolation artifacts, while actively relaxing continuity requirements in abruptly changing regions to protect geological boundary features such as faults and pinch-outs from being smoothed out. This approach integrates geological information into the constraint design, making the data recovery process more consistent with the actual underground geological conditions.

[0108] In some implementations, S44, based on the normalized curvature matrix, adaptively adjusts the basic weights of the lateral constraints and the basic threshold of the inter-channel difference to obtain an adaptive lateral constraint set, including:

[0109] The basic weights of the lateral constraints are adaptively adjusted based on the normalized curvature matrix to satisfy:

[0110] ;

[0111] in, For earthquake data in Lateral constraint weights for location, The basic weights of the lateral constraints, The curvature sensitivity coefficient, In the normalized curvature matrix The normalized curvature value of the position. This is the minimum weight lower bound;

[0112] The inter-channel difference baseline threshold is adaptively adjusted based on the normalized curvature matrix to satisfy:

[0113] and

[0114] in, For earthquake data in Inter-channel difference threshold at location This is the basic threshold for the inter-channel difference. This is the threshold amplification factor. This represents the upper limit of the inter-channel difference threshold.

[0115] S45. Project the frequency domain sparse projection result onto the adaptive lateral constraint set to obtain the lateral constraint projection result. The lateral constraint set requires that the sum of the absolute values ​​of the column-direction second-order difference results of the input data does not exceed a preset inter-channel difference threshold. The larger the curvature value of the normalized curvature matrix, the smaller the lateral constraint weight and the larger the inter-channel difference threshold.

[0116] Specifically, projecting the frequency domain sparse projection result onto the adaptive lateral constraint set refers to performing a mathematical transformation operation on the current data to satisfy differentiated constraint conditions. This operation adjusts the data matrix based on the lateral constraint weights and inter-channel difference thresholds set at each position, ensuring that the adjusted data satisfies the corresponding inter-channel difference constraints at each position, while minimizing the adjustment magnitude to preserve the original data characteristics. The data obtained after this projection operation is the lateral constraint projection result.

[0117] Under the influence of an adaptive lateral constraint set, the projection operation performs adjustments of varying intensity in different regions. In gently sloping regions, due to larger weights and smaller thresholds, the projection operation forces strong lateral continuity, making waveforms between adjacent traces more consistent, thus effectively suppressing isolated noise and spurious phase axes generated during missing trace recovery. In steeply changing regions, due to smaller weights and larger thresholds, the projection operation allows for the preservation of significant inter-trace differences, ensuring the complete preservation of geological features such as wave group relationships on both sides of the fault and amplitude variations at pinch-out points. This projection operation can be implemented using an iterative shrinkage method based on convex set projection theory or a gradient descent solution method based on optimization theory. Both methods can maintain closeness to the original data while satisfying the differentiated constraints. The projected data, while preserving frequency domain sparsity, further achieves lateral continuity matching geological features, ensuring that the missing trace recovery results conform to both the overall statistical regularity of seismic data and respect the individual characteristics of local geological structures.

[0118] In some embodiments, projecting the frequency domain sparse projection result onto the adaptive lateral constraint set to obtain a lateral constraint projection result satisfies:

[0119] ;

[0120] ;

[0121] ;

[0122] in, The result is a lateral constraint projection. This refers to the frequency domain sparse projection result. For symbolic functions, It is a second-order difference matrix. This is the transpose of a second-order difference matrix. It is a norm of 1.

[0123] The set of lateral constraints is:

[0124] ;

[0125] ;

[0126] First Road With the Last Way One-sided second-order difference correction is used. ; ; for Norms are used to enhance the ability to suppress inter-channel mutation signals.

[0127] Specifically, the core of projecting onto the lateral constraint set C is to transform the input data... The goal is to map the projection to the nearest point in the lateral constraint set C, while satisfying the lateral continuity constraint and minimizing the difference between the projection result and the input data. Projection operator Essentially, it involves solving the following optimization problem:

[0128] ;

[0129] In the formula The data after projection. for Norm.

[0130] Introducing Lagrange multipliers Constructing the Lagrangian function transforms the constrained optimization problem into an unconstrained optimization problem:

[0131] ;

[0132] because Since the norm is not differentiable at zero, a subgradient is used instead of a conventional gradient to solve for the extrema. about Finding the subgradient can be decomposed into two calculations:

[0133] a, Normative terms The gradient is ;

[0134] b. According to convex analysis theory, for matrix forms Normative terms ( (where B is a variable matrix and B is a fixed matrix), and the gradient is... Substitute ,have to The subgradient is .

[0135] in, For symbolic functions .

[0136] Setting the subgradient of the Lagrange function to zero satisfies the extremum condition:

[0137] ;

[0138] After sorting, we get:

[0139] ;

[0140] Minimize the inter-channel difference energy using gradient descent, and input data Projecting onto the convex set C, the expression is:

[0141] ;

[0142] in These are Lagrange multipliers (used to balance lateral constraints and fidelity terms). This is the transpose of a second-order difference matrix. It is a symbolic function.

[0143] In some embodiments, projecting the initial reconstructed data onto a preset frequency-domain sparse constraint set to obtain a frequency-domain sparse projection result includes:

[0144] ;

[0145] ;

[0146] in, This is the result of sparse projection in the frequency domain. The initial reconstruction data, For sparse transformation, For element-wise multiplication, Dynamic updates are adopted using an exponential decay strategy. As the initial threshold, The minimum threshold, Number of iterations , The maximum number of iterations, As an indicator function, it represents when If the value is 1, then the value is 0; otherwise, the value is 0.

[0147] The frequency domain sparse constraint set is:

[0148] ;

[0149] in, To preset sparsity, It is a zero norm.

[0150] In some embodiments, the step of projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result satisfies:

[0151] ;

[0152] in, To constrain the projection results of the data, This refers to the projection result of the lateral constraint. The sampled mask matrix, For element-wise multiplication, For the earthquake data, It is the identity matrix. The number of time sampling points, This represents the number of earthquake traces.

[0153] The data constraint set is as follows: .

[0154] In some implementations, the convergence condition is: ,in, It is the Frobenius norm. for The data constraint projection results from the previous iteration.

[0155] For example, the iteration process is as follows:

[0156] Initialization: Set the initial reconstruction result Set the maximum number of iterations. Horizontal constraint weights Initial frequency domain threshold .

[0157] right , Perform the following projection operations in sequence:

[0158] Iterative updates:

[0159] Frequency domain sparse projection: calculation ;

[0160] Phased lateral constraint projection: If (Basic convergence phase): Using fixed basic parameters , ,calculate ;like (Curvature Adaptive Stage): Adjustment based on normalized curvature matrix , ,calculate ;

[0161] Data constraint projection: Based on the results of the previous step, calculate ;

[0162] Termination and Output: When the convergence condition is met ( When the Frobenius norm is reached or the maximum number of iterations N is reached, the iteration terminates and the final reconstruction result is output. .

[0163] If the condition is not met, the frequency domain threshold is updated according to the exponential decay formula. ,make Proceed to the next iteration.

[0164] Interpolation result output and verification: Output the complete reconstructed seismic data. The interpolation effect is evaluated by calculating the relative error between the interpolation result and the original data and the peak signal-to-noise ratio. The smaller the relative error and the larger the peak signal-to-noise ratio, the higher the interpolation accuracy.

[0165] Technical effectiveness verification:

[0166] To comprehensively verify the effectiveness, noise resistance, and applicability of the seismic data convex set projection interpolation method based on lateral constraints of this invention in complex geological scenarios, single-shot seismic records corresponding to the Marmousi model were selected as test data for comparative experiments. The traditional convex set projection interpolation method (AK-POCS) was used as a reference, and the performance of the method was evaluated from both qualitative and quantitative dimensions.

[0167] The Marmousi model incorporates diverse geological features such as complex block structures, abrupt lithological interface zones, and gently sloping strata. Its single-shot record's phase axis exhibits both "local continuity" and "global complexity," accurately verifying the interpolation algorithm's ability to model inter-trace correlations and its noise resistance. The specific parameters of this single-shot record are as follows: time sampling rate 1ms, time duration 3000ms, number of seismic traces 400, and trace spacing 25m. The data dimensions conform to the typical characteristics of actual seismic exploration acquisition scenarios. To ensure the fairness and effectiveness of the comparative experiment, the core experimental parameters are uniformly set: maximum number of iterations N=100; the sparse transformation adopts the FK transform, consistent with the traditional AK-POCS method; the frequency domain threshold is dynamically updated using an exponential decay strategy to ensure the rationality of sparse constraints during iteration; the lateral constraint weights are set according to the lateral variation of the seismic record's phase axis—smaller lateral variations result in larger lateral constraint weights, and vice versa.

[0168] like Figure 2 As shown, Figure 2 A comparison chart showing the interpolation effect when the synthesized pre-stack set data is 30% missing. Figure 2 (a) is the original synthetic seismic profile; Figure 2 (b) Seismic data with 30% random missing data; Figure 2 (c) is the interpolation result of the method of the present invention; Figure 2 (d) shows the interpolation results of the traditional method (AK-POCS); Figure 2 (e) represents the interpolation error of the method of the present invention; Figure 2 (f) represents the interpolation error of the traditional method. When 30% of the data is missing, the interpolation result of the method of this invention ( Figure 2 (c) shows significantly better continuity of the in-phase axis than the traditional AK-POCS method. Figure 2 (d)), Interpolation error diagram ( Figure 2 (e) The amplitude is smaller, especially in the region of the flat phase axis (red elliptical region), and the missing data recovery effect is closer to the original data;

[0169] Figure 3 The results show the changing trends of different indicators of the patented method and the AK-POCS algorithm with the number of iterations when 30% of the data is missing. The relative error and peak signal-to-noise ratio are both better than those of the AK-POCS algorithm.

[0170] Figure 4 The FK spectrum of different interpolation results when 30% of the data is missing. Figure 4 (a) is the FK spectrum of the original complete data; Figure 4 (b) is the FK spectrum of the AK-POCS algorithm; Figure 4(c) shows the FK spectrum of the seismic data after interpolation using the method of this invention. As can be seen from the figure, the AK-POCS algorithm introduces a large amount of random noise into the FK spectrum, resulting in a greater difference compared to the FK spectrum of the original data.

[0171] Figure 5 A comparison chart showing the interpolation effect when the synthesized pre-stack set data is 50% missing. Figure 5 (a) is the original synthetic seismic profile; Figure 5 (b) Seismic data with 50% random missing data; Figure 5 (c) is the interpolation result of the method of the present invention; Figure 5 (d) shows the interpolation results of the traditional method (AK-POCS); Figure 5 (e) represents the interpolation error of the method of the present invention; Figure 5 (f) represents the interpolation error of the traditional method. By comparing the error plots, it can be seen that under a high missing percentage, the interpolation results of the traditional AK-POCS method ( Figure 5 (d) Obvious artifacts and phase axis breaks appear. The interpolation results of the method of the present invention have a higher signal-to-noise ratio and introduce smaller interpolation errors (especially in the red rectangular area). At the same time, it has a greater advantage in maintaining the continuity of the phase axis (red elliptical area).

[0172] Figure 6 The results show the changing trends of different indicators of the patented method and the AK-POCS algorithm with the number of iterations under the condition of 50% missing data. The relative error and peak signal-to-noise ratio are both better than those of the AK-POCS algorithm.

[0173] Figure 7 The FK spectrum is the result of different interpolation when 50% of the data is missing. Figure 7 (a) is the FK spectrum of the original complete data; Figure 7 (b) is the FK spectrum of the AK-POCS algorithm; Figure 7 (c) shows the FK spectrum of the seismic data after interpolation using the method of this invention. As can be seen from the figure, the FK spectrum of the AK-POCS algorithm is almost completely masked by noise, while the FK spectrum of the method of this patent still maintains good consistency with the original data.

[0174] Therefore, under different missing proportions, the relative error of the method of the present invention is always lower than that of the traditional AK-POCS method, and the peak signal-to-noise ratio is always higher than that of the traditional method. Moreover, the advantage gradually increases with the number of iterations, indicating that the convergence stability and interpolation accuracy of the method of the present invention are better. Figure 3 , Figure 6 The FK spectrum of the interpolation results obtained by the traditional AK-POCS method introduces a large amount of random noise. Figure 4 (b) Figure 7 (b)), while the FK spectrum of the interpolation result of the method of the present invention ( Figure 4(c) Figure 7 (c) and the original data FK spectrum ( Figure 4 (a) Figure 7 (a) Maintaining a high degree of consistency verifies the noise suppression capability of the method of the present invention.

[0175] Example 2

[0176] Please see Figure 8 This invention provides a triple convex set projection seismic data interpolation device, comprising:

[0177] The seismic data module is used to acquire seismic data containing missing traces, the seismic data including multiple time sampling points and multiple seismic traces;

[0178] An initialization module is used to obtain a mask matrix and initial reconstruction data based on the seismic data. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0, and the corresponding value is known to be 1. The seismic data containing the missing trace is used as the initial reconstruction data.

[0179] The first projection module is used to project the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity.

[0180] The second projection module is used to project the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces.

[0181] The third projection module is used to project the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix.

[0182] The iterative module is used to take the data constraint projection result as the initial reconstruction data, repeat the steps of projecting the initial reconstruction data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is output as the final interpolation result.

[0183] It should be noted that each module and unit in the triple convex set projection seismic data interpolation device in this embodiment corresponds one-to-one with each step in the triple convex set projection seismic data interpolation method in the aforementioned embodiment. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned triple convex set projection seismic data interpolation method, and will not be repeated here.

[0184] Example 3

[0185] Please see Figure 9 This embodiment provides an electronic device, including at least one processor 901 and a memory 902. Optionally, the device further includes a communication component 903. The processor 901, memory 902, and communication component 903 are connected via a bus 904.

[0186] In a specific implementation, at least one processor 901 executes computer execution instructions stored in memory 902, causing at least one processor 901 to perform the above-described method.

[0187] The specific implementation process of processor 901 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0188] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0189] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0190] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0191] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0192] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0193] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0194] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0195] The division of units is merely a logical functional division; 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 indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0196] 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.

[0197] In addition, 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.

[0198] If a function 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, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0199] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0200] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for interpolating seismic data using triple convex set projection, characterized in that, include: Acquire seismic data containing missing traces, the seismic data including multiple time sampling points and multiple seismic traces; Based on the seismic data, a mask matrix and initial reconstruction data are obtained. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0, and the corresponding value is known to be 1. The seismic data containing the missing trace is used as the initial reconstruction data. The initial reconstructed data is projected onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity. The frequency domain sparse projection result is projected onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces. The lateral constraint projection result is projected onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix. Using the data constraint projection result as the initial reconstructed data, repeat the steps of projecting the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is then output as the final interpolation result.

2. The method according to claim 1, characterized in that, The step of projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result includes: The phase axis curvature features are extracted from the seismic data to generate a normalized curvature matrix of the same dimension as the seismic data. The element values ​​of the normalized curvature matrix are mapped to the interval [0,1], where 0 represents a very gentle phase axis and 1 represents a steep change or break in the phase axis. Determine whether the current iteration count has reached the preset base iteration count; If the current iteration number does not reach the preset basic iteration number, the frequency domain sparse projection result is projected onto a preset lateral constraint set using fixed basic parameters to obtain the lateral constraint projection result. The fixed basic parameters are the preset lateral constraint basic weight and the inter-channel difference basic threshold. If the current iteration number reaches the preset basic iteration number, the basic weight of the lateral constraint and the basic threshold of the inter-path difference are adaptively adjusted based on the normalized curvature matrix to obtain an adaptive lateral constraint set. The frequency domain sparse projection result is projected onto the adaptive lateral constraint set to obtain the lateral constraint projection result. The lateral constraint set requires that the sum of the absolute values ​​of the column-direction second-order difference results of the input data does not exceed a preset inter-channel difference threshold. The larger the curvature value of the normalized curvature matrix, the smaller the lateral constraint weight and the larger the inter-channel difference threshold.

3. The method according to claim 2, characterized in that, The step of extracting in-phase axis curvature features from the seismic data and generating a normalized curvature matrix of the same dimension as the seismic data includes: Calculate the lateral amplitude gradient of the initial reconstructed data in the interchannel direction. and the time amplitude gradient in the time direction ; The transverse amplitude gradient is calculated using the Laplace operator. and the time amplitude gradient The second rate of change gives the position. curvature value ,in, For spatial coordinates, For time; The curvature value at each position is normalized and mapped to the [0,1] interval to obtain the normalized curvature value; The normalized curvature matrix is ​​obtained based on the normalized curvature value at each position.

4. The method according to claim 2, characterized in that, The adaptive adjustment of the basic weights of the lateral constraints and the basic threshold of the inter-channel difference based on the normalized curvature matrix to obtain the adaptive lateral constraint set includes: The basic weights of the lateral constraints are adaptively adjusted based on the normalized curvature matrix to satisfy: ； in, For earthquake data in Lateral constraint weights for location, The basic weights of the lateral constraints, The curvature sensitivity coefficient, In the normalized curvature matrix The normalized curvature value of the position. This is the minimum weight lower bound; The inter-channel difference baseline threshold is adaptively adjusted based on the normalized curvature matrix to satisfy: and in, For earthquake data in Inter-channel difference threshold at location This is the basic threshold for the inter-channel difference. This is the threshold amplification factor. This represents the upper limit of the inter-channel difference threshold.

5. The method according to claim 2, characterized in that, The step of projecting the frequency domain sparse projection result onto the adaptive lateral constraint set to obtain the lateral constraint projection result satisfies: ； ； ； in, The result is a lateral constraint projection. This refers to the frequency domain sparse projection result. For symbolic functions, It is a second-order difference matrix. This is the transpose of a second-order difference matrix. It is a norm of 1.

6. The method according to claim 5, characterized in that, The set of lateral constraints is: ； ； First Road With the Last Way One-sided second-order difference correction is used. ; ; for Norms are used to enhance the ability to suppress inter-channel mutation signals.

7. The method according to claim 1, characterized in that, The step of projecting the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result includes: ； ； in, This is the result of sparse projection in the frequency domain. The initial reconstruction data, For sparse transformation, For element-wise multiplication, Dynamic updates are adopted using an exponential decay strategy. As the initial threshold, The minimum threshold, Number of iterations , The maximum number of iterations, As an indicator function, it represents when If the value is 1, then the value is 0; otherwise, the value is 0.

8. The method according to claim 7, characterized in that, The frequency domain sparse constraint set is: ； in, To preset sparsity, It is a zero norm.

9. The method according to claim 1, characterized in that, The process of projecting the lateral constraint projection result onto a preset data constraint set yields a data constraint projection result that satisfies the following: ； in, To constrain the projection results of the data, This refers to the projection result of the lateral constraint. The sampled mask matrix, For the earthquake data, It is the identity matrix. The number of time sampling points, This represents the number of earthquake traces.

10. The method according to claim 9, characterized in that, The data constraint set is as follows: .

11. The method according to claim 1, characterized in that, The convergence condition is: ,in, It is the Frobenius norm. for The data constraint projection results from the previous iteration.

12. A triple convex set projection seismic data interpolation device, characterized in that, include: The seismic data module is used to acquire seismic data containing missing traces, the seismic data including multiple time sampling points and multiple seismic traces; An initialization module is used to obtain a mask matrix and initial reconstruction data based on the seismic data. The mask matrix has the same dimension as the seismic data. The mask matrix corresponding to the missing trace position is 0, and the corresponding value is known to be 1. The seismic data containing the missing trace is used as the initial reconstruction data. The first projection module is used to project the initial reconstructed data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result. The frequency domain sparse constraint set is used to require that the number of coefficients with amplitudes higher than a dynamic threshold in the input data in a specified sparse transform domain does not exceed a preset sparsity. The second projection module is used to project the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result, wherein the lateral constraint set is used to constrain the lateral continuity between seismic traces. The third projection module is used to project the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result. The data constraint set requires that the input data values ​​remain unchanged on the known values ​​indicated by the mask matrix. The iterative module is used to take the data constraint projection result as the initial reconstruction data, repeat the steps of projecting the initial reconstruction data onto a preset frequency domain sparse constraint set to obtain a frequency domain sparse projection result; projecting the frequency domain sparse projection result onto a preset lateral constraint set to obtain a lateral constraint projection result; and projecting the lateral constraint projection result onto a preset data constraint set to obtain a data constraint projection result, until a preset convergence condition is met or the maximum number of iterations is reached. The data constraint projection result obtained in the last iteration is output as the final interpolation result.

13. An electronic device, characterized in that, include: At least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement the method as described in any one of claims 1-10.

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