Stable deconvolution method based on mixed norm constraint and frequency band optimization

Abstract

The invention belongs to the field of seismic data processing, relates to a stable deconvolution method based on mixed norm constraint and frequency band optimization, and aims to solve the problems that the prior art is easily interfered by noise and is insufficient in data resolution and dynamic optimization in a low signal-to-noise ratio and complex geological environment. The method comprises the following steps: obtaining a linearization frequency division operator according to collected seismic data; based on a linearized frequency division operator, establishing a stable deconvolution objective function of sparsity constraint and mixed norm constraint; decomposing the target function into a plurality of sub-problems based on an ADMM algorithm, alternately optimizing and updating each variable, and solving an approximate optimal solution; and stopping iteration until a termination criterion is met, taking the variable obtained at the last time as an approximate optimal solution, and outputting a stable deconvolution result. According to the method, the mixed norm sparsity constraint and the linearization frequency division operator are introduced, so that the sparsity of data can be effectively kept, meanwhile, the dominant frequency band range is accurately controlled, and the authenticity and precision of a deconvolution result are ensured.

Description

Background Art

[0002] In the field of seismic exploration, the resolution of seismic data is the core indicator for achieving fine analysis of underground geological structures. It directly determines the accuracy of precise identification of underground structures and is of key significance for oil and gas resource exploration, geological disaster assessment, etc. As an important means to improve the resolution of seismic data, the traditional deconvolution method is committed to restoring the original pulse characteristics of the reflected wave by estimating the autocorrelation function of seismic data, achieving the purpose of removing multiple reflections and signal distortion, and effectively enhancing the resolution of seismic data to a certain extent.

[0003] However, in actual application scenarios, the existing traditional deconvolution methods have exposed many limitations. First, under low signal-to-noise ratio conditions, it is difficult for traditional deconvolution methods to effectively distinguish between noise and signals. Random noise can easily interfere with the deconvolution process, resulting in signal distortion, which seriously affects the accuracy of the deconvolution results and reduces the imaging accuracy. Secondly, for key reservoir geological features such as small-scale faults, fractures and caves that are widely present in complex geological bodies, traditional methods are limited by fixed parameter models and cannot capture the weak phase and amplitude changes in the signal. Especially in low signal-to-noise ratio environments, subtle geological response features are easily submerged, resulting in missing details or blurred morphology in reservoir characterization. Third, the traditional linear deconvolution algorithm uses a static processing flow with preset parameters. It lacks the ability to adaptively optimize the reflection coefficient according to the local characteristics of seismic data. It is difficult to adapt to the non-stationary seismic response generated by complex geological interfaces, and there are obvious imaging deviations when characterizing complex structures such as reverse faults and salt dome structures. Finally, the traditional deconvolution method has obvious defects in frequency band control and only relies on L 1 or L 2 The single norm constraint cannot effectively limit the frequency band range of the deconvolution result, which can easily lead to excessive resolution improvement and infinite frequency band expansion, thus generating artifacts such as high-frequency noise and false event axes.

[0004] In summary, the current technology's processing bottlenecks under low signal-to-noise ratio and complex geological conditions have become a key factor restricting the improvement of seismic exploration accuracy. In particular, there are significant deficiencies in core technical links such as restoring small-scale geological features, enhancing resolution, and avoiding false images. It is urgent to propose a new optimization method to overcome the above technical challenges and further improve the accuracy and resolution of seismic data. Summary of the invention

[0005] In order to solve the above problems in the prior art, that is, to solve the problems that the prior art is susceptible to noise interference, insufficient seismic data resolution and insufficient dynamic optimization capability under low signal-to-noise ratio and complex geological environment, the first aspect of the present invention proposes a stable deconvolution method based on hybrid norm constraint and frequency band optimization, the method comprising the following steps: Obtain seismic data and perform preprocessing, and obtain a linearized frequency-divided operator based on the preprocessed seismic data; With the goal of minimizing the matching error, based on the linearized frequency-divided operator, establish a stable deconvolution objective function with sparsity constraints and mixed norm constraints; Based on the alternating direction method of multipliers framework, decompose the stable deconvolution objective function into several sub-problems, and solve the approximate optimal solution by alternately optimizing and updating each variable; The variables include reflection coefficients, auxiliary variables, and linearized frequency-divided operators; When the termination criterion is met, the iteration terminates, and the variables obtained in the last iteration are used as the approximate optimal solution of the stable deconvolution objective function, and the output is the stable deconvolution result.

[0006] In some preferred embodiments, to obtain a linearized frequency-divided operator based on the seismic data, the method is as follows: A 1. Perform Fourier transform on the preprocessed seismic data to obtain a frequency-domain signal; A 2. Based on the center frequency and bandwidth, define a zero-phase band-pass filter, and obtain a multi-band-pass filter by weighting the zero-phase band-pass filter; A 3. Filter the frequency-domain signal based on the multi-band-pass filter, and then obtain a time-domain signal through inverse Fourier transform and linearize it to obtain a linearized frequency-divided operator.

[0007] In some preferred embodiments, with the goal of minimizing the matching error, based on the linearized frequency-divided operator, establish a stable deconvolution objective function with sparsity constraints and mixed norm constraints, and the method is as follows: ; Among them, represents the matching error between the reflection coefficient and the observed data; represents the sparsity of the reflection coefficient under the L 1-norm; is L 2-norm constraint; is the original post-stack seismic data, is the balance factor, used to adjust the weights of different constraint terms; is the sparsity constraint term weight, is the auxiliary vector, is the seismic wavelet matrix, is the linearized frequency-divided operator; is the objective function for jointly optimizing the variables r and x .

[0008] In some preferred embodiments, to solve the approximate optimal solution, the method is as follows: B 1. Initialize the parameters, set the initial value of the auxiliary vector to 0, and the initial value of the reflection coefficient vector to , and define the regularization parameter and the balance factor ; B 2. Solve for the reflection coefficient: ; where k is the iteration number index, is the reflection coefficient of the k+ first iteration, is the auxiliary vector of the k iteration, is the linearized frequency division operator of the k iteration; is the optimal value solution function for minimizing the objective function r ; B 3. Based on the reflection coefficient, in combination with the soft threshold method, determine the auxiliary vector: ; where is the auxiliary vector of the k+ first iteration; is the optimal value solution function for minimizing the objective function x ; B 4. Update the linearized frequency division operator according to the updated auxiliary vector; ; where is the linearized frequency division operator of the k+ first iteration; B 5. When the algorithm converges, obtain the approximate optimal solution of the stable deconvolution objective function; otherwise, return to step B 2 for the next iteration.

[0009] A second aspect of the present invention proposes a stable deconvolution system based on hybrid norm constraint and frequency band optimization, and the system includes: A data acquisition module configured to acquire seismic data and perform preprocessing; A linearized frequency division operator generation module configured to obtain a linearized frequency division operator based on the preprocessed seismic data; A target function generation module, configured to establish a stable deconvolution target function with sparsity constraints and mixed norm constraints based on a linearized frequency division operator with the goal of minimizing the matching error; ADMM A solution module, configured to decompose the stable deconvolution target function into several sub-problems based on the alternating direction method of multipliers framework, and solve an approximate optimal solution by alternately optimizing and updating each variable; the variables include reflection coefficients, auxiliary variables, and a linearized frequency division operator; when the termination criterion is met, the iteration terminates, and the variables obtained in the last iteration are used as the approximate optimal solution of the stable deconvolution target function and output as the stable deconvolution result.

[0010] A third aspect of the present invention proposes an electronic device, including: At least one processor; and A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned stable deconvolution method based on mixed norm constraints and frequency band optimization.

[0011] Advantages of the present invention: Based on mixed norm sparsity constraints and a linearized frequency division operator, combined with an iterative optimization mechanism, the output deconvolution result not only retains the dominant frequency band characteristics of seismic data but also can finely restore the details of the geological structure, such as geological features like small and medium-scale fractures, fissures, and cavities, effectively improving the imaging accuracy and making the deconvolution result clearer and more accurate; it avoids problems such as the inability of traditional deconvolution methods to accurately restore complex geological structures and inaccurate frequency band control, is applicable to the fine identification of details such as small and medium-scale fractures in complex geological environments, and can effectively improve the fracture identification accuracy and the reliability of reservoir prediction; Based on the frequency band optimization operator, the high signal-to-noise ratio (SNR) frequency band is dynamically selected through a weight formula, suppressing the contribution of the low signal-to-noise ratio frequency band; further, through the combination of mixed norm sparsity constraints and a linearized frequency division operator, the output deconvolution result can not only maintain the sparsity of the reflection coefficient but also effectively control the frequency band range, avoiding problems such as excessive enhancement or distortion of frequency components, ensuring that the dominant frequency band range during the deconvolution process is consistent with the actual seismic data, and avoiding problems of structural and lithological artifacts caused by traditional deconvolution methods over-improving the resolution, thus ensuring the authenticity and accuracy of the deconvolution result; The linearized frequency division operator is incorporated into the ADMM iteration framework as an optimization variable, enabling its dynamic update during the reflection coefficient estimation process, overcoming the limitations of traditional methods that use fixed operators, and making the optimization process more robust and adaptive. By optimizing the reflection coefficient and precisely controlling the frequency band range, the continuity and identifiability of the fault can be effectively enhanced, especially in a low signal-to-noise ratio environment. An adaptive parameter adjustment mechanism is provided to dynamically adjust the regularization parameter according to the data characteristics of the work area, ensuring an ideal deconvolution effect under different signal-to-noise ratio conditions and taking into account the requirements of both high and low signal-to-noise ratio scenarios. Brief Description of the Drawings

[0012] Other features, objects, and advantages of the present application will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings. Figure 1 is a flowchart of the stable deconvolution method based on hybrid norm constraint and frequency band optimization of the present invention; Figure 2 is a map of the original post-stack data in the shallow layer of the work area in an embodiment of the present invention; Figure 3 is a map of the processed data of stable deconvolution in the shallow layer of the work area in an embodiment of the present invention; Figure 4 is a map of the original post-stack data of any line in the deep layer of the work area in an embodiment of the present invention; Figure 5 is a map of the processed data of stable deconvolution of any line in the deep layer of the work area in an embodiment of the present invention; Figure 6 is the original RTM data coherence body attribute map of a certain layer in the work area; Figure 7 is the data coherence body attribute map of stable deconvolution of a certain layer in the work area in an embodiment of the present invention. Detailed Description of the Embodiments

[0013] The present application will be further described in detail below with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related invention and are not intended to limit the invention. Additionally, it should be noted that for the convenience of description, only parts related to the relevant invention are shown in the drawings.

[0014] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and embodiments.

[0015] The present invention constructs an iterative objective function containing a mixed - norm constraint, combines a linearized frequency - division operator to dynamically balance the target dominant frequency band, solves for the high - resolution reflection coefficient, and finally outputs seismic data with excellent amplitude preservation and a reasonable frequency band; uses the linearized frequency - division operator to perform frequency division on seismic data to accurately extract the target dominant frequency components; and by combining the mixed - norm constraint, optimizes the sparsity of the reflection coefficient, enabling the deconvolution result to not only maintain sparsity but also accurately match the dominant frequency band in the seismic data, thereby preventing distortion or over - enhancement of frequency components during the deconvolution process.

[0016] A stable deconvolution method based on mixed - norm constraint and frequency - band optimization of the present invention includes the following steps: S 1. Obtain seismic data and perform pre - processing, and obtain a linearized frequency - division operator based on the pre - processed seismic data; S 2. With the goal of minimizing the matching error, based on the linearized frequency - division operator, establish a stable deconvolution objective function with sparsity constraint and mixed - norm constraint; S 3. Based on the alternating direction method of multipliers (ADMM) framework, decompose the stable deconvolution objective function into several sub - problems, and solve for the approximate optimal solution by alternately optimizing and updating each variable; The variables include the reflection coefficient, auxiliary variables, and the linearized frequency - division operator; S 4. When the termination criterion is met, terminate the iteration, and use the variables obtained in the last iteration as the approximate optimal solution of the stable deconvolution objective function, and output it as the stable deconvolution result.

[0017] To more clearly illustrate the stable deconvolution method of the present invention based on mixed - norm constraint and frequency - band optimization, the following will detail each step in Figure 1 the embodiments of the present invention.

[0018] The stable deconvolution method based on mixed - norm constraint and frequency - band optimization in the first embodiment of the present invention includes the following steps S Steps 1~ S 4 are described in detail as follows: S 1. Obtain seismic data and perform pre - processing, obtain the original post - stack seismic data based on the original seismic data, and obtain a linearized frequency - division operator based on the original post - stack seismic data. The method is as follows: A 1. Perform a Fourier transform on the original post - stack seismic data to obtain a frequency - domain signal; A 2. Based on the central frequency and bandwidth, define a zero - phase band - pass filter, and obtain a multi - band - pass filter by weighting the zero - phase band - pass filter; A 3. Filter the frequency-domain signal based on the multi-bandpass filter, then obtain the time-domain signal through inverse Fourier transform and linearize it to obtain a linearized frequency-division operator.

[0019] Preferably, to obtain the multi-bandpass filter, the method is as follows: Define a zero-phase bandpass filter : ; where is the center frequency, is the bandwidth, is the frequency variable of the frequency band; extract the dominant frequency band from the original data and adjust the center frequency and the bandwidth according to the spectral characteristics of the actual data; Select the dominant frequency band according to the conformity of different frequency bands to the geological structure, and perform weighted superposition: ; where is the zero-phase bandpass filter corresponding to each frequency band, is the number of frequency bands; is the weight corresponding to each frequency band.

[0020] Further preferably, the weight is dynamically adjusted according to the conformity of the frequency band to the target geological structure, and the method is as follows: ; where is the adaptive weight of the th frequency band, is the signal-to-noise ratio of the th frequency band, is the th frequency band and the correlation coefficient of the target geological structure, is the corresponding .

[0021] Further preferably, the linearized frequency-division operator is specifically: ; where is the representation of the Tukey windowing function in the frequency domain, reducing the spectral leakage and oscillation generated when the frequency-domain signal is truncated, i.e., the Gibbs effect; is the Fourier transform of the original seismic data, is the inverse Fourier transform.

[0022] In this application, the linearized frequency division operator preserves the linear characteristics of the target frequency in the seismic record and avoids phase distortion. By optimizing data in different frequency bands, analyzing the compliance of data in different frequency bands with the target geological structure, the filtering operator is finally determined to obtain the dominant frequency components. By introducing the linearized frequency division operator, not only the frequency range in the deconvolution process is controlled, but also the sparsity of the reflection coefficient within the target frequency band is ensured. In this way, during the deconvolution process, both the artifacts caused by excessive enhancement of frequency components are avoided, and the deconvolution result is ensured not to deviate from the actual seismic data frequency band.

[0023] S 2. With the goal of minimizing the matching error, based on the linearized frequency division operator, a stable deconvolution objective function with sparsity constraints and mixed norm constraints is established: ; where represents the matching error between the reflection coefficient and the observed data; represents the sparsity of the reflection coefficient under the L 1-norm; is the L 2-norm constraint; is the original post-stack seismic data, is the balance factor used to adjust the weights of different constraint terms; is the weight of the sparsity constraint term, is the auxiliary vector, is the seismic wavelet matrix, is the linearized frequency division operator; is the objective function for jointly optimizing the variables r and x.

[0024] The optimization objective of this objective function consists of three parts: the first term represents the matching error between the reflection coefficient and the observed data. By minimizing this term, the characteristics of the real seismic data can be maximally retained; the second term uses the L 1-norm to maintain the sparsity of the reflection coefficient, ensuring that only the components that make important contributions to seismic reflections are retained during the optimization process, and noise and non-dominant frequency band interference are removed; the third term L the 2-norm constraint constrains the relationship between the auxiliary vector and the linearized frequency division operator through the balance term so that the reflection coefficient matches the frequency-divided signal within the dominant frequency band, thereby maintaining the stability and consistency of the solution during the iteration process.

[0025] By introducing the L 1 and L 2 mixed norm constraints of the reflection coefficient during the deconvolution process, using LThe 1-norm preserves the sparsity of the deconvolution result, thereby reducing random errors and improving resolution. Considering the actual data situation, the dominant frequency band in seismic data is preferably selected, and the L2-norm is used to improve the conformity between the deconvolution result and the dominant frequency band data, ensuring the fidelity. Through these two constraints, both the resolution of seismic data can be improved, and the structural and lithological artifacts caused by excessive resolution improvement can be avoided, thus ensuring the resolution and accuracy of the deconvolution result.

[0026] S 3. Decompose the stable deconvolution objective function into several sub-problems based on the alternating direction method of multipliers (ADMM) framework, and solve the approximate optimal solution by alternately optimizing and updating each variable. The variables include the reflection coefficient, the auxiliary variable, and the linearized frequency division operator.

[0027] Preferably, the method for solving the approximate optimal solution is as follows: B 1. Perform parameter initialization. Let the initial value of the auxiliary vector be and the initial value of the reflection coefficient vector be . Define the regularization parameter and the balancing factor . ; B 2. Solve for the reflection coefficient , and update the reflection coefficient to : ; where k is the iteration index, is the reflection coefficient at the k+ -th iteration, is the auxiliary vector at the k -th iteration, and is the linearized frequency division operator at the k -th iteration; is the optimal value solving function for minimizing the objective function r . B 3. Based on the reflection coefficient and combined with the soft thresholding method, update the auxiliary vector to : Fix the reflection coefficient vector , and use the soft thresholding method to solve the L 1-norm problem: ; where is the auxiliary vector at the k+ -th iteration; is the optimal value solving function for minimizing the objective function x . B 4. Update the linearized frequency division operator according to the updated auxiliary vector; Explicitly update the linearized frequency division operator to to balance the constraint deviation: ; where is the linearized frequency division operator for the k+ 1st iteration, adjust the balance of the constraint conditions to further optimize the estimation of the auxiliary vector; B 5. When the algorithm converges, obtain an approximate optimal solution of the stable deconvolution objective function; otherwise, return to step B 2 for the next iteration.

[0028] Preferably, in this embodiment, when solving the linear optimization problem of the reflection coefficient, the conjugate gradient method is used to accelerate the solution process.

[0029] Preferably, in this embodiment, use L the 1-norm to sparsify the auxiliary vector to ensure that only important geological features are retained. During this process, control the sparsity, with typical values ranging from 0.1 to 1.0, and the soft threshold is , with the value set to 1:3 to 1:5 to control the sparsity degree of the reflection coefficient. The higher the threshold, the fewer the retained reflection coefficients and the stronger the sparsity.

[0030] The hybrid norm of the present invention avoids overfitting or frequency band distortion caused by a single constraint by coordinating sparsity and frequency band matching constraints; while the linearized frequency division operator accurately extracts the dominant frequency components matching the target geological structure through dynamic optimization of multi-frequency band weights and window filtering, and restricts the sparsity of the deconvolution process only within the effective frequency band. The combination of the two enables the present invention to suppress noise interference while avoiding high-frequency oscillation or phase distortion problems in traditional methods, thereby achieving sharpened fault boundaries and improved thin layer resolution under low signal-to-noise ratio conditions.

[0031] S 4. When the termination criterion is met, terminate the iteration, take the variable obtained in the last iteration as the approximate optimal solution of the stable deconvolution objective function, and output it as the stable deconvolution result.

[0032] Preferably, when the algorithm converges, the termination criterion is met: ; where k is the iteration number index, is the reflection coefficient for the k+ 1st iteration, is thek The reflection coefficient of the next iteration tol is a preset threshold value.

[0033] Preferably, in this embodiment, the preset threshold value tol is taken as 10 -5 , and for low signal-to-noise ratio data, it can be relaxed to 10 -4 to accelerate convergence.

[0034] By continuously iteratively optimizing the reflection coefficient and linearizing the frequency division operator, not only the frequency range in the deconvolution process is controlled, but also the sparsity of the reflection coefficient within the target dominant frequency range is ensured; multiple reflections and distortion components are gradually removed, making the seismic data clearer after each round of iteration. In the deconvolution process, it not only avoids the structural and lithological artifacts caused by excessive enhancement of frequency components, but also ensures that the deconvolution result does not deviate from the actual seismic data frequency band; especially in a low signal-to-noise ratio environment, the present invention can better restore the details of small-scale fractures and complex geological bodies, effectively reduce noise interference, and improve the imaging accuracy. Generally speaking, the present invention improves the quality and usability of seismic data by optimizing the sparsity of the reflection coefficient. Especially under low signal-to-noise ratio conditions, it demonstrates its unique advantages and provides a more reliable technical guarantee for seismic exploration and underground structure identification.

[0035] Preferably, in this embodiment, a stable deconvolution method based on hybrid norm constraint and frequency band optimization is adopted to test the effectiveness of the present invention on the actual RTM post-stack data of a certain work area.

[0036] As Figure 2 shown, it shows the post-stack profile of a line in the shallow area of this work area. The data contains 331 seismic traces, 1200 time sampling points, the sampling interval is 1 millisecond, and the set parameters are μ = 0.3 , λ = 1.2, and the soft threshold is 0.25. In terms of frequency band selection, according to the actual spectral characteristics analysis, four main frequency bands are selected, and they are adaptively weighted according to their contribution degrees to the seismic data: the low frequency band (0 - 10 Hz ) retains the macroscopic geological information; the mid-low frequency band (11 - 30 Hz ) reflects the response of medium-scale geological bodies, balancing resolution and stability; the mid-high frequency band (31 - 45 Hz ) usually contains the details of small-scale fractures, but may be accompanied by higher noise. Therefore, the weighting algorithm dynamically adjusts its weight according to the contribution degree of the frequency band and the noise level to retain the effective signal and suppress noise; the high frequency band (46 - 60 Hz ) is mainly high-frequency noise, so the algorithm assigns a low weight to improve the signal-to-noise ratio. After being processed by this method, as Figure 3As shown, the fault features (indicated by arrows) become clearer, and the continuity and distinguishability of the in-phase axis are significantly improved compared to the original RTM post-stack data.

[0037] For example, Figure 4 as shown, the post-stack profile of an arbitrary line in the deep area of the work area is subjected to stable deconvolution. The data contains 291 seismic traces, 1200 time sampling points, and the sampling interval is 1 millisecond. The processing results are as shown in Figure 5 As shown, the fault features (indicated by arrows) are more distinguishable, and the continuity and structural details of the in-phase axis are improved compared to the original RTM data. This improvement not only enhances the resolution of the seismic imaging profile but also further verifies the effectiveness of the algorithm of the present invention in improving data quality, especially in enhancing fault resolution and detail presentation, providing a more reliable basis for geological analysis.

[0038] Seismic attribute volume analysis is performed on the data before and after processing. For example, Figure 6 as shown, it is the coherence volume attribute of the original RTM data of a certain horizon in this work area, Figure 7 while

[0039] shows the coherence volume attribute after being processed by the method of the present invention. It can be clearly seen by comparison that the processed data makes the overall structure of the fault zone clearer, the continuity and distribution characteristics of the faults more prominent, especially in the performance of small-scale faults and local structures. Compared with the unprocessed data, the processed data has higher resolution, thus making the identification and analysis of complex geological bodies more accurate and providing more effective support for geological exploration.

[0040] In the above embodiments, although the various steps are described in the above sequential order, those skilled in the art can understand that in order to achieve the effects of this embodiment, different steps do not have to be executed in such an order. They can be executed simultaneously (in parallel) or in a reversed order, and these simple changes are all within the protection scope of the present invention.

[0040] The stable deconvolution system based on hybrid norm constraint and frequency band optimization according to the second embodiment of the present invention, the system includes: A data acquisition module configured to acquire seismic data and perform preprocessing; A linearized frequency-divided operator generation module configured to obtain a linearized frequency-divided operator based on the preprocessed seismic data; A target function generation module configured to establish a stable deconvolution target function with sparsity constraint and hybrid norm constraint based on the linearized frequency-divided operator with the goal of minimizing the matching error; ADMMA solution module, configured to decompose the stable deconvolution objective function into several sub-problems based on the alternating direction method of multipliers framework, and solve an approximate optimal solution by alternately optimizing and updating each variable; the variables include reflection coefficients, auxiliary variables, and linearized frequency division operators; when the termination criterion is met, the iteration terminates, and the variables obtained in the last iteration are used as the approximate optimal solution of the stable deconvolution objective function and output as the stable deconvolution result.

[0041] It should be noted that the stable deconvolution system based on mixed norm constraint and frequency band optimization provided in the above embodiments is only illustrated by dividing the above functional modules. In actual applications, the above functions can be allocated to different functional modules according to needs, that is, the modules or steps in the embodiments of the present invention can be further decomposed or combined. For example, the modules in the above embodiments can be combined into one module, or further split into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing each module or step, and are not regarded as an improper limitation of the present invention.

[0042] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working process and related descriptions of the above-described system can refer to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0043] An electronic device according to a third embodiment of the present invention includes: At least one processor; and A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned stable deconvolution method based on mixed norm constraint and frequency band optimization.

[0044] A computer-readable storage medium according to a fourth embodiment of the present invention stores computer instructions, and the computer instructions are used to be executed by a computer to implement the above-mentioned stable deconvolution method based on mixed norm constraint and frequency band optimization.

[0045] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working process and related descriptions of the above-described electronic device and computer-readable storage medium can refer to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0046] Those skilled in the art should be able to realize that the modules and method steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of both. The programs corresponding to the software modules and method steps can be placed in random access memory ( RAM ), internal memory, read-only memory ( ROM ), electrically programmable ROM , electrically erasable programmable ROM , registers, hard disks, removable disks, CD - ROM ), or any other form of storage medium known in the art. To clearly illustrate the interchangeability of electronic hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in the form of electronic 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 implementation should not be considered to exceed the scope of the present invention.

[0047] Computer program code for performing the operations of the present application can be written in one or more programming languages or combinations thereof. The above programming languages include object-oriented programming languages - such as Java , Smalltalk , C ++, and also include conventional procedural programming languages - such as the " C " language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network - including a local area network ( LAN ) or a wide area network ( WAN ), or can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0048] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functions, and operations of possible implementations of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code that contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions noted in the blocks may occur in a different order than that noted in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0049] The terms "first", "second", etc. are used to distinguish similar objects and not to describe or indicate a specific order or sequence.

[0050] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device that comprises a series of elements includes not only those elements but also other elements not expressly listed, or elements that are inherent to those process, method, article, or apparatus / device.

[0051] So far, the technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A stable deconvolution method based on mixed norm constraint and frequency band optimization, characterized in that The method comprises the following steps: Obtain seismic data and perform preprocessing, and obtain a linearized frequency-divided operator based on the preprocessed seismic data; With the goal of minimizing the matching error, based on the linearized frequency-divided operator, establish a stable deconvolution objective function with sparsity constraints and mixed-norm constraints; Based on the alternating direction method of multipliers (ADMM) framework, decompose the stable deconvolution objective function into several sub-problems, and solve for an approximate optimal solution by alternately optimizing and updating each variable; the variables include reflection coefficients, auxiliary variables, and the linearized frequency-divided operator; When the termination criterion is met, the iteration terminates, and the variables obtained in the last iteration are used as the approximate optimal solution of the stable deconvolution objective function, and the output is the stable deconvolution result.

2. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 1, wherein The method for obtaining a linearized frequency-divided operator based on the seismic data is as follows: A 1. Perform Fourier transform on the preprocessed seismic data to obtain the frequency-domain signal; A 2. Define a zero-phase band-pass filter based on the center frequency and bandwidth, and weight the zero-phase band-pass filter to obtain a multi-band-pass filter; A 3. Filter the frequency-domain signal based on the multi-bandpass filter, then obtain the time-domain signal through inverse Fourier transform and linearize it to obtain a linearized frequency division operator.

3. The stable deconvolution method based on mixed norm constraint and frequency band optimization according to claim 2, wherein The method for obtaining a multi-bandpass filter is as follows: Define zero-phase band-pass filter : ； Among them, is the center frequency, is the bandwidth, is the frequency variable of the frequency band; Select dominant frequency bands according to the compliance of different frequency bands with the geological structure, and perform weighted superposition: ； Among them, is a zero-phase band-pass filter corresponding to each frequency band, is the number of frequency bands; is the weight corresponding to each frequency band.

4. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 3, wherein The weight is dynamically adjusted according to the degree of conformity between the frequency band and the target geological structure. The method is as follows: ； Among them, is the adaptive weight of the th frequency band, is the signal-to-noise ratio of the th frequency band, is the correlation coefficient between the th frequency band and the target geological structure, is the corresponding .

5. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 3, wherein The linearized frequency-divided operator is specifically: ； Among them, is Tukey the representation of the window function in the frequency domain, is the Fourier transform of the original seismic data, is the inverse Fourier transform.

6. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 1, characterized in that With the goal of minimizing the matching error, based on the linearized frequency-divided operator, the method for establishing a stable deconvolution objective function with sparsity constraints and mixed-norm constraints is as follows: ； Among them, represents the matching error between the reflection coefficient and the observed data; represents the sparsity of the reflection coefficient under the L 1-norm; is the L 2-norm constraint; is the original post-stack seismic data, is the balancing factor, used to adjust the weights of different constraint terms; is the weight of the sparsity constraint term, is the auxiliary vector, is the seismic wavelet matrix, is the linearized frequency-divided operator; is the objective function for jointly optimizing the variables r and x ​ 7. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 6, wherein The method for solving for an approximate optimal solution is as follows: B 1. Initialize the parameters. Let the initial value of the auxiliary vector be 0 and the initial value of the reflection coefficient vector be , and define the regularization parameter and the balance factor ; B 2. Solve for the reflection coefficient: ； Among them, k is the iteration number index, is the reflection coefficient of the k+ 1st iteration, is the auxiliary vector of the k th iteration, is the linearized frequency division operator of the k th iteration; is the optimal value solving function for minimizing the objective function r ; B 3. Determine an auxiliary vector based on the reflection coefficient and in combination with a soft threshold method: ； Among them, is the auxiliary vector for the k+ first iteration; is the optimal value solving function for minimizing the objective function x ; B 4. Update the linearized frequency division operator according to the updated auxiliary vector; ； Among them, is the linearized frequency division operator for the k+ first iteration; B 5. When the algorithm converges, an approximate optimal solution of the stable deconvolution objective function is obtained; otherwise, return to step B 2 for the next round of iteration.

8. The stable deconvolution method based on hybrid norm constraint and frequency band optimization according to claim 7, wherein When the algorithm converges, the termination criterion is met: ； Among them, k is the iteration number index, is the reflection coefficient of the k+ first iteration, is the reflection coefficient of the k th iteration, tol is the preset threshold.

9. A stable deconvolution system based on hybrid norm constraint and frequency band optimization, characterized in that, The system comprises: A data acquisition module configured to obtain seismic data and perform preprocessing; A linearized frequency-divided operator generation module configured to obtain a linearized frequency-divided operator based on the preprocessed seismic data; An objective function generation module configured to, with the goal of minimizing the matching error, based on the linearized frequency-divided operator, establish a stable deconvolution objective function with sparsity constraints and mixed-norm constraints; ADMM A solution module, configured to decompose the stable deconvolution objective function into a number of sub-problems based on the alternating direction method of multipliers framework, update each variable by alternating optimization, and solve for an approximate optimal solution; the variables include reflection coefficients, auxiliary variables, and linearized frequency division operators; when a termination criterion is met, the iteration terminates, and the variables obtained in the last iteration are used as the approximate optimal solution of the stable deconvolution objective function, and the output is the stable deconvolution result.

10. An electronic device, characterized in that, Comprises: At least one processor; And A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the stable deconvolution method based on mixed-norm constraints and frequency-band optimization according to any one of claims 1-8.

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