Method and device for quickly imaging stratigraphic structure by using variable-frequency wavelet convolution
The stratigraphic structure is imaged through the variable frequency wave convolution method, which solves the problem of low forward simulation efficiency of stratigraphic structure in seismic data processing, and realizes rapid imaging and accurate multiple wave prediction, which is suitable for the processing of seismic data of complex underground geological structures.
Patent Information
- Application Number
- CN202410113218.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-01-26
- Publication Date
- 2025-07-29
AI Technical Summary
When processing seismic data, conventional methods have low imaging efficiency for forward simulation of stratigraphic structures, especially in stratigraphic complexes with complex fracture structures, which requires repeated modification of the velocity model, resulting in too long processing time.
The variable frequency wave convolution method is adopted to perform convolutional calculations on the reflective coefficient data body and the layer-controlled variable frequency waves to generate an imaging data body, which objectively reflects the main frequency response characteristics of the underground structure.
The forward simulation imaging speed of stratigraphic structure interpretation has been greatly improved, and the imaging process can be completed within ten minutes, providing reliable technical support for multiple wave prediction of earthquake data in complex underground geological structures, meeting the needs of fine processing of earthquake data.
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Figure CN120386031A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of processing seismic data in physical exploration of spheres, and particularly to a method and device for quickly imaging formation structures by using convolution of frequency-variable wavelets. Background Art
[0002] In the processing of seismic data, prediction and suppression of multiple waves have become routine tasks. Precise prediction of multiple waves usually requires establishing a formation structure model and imaging it. Therefore, using the imaging data of the formation interpretation model to predict multiple waves and analyzing their influence on the target layer has become an important means of processing. Usually, a velocity model is established using the interpreted formation, forward modeling is performed using the acoustic wave equation, then the single-shot data after simulation is subjected to migration imaging, and then the multiple waves are predicted using the imaging data after simulation to analyze the influence range of the multiple waves on the target layer. Completing this process often takes 1-2 days. However, for formations with complex fault structures, the velocity model needs to be repeatedly modified, and the completion time will be longer, resulting in low efficiency. Therefore, there is an urgent need for a method and device that can quickly image formation structures to provide a reliable basis for efficiently and accurately predicting the influence of multiple waves on the target layer.
[0003] Based on this technical background, the present invention has studied a method and device for quickly imaging formation structures by using convolution of frequency-variable wavelets. Summary of the Invention
[0004] Aiming at the deficiencies of the prior art, the present invention provides a method and device for quickly imaging formation structures by using convolution of frequency-variable wavelets. This method obtains an imaging data volume through convolution operation on the reflection coefficient data volume and the layer-controlled frequency-variable wavelet, objectively reflecting the main frequency response characteristics of the underground structure, solving the problem of low efficiency in forward modeling and imaging formation structures using conventional methods, providing strong technical support for the prediction and processing of multiple waves in seismic data of complex underground geological structures, and meeting the requirements of fine processing of seismic data.
[0005] To achieve the above object, the first aspect of the present invention provides a method for quickly imaging formation structures by using convolution of frequency-variable wavelets, including:
[0006] Obtaining a reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple wave suppression and well logging information;
[0007] Generating a layer-controlled frequency-variable wavelet using a wavelet processing tool based on the main frequency of each interpreted formation;
[0008] Performing convolution operation on the reflection coefficient data volume and the layer-controlled frequency-variable wavelet to obtain an imaging data volume.
[0009] The second aspect of the present invention provides a device for quickly imaging a formation structure by using frequency-variable wavelet convolution, including:
[0010] A data volume acquisition module, configured to obtain a reflection coefficient data volume of a formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple wave suppression and well logging information;
[0011] A frequency-variable wavelet generation module, configured to generate a layer-controlled frequency-variable wavelet by using a wavelet processing tool based on the main frequency of each interpreted formation;
[0012] A convolution operation module, configured to perform convolution operation on the reflection coefficient data volume and the layer-controlled frequency-variable wavelet to obtain an imaging data volume.
[0013] The third aspect of the present invention provides an electronic device, which includes:
[0014] A memory, storing executable instructions;
[0015] A processor, which runs the executable instructions in the memory to implement the method for quickly imaging a formation structure by using frequency-variable wavelet convolution according to the first aspect.
[0016] The fourth aspect of the present invention provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, it implements the method for quickly imaging a formation structure by using frequency-variable wavelet convolution according to the first aspect.
[0017] The beneficial effects of the present invention include:
[0018] (1) The method for quickly imaging a formation structure by using frequency-variable wavelet convolution proposed by the present invention obtains an imaging data volume by performing convolution operation on the reflection coefficient data volume and the layer-controlled frequency-variable wavelet, objectively reflects the main frequency response characteristics of the underground structure, solves the problem of low efficiency in forward modeling and imaging of formation structures by using conventional methods, provides strong technical support for multiple wave prediction and processing of seismic data of complex underground geological structures, and meets the requirements of fine processing of seismic data.
[0019] (2) The method for quickly imaging a formation structure by using frequency-variable wavelet convolution proposed by the present invention is based on the Ricker wavelet and uses the convolution method to quickly image the formation structure, objectively reflects the main frequency response characteristics of the underground structure, greatly improves the forward modeling and imaging speed of formation structure interpretation, can complete the entire imaging process within ten minutes, and provides a more practical supporting technology for accurate prediction of multiple waves of imaging data of complex underground geological structures.
[0020] Other features and advantages of the present invention will be described in detail in the following specific implementation part. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] The above and other objects, features, and advantages of the present invention will become more apparent by describing the exemplary embodiments of the present invention in more detail with reference to the accompanying drawings.
[0022] Figure 1 It is a schematic flow diagram of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0023] Figure 2 It is a schematic diagram of a directed acyclic graph for calculating a path in a Spark framework in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0024] Figure 3 It is a schematic diagram of formation frequency spectrum analysis and main frequency statistics after calibration in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0025] Figure 4 It is a quality control chart of interpreted structural formations and reflection coefficient information in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0026] Figure 5 It is a schematic diagram of a variable-frequency wavelet device and its Ricker wavelet curves with different main frequencies in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0027] Figure 6 It is a schematic diagram for comparing wavelet convolution imaging profiles in different ways in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention.
[0028] Figure 7 It is a schematic diagram of the effect of multiple wave prediction on a variable wavelet convolution imaging profile in a specific embodiment of a method for quickly imaging a formation structure using variable-frequency wavelet convolution proposed by the present invention. Specific Embodiment
[0029] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein.
[0030] The present invention provides a method for quickly imaging a formation structure using variable-frequency wavelet convolution, as Figure 1 shown, including:
[0031] Obtaining a reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple wave suppression and well logging information;
[0032] Based on the main frequency of each interpreted formation, a layer-controlled variable-frequency wavelet is generated using a wavelet processing tool;
[0033] The imaging data volume is obtained by performing convolution operation on the reflection coefficient data volume and the layer-controlled variable-frequency wavelet.
[0034] In the present invention, the imaging data volume is obtained by performing convolution operation on the reflection coefficient data volume and the layer-controlled variable-frequency wavelet, objectively reflecting the main frequency response characteristics of the underground structure, solving the problem of low efficiency in forward modeling and imaging of formation structures using conventional methods, providing strong technical support for the prediction and processing of multiple waves in seismic data of complex underground geological structures, and meeting the requirements of fine processing of seismic data.
[0035] According to the present invention, obtaining the reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume and well logging information includes:
[0036] Based on the pre-multiple suppression migration imaging data volume, a data volume containing only spatial grid information is obtained;
[0037] Based on the pre-multiple suppression migration imaging data volume, structural formation information and the main frequency of each interpreted formation are obtained;
[0038] The structural formation information is placed into the data volume containing only spatial grid information to obtain an intermediate data volume;
[0039] The intermediate data volume is transformed into the reflection coefficient data volume of the formation using the reflection coefficient of the well logging information.
[0040] According to the present invention, obtaining the structural formation information and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume includes;
[0041] Based on the pre-multiple suppression migration imaging data volume, fine interpretation of the structural horizons of the calibrated formation is carried out in sequence, structural formation meshing is performed to obtain structural formation information, and hourly window statistical analysis is performed on the calibrated formation to obtain the main frequency of each interpreted formation.
[0042] According to the present invention, generating a layer-controlled variable-frequency wavelet based on the main frequency of each interpreted formation includes:
[0043] Using a wavelet processing tool, based on the main frequency of each interpreted formation, Ricker wavelets with different main frequencies for each formation are generated;
[0044] Create a layer-controlled variable-frequency wavelet device;
[0045] Based on the Ricker wavelets with different main frequencies for each formation, a layer-controlled variable-frequency wavelet is generated using the layer-controlled variable-frequency wavelet device.
[0046] Preferably, the imaging method of the present invention further includes the following steps:
[0047] Analyze the imaging data volume to obtain an analysis result.
[0048] According to the present invention, if the analysis result does not conform to the underground geological understanding, re-perform a fine interpretation of the structural horizons for the calibrated strata, and repeat the subsequent related operations until the analysis result conforms to the underground geological understanding.
[0049] According to the present invention, if the analysis result conforms to the underground geological understanding, perform subsequent multiple wave prediction processing work.
[0050] In the present invention, based on the Ricker wavelet, the method of convolution is used to perform rapid imaging of the stratigraphic structure, objectively reflecting the main frequency response characteristics of the underground structure, greatly improving the forward modeling imaging speed of stratigraphic structure interpretation, and the entire imaging process can be completed within ten minutes, providing a more practical supporting technology for the accurate prediction of multiple waves in complex underground geological structure imaging data.
[0051] The present invention will be described in more detail below through embodiments.
[0052] Embodiment 1:
[0053] As Figure 2 shown, this embodiment provides a method for rapid imaging of stratigraphic structure using variable-frequency wavelet convolution, and the specific steps are as follows:
[0054] 1) Load the migration imaging data volume before multiple wave suppression into the interpretation workstation, and create a data volume DATA1 in the processing system that only contains spatial grid information;
[0055] 2) Perform a fine interpretation of the structural horizons for the calibrated strata, and use a small time window to statistically analyze the main frequency f of each interpreted stratum n As Figure 3 shown;
[0056] 3) Grid the finely interpreted structural strata, and place the structural stratum information into the grid data volume DATA1 to form a data volume DATA2, as Figure 4 shown in a;
[0057] 4) Use the reflection coefficient in the logging information, as shown in Table 1 and Figure 4 shown in b, to convert DATA2 into a data volume DATA3 containing the reflection coefficient, as Figure 4 shown in c;
[0058] 5) Use the wavelet processing tool to generate Ricker wavelets with different main frequencies for each stratum according to the main frequency f of each interpreted stratum n , create a layer-controlled variable-frequency wavelet device WD, as Figure 5 shown in a, and the variable-frequency wavelet device can provide different wavelets W for different stratan , as shown in Figure 5 b, the imaging result can better reflect the main frequency characteristics of the formation;
[0059] 6) Convolve DATA3 and W n to obtain an imaging data volume DATA4, as shown in Figure 6 ;
[0060] 7) Provide DATA4 to the structural stratigraphic interpreter for analysis to determine whether it conforms to the underground geological understanding. If not, let the geological interpreter modify the structural stratigraphy again. If it conforms, subsequent multiple-wave prediction processing work can be carried out.
[0061] In this embodiment, Figure 6 is a comparison of the imaging profiles of different-wavelet convolutions. It can be seen that the variable-wavelet convolution with reflection coefficient for structural stratigraphic imaging is more consistent with the amplitude strength relationship of the actual seismic imaging in Figure 3 a and can reflect the main frequency response characteristics of the underground structure; from Figure 7 the perspective of multiple-wave prediction effect, the multiple waves have a greater impact on the imaging of high-steep structures (indicated by the arrows), which conforms to the understanding of the geological interpreter, indicating the reliability of the method for rapid imaging of formation structures by using variable-frequency wavelet convolution proposed by the present invention.
[0062] Table 1 Statistical table of main frequency and reflection coefficient of formation analysis
[0063]
[0064] Embodiment 2:
[0065] As shown in Figure 1 , a method for rapid imaging of formation structures by using variable-frequency wavelet convolution in this embodiment is as follows:
[0066] Obtain the reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple-wave suppression and well logging information;
[0067] Generate layer-controlled variable-frequency wavelets by using wavelet processing tools based on the main frequency of each interpreted formation;
[0068] Perform convolution operation on the reflection coefficient data volume and the layer-controlled variable-frequency wavelets to obtain an imaging data volume;
[0069] In this embodiment, obtaining the reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple-wave suppression and well logging information includes:
[0070] Obtain a data volume containing only spatial grid information based on the migration imaging data volume before multiple-wave suppression;
[0071] Obtain the structural stratigraphic information and the main frequency of each interpreted formation based on the migration imaging data volume before multiple suppression;
[0072] Place the structural stratigraphic information into the data volume containing only spatial grid information to obtain an intermediate data volume;
[0073] Use the reflection coefficient of well logging information to transform the intermediate data volume into the reflection coefficient data volume of the formation;
[0074] In this embodiment, obtaining the structural stratigraphic information and the main frequency of each interpreted formation based on the migration imaging data volume before multiple suppression includes;
[0075] Based on the migration imaging data volume before multiple suppression, perform fine interpretation of the structural horizons on the calibrated formation in sequence, perform structural stratigraphic meshing to obtain the structural stratigraphic information, and perform small time window statistical analysis on the calibrated formation to obtain the main frequency of each interpreted formation;
[0076] In this embodiment, based on the main frequency of each interpreted formation, generating a layer-controlled variable-frequency wavelet using a wavelet processing tool includes:
[0077] Use a wavelet processing tool to generate Ricker wavelets with different main frequencies for each formation according to the main frequency of each interpreted formation;
[0078] Create a layer-controlled variable-frequency wavelet device;
[0079] Based on the Ricker wavelets with different main frequencies for each formation, use the layer-controlled variable-frequency wavelet device to generate a layer-controlled variable-frequency wavelet;
[0080] The method in this embodiment further includes:
[0081] Analyze the imaging data volume to obtain an analysis result;
[0082] If the analysis result does not conform to the underground geological understanding, re-perform fine interpretation of the structural horizons on the calibrated formation, and repeat the subsequent related operations until the analysis result conforms to the underground geological understanding;
[0083] If the analysis result conforms to the underground geological understanding, perform the subsequent multiple prediction processing work.
[0084] Embodiment 3:
[0085] This embodiment provides a device for quickly imaging formation structures using variable-frequency wavelet convolution, including:
[0086] A data volume acquisition module, configured to obtain the reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the migration imaging data volume before multiple suppression and well logging information;
[0087] A variable-frequency wavelet generation module, configured to generate a layer-controlled variable-frequency wavelet using a wavelet processing tool based on the main frequency of each interpreted formation;
[0088] A convolution operation module for performing a convolution operation on a reflection coefficient data volume and a layer-controlled variable-frequency wavelet to obtain an imaging data volume;
[0089] In this embodiment, obtaining the reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the pre-multiple-wave-suppression migration imaging data volume and well logging information includes:
[0090] Obtaining a data volume containing only spatial grid information based on the pre-multiple-wave-suppression migration imaging data volume;
[0091] Obtaining structural formation information and the main frequency of each interpreted formation based on the pre-multiple-wave-suppression migration imaging data volume;
[0092] Placing the structural formation information into the data volume containing only spatial grid information to obtain an intermediate data volume;
[0093] Converting the intermediate data volume into the reflection coefficient data volume of the formation by using the reflection coefficient of the well logging information;
[0094] In this embodiment, obtaining the structural formation information and the main frequency of each interpreted formation based on the pre-multiple-wave-suppression migration imaging data volume includes;
[0095] Based on the pre-multiple-wave-suppression migration imaging data volume, performing a fine interpretation of the structural horizons on the calibrated formation in sequence, performing structural formation grid division to obtain the structural formation information, and performing a small-time-window statistical analysis on the calibrated formation to obtain the main frequency of each interpreted formation;
[0096] In this embodiment, generating a layer-controlled variable-frequency wavelet based on the main frequency of each interpreted formation by using a wavelet processing tool includes:
[0097] Using the wavelet processing tool to generate a Ricker wavelet with different main frequencies for each formation according to the main frequency of each interpreted formation;
[0098] Creating a layer-controlled variable-frequency wavelet device;
[0099] Generating a layer-controlled variable-frequency wavelet by using the layer-controlled variable-frequency wavelet device based on the Ricker wavelets with different main frequencies for each formation;
[0100] The method in this embodiment further includes:
[0101] Analyzing the imaging data volume to obtain an analysis result;
[0102] If the analysis result does not conform to the underground geological understanding, re-performing a fine interpretation of the structural horizons on the calibrated formation, and repeating the subsequent related operations until the analysis result conforms to the underground geological understanding;
[0103] If the analysis result conforms to the underground geological understanding, perform subsequent multiple-wave prediction processing work.
[0104] Example 4:
[0105] An embodiment of the present invention provides an electronic device including a memory and a processor.
[0106] The memory stores executable instructions.
[0107] The processor runs the executable instructions in the memory to implement a method for quickly imaging the formation structure using frequency-variable wavelet convolution.
[0108] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, and the computer program products may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory, etc. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.
[0109] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In an embodiment of the present invention, the processor is used to run the computer-readable instructions stored in the memory.
[0110] Those skilled in the art should understand that, in order to solve the technical problem of how to obtain a good user experience effect, this embodiment may also include well-known structures such as communication buses, interfaces, etc., and these well-known structures should also be included in the protection scope of the present invention.
[0111] For the detailed description of this embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, and details will not be repeated here.
[0112] Example 5:
[0113] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, it implements a method for quickly imaging the formation structure using frequency-variable wavelet convolution.
[0114] According to the computer-readable storage medium of the embodiment of the present invention, non-temporary computer-readable instructions are stored thereon. When the non-temporary computer-readable instructions are run by a processor, all or part of the steps of the methods of the foregoing embodiments of the present invention are executed.
[0115] The above computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROMs and DVDs), magneto-optical storage media (e.g., MOs), magnetic storage media (e.g., magnetic tapes or external hard drives), media with built-in rewritable non-volatile memories (e.g., memory cards), and media with built-in ROMs (e.g., ROM cartridges).
[0116] The method for rapidly imaging a formation structure by using frequency-converted wavelet convolution proposed in an embodiment of the present invention obtains an imaging data volume through a convolution operation on a reflection coefficient data volume and a layer-controlled frequency-converted wavelet, objectively reflecting the main frequency response characteristics of the underground structure, solving the problem of low efficiency in forward modeling and imaging of formation structures using conventional methods, providing strong technical support for the prediction and processing of multiple waves in seismic data of complex underground geological structures, and meeting the requirements for fine processing of seismic data.
[0117] The embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art in the technical field without departing from the scope and spirit of the described embodiments.
Claims
1. A method for quickly imaging formation structures using convolutional frequency-variable wavelets, characterized in that, Comprising: Obtaining a reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume and well logging information; Generating a layer-controlled variable-frequency wavelet based on the main frequency of each interpreted formation by using a wavelet processing tool; Performing convolution operation on the reflection coefficient data volume and the layer-controlled variable-frequency wavelet to obtain an imaging data volume.
2. The method according to claim 1, characterized in that, Obtaining a reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume and well logging information includes: Obtaining a data volume containing only spatial grid information based on the pre-multiple suppression migration imaging data volume; Obtaining structural formation information and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume; Placing the structural formation information into the data volume containing only spatial grid information to obtain an intermediate data volume; Converting the intermediate data volume into the reflection coefficient data volume of the formation by using the reflection coefficient of the well logging information.
3. The method according to claim 2, wherein Obtaining structural formation information and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume includes; Based on the pre-multiple suppression migration imaging data volume, successively performing fine interpretation of structural horizons on the calibrated formation, gridifying the structural formation to obtain structural formation information, and performing small-hour window statistical analysis on the calibrated formation to obtain the main frequency of each interpreted formation.
4. The method according to claim 3, characterized in that, Generating a layer-controlled variable-frequency wavelet based on the main frequency of each interpreted formation by using a wavelet processing tool includes: Using a wavelet processing tool to generate Ricker wavelets with different main frequencies for each formation according to the main frequency of each interpreted formation; Creating a layer-controlled variable-frequency wavelet device; Generating a layer-controlled variable-frequency wavelet based on the Ricker wavelets with different main frequencies for each formation by using the layer-controlled variable-frequency wavelet device.
5. The method according to claim 4, wherein Further comprising: Analyzing the imaging data volume to obtain an analysis result.
6. The method according to claim 5, wherein If the analysis result does not conform to the underground geological understanding, re-performing fine interpretation of structural horizons on the calibrated formation, and repeating the subsequent related operations until the analysis result conforms to the underground geological understanding.
7. The method according to claim 6, characterized in that, If the analysis result conforms to the underground geological understanding, performing subsequent multiple wave prediction processing work.
8. A fast imaging device for formation structure using variable-frequency wavelet convolution, characterized in that, Comprising: A data volume acquisition module for obtaining a reflection coefficient data volume of the formation and the main frequency of each interpreted formation based on the pre-multiple suppression migration imaging data volume and well logging information; A variable-frequency wavelet generation module for generating a layer-controlled variable-frequency wavelet based on the main frequency of each interpreted formation by using a wavelet processing tool; A convolution operation module for performing convolution operation on the reflection coefficient data volume and the layer-controlled variable-frequency wavelet to obtain an imaging data volume.
9. An electronic device, characterized in that, The electronic device includes: A memory storing executable instructions; A processor, the processor running the executable instructions in the memory to implement the method for quickly imaging the formation structure by using variable-frequency wavelet convolution according to any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the method for quickly imaging the formation structure by using variable-frequency wavelet convolution according to any one of claims 1-7.