Frequency expansion method, device and readable storage medium based on fast sparse inversion

Abstract

The present invention provides a frequency expansion method, device, and readable storage medium based on rapid sparse inversion, belonging to the technical field of seismic data processing. The method comprises: obtaining pre-stack seismic data; filtering the pre-stack seismic data using a filter operator to obtain filtered pre-stack seismic data; performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data; constructing a frequency inversion objective function based on the filtered pre-stack seismic data and a sparse inversion algorithm, with the transformed pre-stack seismic data as a constraint; iterating the frequency inversion objective function using a Lagrange multiplier method, updating the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is less than a preset update threshold or the number of iterations reaches a preset iteration threshold, and outputting the updated filtered pre-stack seismic data. The method has the advantages of high frequency inversion accuracy and data signal-to-noise ratio, can reduce the amount of calculation in the data processing process, and lowers the computational cost.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic data processing, and in particular to a frequency expansion method based on fast sparse inversion, a frequency expansion device based on fast sparse inversion, an electronic device and a readable storage medium. Background Art

[0002] During land-based seismic data acquisition, the collected data often lose low-frequency components due to the filtering effects of the earth, the limitations of artificial seismic sources, and interference from detector distortion and surface waves. In marine data processing, however, the lack of low-frequency components in the source itself, the low-frequency response of the detectors, and interference from ghost waves can lead to a loss of low-frequency and some high-frequency information. This loss of low-frequency components can easily lead to local minima in full waveform inversion results, significantly reducing the accuracy of seismic signal processing and interpretation. The loss of high-frequency components can also reduce processing resolution. Therefore, there is an urgent need for new technologies to extend seismic data at both low and high frequencies to improve the quality of subsequent data processing. Summary of the Invention

[0003] The purpose of the embodiments of the present invention is to provide a frequency expansion method, device and readable storage medium based on fast sparse inversion, so as to at least solve the above-mentioned problems that the lack of low-frequency components in seismic data will make the full waveform inversion results prone to local minima, greatly reducing the accuracy of seismic signal processing and interpretation, and the lack of high-frequency components will reduce the processing resolution.

[0004] In order to achieve the above object, the first aspect of the present invention provides a frequency expansion method based on fast sparse inversion, the method comprising:

[0005] Acquire pre-stack seismic data;

[0006] Filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0007] Performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0008] Based on the filtered pre-stack seismic data and a sparse inversion algorithm, a frequency inversion objective function is constructed with the transformed pre-stack seismic data as a constraint condition;

[0009] The frequency inversion objective function is iteratively solved using the Lagrange multiplier method, and the filtered pre-stack seismic data is updated until the update amount of the updated filtered pre-stack seismic data is less than a preset update threshold or the number of iterations reaches a preset iteration threshold. The updated filtered pre-stack seismic data is then output as the pre-stack seismic data after frequency expansion.

[0010] Optionally, before filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data, the method further includes:

[0011] Based on the effective frequency band of pre-stack seismic data, the frequency band where the noise is located and the frequency band to be inverted, a filtering operator is constructed;

[0012] The expression of the filtering operator is:

[0013] .

[0014] Optionally, the method is characterized in that performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data comprises:

[0015] The transformed pre-stack seismic data are obtained using the following calculation formula:

[0016] ;

[0017] in, is the transformed pre-stack seismic data; is the filtered pre-stack seismic data; n is the temporal number of the seismic data sampling points; j is an imaginary unit; k is the number of seismic data in the frequency domain, and .

[0018] Optionally, the sparse inversion algorithm is an L1 sparse inversion algorithm;

[0019] The Lagrange multiplier method is a double augmented Lagrange multiplier method.

[0020] Optionally, the frequency inversion objective function is expressed as:

[0021] ;

[0022] in, is the frequency inversion objective function; D is the data matrix of filtered pre-stack seismic data.

[0023] Optionally, the constraints of the frequency inversion objective function are:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] in, A is the discrete Fourier transform matrix; D is the data matrix of filtered pre-stack seismic data; B is the data matrix of transformed pre-stack seismic data; j Is an imaginary unit.

[0029] Optionally, update the filtered prestack seismic data using the following formula:

[0030] ;

[0031] in, For the m The data matrix of filtered pre-stack seismic data after iterations; is the sparse inversion parameter; is the preset vector; For the m -The data matrix of filtered prestack seismic data after 1 iteration; For the general All values ​​greater than 1 are set to 1; is the inverse Fourier transform; is the Fourier forward transform; are fitting parameters, and ; B is the data matrix of transformed pre-stack seismic data; N is the latitude of pre-stack seismic data, is a constant.

[0032] A second aspect of the present invention provides a frequency extension device based on fast sparse inversion, the device comprising:

[0033] A data acquisition module, used for acquiring pre-stack seismic data;

[0034] A data filtering module, configured to filter the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0035] a data denoising module, performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0036] An objective function establishment module is used to construct a frequency inversion objective function based on the filtered pre-stack seismic data and a sparse inversion algorithm, with the transformed pre-stack seismic data as a constraint condition;

[0037] The frequency expansion module is used to iteratively solve the frequency inversion objective function using the Lagrange multiplier method and update the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is less than the preset update threshold or the number of iterations reaches the preset iteration threshold, and then output the updated filtered pre-stack seismic data as the pre-stack seismic data after frequency expansion.

[0038] A third aspect of the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned frequency expansion method based on fast sparse inversion when executing the computer program.

[0039] On the other hand, the present invention further provides a readable storage medium having instructions stored thereon, the instructions being used to enable a machine to execute the above-mentioned frequency expansion method based on fast sparse inversion.

[0040] This technical solution can extend the frequency of missing data while keeping the original frequency components of the data unchanged. It has high frequency inversion accuracy and data signal-to-noise ratio, and can reduce the amount of calculation in the data processing process and reduce computing costs.

[0041] Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following detailed description, they are used to explain the embodiments of the present invention, but do not constitute a limitation of the embodiments of the present invention. In the accompanying drawings:

[0043] Figure 1 is a flow chart of a frequency expansion method based on fast sparse inversion provided by the present invention;

[0044] Figure 2 is a schematic diagram of pre-stack data and its spectrum provided by the present invention;

[0045] Figure 3 is a schematic diagram of pre-stack data and its spectrum after inversion provided by the present invention;

[0046] Figure 4 is a schematic diagram of pre-stack data with noise and its spectrum provided by the present invention;

[0047] Figure 5 Schematic diagram of pre-stack data and its spectrum after the noise band is padded provided by the present invention;

[0048] Figure 6 It is a schematic diagram of the single shot model data and its spectrum provided by the present invention;

[0049] Figure 7 Schematic diagram of filtered single shot model data and its spectrum provided by the present invention;

[0050] Figure 8 Schematic diagram of single-shot model data and its spectrum after frequency expansion provided by the present invention;

[0051] Figure 9 This is a schematic diagram comparing the low-frequency components of the original data provided by the present invention and the low-frequency components after extension of this solution;

[0052] Figure 10 It is a structural diagram of a frequency expansion device based on fast sparse inversion provided by an embodiment of the present invention.

[0053] Description of Reference Numerals

[0054] 10-data acquisition module; 20-data filtering module; 30-data denoising module;

[0055] 40-adjustment feedback device; 50-frequency expansion module. DETAILED DESCRIPTION

[0056] The following describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0057] Figure 1 is a flow chart of a frequency expansion method based on fast sparse inversion provided by the present invention; Figure 2 is a schematic diagram of pre-stack data and its spectrum provided by the present invention; Figure 3 is a schematic diagram of pre-stack data and its spectrum after inversion provided by the present invention; Figure 4 is a schematic diagram of pre-stack data with noise and its spectrum provided by the present invention; Figure 5 Schematic diagram of pre-stack data and its spectrum after the noise band is padded provided by the present invention; Figure 6 It is a schematic diagram of the single shot model data and its spectrum provided by the present invention; Figure 7 Schematic diagram of filtered single shot model data and its spectrum provided by the present invention; Figure 8 Schematic diagram of single-shot model data and its spectrum after frequency expansion provided by the present invention; Figure 9 This is a schematic diagram comparing the low-frequency components of the original data provided by the present invention and the low-frequency components after extension of this solution; Figure 10 It is a structural diagram of a frequency expansion device based on fast sparse inversion provided by an embodiment of the present invention.

[0058] like Figure 1As shown, an embodiment of the present invention provides a frequency expansion method based on fast sparse inversion, the method comprising:

[0059] Step 1: Obtain pre-stack seismic data;

[0060] Specifically, in this embodiment, Figure 2 As shown in (a), prestack seismic data refers to the raw seismic data acquired during seismic exploration. This data is obtained by transmitting a source signal underground through a seismic instrument and then receiving signals reflected and refracted by the subsurface rock. Prestack seismic data contains information about the reflection and refraction of the subsurface rock and can be used to study subsurface structure, lithology, and the distribution of oil and gas resources. Prestack seismic data processing is a key step in seismic exploration. During processing, the raw data must first be denoised to remove noise interference from the signal. Next, time-distance conversion is performed to convert the time information in the seismic records into subsurface depth information. Next, stacking is performed to combine multiple seismic records to enhance the intensity of the subsurface reflection information. Finally, velocity modeling and migration processing are required to obtain more accurate subsurface structural information. Prestack seismic data processing allows seismic explorers to obtain detailed information about the subsurface structure, providing important insights for oil and gas exploration, geological disaster prediction, and other areas. Prestack seismic data can also be used in earthquake research and monitoring, helping to understand the patterns and trends of seismic activity and improving the accuracy of earthquake early warnings.

[0061] Step 2: filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0062] In this embodiment, a filtering operator is constructed based on the effective frequency band of pre-stack seismic data, the frequency band where noise is located, and the frequency band to be inverted. The filtering operator is used to perform denoising. The filtering operator acts on the frequency domain data to filter out the frequency band containing noise in the data and suppress abnormal energy noise to ensure data accuracy.

[0063] The frequency value of the effective signal is set to 1, and the frequency value of the noise is set to 0. The expression of the filtering operator is:

[0064] .

[0065] Step 3: performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0066] In this embodiment, the following calculation formula is used to obtain the transformed pre-stack seismic data:

[0067] ;

[0068] in, is the transformed pre-stack seismic data, such as Figure 2 (b) shows the spectrum of the prestack seismic data after transformation; is the filtered pre-stack seismic data, such as Figure 2 (a) n is the temporal number of the seismic data sampling points; j is an imaginary unit; k is the number of seismic data in the frequency domain, and .

[0069] Step 4: Based on the filtered pre-stack seismic data and the sparse inversion algorithm, a frequency inversion objective function is constructed with the transformed pre-stack seismic data as a constraint condition;

[0070] In this embodiment, the sparse inversion algorithm is the L1 sparse inversion algorithm, which has the advantages of high inversion accuracy, less multi-solution, and low requirements on the number of well logs and the uniformity of distribution.

[0071] Among them, the expression of the frequency inversion objective function is:

[0072] ;

[0073] in, is the frequency inversion objective function; D is the data matrix of filtered pre-stack seismic data.

[0074] Using the above method, the value of the minimum solution of the L1 norm of the original data is solved, that is, the sparsest solution of data D is solved to invert the frequency of data missing. When the data D is sparser, the waveform of the seismic record is closer to the unit pulse and its frequency band is wider.

[0075] In this embodiment, the constraints of the frequency inversion objective function are:

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] in, A For the discrete Fourier transform matrix, the fast Fourier transform can be used to reduce the computational complexity from Reduce to , reduce the amount of calculation and improve the calculation efficiency; D is the data matrix of filtered pre-stack seismic data; B is the data matrix of transformed pre-stack seismic data; is the transformed pre-stack seismic data; is the filtered pre-stack seismic data; n is the temporal number of the seismic data sampling points; j Is an imaginary unit.

[0081] Specifically, As a constraint condition of the frequency inversion objective function, it ensures that the effective frequency of the original data conforms to the relationship between the forward and inverse Fourier transforms and does not change the signal of the original data.

[0082] Step 5: Use the Lagrange multiplier method to iteratively solve the frequency inversion objective function and update the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is less than the preset update threshold or the number of iterations reaches the preset iteration threshold, and then output the updated filtered pre-stack seismic data as the pre-stack seismic data after frequency expansion.

[0083] Specifically, in this embodiment, the Lagrangian multiplier method is the double augmented Lagrangian multiplier method. Numerous methods exist for L1 inversion in the prior art, with the augmented Lagrangian method (ALM) being a popular choice due to its robustness and low computational cost per iteration. However, the ALM typically requires a large number of iterations to converge. In contrast, the double augmented Lagrangian method (DALM) requires fewer iterations to converge, but its cost is higher due to the need for matrix inversion.

[0084] In addition, the following formula is used to update the filtered prestack seismic data:

[0085] ;

[0086] in, For the m The data matrix of filtered pre-stack seismic data after iterations; is the sparse inversion parameter; is the preset vector; For the m -The data matrix of filtered prestack seismic data after 1 iteration; For the general All values ​​greater than 1 are set to 1, and the original signs are retained; is the inverse Fourier transform; is the Fourier forward transform; is the fitting parameter, and ; B is the data matrix of transformed pre-stack seismic data; N is the latitude of pre-stack seismic data, is a constant.

[0087] By adopting the above scheme, under the premise of ensuring the accuracy of frequency inversion, the computational cost of DALM L1 inversion is significantly reduced. Thus, the noise frequency in the data is eliminated, and the missing frequency is inverted based on the L1 time domain sparsity. From the three examples provided in this application, it can be clearly seen that when the data meets the time domain sparsity assumption, the frequency of missing data can be well extended. When the DALM algorithm is used to implement frequency inversion, the amount of calculation in the iterative process can be reduced by optimizing the matrix operation. The constraint condition used when inverting the missing frequency is to keep the original frequency component of the data unchanged, so this technology can well protect the original frequency component. Before frequency inversion, the original data is filtered to suppress the abnormal energy noise in the data. During the inversion process, the effective frequency destroyed by the filtering effect can also be extended, so this technology can improve the data signal-to-noise ratio to a certain extent.

[0088] This invention demonstrates that in this specific case, the Fast Fourier Transform (FFT) can be used to bypass the matrix inversion step (usually complexity), and the complexity of the corresponding matrix multiplication process in each iteration is changed from Reduce to , where N represents the number of samples.

[0089] In this embodiment, Figure 3 The results are shown after the missing frequencies are expanded based on the fast sparse inversion frequency. Figure 3 (a) It can be seen that the phase axis of the seismic data is suppressed. Figure 3 As can be seen in (b), the processed spectrum not only expands the high-frequency components but also remains completely consistent with the effective frequency band of the original data. This is because the constraints used in this technology ensure that the original frequency of the data can always conform to the Fourier transform relationship.

[0090] By analyzing the model data with abnormal noise Figure 4 (a) To test, the original data spectrum is as follows: Figure 4 (b) shows that the input data lacks low-frequency data below 4Hz and high-frequency data above 16Hz, and contains abnormal energy noise in the range of 9-12Hz. After processing by this technology, the test results can be seen, such as Figure 5 (a) and Figure 5 As shown in (b), it can not only invert the missing low-frequency and high-frequency components, but also has a good suppression effect on abnormal energy noise.

[0091] In order to test the applicability of this method, more complex model data tests were added.

[0092] Figure 6 (a) is a simulated single shot record, Figure 6The blue solid line in (b) is the spectrum of the model data. A high-pass filter is used to filter out the low-frequency components below 5 Hz in the original data. Figure 7 As shown in (a), Figure 7 The green solid line in (b) is the spectrum of the model data after filtering. This technology is used to extend the low-frequency data below 5Hz. Figure 8 (a) is the single shot data after frequency extension, Figure 8 The red solid line in (b) is the spectrum of the data after frequency extension. From the spectrum, we can see that the extended low frequency is very close to the low frequency of the original data, which verifies the correctness of this technology. Figure 9 (a) and the low-frequency components inverted by this technique Figure 9 (b) We can see that the two are also very close in the gun records, which further verifies the correctness of this method.

[0093] like Figure 10 As shown, an embodiment of the present invention provides a frequency expansion device based on fast sparse inversion, the device comprising:

[0094] A data acquisition module 10 is used to acquire pre-stack seismic data;

[0095] A data filtering module 20 is configured to filter the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0096] A data denoising module 30 performs Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0097] An objective function establishment module 40 is used to construct a frequency inversion objective function based on the filtered pre-stack seismic data and a sparse inversion algorithm, with the transformed pre-stack seismic data as a constraint condition;

[0098] The frequency expansion module 50 is used to iteratively solve the frequency inversion objective function using the Lagrange multiplier method and update the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is less than a preset update threshold or the number of iterations reaches a preset iteration threshold, and output the updated filtered pre-stack seismic data as the pre-stack seismic data after frequency expansion.

[0099] An embodiment of the present invention further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned frequency expansion method based on fast sparse inversion when executing the computer program.

[0100] An embodiment of the present invention further provides a readable storage medium having instructions stored thereon, the instructions being used to enable a machine to execute the above-mentioned frequency expansion method based on fast sparse inversion.

[0101] Those skilled in the art will appreciate that all or part of the steps in the methods described in the aforementioned embodiments can be performed by instructing the relevant hardware through a program. The program, stored in a storage medium, includes instructions for causing a microcontroller, chip, or processor to execute all or part of the steps in the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0102] Those skilled in the art can clearly understand that, for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other and are not used to limit the scope of protection of this application.

[0103] The above describes in detail the optional embodiments of the present invention in conjunction with the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the technical concept of the embodiments of the present invention, a variety of simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the scope of protection of the embodiments of the present invention. It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner unless there is any contradiction. In order to avoid unnecessary repetition, the embodiments of the present invention will no longer describe the various possible combinations separately.

[0104] In addition, the various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the embodiments of the present invention, they should also be regarded as the contents disclosed in the embodiments of the present invention.

Claims

1. A frequency expansion method based on fast sparse inversion, characterized in that: The method comprises: Acquire pre-stack seismic data; Filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data; Performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data; Based on the filtered pre-stack seismic data and a sparse inversion algorithm, a frequency inversion objective function is constructed with the transformed pre-stack seismic data as a constraint condition; The frequency inversion objective function is iteratively solved using the Lagrange multiplier method, and the filtered pre-stack seismic data is updated until the update amount of the updated filtered pre-stack seismic data is less than a preset update threshold or the number of iterations reaches a preset iteration threshold, and the updated filtered pre-stack seismic data is output as the pre-stack seismic data after frequency expansion; The following formula is used to update the filtered pre-stack seismic data: ； in, For the m The data matrix of filtered pre-stack seismic data after iterations; is the sparse inversion parameter; is the preset vector; For the m -The data matrix of filtered prestack seismic data after 1 iteration; For the general All values ​​greater than 1 are set to 1; is the inverse Fourier transform; is the Fourier forward transform; are fitting parameters, and ; B is the data matrix of transformed pre-stack seismic data; N is the latitude of prestack seismic data; is a constant.

2. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: Before filtering the pre-stack seismic data using a pre-built filter operator to obtain filtered pre-stack seismic data, the method further includes: Based on the effective frequency band of pre-stack seismic data, the frequency band where the noise is located and the frequency band to be inverted, a filtering operator is constructed; The expression of the filtering operator is: 。 3. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: Performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data, comprising: The transformed pre-stack seismic data are obtained using the following calculation formula: ； in, is the transformed pre-stack seismic data; is the filtered pre-stack seismic data; n is the temporal number of the seismic data sampling points; j is an imaginary unit; k is the number of seismic data in the frequency domain, and .

4. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: The sparse inversion algorithm is an L1 sparse inversion algorithm; The Lagrange multiplier method is a double augmented Lagrange multiplier method.

5. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: The expression of the frequency inversion objective function is: ； in, is the frequency inversion objective function; D is the data matrix of filtered pre-stack seismic data.

6. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: The constraints of the frequency inversion objective function are: ； ； ； ； in, A is the discrete Fourier transform matrix; D is the data matrix of filtered pre-stack seismic data; B is the data matrix of transformed pre-stack seismic data; is the transformed pre-stack seismic data; is the filtered pre-stack seismic data; n is the temporal number of the seismic data sampling points; j Is an imaginary unit.

7. A frequency expansion device based on fast sparse inversion, characterized in that: The device comprises: A data acquisition module, used for acquiring pre-stack seismic data; A data filtering module, configured to filter the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data; a data denoising module, performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data; An objective function establishment module is used to construct a frequency inversion objective function based on the filtered pre-stack seismic data and a sparse inversion algorithm, with the transformed pre-stack seismic data as a constraint condition; A frequency expansion module is used to iteratively solve the frequency inversion objective function using the Lagrange multiplier method and update the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is less than a preset update threshold or the number of iterations reaches a preset iteration threshold, and output the updated filtered pre-stack seismic data as the pre-stack seismic data after frequency expansion; The following formula is used to update the filtered pre-stack seismic data: ； in, For the m The data matrix of filtered pre-stack seismic data after iterations; is the sparse inversion parameter; is the preset vector; For the m -The data matrix of filtered prestack seismic data after 1 iteration; For the general All values ​​greater than 1 are set to 1; is the inverse Fourier transform; is the Fourier forward transform; are fitting parameters, and ; B is the data matrix of transformed pre-stack seismic data; N is the latitude of prestack seismic data; is a constant.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the frequency expansion method based on fast sparse inversion according to any one of claims 1 to 6 is implemented.

9. A readable storage medium having instructions stored thereon, wherein the instructions are used to enable a machine to execute the frequency expansion method based on fast sparse inversion according to any one of claims 1 to 6.

Images