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

Abstract

The present invention relates to the technical field of seismic data processing, and provides a frequency expansion method and apparatus based on fast sparse inversion, and a readable storage medium. The method comprises: acquiring pre-stack seismic data; filtering the pre-stack seismic data by 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; on the basis of the filtered pre-stack seismic data and a sparse inversion algorithm, constructing a frequency inversion objective function by taking the transformed pre-stack seismic data as a constraint condition; and iterating the frequency inversion objective function by 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 smaller 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 precision and a high data signal-to-noise ratio, a reduced calculation amount in a data processing process, and a reduced calculation cost.

Description

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

[0003] Summary of the Invention

[0004] 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.

[0005] 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:

[0006] Acquire pre-stack seismic data;

[0007] Filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0008] Performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0009] 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;

[0010] 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.

[0011] 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:

[0012] 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;

[0013] The expression of the filtering operator is:

[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] Where b[k] is the transformed pre-stack seismic data; d[n] is the filtered pre-stack seismic data; n is the temporal number of the seismic data sampling point; j is the imaginary unit; k is the number of the seismic data in the frequency domain, and 0≤k≤N-1.

[0017] Optionally, the sparse inversion algorithm is an L1 sparse inversion algorithm;

[0018] The Lagrange multiplier method is a double augmented Lagrange multiplier method.

[0019] Optionally, the frequency inversion objective function is expressed as:

[0020] Where J(x) is the frequency inversion objective function; D is the data matrix of filtered pre-stack seismic data.

[0021] Optionally, the constraint condition of the frequency inversion objective function is: A*D=B; D=[d[0] d[1]...d[N-1]]; B=[b[0] b[1]...b[N-1]];

[0022] Wherein, A is the discrete Fourier transform matrix; D is the data matrix of the pre-stack seismic data after filtering; B is the data matrix of the pre-stack seismic data after Fourier transform; and j is the imaginary unit.

[0023] Optionally, update the filtered prestack seismic data using the following formula:

[0024] Among them, D (m) is the data matrix of filtered prestack seismic data after the mth iteration; β is the sparse inversion parameter; u is the preset vector; D (m-1) is the data matrix of filtered pre-stack seismic data after the m-1th iteration; For the general All values ​​greater than 1 are set to 1; IFFT() is the inverse Fourier transform; FFT() is the forward Fourier transform; α is the fitting parameter, and α<1; B is the data matrix of the transformed pre-stack seismic data; N is the latitude of the pre-stack seismic data, and O(N) is a constant.

[0025] A second aspect of the present invention provides a frequency extension device based on fast sparse inversion, the device comprising:

[0026] A data acquisition module, used for acquiring pre-stack seismic data;

[0027] 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;

[0028] A Fourier transform module performs Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0029] 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;

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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

[0035] 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:

[0036] FIG1 is a flow chart of a frequency expansion method based on fast sparse inversion provided by the present invention;

[0037] FIG2 is a schematic diagram of pre-stack data and its spectrum provided by the present invention;

[0038] FIG3 is a schematic diagram of pre-stack data and its spectrum after inversion provided by the present invention;

[0039] FIG4 is a schematic diagram of pre-stack data with noise and its spectrum provided by the present invention;

[0040] FIG5 is a schematic diagram of pre-stack data and its spectrum after the noise band is padded provided by the present invention;

[0041] FIG6 is a schematic diagram of single shot model data and its spectrum provided by the present invention;

[0042] FIG7 is a schematic diagram of filtered single shot model data and its spectrum provided by the present invention;

[0043] FIG8 is a schematic diagram of single-shot model data and its spectrum after frequency expansion provided by the present invention;

[0044] FIG9 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 the present solution;

[0045] FIG10 is a schematic structural diagram of a frequency expansion device based on fast sparse inversion provided by an embodiment of the present invention.

[0046] Description of the accompanying drawings: 10 - data acquisition module; 20 - data filtering module; 30 - Fourier transform module; 40 - adjustment feedback device; 50 - frequency expansion module. DETAILED DESCRIPTION

[0047] 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.

[0048] Figure 1 is a flow chart of the frequency expansion method based on fast sparse inversion provided by the present invention; Figure 2 is a schematic diagram of the pre-stack data and its spectrum provided by the present invention; Figure 3 is a schematic diagram of the pre-stack data and its spectrum after inversion provided by the present invention; Figure 4 is a schematic diagram of the pre-stack data with noise and its spectrum provided by the present invention; Figure 5 is a schematic diagram of the pre-stack data and its spectrum after the noise frequency band is padded provided by the present invention; Figure 6 is a schematic diagram of the single-shot model data and its spectrum provided by the present invention; Figure 7 is a schematic diagram of the filtered single-shot model data and its spectrum provided by the present invention; Figure 8 is a schematic diagram of the single-shot model data and its spectrum after frequency expansion provided by the present invention; Figure 9 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 scheme; Figure 10 is a structural schematic diagram of the frequency expansion device based on fast sparse inversion provided by an embodiment of the present invention.

[0049] As shown in FIG1 , an embodiment of the present invention provides a frequency expansion method based on fast sparse inversion, the method comprising:

[0050] Step 1: Obtain pre-stack seismic data;

[0051] Specifically, in this embodiment, as shown in Figure 2(a), pre-stack seismic data refers to the raw seismic recording 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 underground rock. Pre-stack seismic data contains information about the reflection and refraction of the underground rock and can be used to study underground structure, lithology, and the distribution of resources such as oil and gas. Processing pre-stack seismic data 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 recordings into underground depth information. Next, stacking is performed to combine multiple seismic recordings to enhance the intensity of the underground reflection information. Finally, velocity modeling and migration processing are required to obtain more accurate information about the underground structure. By processing pre-stack seismic data, seismic explorers can obtain detailed information about the underground structure, providing important information for oil and gas exploration, geological disaster prediction, and other areas. Pre-stack seismic data can also be used for earthquake research and monitoring, helping to understand the patterns and trends of seismic activity and improving the accuracy of earthquake early warnings.

[0052] Step 2: filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data;

[0053] 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.

[0054] 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:

[0055] Step 3: performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0056] In this embodiment, the following calculation formula is used to obtain the transformed pre-stack seismic data:

[0057] Where b[k] is the transformed pre-stack seismic data, as shown in Figure 2(b), which is the frequency spectrum of the transformed pre-stack seismic data; d[n] is the filtered pre-stack seismic data, as shown in Figure 2(a); n is the temporal number of the seismic data sampling point; j is the imaginary unit; k is the number of the seismic data in the frequency domain, and 0≤k≤N-1.

[0058] 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;

[0059] 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.

[0060] Among them, the expression of the frequency inversion objective function is:

[0061] Where J(x) is the frequency inversion objective function; D is the data matrix of filtered pre-stack seismic data.

[0062] 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.

[0063] In this embodiment, the constraints of the frequency inversion objective function are: A*D=B; D=[d[0] d[1]...d[N-1]]; B=[b[0]b[1]...b[N-1]];

[0064] Among them, A is the discrete Fourier transform matrix, and the fast Fourier transform can be used to reduce the computational complexity from N 2 Reduced to Nlog(N), reducing the amount of calculation and improving the calculation efficiency; D is the data matrix of pre-stack seismic data after filtering; B is the data matrix of pre-stack seismic data after Fourier transform; b[k] is the transformed pre-stack seismic data; d[n] is the filtered pre-stack seismic data; n is the time number of the seismic data sampling point; j is the imaginary unit.

[0065] Specifically, A*D=B is used as the constraint condition of the frequency inversion objective function to ensure 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.

[0066] 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.

[0067] 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.

[0068] In addition, the following formula is used to update the filtered prestack seismic data:

[0069] Among them, D (m) is the data matrix of filtered prestack seismic data after the mth iteration; β is the sparse inversion parameter; u is the preset vector; D (m-1) is the data matrix of filtered pre-stack seismic data after the m-1th iteration; For the general All values ​​greater than 1 are set to 1 and the original signs are retained; IFFT() is the inverse Fourier transform; FFT() is the forward Fourier transform; α is the fitting parameter, and α<1; B is the data matrix of the transformed pre-stack seismic data; N is the latitude of the pre-stack seismic data, and O(N) is a constant.

[0070] By adopting the above scheme, the computational cost of DALM L1 inversion is significantly reduced under the premise of ensuring the accuracy of frequency inversion. 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 by the present invention, 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 adopted 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. Therefore, this technology can improve the data signal-to-noise ratio to a certain extent.

[0071] The present invention demonstrates that in this specific case, the Fast Fourier Transform (FFT) can be used to bypass the matrix inversion step (typically N 3 complexity), and the complexity of the corresponding matrix multiplication process in each iteration is changed from N 2 Reduced to Nlog(N), where N represents the number of samples.

[0072] In this embodiment, Figure 3 shows the results of frequency expansion of missing frequencies based on fast sparse inversion. As can be seen in Figure 3(a), the events of the seismic data are suppressed. Figure 3(b) shows that 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 technique ensure that the original frequency of the data always conforms to the Fourier transform relationship.

[0073] By testing the model data with abnormal noise (Figure 4(a), the original data spectrum (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 9-12Hz range. After processing with this technology, the test results (Figures 5(a) and 5(b)) show that it not only recovers the missing low-frequency and high-frequency components but also effectively suppresses the abnormal energy noise.

[0074] In order to test the applicability of this method, more complex model data tests were added.

[0075] Figure 6(a) shows a simulated single-shot record. The solid line indicated by the arrow in Figure 6(b) is the spectrum of the model data. A high-pass filter was used to filter out low-frequency components below 5 Hz in the original data, as shown in Figure 7(a). The solid line indicated by the arrow in Figure 7(b) is the spectrum of the filtered model data. This technique was used to extend the low-frequency data below 5 Hz. Figure 8(a) shows the single-shot data after frequency extension, and the solid line indicated by the arrow in Figure 8(b) is the spectrum of the data after frequency extension. The spectrum shows that the extended low-frequency components are very close to those of the original data, verifying the correctness of this technique. Comparing the low-frequency components below 5 Hz in the original data (Figure 9(a)) with the low-frequency components inverted by this technique (Figure 9(b)), we can see that they are also very close in the shot records, further verifying the correctness of this method.

[0076] As shown in FIG10 , an embodiment of the present invention provides a frequency extension device based on fast sparse inversion, the device comprising:

[0077] A data acquisition module 10 is used to acquire pre-stack seismic data;

[0078] 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;

[0079] A Fourier transform module 30 performs Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data;

[0080] 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;

[0081] 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.

[0082] 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.

[0083] 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.

[0084] Those skilled in the art will appreciate that all or part of the steps in the methods of the aforementioned embodiments can be accomplished by instructing the relevant hardware through a program, which is stored in a storage medium and includes a number of instructions for causing a single-chip microcomputer, chip, or processor to execute all or part of the steps of 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 disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0085] 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 the present invention.

[0086] 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.

[0087] 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-constructed filter operator to obtain filtered pre-stack seismic data; Performing Fourier transformation on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data; Based on the filtered prestack seismic data and the sparse inversion algorithm, a frequency inversion objective function is constructed with the transformed prestack 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.

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-constructed 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 transformation on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data includes: The transformed pre-stack seismic data is obtained using the following calculation formula: Wherein, b[k] is the transformed pre-stack seismic data; d[n] is the filtered pre-stack seismic data; n is the time number of the seismic data sampling point; j is the imaginary unit; k is the number of the seismic data in the frequency domain, And 0≤k≤N-1.

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: Wherein, J(x) is the frequency inversion objective function; D is the data matrix of pre-stack seismic data after filtering.

6. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: The constraint conditions of the frequency inversion objective function are: A*D=B; D=[d[0] d[1] ... d[N-1]]; B=[b[0] b[1] ... b[N-1]]; Wherein, A is the discrete Fourier transform matrix; D is the data matrix of the filtered prestack seismic data; B is the data matrix of the transformed prestack seismic data; b[k] is the transformed prestack seismic data; d[n] is the filtered prestack seismic data; n is the temporal number of the seismic data sampling point; j is the imaginary unit.

7. The frequency expansion method based on fast sparse inversion according to claim 1, characterized in that: The following formula is used to update the filtered prestack seismic data: Among them, D (m) is the data matrix of filtered prestack seismic data after the mth iteration; β is the sparse inversion parameter; u is the preset vector; D (m-1) is the data matrix of filtered pre-stack seismic data after the m-1th iteration; For the general All values ​​greater than 1 are set to 1; IFFT() is the inverse Fourier transform; FFT() is the forward Fourier transform; α is the fitting parameter, and α<1; B is the data matrix of the transformed prestack seismic data; N is the latitude of the prestack seismic data; O(N) is a constant.

8. 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, used for filtering the pre-stack seismic data using a pre-built filtering operator to obtain filtered pre-stack seismic data; A Fourier transform module performs 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 prestack seismic data and the sparse inversion algorithm, taking the transformed prestack seismic data as a constraint condition; 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 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.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the frequency expansion method based on fast sparse inversion described in any one of claims 1 to 7 is implemented.

10. A readable storage medium having instructions stored thereon, the instructions being used to enable a machine to execute the frequency expansion method based on fast sparse inversion as described in any one of claims 1 to 7.

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