Method, system and device for improving seismic data resolution and medium

Abstract

The invention belongs to the technical field of oil-gas exploration seismic data processing, and particularly discloses a method, a system, equipment and a medium for improving seismic data resolution. The method comprises the following steps: giving an order, expressing a resolution improving operator in a Legendre polynomial orthogonal decomposition form, and obtaining a frequency domain resolution improving result mathematical expression expressed by a Legendre polynomial; a frequency band expected to be output is given, an expected frequency spectrum for improving the resolution ratio is designed, and a mathematical expression of Legendre polynomial coefficients is obtained through a least square method; calculating the amplitude spectrum of the seismic data, substituting the amplitude spectrum into the mathematical expression of the Legendre polynomial coefficient, and obtaining each coefficient value; various coefficient values are substituted into a mathematical expression of a frequency domain resolution improving result and are inversely transformed into a time domain to obtain a final result. According to the method, a high-resolution broadband seismic data result can be obtained, seismic wavelets do not need to be estimated, parameter setting is few, and quality control is convenient.

Description

Technical Field

[0001] The present invention belongs to the technical field of oil and gas exploration seismic data processing, and in particular relates to a method, system, equipment and medium for improving the resolution of seismic data. Background Art

[0002] Affected by factors such as seismic acquisition, near-surface and underground strata absorption, the resolution of seismic data is relatively low. For the exploration of thin-bed lithologic oil and gas reservoirs in continental fast-changing sedimentary environments, the resolution of seismic data is far from meeting the needs of geological research. It is necessary to process seismic data to improve its resolution.

[0003] With the advancement of seismic data processing concepts and technologies, seismic data resolution improvement is moving towards broadband processing, that is, effectively compensating for the low-frequency and high-frequency energy of seismic data, thereby making the information in each frequency band in the seismic data richer, reducing visual illusions in the data, and obtaining clearer and more realistic data results, laying the foundation for the subsequent comprehensive geological utilization of seismic data.

[0004] Traditional methods of improving resolution, such as predictive deconvolution and inverse Q filtering, can effectively improve the high-frequency energy in seismic data and increase the main frequency of the data, thereby obtaining high-resolution seismic profiles. However, these methods often suppress the low-frequency information in the data while improving the high-frequency energy and main frequency of seismic data, resulting in low or missing low-frequency energy in the data, making it difficult to obtain ideal broadband processing results. Summary of the invention

[0005] The purpose of the present invention is to provide a method for improving the resolution of seismic data, which can not only improve the high-frequency energy of the seismic data but also effectively compensate for the low-frequency energy of the seismic data, thereby obtaining a high-resolution broadband processing result.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme: A method for improving the resolution of seismic data comprises the following steps: Step 1. Given an order, the resolution enhancement operator is expressed in the form of Legendre polynomial orthogonal decomposition, and a mathematical expression of the Legendre polynomial representation of the frequency domain resolution enhancement result is obtained; Step 2. Given the desired output frequency band, design the desired spectrum with improved resolution, and use the least square method to obtain the mathematical expression of the Legendre polynomial coefficients; Step 3. Calculate the amplitude spectrum of the seismic data, and substitute it into the mathematical expression of the Legendre polynomial coefficients obtained in step 2 to obtain the values ​​of each coefficient; Step 4. Substitute the coefficient values ​​calculated in step 3 into the mathematical expression represented by the Legendre polynomial of the frequency domain resolution enhancement result obtained in step 1 and inversely transform to the time domain to obtain the final result.

[0007] In addition, based on the above method for improving the resolution of seismic data, the present invention also proposes a system for improving the resolution of seismic data adapted thereto, which adopts the following technical solution: A system for improving the resolution of seismic data, comprising the following modules: The frequency domain resolution enhancement calculation module calculates the frequency spectrum of the seismic data after the resolution enhancement based on the amplitude spectrum of the seismic data, the order of the Legendre polynomial decomposition, and the coefficient values ​​of the Legendre polynomials; The module for calculating the coefficient values ​​of Legendre polynomials is used to calculate the coefficient values ​​of Legendre polynomials by using the least square method according to the amplitude spectrum of seismic data, cutoff frequency, the order of Legendre polynomials, the frequency range and amplitude spectrum amplitude control constant given by the user; A module for calculating the amplitude spectrum and cutoff frequency of seismic data, which performs Fourier transform on the seismic data to obtain the spectrum of the seismic data, performs modulo processing on the spectrum of the seismic data to obtain the amplitude spectrum of the seismic data, and calculates the cutoff frequency using the sampling interval, and uses the calculated amplitude spectrum and cutoff frequency of the seismic data as input parameters of the module for calculating the coefficient values ​​of each item of Legendre polynomial; And a time domain resolution improvement result calculation module, which inputs the Legendre polynomial coefficient values ​​calculated by the Legendre polynomial coefficient value calculation module into the frequency domain resolution improvement calculation module, and combines the amplitude spectrum of the seismic data and the order of the Legendre polynomial decomposition to calculate the spectrum of the seismic data after the resolution is improved, and further performs an inverse Fourier transform on the spectrum and takes the real part as the final output result of the resolution improvement.

[0008] In addition, based on the above method for improving the resolution of seismic data, the present invention also proposes a computer device, which includes a memory and one or more processors.

[0009] The memory stores executable codes, and when the processor executes the executable codes, the executable codes are used to implement the steps of the above-mentioned method for improving the resolution of seismic data.

[0010] In addition, based on the above method for improving the resolution of seismic data, the present invention also proposes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the above method for improving the resolution of seismic data.

[0011] The present invention has the following advantages: The present invention relates to a method for improving the resolution of seismic data, which expresses a resolution improvement operator in the form of orthogonal decomposition of Legendre polynomials, solves the resolution improvement operator based on a given desired output frequency band in the least squares sense, and thus performs resolution improvement processing. The frequency band range for improving the resolution of the method is given by the user, and the user can control the resolution improvement capability. The user can determine the range of low and high frequency end energy compensation based on the signal-to-noise ratio of the seismic data and the continuity of the reflection wave event axis of the processing result, thereby obtaining a high-resolution broadband processing result. In addition, the method does not require estimation of sub-waves, has fewer parameter settings, has a high degree of differentiation of the effects of each parameter, is convenient for quality control, and is convenient for parameter optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a flow chart of a method for improving the resolution of seismic data in Embodiment 1 of the present invention; Figure 2 The waveform comparison diagram of synthetic seismic records before and after resolution enhancement processing in Example 1 of the present invention is shown; wherein, (a) shows the seismic wavelet used to make synthetic seismic records; (b) shows the amplitude spectrum of the seismic wavelet; (c) shows the synthetic seismic records and the reflection coefficient used to make the synthetic seismic records; (d) shows the comparison diagram of the reflection coefficient before and after the [0,50Hz] low-pass filtering and the amplitude amplification by 20 times; (e) shows the comparison diagram of the result of the synthetic seismic record resolution enhancement processing using the method of the present invention and the theoretical reflection coefficient; Figure 3 A comparison diagram of the amplitude spectra of synthetic seismic records before and after resolution improvement in Example 1 of the present invention; Figure 4 A comparison diagram of the resolution enhancement processing result of the synthetic seismic record in Example 1 of the present invention and the amplitude spectrum after the reflection coefficient is low-pass filtered at 0-50Hz and the amplitude is amplified by 20 times; Figure 5 This is a waveform variable area display diagram of actual post-stack seismic data in Example 2 of the present invention; Figure 6 This is a waveform variable area display diagram of the resolution improvement processing result of the actual post-stack seismic data in Example 2 of the present invention; Figure 7 This is a comparison diagram of the amplitude spectra of the actual post-stack seismic data before and after resolution enhancement processing in Example 2 of the present invention. DETAILED DESCRIPTION

[0013] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment 1 describes a method for improving the resolution of seismic data to achieve the purpose of high-resolution broadband processing of seismic data. The method of the present invention does not require estimation of seismic wavelets, has fewer parameter settings, has a high degree of differentiation of the effects of each parameter, is convenient for quality control, and facilitates parameter optimization.

[0014] like Figure 1 As shown, the method for improving the resolution of seismic data in this embodiment includes the following steps: Step 1. Given an order, the resolution enhancement operator is expressed in the form of Legendre polynomial orthogonal decomposition, and the mathematical expression of the Legendre polynomial representation of the frequency domain resolution enhancement result is obtained.

[0015] Step 1.1. Use represents a one-dimensional seismic record, where Indicates time, the frequency spectrum of earthquake records is expressed as Indicates that Indicates frequency. The operator for improving the resolution of earthquake records is represented. The earthquake records after improving the resolution can be expressed in the frequency domain as follows: (1) in, Spectrum showing the seismic data after resolution enhancement.

[0016] Step 1.2. The frequency range of the seismic data is denoted by ,in, Indicates the starting frequency of the data, represents the cutoff frequency of the data. Then any frequency within this frequency range can be mapped to the interval of Legendre polynomials by the following formula superior, (2) in, The variable Standardized transformation function for projection to the orthogonal space of Legendre polynomials, making it suitable for orthogonal expansion and projection calculation; Step 1.3. Let the frequency domain resolution enhancement operator of the seismic record be The order of the orthogonal decomposition of Legendre polynomials is ,So It is expressed as: (3) in, are the coefficients of Legendre polynomials, Indicates the number of times The Legendre polynomial of is expressed as: (4) Among them, the symbol Indicates rounding down.

[0017] In addition, by substituting formula (3) into formula (1), the frequency domain mathematical expression after improving the resolution is obtained as follows: (5) Step 2. Given the desired output frequency band, design the desired spectrum with improved resolution, and use the least squares method to obtain the mathematical expression of the Legendre polynomial coefficients.

[0018] Step 2.1. Based on the given desired output frequency band, design the desired spectrum after improving the resolution; Let the frequency range of the given desired output be , assuming that the reflection coefficient of the seismic record has the characteristics of a white noise spectrum, the mathematical expression of the expected amplitude spectrum after the resolution is improved is as follows: (6) in, represents the expected spectrum after improving the resolution, and the symbol Indicates modulo processing, is the amplitude spectrum amplitude control constant. To increase the minimum frequency of resolution processing, The highest frequency processed to increase resolution, the energy of other frequencies remains unchanged; parameters , and The value of is related to the signal-to-noise ratio of the seismic data and is determined through parameter experiments in actual processing.

[0019] Step 2.2. Use the least square method to solve the mathematical expression of Legendre polynomial coefficients; Amplitude spectrum after improving the resolution of seismic data and the expected amplitude spectrum The error energy is To express, then: (7) make: , , , (8) Then formula (7) can be rewritten into the following matrix form: (9) Use the least squares method to find the parameters that make the following equation true The value of (10) Right now: (11) Further deduction and solution yield: (12) Among them, the matrix The elements of are the coefficients of the Legendre polynomials , , , Formula (12) is the mathematical expression for calculating the coefficients of Legendre polynomials.

[0020] Step 3. Calculate the amplitude spectrum of the seismic data and substitute it into the mathematical expression of the Legendre polynomial coefficients derived in step 2 to obtain the values ​​of each coefficient.

[0021] Step 3.1. Based on the analysis of seismic data frequency band and data signal-to-noise ratio, set the frequency range parameters after the resolution is improved. and parameters , and put it into formula (8) to calculate the matrix .

[0022] Step 3.2. Perform Fourier transform on the seismic data to obtain the spectrum of the seismic data , and take the modulus to get the amplitude spectrum , and put it into formula (8) to calculate the matrix .

[0023] Step 3.3. Calculate the cutoff frequency of seismic data according to the sampling interval of seismic data: , (13) in, is the sampling interval of seismic data, in ms.

[0024] make ,Will and Substitute into formula (2) and combine with formula (4) to calculate the Legendre polynomials of each degree The value of , given the Legendre polynomial order ,Will and Substitute into formula (8) to calculate the matrix .

[0025] Step 3.4. Transform the matrix , and Substituting into formula (12) we get the coefficient matrix , and then get the coefficients of the Legendre polynomials .

[0026] Step 4. Substitute the coefficient values ​​of the Legendre polynomials calculated in step 3 into the frequency domain mathematical expression with improved resolution derived in step 1 and inversely transform to the time domain to obtain the final result output.

[0027] Step 4.1. Calculate the spectrum of the seismic data after the resolution is improved; The spectrum of the seismic data calculated in step 3 and Legendre polynomials The values ​​of and the calculated Legendre polynomial coefficients , together with the given Legendre polynomial order Substitute them into formula (5) in step 1 to obtain the spectrum of the seismic data with improved resolution .

[0028] Step 4.2. Calculate the final result after improving the resolution; The spectrum of the seismic data calculated in step 4.1 The final resolution enhancement result is obtained by processing as follows: (13) in, represents the time domain result with improved resolution, symbol represents the inverse Fourier transform, Indicates taking the real part. Output is the final result of the resolution enhancement process.

[0029] The method of the present invention can reasonably broaden the frequency band of seismic data, improve the resolution of data, improve the spatial continuity and interpretability of thin reservoir phase axis, thereby improving the recognition and identification ability of thin reservoirs in seismic data bodies, and providing a high-resolution broadband data basis for subsequent interpretation of seismic data and geological reservoir exploration and development. The method does not require estimating wavelets, avoids the complex parameter quality control process of wavelet estimation and other links, has fewer parameter settings, high differentiation of the effects of various parameters, convenient quality control, and convenient parameter optimization.

[0030] In addition, the present invention also provides two specific examples to verify the effectiveness of the method proposed in the present invention.

[0031] In specific examples 1 and 2, the method for improving the resolution of seismic data according to the present invention is described in combination with synthetic seismic records and actual post-stack seismic data, respectively.

[0032] Example 1 Figure 2The waveform comparison diagrams of the synthetic seismic record in Example 1 of the present invention before and after the resolution enhancement processing are shown. The black line in (c) is the waveform display of the synthetic seismic record obtained by convolving the seismic wavelet in (a) and the reflection coefficient sequence (gray line) in (c). (b) is the amplitude spectrum of the seismic wavelet in (a). It can be seen from the figure that the main frequency of the seismic wavelet is 15 Hz, and the frequency band of the wavelet is relatively narrow, which leads to the low resolution of the synthetic seismic record in (c). Two close reflection coefficients cannot be distinguished on the waveform of the synthetic seismic record. The black line in (e) is the result of the synthetic seismic record in (c) after the resolution enhancement processing is performed using the method of the present invention. The order of the Legendre polynomial orthogonal decomposition used is To 30, increase the band parameter in the resolution operator for ,parameter 3. Comparing the waveform of the resolution-enhanced result in (e) with the reflection coefficient sequence, it can be seen that the waveform after the resolution is improved is consistent with the reflection coefficient sequence, and most of the reflection coefficient sequences that are relatively close can be identified and recognized by the waveform of the resolution-enhanced result. Comparing the consistency of the waveform and the reflection coefficient before and after the resolution-enhanced processing in (c) and (e), it can be seen from the figure that the resolution ability of the seismic data is significantly improved after the processing by the method of the present invention, and the consistency of the seismic data waveform and the reflection coefficient is significantly improved. After the resolution-enhanced processing, the resolvable waveform at the position indicated by the arrow in the figure is more matched with the true reflection coefficient, and the consistency between the waveform and the reflection coefficient strength is restored to a certain extent.

[0033] Since the frequency band of the result after improving the resolution is inconsistent with the frequency band range of the reflection coefficient, in order to further verify the amplitude preservation of this method, the real reflection coefficient sequence is processed by 0-50Hz low-pass filtering as the theoretical value. The results are shown in Figure 2 The waveform shown in (d) in the figure. Since the amplitude of the reflection coefficient low-pass filtering result is small, for the sake of comparison, the amplitude of the low-pass filtering result in (d) is multiplied by 20 for amplification. The theoretical value of the reflection coefficient after low-pass filtering is compared with the waveform of the seismic record after the resolution is improved to verify the amplitude preservation of the resolution improvement processing. By comparing (d) and (e), it can be seen that the waveform of the synthetic seismic record after the resolution is improved is very similar to the waveform after the theoretical reflection coefficient is low-pass filtered, and the relationship between the strength of the amplitude is basically the same, which shows that the resolution improvement method has good amplitude preservation. In order to more accurately verify the amplitude preservation ability of this method after improving the resolution, the correlation coefficient between the seismic record and the theoretical reflection coefficient is calculated. Figure 2 The correlation coefficient between the synthetic record before processing and the theoretical reflection coefficient is 0.2021 (e.g. Figure 2 In (c), the correlation coefficient between the theoretical reflection coefficient low-pass filter result and the theoretical reflection coefficient is 0.3090 (e.g. Figure 2In (d), the correlation coefficient between the resolution improvement result and the theoretical reflection coefficient is 0.3044 (e.g. Figure 2 (e)). From the numerical comparison of the correlation coefficients, it can be seen that after the resolution is improved, the correlation between the seismic record waveform and the reflection coefficient sequence is improved, and the correlation coefficient calculated after the resolution is improved is very close to the correlation coefficient calculated by the low-pass filtering result of the reflection coefficient, which verifies that the processing result of improving the resolution using this method has good amplitude preservation.

[0034] Figure 3 A comparison of the amplitude spectrum of synthetic seismic records before and after the resolution is improved is given. From this figure, the amplitude spectrum amplitude control constant can be quality controlled The selection of constant The value of must satisfy the requirement that the amplitude near the main frequency of the amplitude spectrum before processing (about 15Hz) remains basically the same as the amplitude of the amplitude spectrum after processing. The best value is 3. and The value of is chosen to satisfy the premise that the processing result has a high signal-to-noise ratio, and the wider the frequency band, the better. The order of the orthogonal decomposition of Legendre polynomials is preferably a smaller order that does not have notches in the amplitude spectrum after resolution processing, and the energy at the low, medium and high frequency ends is relatively balanced. Figure 3 Further comparison of the amplitude spectra before and after processing shows that the amplitude spectrum band of the synthetic seismic record before processing is relatively narrow, with a frequency range of approximately 6-32 Hz. After resolution-enhanced processing, the frequency band range is approximately 2-52 Hz, and the frequency band of the seismic data is widened by approximately 20 Hz, indicating that relatively broadband seismic data is obtained after resolution-enhanced processing.

[0035] Figure 4 This is a comparison chart of the amplitude spectra of the synthetic seismic record resolution improvement results and the theoretical value (the result after 0-50Hz low-pass filtering of the reflection coefficient * 20 coefficient); it can be seen from the figure that the amplitude spectrum after the resolution improvement is very consistent with the amplitude spectrum of the theoretical value, and the relative strength relationship between the reflection coefficient amplitude spectra is basically maintained, which indirectly reflects that the resolution improvement method has good amplitude preservation.

[0036] The above comparative analysis shows that the method of the present invention can broaden the frequency band of seismic data, improve the resolution of seismic data, maintain the strong-weak relationship between the reflection coefficient amplitude spectrum, restore the consistency between the waveform and the reflection coefficient strength, and has good amplitude preservation characteristics.

[0037] Example 2 Figure 5This is a waveform variable area display diagram of actual post-stack seismic data in a certain exploration area. The resolution of the seismic data in the figure is insufficient, the continuity and spatial interpretability of the event axis are poor, and there is a set of thin interlayers at the position shown by the black rectangular box. Due to the insufficient resolution of the data, the waveform of the thin interlayer is intermittent, which brings difficulties to the subsequent seismic data interpretation and needs to be processed to improve the resolution. Figure 6 The waveform variable area display of the actual post-stack seismic data after the resolution is improved by the method of the present invention is given. From the summary, it can be seen from the figure that whether it is a strong reflection wave event axis or a weak reflection wave event axis, their continuity has been greatly improved, and the event axis can be continuously tracked in space. Compared with before processing, the continuity of the event axis has been improved, and the spatial interpretability of the thin layer in the section has been improved. Further comparison of the position of the thin interlayer shown in the rectangular box before and after processing shows that the number of events in the rectangular box has changed from 2-3 sets that are difficult to distinguish before processing to 3 sets of events with clear resolution after processing. The waveform of the thin interlayer can be clearly distinguished, the waveform of the event axis is clear, the continuity is good, and the resolution improvement effect is obvious. Figure 7 The amplitude spectrum comparison diagram of the actual post-stack seismic data before and after resolution enhancement processing is shown in the figure. It can be seen from the figure that the frequency band of the original data is relatively narrow, and the main frequency is about 30Hz. After the resolution enhancement processing by the method of the present invention, the energy of the low-frequency end and the high-frequency end of the data are well compensated and improved, and the frequency band of the data is relatively wide. After the processing, the frequency band of the data is widened by nearly 18Hz, and the main frequency is increased by about 6Hz, and a relatively wide-band resolution enhancement processing result is obtained. This verifies the effectiveness of the method of the present invention and the ability to improve the resolution of actual data.

[0038] Example 2

[0039] This embodiment 2 describes a system for improving the resolution of seismic data, which is based on the same inventive concept as the method for improving the resolution of seismic data in the above embodiment 1.

[0040] A system for improving the resolution of seismic data, comprising the following modules: The frequency domain resolution enhancement calculation module calculates the frequency spectrum of the seismic data after the resolution enhancement based on the amplitude spectrum of the seismic data, the order of the Legendre polynomial decomposition, and the coefficient values ​​of the Legendre polynomials; The module for calculating the coefficient values ​​of Legendre polynomials is used to calculate the coefficient values ​​of Legendre polynomials by using the least square method according to the amplitude spectrum of seismic data, cutoff frequency, the order of Legendre polynomials, the frequency range and amplitude spectrum amplitude control constant given by the user; A module for calculating the amplitude spectrum and cutoff frequency of seismic data, which performs Fourier transform on the seismic data to obtain the spectrum of the seismic data, performs modulo processing on the spectrum of the seismic data to obtain the amplitude spectrum of the seismic data, and calculates the cutoff frequency using the sampling interval, and uses the calculated amplitude spectrum and cutoff frequency of the seismic data as input parameters of the module for calculating the coefficient values ​​of each item of Legendre polynomial; And the time domain resolution improvement result calculation module inputs the Legendre polynomial coefficient values ​​calculated by the Legendre polynomial coefficient value calculation module into the frequency domain resolution improvement calculation module, and calculates the spectrum of the seismic data after the resolution is improved in combination with other input parameters, and further performs inverse Fourier transformation on the spectrum and takes the real part as the final output result of the resolution improvement.

[0041] It should be noted that, in the system for improving the resolution of seismic data, the implementation process of the functions and effects of each functional module is specifically described in the implementation process of the corresponding steps in the method in the above embodiment 1, and will not be repeated here.

[0042] Example 3 This embodiment 3 describes a computer device, which includes a memory and one or more processors. The memory stores executable codes, and when the processor executes the executable codes, the steps of the method for improving the resolution of seismic data in the above embodiment 1 are implemented.

[0043] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0044] Example 4 This embodiment 4 describes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the method for improving the resolution of seismic data in the above-mentioned embodiment 1.

[0045] The computer-readable storage medium may be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc., equipped on the device.

[0046] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A method for improving the resolution of seismic data, characterized in that: The steps include: Step 1. Given an order, the resolution enhancement operator is expressed in the form of Legendre polynomial orthogonal decomposition, and a mathematical expression of the Legendre polynomial representation of the frequency domain resolution enhancement result is obtained; Step 2. Given the desired output frequency band, design the desired spectrum with improved resolution, and use the least square method to obtain the mathematical expression of the Legendre polynomial coefficients; Step 3. Calculate the amplitude spectrum of the seismic data, and substitute it into the mathematical expression of the Legendre polynomial coefficients obtained in step 2 to obtain the values ​​of each coefficient; Step 4. Substitute the coefficient values ​​calculated in step 3 into the mathematical expression represented by the Legendre polynomial of the frequency domain resolution enhancement result obtained in step 1 and inversely transform to the time domain to obtain the final result.

2. The method for improving the resolution of seismic data according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.

1. Use represents a one-dimensional seismic record, where Indicates time, the frequency spectrum of earthquake records is expressed as Indicates that Indicates frequency; The frequency domain resolution enhancement operator of the seismic record is represented by the following frequency domain form of the seismic record after resolution enhancement: （1） in, The spectrum representing the seismic data after the resolution is increased; Step 1.

2. The frequency range of seismic data is denoted as ,in, Indicates the starting frequency of the data, Represents the cutoff frequency of the data; any frequency within this frequency range can be mapped to the interval of Legendre polynomials by the following formula superior, （2） in, The variable Normalized transformation function projected onto the orthogonal space of Legendre polynomials; Step 1.

3. Let the frequency domain resolution enhancement operator of the seismic record be The order of the orthogonal decomposition of Legendre polynomials is ,So It is expressed as: （3） in, are the coefficients of the Legendre polynomials, Indicates the number of times The Legendre polynomial of is expressed as: （4） Among them, the symbol Indicates rounding down; Step 1.

4. Substitute formula (3) into formula (1) to obtain the mathematical expression after the frequency domain resolution is improved as follows: （5）。 3. The method for improving the resolution of seismic data according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.

1. Based on the given desired output frequency band, design the desired spectrum after improving the resolution; Let the frequency band of the desired output be , assuming that the reflection coefficient of the seismic record has the characteristics of a white noise spectrum, the mathematical expression of the expected amplitude spectrum after the resolution is improved is as follows: （6） in, represents the expected spectrum after improving the resolution, and the symbol Indicates modulo processing, is the amplitude spectrum amplitude control constant, To increase the minimum frequency of resolution processing, The highest frequency processed to increase resolution; Step 2.

2. Use the least square method to solve the mathematical expression of Legendre polynomial coefficients; Amplitude spectrum after improving the resolution of seismic data Expected Amplitude Spectrum The error energy is Indicates that, then, (7) Order: ， , ， （8） Then formula (7) can be rewritten into the following matrix form: （9） Use the least squares method to find the parameters that make the following equation true The value of （10） Right now: （11） Further solving gives: （12） Among them, the matrix The elements of are the coefficients of the Legendre polynomials , , , ; Formula (12) is the mathematical expression for calculating the coefficients of Legendre polynomials.

4. The method for improving the resolution of seismic data according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3.

1. Based on the analysis of seismic data frequency band and data signal-to-noise ratio, set the frequency range parameters after the resolution is improved. and parameters , and put it into formula (8) to calculate the matrix ; Step 3.

2. Perform Fourier transform on the seismic data to obtain the spectrum of the seismic data , and take the modulus to get its amplitude spectrum , and put it into formula (8) to calculate the matrix ; Step 3.

3. Calculate the cutoff frequency of seismic data according to the sampling interval of seismic data: , （13） in, is the sampling interval of seismic data, in ms; The starting frequency of seismic data is 0 Hz, that is: ,Will and Substitute into formula (2) and combine with formula (4) to calculate the Legendre polynomials of each degree The value of , given the Legendre polynomial order ,Will and Substitute into formula (8) to calculate the matrix ; Step 3.

4. Transform the matrix , and Substitute into formula (12) to obtain the coefficient matrix , and then find the coefficients of the Legendre polynomials .

5. The method for improving the resolution of seismic data according to claim 4, characterized in that: The step 4 is specifically as follows: Step 4.

1. Calculate the spectrum of the seismic data after the resolution is improved; The spectrum of the seismic data calculated in step 3 and Legendre polynomials The values ​​of the coefficients of the Legendre polynomials calculated , together with the order of the given Legendre polynomial Substitute them into formula (5) in step 1 to obtain the spectrum of the seismic data with improved resolution ; Step 4.

2. Calculate the time domain result with improved resolution; The spectrum of the seismic data with improved resolution calculated in step 4.1 The final time domain result with improved resolution is obtained by processing as follows: （13） in, represents the time domain result with improved resolution, symbol represents the inverse Fourier transform, Represents taking the real part, Output is the final result of the resolution enhancement process.

6. A system for improving the resolution of seismic data for implementing the method according to any one of claims 1 to 5, characterized in that: The system for improving the resolution of seismic data comprises: The frequency domain resolution enhancement calculation module calculates the frequency spectrum of the seismic data after the resolution enhancement based on the amplitude spectrum of the seismic data, the order of the Legendre polynomial decomposition, and the coefficient values ​​of the Legendre polynomials; The module for calculating the coefficient values ​​of Legendre polynomials is used to calculate the coefficient values ​​of Legendre polynomials by using the least square method according to the amplitude spectrum of seismic data, cutoff frequency, the order of Legendre polynomials, the frequency range and amplitude spectrum amplitude control constant given by the user; A module for calculating the amplitude spectrum and cutoff frequency of seismic data, which performs Fourier transform on the seismic data to obtain the spectrum of the seismic data, performs modulo processing on the spectrum of the seismic data to obtain the amplitude spectrum of the seismic data, and calculates the cutoff frequency using the sampling interval, and uses the calculated amplitude spectrum and cutoff frequency of the seismic data as input parameters of the module for calculating the coefficient values ​​of each item of Legendre polynomial; And a time domain resolution improvement result calculation module, which inputs the Legendre polynomial coefficient values ​​calculated by the Legendre polynomial coefficient value calculation module into the frequency domain resolution improvement calculation module, and combines the amplitude spectrum of the seismic data and the order of the Legendre polynomial decomposition to calculate the spectrum of the seismic data after the resolution is improved, and further performs an inverse Fourier transform on the spectrum and takes the real part as the final output result of the resolution improvement.

7. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the method for improving the resolution of seismic data as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, it is used to implement the steps of the method for improving the resolution of seismic data as described in any one of claims 1 to 5.

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