A method, system, device and medium for improving the resolution of seismic data

Abstract

The present invention belongs to the technical field of seismic data processing for oil and gas exploration, and particularly discloses a method, system, device and medium for improving seismic data resolution. The method of the present invention includes the following steps: Given the order, represent the resolution improvement operator in the form of orthogonal decomposition of Legendre polynomials to obtain a mathematical expression of the Legendre polynomial representation of the resolution improvement result in the frequency domain; Given the desired output frequency band, design the desired spectrum for resolution improvement, and use the least squares method to obtain a mathematical expression of the Legendre polynomial coefficients; Calculate the amplitude spectrum of the seismic data, substitute it into the mathematical expression of the Legendre polynomial coefficients, and obtain the values of each coefficient; Substitute the values of each coefficient into the mathematical expression of the resolution improvement result in the frequency domain and inverse transform it to the time domain to obtain the final result. The present invention can obtain a high-resolution broadband seismic data result, without estimating the seismic wavelet, with few parameter settings and convenient quality control.

Description

Technical Field

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

[0002] Affected by factors such as seismic acquisition, near-surface and underground formation absorption, the resolution of seismic data is relatively low. For the exploration of thin reservoir lithologic oil and gas reservoirs in continental fast-changing sedimentary environments, the resolution of seismic data far from meets the requirements of geological research. It is necessary to perform resolution improvement processing on seismic data.

[0003] With the progress of seismic data processing concepts and processing technologies, the resolution improvement processing of seismic data has developed towards broadband processing, that is, effectively compensating the low-frequency and high-frequency energies of seismic data, so that the information in each frequency band of seismic data is richer, reducing the visual artifacts in the data, and obtaining a clearer and more faithful data result, laying a foundation for the subsequent comprehensive geological utilization of seismic data.

[0004] Traditional resolution improvement methods, such as predictive deconvolution, inverse Q filtering, etc., can effectively increase the high-frequency energy in seismic data and increase the dominant frequency of the data, thus obtaining a high-resolution seismic profile. However, while these methods increase the high-frequency energy and dominant frequency of seismic data, they often suppress the low-frequency information in the data, resulting in low or missing low-frequency energy in the data, and it is difficult to obtain an ideal broadband processing result. Summary of the Invention

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

[0006] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A method for improving the resolution of seismic data includes the following steps:

[0008] Step 1. Given an order, represent the resolution improvement operator in the form of orthogonal decomposition of Legendre polynomials to obtain a mathematical expression of the Legendre polynomial representation of the resolution improvement result in the frequency domain;

[0009] Step 2. Given the desired output frequency band, design the desired spectrum for resolution improvement, and use the least squares method to obtain a mathematical expression of the Legendre polynomial coefficients;

[0010] Step 3. Calculate the amplitude spectrum of the seismic data, substitute it into the mathematical expression of the Legendre polynomial coefficients obtained in Step 2, and obtain the values of each coefficient;

[0011] Step 4. Substitute the coefficient values calculated in Step 3 into the mathematical expression of the Legendre polynomial representation of the frequency-domain resolution-enhanced result obtained in Step 1, and perform an inverse transformation to the time domain to obtain the final result.

[0012] In addition, based on the above method for enhancing the resolution of seismic data, the present invention also proposes a corresponding system for enhancing the resolution of seismic data, which adopts the following technical solutions:

[0013] A system for enhancing the resolution of seismic data, comprising the following modules:

[0014] A frequency-domain resolution-enhanced calculation module, which calculates the spectrum of the seismic data with enhanced resolution from the amplitude spectrum of the seismic data, the order of the Legendre polynomial decomposition, and the coefficient values of each term of the Legendre polynomial.

[0015] A Legendre polynomial coefficient value calculation module, which calculates the coefficient values of each term of the Legendre polynomial by using the least squares method from the amplitude spectrum of the seismic data, the cut-off frequency, the order of the Legendre polynomial, the frequency range given by the user, and the amplitude spectrum amplitude control constant.

[0016] An amplitude spectrum and cut-off frequency calculation module for seismic data, which performs a Fourier transform on the seismic data to obtain the spectrum of the seismic data, takes the modulus of the spectrum of the seismic data to obtain the amplitude spectrum of the seismic data, and calculates the cut-off frequency by using the sampling interval. The calculated amplitude spectrum and cut-off frequency of the seismic data are used as input parameters for the Legendre polynomial coefficient value calculation module.

[0017] And a time-domain resolution-enhanced result calculation module, which inputs the coefficient values of each term of the Legendre polynomial calculated by the Legendre polynomial coefficient value calculation module into the frequency-domain resolution-enhanced 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 with enhanced resolution. The spectrum is further subjected to an inverse Fourier transform and the real part is taken as the final output result of the resolution enhancement.

[0018] In addition, based on the above method for enhancing the resolution of seismic data, the present invention also proposes a computer device, which includes a memory and one or more processors.

[0019] An executable code is stored in the memory, and when the processor executes the executable code, it is used to implement the steps of the above-mentioned method for enhancing the resolution of seismic data.

[0020] In addition, based on the above method for improving the resolution of seismic data, the present invention also provides a computer-readable storage medium with a program stored thereon. When the program is executed by a processor, it is used to implement the steps of the above-mentioned method for improving the resolution of seismic data.

[0021] The present invention has the following advantages:

[0022] The present invention describes a method for improving the resolution of seismic data, which represents the resolution improvement operator in the form of orthogonal decomposition of Legendre polynomials, and solves the resolution improvement operator based on the given frequency band of the desired output in the least squares sense for resolution improvement processing. The frequency band range for resolution improvement by this method is given by the user, and the resolution improvement ability is controllable by the user. The user can determine the range of energy compensation at the low and high frequency ends according to the signal-to-noise ratio of the seismic data and the continuity of the reflection wave in-phase axis of the processing result, so as to obtain a high-resolution broadband processing result. And this method does not require wavelet estimation, has few parameter settings, high distinguishability of the functions of each parameter, convenient quality control, and is convenient for parameter optimization. Description of the Drawings

[0023] Figure 1 is a flowchart of the method for improving the resolution of seismic data in Embodiment 1 of the present invention;

[0024] Figure 2 is a waveform comparison diagram before and after the resolution improvement processing of the synthetic seismic record in Example 1 of the present invention; among them, (a) shows the seismic wavelet used to make the synthetic seismic record; (b) shows the amplitude spectrum of the seismic wavelet; (c) shows the synthetic seismic record and the reflection coefficient used to make the synthetic seismic record; (d) shows the comparison diagram before and after the [0, 50Hz] low-pass filtering of the reflection coefficient and the amplitude amplification by 20 times; (e) shows the comparison diagram between the result of the resolution improvement processing of the synthetic seismic record using the method of the present invention and the theoretical reflection coefficient;

[0025] Figure 3 is an amplitude spectrum comparison diagram before and after the resolution improvement of the synthetic seismic record in Example 1 of the present invention;

[0026] Figure 4 is an amplitude spectrum comparison diagram between the result of the resolution improvement processing of the synthetic seismic record in Example 1 of the present invention and the amplitude spectrum after the 0-50Hz low-pass filtering of the reflection coefficient and the amplitude amplification by 20 times;

[0027] Figure 5 is a waveform variable area display diagram of the post-stack actual seismic data in Example 2 of the present invention;

[0028] Figure 6 is a waveform variable area display diagram of the result of the resolution improvement processing of the post-stack actual seismic data in Example 2 of the present invention;

[0029] Figure 7 This is the comparison chart of the amplitude spectra before and after the resolution improvement processing of the post-stack actual seismic data in Example 2 of the present invention. Detailed implementation manners

[0030] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners:

[0031] Example 1

[0032] This Example 1 describes a method for improving the resolution of seismic data to achieve the purpose of wide-band processing of high-resolution seismic data. The method of the present invention does not require estimating the seismic wavelet, has few parameter settings, high distinguishability of the functions of each parameter, convenient quality control, and is convenient for optimizing the parameters.

[0033] As Figure 1 shown, the method for improving the resolution of seismic data in this example includes the following steps:

[0034] Step 1. Given the order, represent the resolution improvement operator in the form of the orthogonal decomposition of Legendre polynomials to obtain the mathematical expression of the Legendre polynomial representation of the resolution improvement result in the frequency domain.

[0035] Step 1.1. Use to represent the one-dimensional seismic record, where represents time, and the spectrum of the seismic record is represented by where represents frequency. Use to represent the resolution improvement operator of the seismic record. The seismic record after resolution improvement can be expressed in the following frequency domain form:

[0036] (1)

[0037] where represents the spectrum of the seismic data after resolution improvement.

[0038] Step 1.2. Denote the frequency range of the seismic data as , where represents the starting frequency of the data, and represents the cut-off frequency of the data. Then any frequency within this frequency range can be mapped to the interval of the Legendre polynomial through the following formula,

[0039] (2)

[0040] where is the variable The normalized transformation function projected onto the orthogonal space composed of Legendre polynomials, making it applicable to orthogonal expansion and projection calculations;

[0041] Step 1.3. Let the frequency-domain high-resolution operator of the seismic record The order of the Legendre polynomial orthogonal decomposition is , then It is expressed as:

[0042] (3)

[0043] Among them, is the coefficient of the Legendre polynomial, represents the degree of Legendre polynomial, and its mathematical expression is:

[0044] (4)

[0045] Among them, the symbol represents rounding down.

[0046] In addition, substituting formula (3) into formula (1) gives the mathematical expression of the frequency domain after high resolution as follows,

[0047] (5)

[0048] Step 2. Given the frequency band of the expected output, design the expected spectrum for high resolution, and obtain the mathematical expression of the Legendre polynomial coefficients using the least squares method.

[0049] Step 2.1. Design the expected spectrum for high resolution according to the given frequency band of the expected output;

[0050] Let the given frequency range of the expected output be denoted as , assuming that the reflection coefficient of the seismic record has the characteristics of a white noise spectrum, then the mathematical expression of the designed expected amplitude spectrum for high resolution is as follows:

[0051] (6)

[0052] Among them, represents the expected spectrum for high resolution, the symbol represents modulus processing, is the amplitude spectrum amplitude control constant. is the lowest frequency for high-resolution processing, is the highest frequency for high-resolution processing, and the energy of other frequencies remains unchanged; the parameters , and Its value is related to the signal-to-noise ratio of seismic data and is determined through parametric experiments during actual processing.

[0053] Step 2.2. Solve the mathematical expression of the Legendre polynomial coefficients using the least squares method;

[0054] The amplitude spectrum after processing to improve the resolution of seismic data and the desired amplitude spectrum The error energy of is represented by

[0055] (7)

[0056] Let:

[0057] , ,

[0058] , (8)

[0059] Then formula (7) can be rewritten in the following matrix form:

[0060] (9)

[0061] Use the least squares method to solve for the parameters such that the following equation holds,

[0062] (10)

[0063] That is:

[0064] (11)

[0065] Further derivation and solution yield:

[0066] (12)

[0067] Among them, the elements of the matrix are the coefficients of each term of the Legendre polynomial , , , . Formula (12) is the mathematical expression for calculating the coefficients of each term of the Legendre polynomial.

[0068] 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.

[0069] Step 3.1. Based on the analysis of the seismic data frequency band and data signal-to-noise ratio, set the frequency range parameters after improving the resolution and parameters , and substitute them into Equation (8) to calculate the matrix .

[0070] Step 3.2. Perform Fourier transform on the seismic data to obtain the spectrum of the seismic data , and take the modulus to obtain the amplitude spectrum , and substitute them into Equation (8) to calculate the matrix .

[0071] Step 3.3. According to the sampling interval of the seismic data, calculate the cut-off frequency of the seismic data according to the following formula ,

[0072] (13)

[0073] where is the sampling interval of the seismic data, with the unit of ms

[0074] Let , substitute and into Equation (2), and combine with Equation (4) to calculate each Legendre polynomial value. Given the order of the Legendre polynomial , substitute and into Equation (8) to calculate the matrix .

[0075] Step 3.4. Substitute the matrices , and into Equation (12) to obtain the coefficient matrix , and then obtain the coefficients of each term of the Legendre polynomial .

[0076] Step 4. Substitute the coefficient values of each term of the Legendre polynomial calculated in Step 3 into the frequency-domain mathematical expression with improved resolution derived in Step 1 and perform inverse transformation to the time domain to obtain the final result for output

[0077] Step 4.1. Calculate the spectrum of the seismic data with improved resolution

[0078] Substitute the spectrum of the seismic data calculated in Step 3, the values of each Legendre polynomial , the calculated coefficients of each Legendre polynomial , together with the given order of the Legendre polynomial into Equation (5) in Step 1, so as to obtain the spectrum of the seismic data with improved resolution .

[0079] Step 4.2. Calculate the final result after improving the resolution;

[0080] The spectrum of the seismic data calculated in Step 4.1 is processed according to the following formula to obtain the final resolution improvement result,

[0081] (13)

[0082] where, represents the time-domain result of improving the resolution, and the symbol represents the inverse Fourier transform, represents taking the real part. Take as the output as the final result of the resolution improvement process.

[0083] The method of the present invention can reasonably broaden the frequency band of seismic data, improve the resolution of the data, improve the spatial continuity and interpretability of the in-phase axis of thin reservoirs, thereby improving the recognition and identification ability of thin reservoirs in the seismic data volume, and providing a high-resolution broadband data basis for the subsequent interpretation of seismic data and geological reservoir exploration and development. This method does not require wavelet estimation, avoids the complex parameter quality control process in links such as wavelet estimation, has few parameter settings, high discrimination of the functions of each parameter, convenient quality control, and is convenient for parameter optimization.

[0084] In addition, the present invention also gives two specific examples to verify the effectiveness of the method proposed by the present invention.

[0085] In Specific Example 1 and Example 2, the method for improving the resolution of seismic data described in the present invention is described in combination with synthetic seismic records and actual post-stack seismic data respectively.

[0086] Example 1

[0087] Figure 2 is a waveform comparison diagram before and after the resolution improvement process of the synthetic seismic record in Example 1 of the present invention. The black line in (c) is the waveform display of the synthetic seismic record obtained by convolving the seismic wavelet in (a) with 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 this seismic wavelet is 15 Hz and the frequency band of the wavelet is relatively narrow, which results in a low resolution of the synthetic seismic record in (c), and two relatively close reflection coefficients cannot be distinguished on the waveform of the synthetic seismic record. The black line in (e) is the result after processing the synthetic seismic record in (c) using the method of the present invention to improve the resolution. The order of the Legendre polynomial orthogonal decomposition used is 30, and the frequency band parameter in the resolution improvement operator is , and the parameter is 3. Comparing the waveforms of the enhanced resolution results in (e) with the reflection coefficient sequences, it can be seen that the waveforms after enhanced resolution match the reflection coefficient sequences. Most of the relatively close reflection coefficient sequences can be identified and distinguished by the waveforms of the enhanced resolution results. Comparing the waveform and reflection coefficient matching before and after the enhanced resolution processing in (c) and (e), it can be seen from the figure that the resolution ability of the seismic data processed by the method of the present invention is significantly improved, and the matching of the seismic data waveform and the reflection coefficient is significantly improved. After the enhanced resolution processing, the waveforms at the positions indicated by the arrows in the figure are more matched with the true reflection coefficients, and to a certain extent, the consistency between the waveform and the strength of the reflection coefficient is restored.

[0088] Since the frequency band of the results after enhanced resolution is inconsistent with the frequency band range of the reflection coefficients, in order to further verify the amplitude preservation property of this method, the true reflection coefficient sequence is subjected to low-pass filtering processing with 0 - 50 Hz as the theoretical value, and the result is as Figure 2 shown in the waveform of (d). Since the amplitude of the low-pass filtering result of the reflection coefficient is small, for the convenience of comparison, the amplitude of the low-pass filtering result in (d) is multiplied by 20 for amplification processing. The theoretical value after low-pass filtering of the reflection coefficient is compared with the waveform of the seismic record after enhanced resolution to verify the amplitude preservation property of the enhanced resolution processing. Comparing (d) and (e), it can be seen that the waveforms of the synthetic seismic record after enhanced resolution are very similar to the waveforms after low-pass filtering of the theoretical reflection coefficients, and the strength relationship of the amplitudes is basically completely consistent, thus indicating that this enhanced resolution method has good amplitude preservation property. In order to more accurately verify the amplitude preservation ability of this method after enhanced 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 in [reference] is 0.2021 (as shown in (c) in Figure 2 [reference]), the correlation coefficient between the low-pass filtering result of the theoretical reflection coefficient and the theoretical reflection coefficient is 0.3090 (as shown in (d) in Figure 2 [reference]), and the correlation coefficient between the result of enhanced resolution and the theoretical reflection coefficient is 0.3044 (as shown in (e) in Figure 2 [reference]). From the numerical comparison of the correlation coefficients, it can be seen that after the enhanced resolution processing, the correlation between the seismic record waveform and the reflection coefficient sequence has been improved, and the correlation coefficient calculated after enhanced resolution is very close to the correlation coefficient calculated from the low-pass filtering result of the reflection coefficient, thus verifying that the processing result of enhancing the resolution by using this method has good amplitude preservation property.

[0089] Figure 3 The comparison chart of the amplitude spectra before and after enhancing the resolution of the synthetic seismic record is given. From this chart, the selection of the amplitude spectrum amplitude control constant can be quality controlled, and the constant The value of should be preferably 3. For the resolution improvement parameters and , their values should be such that, on the premise of ensuring a relatively high signal-to-noise ratio of the processing result, the wider the frequency band, the better. For the order of the Legendre polynomial orthogonal decomposition, a relatively small order is preferred, under the condition that there are no frequency dips in the amplitude spectrum after the resolution improvement processing and the energy at the low, medium, and high frequency ends is relatively balanced. From Figure 3 , by further comparing the amplitude spectra before and after processing, it can be seen that the frequency band of the amplitude spectrum of the synthetic seismogram before processing is relatively narrow, with a frequency range of approximately 6 - 32 Hz. After the resolution improvement processing, the frequency band range is approximately 2 - 52 Hz, and the frequency band of the seismic data is broadened by approximately 20 Hz, indicating that relatively broadband seismic data is obtained after the resolution improvement processing.

[0090] Figure 4 Figure

[0091] is a comparison diagram of the amplitude spectra of the resolution improvement processing result of the synthetic seismogram and the theoretical value (the result after low-pass filtering the reflection coefficient from 0 - 50 Hz * 20 coefficients). It can be seen from the figure that the amplitude spectrum after the resolution improvement is highly consistent with the theoretical amplitude spectrum, basically maintaining the relative strength relationship between the amplitude spectra of the reflection coefficients, which reflects from the side that the resolution improvement method has good amplitude preservation.

[0092] Example 2

[0093] Figure 5 Figure Figure 6The waveform variable area display after the post-stack actual seismic data is processed by the method of the present invention to improve the resolution is given. Generally speaking, it can be seen from this figure that whether it is the in-phase axis of strong reflection waves or the in-phase axis of weak reflection waves, their continuity has been greatly improved. The in-phase axis can be continuously traced in space. Compared with before processing, the continuity of the in-phase axis has been improved, and the spatial interpretability of thin layers in the section has been enhanced. Further comparing the positions of thin interbedded layers shown by the rectangular frames before and after processing, it can be seen that the number of in-phase axes within the rectangular frame has changed from 2-3 sets that were difficult to distinguish before processing to 3 sets of in-phase axes that can be clearly resolved after processing. The waveforms of the thin interbedded layers can be clearly distinguished, the waveforms of the in-phase axes are clear, and the continuity is good, and the effect of improving the resolution is obvious. Figure 7 It is a comparison diagram of the amplitude spectra before and after the resolution of the post-stack actual seismic data is improved. It can be seen from the figure that the frequency band of the original data is relatively narrow, and the main frequency is about 30 Hz. After the resolution is improved by the method of the present invention, the energy at both the low-frequency end and the high-frequency end of the data has been well compensated and enhanced. The frequency band of the data is relatively wide. After processing, the frequency band of the data has been broadened by nearly 18 Hz, and the main frequency has been increased by about 6 Hz, and a relatively broadband resolution improvement processing result has been obtained. Thus, the effectiveness of the method of the present invention and the ability to improve the resolution of actual data are verified.

[0094] Embodiment 2

[0095] This Embodiment 2 describes a system for improving the resolution of seismic data. This system is based on the same inventive concept as the method for improving the resolution of seismic data in the above Embodiment 1.

[0096] A system for improving the resolution of seismic data includes the following modules:

[0097] Frequency domain resolution improvement calculation module, which calculates the spectrum of the seismic data after resolution improvement from the amplitude spectrum of the seismic data, the order of the Legendre polynomial decomposition, and the coefficient values of each term of the Legendre polynomial.

[0098] Coefficient value calculation module for each term of the Legendre polynomial, which calculates the coefficient values of each term of the Legendre polynomial by using the least squares method from the amplitude spectrum of the seismic data, the cut-off frequency, the order of the Legendre polynomial, the given frequency range by the user, and the amplitude spectrum amplitude control constant.

[0099] Amplitude spectrum and cut-off frequency calculation module for seismic data, which performs Fourier transform on the seismic data to obtain the spectrum of the seismic data, takes the modulus of the spectrum of the seismic data to obtain the amplitude spectrum of the seismic data, and calculates the cut-off frequency by using the sampling interval. The calculated amplitude spectrum and cut-off frequency of the seismic data are used as input parameters for the coefficient value calculation module of each term of the Legendre polynomial.

[0100] 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 for each term into the frequency-domain resolution improvement calculation module, and combines other input parameters to calculate the spectrum of the seismic data after resolution improvement. Further perform an inverse Fourier transform on this spectrum and take the real part as the final output result of the resolution improvement.

[0101] It should be noted that in the system for improving the resolution of seismic data, the implementation processes of the functions and roles of each functional module are specifically described in the corresponding steps of the method in the above-mentioned Embodiment 1, and will not be elaborated here.

[0102] Embodiment 3

[0103] This Embodiment 3 describes a computer device, which includes a memory and one or more processors. An executable code is stored in the memory. When the processor executes the executable code, it is used to implement the steps of the method for improving the resolution of seismic data in the above-mentioned Embodiment 1.

[0104] In this embodiment, the computer device is any device or apparatus with data processing capabilities, which will not be elaborated here.

[0105] Embodiment 4

[0106] 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.

[0107] This computer-readable storage medium can 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.

[0108] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to listing the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any person skilled in the art under the teaching of this specification fall within the substantial 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 the seismic data is denoted by ,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 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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