High-resolution time-varying spectrum simulation method, device, electronic equipment and medium

Abstract

The present application discloses a high-resolution time-varying spectrum simulation method, device, electronic device, and medium. The method may include: performing a Gabor transform on seismic data to obtain a time-frequency amplitude spectrum and a time-frequency logarithmic spectrum; performing nonlinear smoothing on the time-frequency logarithmic spectrum to obtain a mean-filtered time-frequency logarithmic spectrum; obtaining the attenuation trend of the time-frequency logarithmic spectrum in the time direction and calculating the time-varying wavelet time-frequency logarithmic spectrum; calculating the time-varying wavelet amplitude spectrum based on the time-varying wavelet time-frequency logarithmic spectrum; calculating the frequency band widening at the low-frequency and high-frequency ends of the time-varying wavelet to determine the expected output of the time-varying wavelet; calculating a high-resolution operator based on the time-varying wavelet amplitude spectrum and the expected output of the time-varying wavelet; and calculating the high-resolution time-varying spectrum result. The present invention designs a reasonable high-resolution operator based on the time-varying signal-to-noise ratio characteristics of the data, achieving the purpose of reasonably improving the resolution of shallow, medium, and deep data and easily controlling parameters, thereby providing a high-resolution data foundation for subsequent inversion and interpretation.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas geophysics technology, and more specifically, to a high-resolution time-varying spectrum simulation method, device, electronic equipment and medium. Background Art

[0002] When seismic waves propagate through underground media, they absorb and attenuate their energy due to the medium's inelasticity, with high-frequency energy attenuated more severely. This causes the seismic wavelet to be time-varying, leading to a gradual decrease in the resolution of seismic data. Observed seismic data is noisy, so to effectively improve the resolution of seismic data in noisy environments, it is essential to perform relatively accurate time-varying wavelet estimation and design appropriate resolution-enhancing operators.

[0003] Currently, researchers are mainly working on improving seismic resolution from two aspects: time-varying sub-wave spectrum estimation and deconvolution operator design.

[0004] (1) Time-varying wavelet amplitude spectrum estimation: Seismic data are time-varying. To perform time-varying amplitude spectrum estimation, the seismic data must be transformed into the time-frequency domain and the frequency domain spectrum simulation concept must be applied to the time-frequency domain. Time-varying wavelet amplitude spectrum estimation can be performed based on Gabor transform, S transform, and generalized S transform.

[0005] (2) Design of resolution-enhancing operators: The commonly used time-varying resolution-enhancing operator design is generally to flatten the spectrum of the instantaneous wavelet in the time-frequency domain so that the expected output of the instantaneous wavelet is a unit pulse function.

[0006] The current methods for improving seismic time-frequency domain resolution have the following main problems:

[0007] ① The time-varying wavelet amplitude spectrum estimation is easily affected by the reflection coefficient factor and has poor stability;

[0008] ② It is difficult for the resolution-enhancing operator to adapt to the time-varying signal-to-noise ratio characteristics of the data.

[0009] Therefore, it is necessary to develop a high-resolution time-varying spectrum simulation method, device, electronic equipment and medium.

[0010] The information disclosed in the background technology section of the present invention is only intended to deepen the understanding of the general background technology of the present invention, and should not be regarded as an admission or any form of suggestion that the information constitutes the prior art already known to those skilled in the art. Summary of the Invention

[0011] The present invention proposes a high-resolution time-varying spectrum simulation method, device, electronic equipment and medium, which can design a reasonable resolution improvement operator based on the time-varying characteristics of the data signal-to-noise ratio, achieve the purpose of reasonable improvement of shallow, medium and deep data resolution and easy parameter control, and provide a high-resolution data foundation for subsequent inversion and interpretation.

[0012] In a first aspect, an embodiment of the present disclosure provides a high-resolution time-varying spectrum simulation method, comprising:

[0013] Gabor transform is performed on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum;

[0014] Performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering;

[0015] According to the time-frequency logarithmic spectrum after the mean filtering, the attenuation trend of the time-frequency logarithmic spectrum in the time direction is obtained, and then the time-varying wavelet time-frequency logarithmic spectrum is calculated;

[0016] Calculating the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum;

[0017] Calculate the bandwidth widening of the low-frequency end and the high-frequency end of the time-varying wave, and determine the expected output of the time-varying wavelet;

[0018] calculating a high-resolution operator based on the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output;

[0019] A high-resolution time-varying spectrum result is calculated according to the time-frequency amplitude spectrum and the high-resolution operator.

[0020] Preferably, performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering includes:

[0021] Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering:

[0022] Open a time window for the time-frequency logarithmic spectrum, and sort the data in the time window from small to large;

[0023] Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window;

[0024] The sliding time window obtains the alpha-trim mean filtering output of the time-frequency log spectrum of the current frequency.

[0025] Preferably, with respect to the attenuation trend of the time-frequency logarithmic spectrum in the time direction, polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum:

[0026]

[0027] Among them, Q tf (t i ,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

[0028] Preferably, the time-varying wavelet amplitude spectrum is calculated by formula (2):

[0029] w(t,f)=exp(Q tf (t,f)) (2)

[0030] Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

[0031] Preferably, calculating the bandwidth broadening of the time-varying low-frequency end and the high-frequency end and determining the expected output of the time-varying wavelet includes:

[0032] The band widening amount of the time-varying low-frequency end and high-frequency end is calculated, and the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are respectively moved toward the low-frequency end and the high-frequency end by the corresponding band widening amount. After the movement, the amplitude of the amplitude spectrum missing in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

[0033] Preferably, the high-resolution operator is calculated by formula (3):

[0034]

[0035] Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

[0036] Preferably, the high-resolution time-varying spectrum result is calculated by formula (4):

[0037] x(t)=G -1 [d(t,f)o(t,f)] (4)

[0038] Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

[0039] As a specific implementation of the embodiment of the present disclosure,

[0040] In a second aspect, the present disclosure further provides a high-resolution time-varying spectrum simulation device, comprising:

[0041] Gabor transform module, which performs Gabor transform on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum;

[0042] a nonlinear smoothing processing module, performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering;

[0043] A time-varying wavelet time-frequency logarithmic spectrum calculation module obtains the attenuation trend of the time-frequency logarithmic spectrum in the time direction according to the time-frequency logarithmic spectrum after the mean filtering, and then calculates the time-varying wavelet time-frequency logarithmic spectrum;

[0044] A time-varying wavelet amplitude spectrum calculation module calculates the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum;

[0045] The time-varying wavelet expected output determination module calculates the frequency band widening amount of the time-varying low-frequency end and the high-frequency end to determine the time-varying wavelet expected output;

[0046] A high-resolution operator calculation module calculates a high-resolution operator according to the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output;

[0047] The high-resolution time-varying spectrum result calculation module calculates the high-resolution time-varying spectrum result according to the time-frequency amplitude spectrum and the high-resolution operator.

[0048] Preferably, performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering includes:

[0049] Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering:

[0050] Open a time window for the time-frequency logarithmic spectrum, and sort the data in the time window from small to large;

[0051] Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window;

[0052] The sliding time window obtains the alpha-trim mean filtering output of the time-frequency logarithmic spectrum of the current frequency.

[0053] Preferably, with respect to the attenuation trend of the time-frequency logarithmic spectrum in the time direction, polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum:

[0054]

[0055] Among them, Q tf (t i,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

[0056] Preferably, the time-varying wavelet amplitude spectrum is calculated by formula (2):

[0057] w(t,f)=exp(Q tf (t,f)) (2)

[0058] Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

[0059] Preferably, calculating the bandwidth broadening of the time-varying low-frequency end and the high-frequency end and determining the expected output of the time-varying wavelet includes:

[0060] The band widening amount of the time-varying low-frequency end and high-frequency end is calculated, and the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are respectively moved toward the low-frequency end and the high-frequency end by the corresponding band widening amount. After the movement, the amplitude of the amplitude spectrum missing in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

[0061] Preferably, the high-resolution operator is calculated by formula (3):

[0062]

[0063] Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

[0064] Preferably, the high-resolution time-varying spectrum result is calculated by formula (4):

[0065] x(t)=G -1 [d(t,f)o(t,f)] (4)

[0066] Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

[0067] In a third aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising:

[0068] a memory storing executable instructions;

[0069] A processor runs the executable instructions in the memory to implement the high-resolution time-varying spectrum simulation method.

[0070] In a fourth aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, implements the high-resolution time-varying spectrum simulation method.

[0071] The methods and apparatus of the present invention have other features and advantages that will be apparent from or will be described in detail in the accompanying drawings and subsequent detailed descriptions incorporated herein, which together serve to explain the specific principles of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0073] Figure 1 A flow chart showing the steps of a high-resolution time-varying spectrum simulation method according to an embodiment of the present invention.

[0074] Figure 2a 、 Figure 2b 、 Figure 2c 、 Figure 2d Schematic diagrams respectively show a simulated reflection coefficient sequence, source wavelet, synthetic stationary seismic record, and the result of attenuating the stationary seismic record using constant Q according to an embodiment of the present invention.

[0075] Figure 3a 、 Figure 3b 、 Figure 3c 、 Figure 3d 、 Figure 3e 、 Figure 3f The time spectrum of the reflection coefficient sequence according to an embodiment of the present invention, the theoretical value of the time spectrum of the time-varying wavelet, the time spectrum of the synthetic seismic record with attenuation, and the time spectrum of the time spectrum of the synthetic seismic record using the spectrum simulation method are respectively shown. Figure 3c The results of direct time-varying sub-spectrum estimation on Figure 3a Schematic diagram of the high-resolution time-varying spectrum obtained by this method after 50-point smoothing in the time direction.

[0076] Figure 4 A schematic diagram showing a high-frequency end band widening amount according to an embodiment of the present invention is shown.

[0077] Figure 5 A schematic diagram showing expected output of a time-varying wavelet according to an embodiment of the present invention is shown.

[0078] Figure 6a 、 Figure 6b Schematic diagrams showing an actual post-stack profile and a high-resolution time-varying spectrum result according to an embodiment of the present invention are shown respectively.

[0079] Figure 7 A block diagram of a high-resolution time-varying spectrum simulation device according to an embodiment of the present invention is shown.

[0080] Description of reference numerals:

[0081] 201. Gabor transform module; 202. Nonlinear smoothing processing module; 203. Time-varying wavelet time-frequency logarithmic spectrum calculation module; 204. Time-varying wavelet amplitude spectrum calculation module; 205. Time-varying wavelet expected output determination module; 206. High-resolution operator calculation module; 207. High-resolution time-varying spectrum result calculation module. DETAILED DESCRIPTION

[0082] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0083] The present invention provides a high-resolution time-varying spectrum simulation method, comprising:

[0084] Gabor transform is performed on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum;

[0085] Perform nonlinear smoothing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering;

[0086] According to the time-frequency logarithmic spectrum after mean filtering, the attenuation trend of the time-frequency logarithmic spectrum in the time direction is obtained, and then the time-varying wavelet time-frequency logarithmic spectrum is calculated;

[0087] Calculate the time-varying wavelet amplitude spectrum based on the time-varying wavelet time-frequency logarithmic spectrum;

[0088] Calculate the bandwidth widening of the low-frequency end and the high-frequency end of the time-varying wave, and determine the expected output of the time-varying wavelet;

[0089] Calculate the high-resolution operator based on the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output;

[0090] Based on the time-frequency amplitude spectrum and high-resolution operators, the high-resolution time-varying spectrum results are calculated.

[0091] In one example, performing nonlinear smoothing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering includes:

[0092] Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering:

[0093] Open a time window for the time-frequency logarithmic spectrum and sort the data in the time window from small to large;

[0094] Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window;

[0095] The sliding time window obtains the alpha-trim mean filter output of the time-frequency logarithmic spectrum of the current frequency.

[0096] In one example, for the attenuation trend of the time-frequency logarithmic spectrum in the time direction, a polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum:

[0097]

[0098] Among them, Q tf (t i ,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

[0099] In one example, the time-varying wavelet amplitude spectrum is calculated using formula (2):

[0100] w(t,f)=exp(Q tf (t,f)) (2)

[0101] Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

[0102] In one example, calculating the bandwidth broadening amounts of the time-varying low-frequency end and the high-frequency end and determining the expected output of the time-varying wavelet includes:

[0103] Calculate the band widening of the time-varying low-frequency and high-frequency ends, and move the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum to the low-frequency and high-frequency ends respectively by the corresponding band widening amount. After the movement, the amplitude of the missing amplitude spectrum in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

[0104] In one example, the high-resolution operator is calculated by formula (3):

[0105]

[0106] Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

[0107] In one example, the high-resolution time-varying spectrum result is calculated by formula (4):

[0108] x(t)=G -1 [d(t,f)o(t,f)] (4)

[0109] Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

[0110] Specifically, Gabor transform is performed on the seismic data and the absolute value is taken to obtain the time-frequency amplitude spectrum d(t,f), where the symbol t represents time and f represents frequency. The logarithm of the time-frequency amplitude spectrum is taken to obtain the time-frequency logarithmic spectrum recorded as log(d(t,f)).

[0111] The alpha-trim mean filter is used to perform nonlinear smoothing on the time-frequency logarithmic spectrum log(d(t,f)) of the earthquake record:

[0112] ① For the time-frequency logarithmic spectrum log(d(t,f0)) of frequency f0, open a time window of a certain length;

[0113] ② Sort the data in the time window from small to large;

[0114] ③ Delete the minimum and maximum values ​​of the α ratio in the total number, where 0<α<0.5;

[0115] ④ Calculate the mean of the remaining part as the filter output at the center of the time window;

[0116] ⑤ Sliding the time window to obtain the alpha-trim mean filter output of the time-frequency logarithmic spectrum log(d(t,f0)) with frequency f0;

[0117] ⑥ Repeat steps ②-⑤ for each frequency of the time-frequency logarithmic spectrum log(d(t,f)) to obtain the time-frequency logarithmic spectrum after mean filtering

[0118] Time-frequency logarithmic spectrum after mean filtering In the sense of least squares, the polynomial of formula (5) is fitted along the time direction to obtain the attenuation trend Q in the time direction of the time-frequency logarithmic spectrum. t (t,f i ):

[0119]

[0120] Among them, Q t (t,f i ) represents the polynomial along the time direction Fitting results, i=1,2,…,Nyquist,f Nyquist is the cutoff frequency, p t is the given polynomial order, which is a positive integer. t The parameter b can be obtained by using the least squares fitting formula of formula (2) j :

[0121]

[0122] Among them, ε t,i Indicates frequency f i The minimum error energy of fitting along the time direction is set as t and b j Substituting into formula (5), we can calculate the time-frequency logarithmic spectrum after trend fitting of each frequency along the time direction, that is, the attenuation trend Q of the time-frequency logarithmic spectrum in the time direction t (t,f).

[0123] Q t (t,f i ) is fitted with a polynomial along the frequency direction by formula (1) to eliminate the oscillation in the frequency direction, and the time-frequency logarithmic spectrum Q of the time-varying wavelet is obtained. tf (t,f). Given parameter p f The value of parameter c can be obtained by using formula (7) k :

[0124]

[0125] Among them, ε f,i Indicates time t i The minimum error energy along the frequency direction is fitted. f and c k Substitute into formula (1) to calculate the time-frequency logarithmic spectrum Q of the time-varying wavelet tf (t,f).

[0126] Time-frequency logarithmic spectrum Q of time-varying wavelet tf (t,f) is processed exponentially, and the amplitude spectrum W(t,f) of the time-varying wavelet is obtained by formula (2).

[0127] Calculate the time-varying bandwidth of the low-frequency end and the high-frequency end, respectively, and record them as I lf (t,f) and I hf (t,f). Among them, I lf (t,f) and I hf (t,f) are time-varying, and their values ​​are determined by the given time-frequency control point parameters (t i ,I lf,i ,I hf,i) is obtained by interpolation calculation. There can be multiple control points, where t i is the time corresponding to the i-th control point, I lf,i Indicates the low-frequency end band widening of the i-th control point, I hf,i The bandwidth expansion of the high-frequency end of the i-th control point is expressed as follows: lf (t,f) and I hf (t, f), the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are moved to the low-frequency end and the high-frequency end respectively by the corresponding band widening amount, and the amplitude of the amplitude spectrum missing in the middle after the movement is set to the amplitude corresponding to the main frequency, which is used as the expected output w′(t, f) of the time-varying wavelet.

[0128] According to the time-varying wavelet amplitude spectrum and the expected output of the time-varying wavelet, the high-resolution operator is calculated by formula (3); according to the time-frequency amplitude spectrum and the high-resolution operator, the high-resolution time-varying spectrum result is calculated by formula (4).

[0129] The present invention also provides a high-resolution time-varying spectrum simulation device, comprising:

[0130] Gabor transform module, which performs Gabor transform on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum;

[0131] A nonlinear smoothing processing module performs nonlinear smoothing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering;

[0132] The time-varying wavelet time-frequency logarithmic spectrum calculation module obtains the attenuation trend of the time-frequency logarithmic spectrum in the time direction according to the time-frequency logarithmic spectrum after mean filtering, and then calculates the time-varying wavelet time-frequency logarithmic spectrum;

[0133] A time-varying wavelet amplitude spectrum calculation module calculates the time-varying wavelet amplitude spectrum based on the time-frequency logarithmic spectrum of the time-varying wavelet;

[0134] The time-varying wavelet expected output determination module calculates the frequency band widening amount of the time-varying low-frequency end and the high-frequency end to determine the time-varying wavelet expected output;

[0135] The high-resolution operator calculation module calculates the high-resolution operator based on the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output;

[0136] The high-resolution time-varying spectrum result calculation module calculates the high-resolution time-varying spectrum result based on the time-frequency amplitude spectrum and the high-resolution operator.

[0137] In one example, performing nonlinear smoothing on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering includes:

[0138] Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering:

[0139] Open a time window for the time-frequency logarithmic spectrum and sort the data in the time window from small to large;

[0140] Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window;

[0141] The sliding time window obtains the alpha-trim mean filter output of the time-frequency logarithmic spectrum of the current frequency.

[0142] In one example, for the attenuation trend of the time-frequency logarithmic spectrum in the time direction, a polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum:

[0143]

[0144] Among them, Q tf (t i ,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

[0145] In one example, the time-varying wavelet amplitude spectrum is calculated using formula (2):

[0146] w(t,f)=exp(Q tf (t,f)) (2)

[0147] Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

[0148] In one example, calculating the bandwidth broadening amounts of the time-varying low-frequency end and the high-frequency end and determining the expected output of the time-varying wavelet includes:

[0149] Calculate the band widening of the time-varying low-frequency and high-frequency ends, and move the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum to the low-frequency and high-frequency ends respectively by the corresponding band widening amount. After the movement, the amplitude of the missing amplitude spectrum in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

[0150] In one example, the high-resolution operator is calculated by formula (3):

[0151]

[0152] Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

[0153] In one example, the high-resolution time-varying spectrum result is calculated by formula (4):

[0154] x(t)=G -1 [d(t,f)o(t,f)] (4)

[0155] Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

[0156] Specifically, Gabor transform is performed on the seismic data and the absolute value is taken to obtain the time-frequency amplitude spectrum d(t,f), where the symbol t represents time and f represents frequency. The logarithm of the time-frequency amplitude spectrum is taken to obtain the time-frequency logarithmic spectrum recorded as log(d(t,f)).

[0157] The alpha-trim mean filter is used to perform nonlinear smoothing on the time-frequency logarithmic spectrum log(d(t,f)) of the earthquake record:

[0158] ① For the time-frequency logarithmic spectrum log(d(t,f0)) of frequency f0, open a time window of a certain length;

[0159] ② Sort the data in the time window from small to large;

[0160] ③ Delete the minimum and maximum values ​​of the α ratio in the total number, where 0<α<0.5;

[0161] ④ Calculate the mean of the remaining part as the filter output at the center of the time window;

[0162] ⑤ Sliding the time window to obtain the alpha-trim mean filter output of the time-frequency logarithmic spectrum log(d(t,f0)) with frequency f0;

[0163] ⑥ Repeat steps ②-⑤ for each frequency of the time-frequency logarithmic spectrum log(d(t,f)) to obtain the time-frequency logarithmic spectrum after mean filtering

[0164] Time-frequency logarithmic spectrum after mean filtering In the sense of least squares, the polynomial of formula (5) is fitted along the time direction to obtain the attenuation trend Q in the time direction of the time-frequency logarithmic spectrum. t (t,f i ):

[0165]

[0166] Among them, Q t (t,f i ) represents the polynomial along the time direction Fitting results, i=1,2,…,Nyquist,f Nyquist is the cutoff frequency, p t is the given polynomial order, which is a positive integer. t The parameter b can be obtained by using the least squares fitting formula of formula (2) j :

[0167]

[0168] Among them, ε t,i Indicates frequency f i The minimum error energy of fitting along the time direction is set as t and b j Substituting into formula (5), we can calculate the time-frequency logarithmic spectrum after trend fitting of each frequency along the time direction, that is, the attenuation trend Q of the time-frequency logarithmic spectrum in the time direction t (t,f).

[0169] Q t (t,f i ) is fitted with a polynomial along the frequency direction by formula (1) to eliminate the oscillation in the frequency direction, and the time-frequency logarithmic spectrum Q of the time-varying wavelet is obtained. tf (t,f). Given parameter p f The value of parameter c can be obtained by using formula (7) k :

[0170]

[0171] Among them, ε f,i Indicates time t i The minimum error energy along the frequency direction is fitted. f and c k Substitute into formula (1) to calculate the time-frequency logarithmic spectrum Q of the time-varying wavelet tf (t,f).

[0172] Time-frequency logarithmic spectrum Q of time-varying wavelet tf (t,f) is processed exponentially, and the amplitude spectrum W(t,f) of the time-varying wavelet is obtained by formula (2).

[0173] Calculate the time-varying bandwidth of the low-frequency end and the high-frequency end, respectively, and record them as I lf (t,f) and I hf (t,f). Among them, I lf (t,f) and I hf (t,f) are time-varying, and their values ​​are determined by the given time-frequency control point parameters (t i ,I lf,i ,I hf,i) is obtained by interpolation calculation. There can be multiple control points, where t i is the time corresponding to the i-th control point, I lf,i Indicates the low-frequency end band widening of the i-th control point, I hf,i The bandwidth expansion of the high-frequency end of the i-th control point is expressed as follows: lf (t,f) and I hf (t, f), the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are moved to the low-frequency end and the high-frequency end respectively by the corresponding band widening amount, and the amplitude of the amplitude spectrum missing in the middle after the movement is set to the amplitude corresponding to the main frequency, which is used as the expected output w′(t, f) of the time-varying wavelet.

[0174] According to the time-varying wavelet amplitude spectrum and the expected output of the time-varying wavelet, the high-resolution operator is calculated by formula (3); according to the time-frequency amplitude spectrum and the high-resolution operator, the high-resolution time-varying spectrum result is calculated by formula (4).

[0175] The present invention also provides an electronic device, which includes: a memory storing executable instructions; and a processor running the executable instructions in the memory to implement the above-mentioned high-resolution time-varying spectrum simulation method.

[0176] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned high-resolution time-varying spectrum simulation method.

[0177] To facilitate understanding of the solutions and effects of the embodiments of the present invention, four specific application examples are given below. Those skilled in the art should understand that these examples are only for facilitating understanding of the present invention, and any specific details thereof are not intended to limit the present invention in any way.

[0178] Example 1

[0179] Figure 1 A flow chart showing the steps of a high-resolution time-varying spectrum simulation method according to an embodiment of the present invention.

[0180] like Figure 1As shown, the high-resolution time-varying spectrum simulation method includes: step 101, performing Gabor transformation on seismic data to obtain a time-frequency amplitude spectrum and a time-frequency logarithmic spectrum; step 102, performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering; step 103, obtaining the attenuation trend of the time-frequency logarithmic spectrum in the time direction according to the time-frequency logarithmic spectrum after mean filtering, and then calculating the time-varying wavelet time-frequency logarithmic spectrum; step 104, calculating the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum; step 105, calculating the frequency band widening amount of the time-varying low-frequency end and the high-frequency end, and determining the expected output of the time-varying wavelet; step 106, calculating the high-resolution operator according to the time-varying wavelet amplitude spectrum and the expected output of the time-varying wavelet; step 107, calculating the high-resolution time-varying spectrum result according to the time-frequency amplitude spectrum and the high-resolution operator.

[0181] Figure 2a 、 Figure 2b 、 Figure 2c 、 Figure 2d Schematic diagrams respectively show a simulated reflection coefficient sequence, source wavelet, synthetic stationary seismic record, and the result of attenuating the stationary seismic record using constant Q according to an embodiment of the present invention.

[0182] Figure 2a-2d In order to verify the synthetic attenuation seismic data designed by the present invention, Figure 2a is the reflection coefficient sequence of the simulated Gauss-Bernoulli distribution, Figure 2b The Ricker wavelet with a main frequency of 40 Hz is used as the source wavelet. Figure 2c for Figure 2a and Figure 2b The unattenuated synthetic seismic record obtained by convolution, Figure 2d For Figure 2c The synthetic record is attenuated using Q=50 to obtain a synthetic attenuated seismic record.

[0183] Figure 3a 、 Figure 3b 、 Figure 3c 、 Figure 3d 、 Figure 3e 、 Figure 3f The time spectrum of the reflection coefficient sequence according to an embodiment of the present invention, the theoretical value of the time spectrum of the time-varying wavelet, the time spectrum of the synthetic seismic record with attenuation, and the time spectrum of the time spectrum of the synthetic seismic record using the spectrum simulation method are respectively shown. Figure 3c The results of direct time-varying sub-spectrum estimation on Figure 3a Schematic diagram of the high-resolution time-varying spectrum obtained by this method after 50-point smoothing in the time direction.

[0184] Figure 3a for Figure 2a The time-frequency amplitude spectrum after Gabor transformation, Figure 3b for Figure 2b The theoretical value of the amplitude spectrum of the time-varying wavelet calculated after Q=50 attenuation, Figure 3c is the time-frequency spectrum of the synthesized seismic record with attenuation after Gabor transformation. Theoretically, Figure 3c equal Figure 3a and Figure 3b The product of Figure 3a 、 Figure 3b and Figure 3c The comparison shows that Figure 3c The local oscillation of the medium time-frequency amplitude spectrum along the time and frequency directions is mainly caused by the reflection coefficient factor, and the main task of time-varying spectrum simulation is to Figure 3c Eliminating the local oscillation of the time-frequency amplitude spectrum, we can obtain Figure 3b The amplitude spectrum of a time-varying wavelet that varies slowly with time and frequency.

[0185] Figure 3d In order to use the traditional spectrum simulation method Figure 3c The time-varying wavelet spectrum obtained by spectrum simulation on each time slice is obtained from Figure 3d The results show that after the traditional spectrum simulation method is used to process the time-frequency amplitude spectrum of the attenuation earthquake record, the violent oscillation in the time direction is effectively alleviated, but the time direction still has rapid changes. Figure 3d and Figure 3b It can be seen that the time-varying wavelet amplitude spectrum estimated by directly applying the traditional spectrum simulation method in the time-frequency domain is significantly different from the theoretical value, which is specifically manifested in the poor stability of the estimation result in the time direction.

[0186] Figure 3e right Figure 3d The results are compared after 50-point smoothing in the time direction. Figure 3b 、 Figure 3d and Figure 3e It can be seen that after smoothing in the time direction, the oscillation of the estimated value of the time-varying wavelet amplitude spectrum in the time direction is alleviated, but there is still a certain difference from the theoretical value, which cannot meet the accuracy requirements of the estimated resolution improvement processing.

[0187] Figure 3f In order to utilize the method of the present invention from Figure 3c The time-varying wavelet amplitude spectrum estimated in Figure 3b and Figure 3f It can be seen that the time-varying wavelet amplitude spectrum estimated by the method of the present invention is consistent with the theoretical value, and the estimated time-varying wavelet amplitude spectrum is very stable, which basically eliminates the Figure 3c There is a local oscillation of the time-frequency amplitude spectrum caused by the reflection coefficient factor, so the time-varying wavelet amplitude spectrum estimated by the present invention has a robust performance.

[0188] Figure 4 A schematic diagram showing a high-frequency end band widening amount according to an embodiment of the present invention is shown.

[0189] Figure 5 A schematic diagram showing expected output of a time-varying wavelet according to an embodiment of the present invention is shown.

[0190] Figure 4 The figure shows the high-frequency band widening calculated by the band widening control points (800ms, 20Hz), (2000ms, 15Hz) and (4000ms, 10Hz). The band widening between the control points is obtained by linear interpolation and smoothing. Figure 5 The expected output (solid line) is constructed by the instantaneous wavelet (dashed line) based on the low-frequency broadening and high-frequency broadening, where the low-frequency broadening and high-frequency broadening are determined by I lf (t,f) and I hf (t,f) is given.

[0191] Figure 6a 、 Figure 6b Schematic diagrams showing an actual post-stack profile and a high-resolution time-varying spectrum result according to an embodiment of the present invention are shown respectively.

[0192] Figure 6a is the actual post-stack section, Figure 6b The method of the present invention is demonstrated to Figure 6a The results after resolution enhancement are compared. Figure 6a and Figure 6b It can be seen that after processing the seismic data using the method of the present invention, the resolution is significantly improved, the signal-to-noise ratio is not significantly reduced, and the continuity and identifiability of the events shown in the box in the figure are significantly improved. This shows that the method of the present invention has high stability and good processing effect.

[0193] The research results show that the time-varying wavelet amplitude spectrum estimated by this method has good stability, the designed resolution improvement operator can adapt to the time-varying signal-to-noise ratio characteristics of the data, and the parameters are easy to adjust and control.

[0194] Example 2

[0195] Figure 7 A block diagram of a high-resolution time-varying spectrum simulation device according to an embodiment of the present invention is shown.

[0196] like Figure 7 As shown, the high-resolution time-varying spectrum simulation device includes:

[0197] Gabor transform module 201, performs Gabor transform on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum;

[0198] A nonlinear smoothing processing module 202 performs nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering;

[0199] The time-varying wavelet time-frequency logarithmic spectrum calculation module 203 obtains the attenuation trend of the time-frequency logarithmic spectrum in the time direction according to the time-frequency logarithmic spectrum after mean filtering, and then calculates the time-varying wavelet time-frequency logarithmic spectrum;

[0200] The time-varying wavelet amplitude spectrum calculation module 204 calculates the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum;

[0201] The time-varying wavelet expected output determination module 205 calculates the frequency band broadening amount of the time-varying low-frequency end and the high-frequency end to determine the time-varying wavelet expected output;

[0202] A high-resolution operator calculation module 206 calculates a high-resolution operator based on the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output;

[0203] The high-resolution time-varying spectrum result calculation module 207 calculates the high-resolution time-varying spectrum result according to the time-frequency amplitude spectrum and the high-resolution operator.

[0204] As an optional solution, nonlinear smoothing is performed on the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering, including:

[0205] Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering:

[0206] Open a time window for the time-frequency logarithmic spectrum and sort the data in the time window from small to large;

[0207] Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window;

[0208] The sliding time window obtains the alpha-trim mean filter output of the time-frequency logarithmic spectrum of the current frequency.

[0209] As an optional solution, according to the attenuation trend of the time-frequency logarithmic spectrum in the time direction, a polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum:

[0210]

[0211] Among them, Q tf (t i ,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

[0212] As an alternative, the time-varying wavelet amplitude spectrum is calculated using formula (2):

[0213] w(t,f)=exp(Q tf (t,f)) (2)

[0214] Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

[0215] As an optional solution, the bandwidth broadening of the low-frequency end and the high-frequency end of the time-varying wave is calculated to determine the expected output of the time-varying wavelet.

[0216] Calculate the band widening of the time-varying low-frequency and high-frequency ends, and move the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum to the low-frequency and high-frequency ends respectively by the corresponding band widening amount. After the movement, the amplitude of the missing amplitude spectrum in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

[0217] As an alternative, the high-resolution operator is calculated using formula (3):

[0218]

[0219] Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

[0220] As an alternative, the high-resolution time-varying spectrum is calculated using formula (4):

[0221] x(t)=G -1 [d(t,f)o(t,f)] (4)

[0222] Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

[0223] Example 3

[0224] The present disclosure provides an electronic device comprising: a memory storing executable instructions; and a processor executing the executable instructions in the memory to implement the above-mentioned high-resolution time-varying spectrum simulation method.

[0225] An electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0226] The memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory. The non-volatile memory may include, for example, read-only memory (ROM), a hard disk, flash memory, etc.

[0227] The processor may be a central processing unit (CPU) or other form of processing unit having data processing capability and / or instruction execution capability, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to execute the computer-readable instructions stored in the memory.

[0228] Those skilled in the art should understand that in order to solve the technical problem of how to obtain a good user experience, this embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the scope of protection of this disclosure.

[0229] For detailed description of this embodiment, please refer to the corresponding description in the aforementioned embodiments, which will not be repeated here.

[0230] Example 4

[0231] An embodiment of the present disclosure provides a computer-readable storage medium storing a computer program, which implements the high-resolution time-varying spectrum simulation method when executed by a processor.

[0232] According to an embodiment of the present disclosure, a computer-readable storage medium stores non-transitory computer-readable instructions, which, when executed by a processor, execute all or part of the steps of the aforementioned methods of the embodiments of the present disclosure.

[0233] The above-mentioned computer-readable storage media include, but are not limited to, optical storage media (e.g., CD-ROMs and DVDs), magneto-optical storage media (e.g., MOs), magnetic storage media (e.g., magnetic tapes or mobile hard disks), media with built-in rewritable non-volatile memory (e.g., memory cards), and media with built-in ROM (e.g., ROM cartridges).

[0234] Those skilled in the art should understand that the above description of the embodiments of the present invention is only for the purpose of illustrative purposes only to illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0235] While various embodiments of the present invention have been described above, the above description is intended to be illustrative, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A high-resolution time-varying spectrum simulation method, characterized in that: include: Gabor transform is performed on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum; Performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering; According to the time-frequency logarithmic spectrum after the mean filtering, the attenuation trend of the time-frequency logarithmic spectrum in the time direction is obtained, and then the time-varying wavelet time-frequency logarithmic spectrum is calculated; Calculating the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum; Calculate the bandwidth widening of the low-frequency end and the high-frequency end of the time-varying wave, and determine the expected output of the time-varying wavelet; calculating a high-resolution operator based on the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output; Calculating a high-resolution time-varying spectrum result according to the time-frequency amplitude spectrum and the high-resolution operator; Calculating the bandwidth widening of the low-frequency end and the high-frequency end of the time-varying wave and determining the expected output of the time-varying wavelet include: The band widening amount of the time-varying low-frequency end and high-frequency end is calculated, and the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are respectively moved toward the low-frequency end and the high-frequency end by the corresponding band widening amount. After the movement, the amplitude of the amplitude spectrum missing in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

2. The high-resolution time-varying spectrum simulation method according to claim 1, wherein: Performing nonlinear smoothing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering includes: Perform the following steps for each frequency of the time-frequency logarithmic spectrum to obtain the time-frequency logarithmic spectrum after mean filtering: Open a time window for the time-frequency logarithmic spectrum, and sort the data in the time window from small to large; Delete the minimum and maximum values ​​of the set proportion in the total data, and calculate the mean of the remaining part as the filter output at the center of the time window; The sliding time window obtains the alpha-trim mean filtering output of the time-frequency log spectrum of the current frequency.

3. The high-resolution time-varying spectrum simulation method according to claim 1, wherein: According to the attenuation trend of the time-frequency logarithmic spectrum in the time direction, a polynomial fitting is performed along the frequency direction using formula (1) to obtain the time-varying wavelet time-frequency logarithmic spectrum: Among them, Q tf (t i ,f) is the time-varying wavelet time-frequency logarithmic spectrum, i=1,2,…,M, M is the number of sampling points for each data channel, p f is the polynomial order, f is the frequency, c k is the fitting coefficient.

4. The high-resolution time-varying spectrum simulation method according to claim 1, wherein: The time-varying wavelet amplitude spectrum is calculated by formula (2): w(t,f)=exp(Q tf (t,f)) (2) Where w(t,f) is the time-varying wavelet amplitude spectrum, Q tf (t i ,f) is the time-frequency logarithmic spectrum of the time-varying wavelet.

5. The high-resolution time-varying spectrum simulation method according to claim 1, wherein: The high-resolution operator is calculated by formula (3): Where o(t,f) is the high-resolution operator, w(t,f) is the time-varying wavelet amplitude spectrum, w′(t,f) is the expected output of the time-varying wavelet, and σ is the stability coefficient.

6. The high-resolution time-varying spectrum simulation method according to claim 5, wherein: The high-resolution time-varying spectrum result is calculated by formula (4): x(t)=G -1 [d(t,f)o(t,f)] (4) Among them, x(t) is the high-resolution time-varying spectrum result, d(t,f) is the time-frequency amplitude spectrum, G -1 represents the inverse Gabor transform.

7. A high-resolution time-varying spectrum simulation device, characterized in that: include: Gabor transform module, which performs Gabor transform on seismic data to obtain time-frequency amplitude spectrum and time-frequency logarithmic spectrum; a nonlinear smoothing processing module, performing nonlinear smoothing processing on the time-frequency logarithmic spectrum to obtain a time-frequency logarithmic spectrum after mean filtering; A time-varying wavelet time-frequency logarithmic spectrum calculation module obtains the attenuation trend of the time-frequency logarithmic spectrum in the time direction according to the time-frequency logarithmic spectrum after the mean filtering, and then calculates the time-varying wavelet time-frequency logarithmic spectrum; A time-varying wavelet amplitude spectrum calculation module calculates the time-varying wavelet amplitude spectrum according to the time-varying wavelet time-frequency logarithmic spectrum; The time-varying wavelet expected output determination module calculates the frequency band widening amount of the time-varying low-frequency end and the high-frequency end to determine the time-varying wavelet expected output; A high-resolution operator calculation module calculates a high-resolution operator according to the time-varying wavelet amplitude spectrum and the time-varying wavelet expected output; A high-resolution time-varying spectrum result calculation module calculates a high-resolution time-varying spectrum result according to the time-frequency amplitude spectrum and the high-resolution operator; Calculating the bandwidth widening of the low-frequency end and the high-frequency end of the time-varying wave and determining the expected output of the time-varying wavelet include: The band widening amount of the time-varying low-frequency end and high-frequency end is calculated, and the amplitude spectra on both sides of the main frequency of the instantaneous wavelet amplitude spectrum are respectively moved toward the low-frequency end and the high-frequency end by the corresponding band widening amount. After the movement, the amplitude of the amplitude spectrum missing in the middle is set to the amplitude corresponding to the main frequency, which is used as the expected output of the time-varying wavelet.

8. An electronic device, characterized in that: The electronic device comprises: a memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the high-resolution time-varying spectrum simulation method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the high-resolution time-varying spectrum simulation method according to any one of claims 1 to 6 is implemented.

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