CN111427089B - Seismic data self-adaptive high-frequency compensation method - Google Patents
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Abstract
The invention relates to a seismic data self-adaptive high-frequency compensation method, which is used for constructing a data-driven amplitude compensation filter according to energy absorption attenuation characteristics reflected by seismic data so as to improve the resolution of the seismic data and carrying out self-adaptive high-frequency component compensation on actual seismic data. The method comprises the following steps: (1) realizing Gabor transformation, and constructing Gabor frequency spectrum slices of the seismic channels; (2) constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function; (3) constructing a high-frequency amplitude compensation filter; (4) realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice; (5) and realizing Gabor inverse transformation, and reconstructing the time domain seismic traces after high-frequency amplitude compensation. The method has the advantages that dependence on a Q model can be eliminated when a filter for improving resolution is constructed, adaptive high-frequency component compensation can be performed on seismic data, the frequency bandwidth of the seismic data is effectively increased, and therefore the capability of identifying the thin mutual reservoir through formation imaging and reservoir inversion of the seismic data is enhanced.
Description
Technical Field
The invention relates to the field of petroleum seismic exploration, in particular to a seismic data self-adaptive high-frequency compensation method.
Background
During the process of underground propagation of the seismic signals, high-frequency energy is gradually absorbed by viscoelastic media, and seismic wavelets displayed on a seismic reflection section are gradually stretched along with the increase of the propagation distance. The stretching phenomenon reduces the resolution of seismic data and has a certain influence on the precision and resolution of formation imaging and oil and gas reservoir inversion. However, the geological target of the global oil-gas-containing basin is more and more complex at present, and a series of problems of thin reservoir, small space span and the like are faced. Therefore, it is highly desirable to improve the resolution of seismic data to effectively describe thin interbed reservoirs of oil and gas accumulation.
The inventor has initiated a stabilizing inverse Q filtering method (A stable and effective approach of inverse Q filtering, Geophysics, vol: 67/2002) in 2002 in the world and has been widely applied in the world. The prior inverse Q filtering methods only correct the phase of the seismic signal (Bickel & Natarajan, 1985; Hargreaves & Calvert, 1991), and the pure phase-corrected inverse Q filtering methods cannot compensate the high-frequency amplitude of the seismic signal. And the Wang's stabilization inverse Q filtering series method improves the resolution ratio of the seismic signals by synchronously realizing amplitude compensation and phase correction. However, this family of methods is a model-driven filtering method, depending on the given Q model, when constructing the amplitude compensation filter. Estimation errors are common in the estimation of the Q model, and the generation of the errors can be influenced by the quality of the seismic data or caused by the estimation method of the Q model. Therefore, the processing method for improving the seismic resolution still needs to be improved, and particularly, the method needs to be capable of getting rid of the dependence on the Q model when a filter for improving the resolution is constructed.
Disclosure of Invention
The invention aims to overcome the defect that the prior art depends on a model, and provides a seismic data self-adaptive high-frequency compensation method.
In order to achieve the purpose, the seismic data self-adaptive high-frequency compensation method is used for constructing a data-driven amplitude compensation filter according to the energy absorption attenuation characteristics reflected by the seismic data, and carrying out self-adaptive high-frequency component compensation on the actual seismic data. The invention provides an amplitude compensation filter constructed according to the self characteristics of seismic signals, so that the high-frequency compensation method is a data-driven filtering processing method, is a method for improving the resolution ratio in seismic data self-adaption, and gets rid of the dependence on a Q model when constructing the filter for improving the resolution ratio.
The method comprises the following steps: (1) realizing Gabor transformation, and constructing Gabor frequency spectrum slices of the seismic channels; (2) constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function; (3) constructing a high-frequency amplitude compensation filter; (4) realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice; (5) and realizing Gabor inverse transformation, and reconstructing the time domain seismic traces after high-frequency amplitude compensation. And (1) realizing Gabor transformation and constructing a Gabor frequency spectrum slice of the seismic channel. The implementation process comprises the following steps: using Gaussian time window functionsg(t) Setting a Gabor slice generation function; apply it to seismic tracess(t) Construction of Gabor time slicess(τ,t)：s(τ,t)= s(t) g(t-τ) In the formulaτIs the time position of the gabor slice; then using Fourier transform to obtain Gabor frequency spectrum sliceS(τƒ), where ƒ represents frequency.
As an optimization, the basic principle followed by constructing the high-frequency amplitude compensation filter in the step (3) is that the multiplication of the fitting function of the compensation filter and the gabor amplitude spectrum is equal to 1; and (3) constructing the high-frequency amplitude compensation filter by using a method of forming a simultaneous equation set by all high-frequency component compensation factors, solving an inverse problem of the simultaneous equation set, and constructing a stable and smooth filter by using a smooth matrix constraint.
As optimization, step (2) constructs an analytic function of the Galois field amplitude spectrum and estimates the peak frequency of the Galois field amplitude spectrum, and the optimization is realized in two steps; carrying out normalization processing on the Gabor frequency spectrum slices of each time window, and fitting the normalized Gabor amplitude spectrum by adopting Wang's generalized wavelet frequency spectrum function:
formula (III) ƒ0Is the natural frequency of the generalized seismic wavelet, anduthen is a fractional order indication of the generalized seismic wavelet; the estimation of the peak frequency is represented in analytical form as follows:
。
in the step (2), in order to construct an analytic function of the gabor amplitude spectrum, the gabor frequency spectrum slices of a plurality of seismic channels can be selected from the transverse space for averaging, and then the normalized gabor frequency spectrum slice with the transverse space average is obtainedW s (ƒ). The amplitude compensation filter obtained by the method can also be applied to seismic traces within a certain span of the transverse space, so that the continuity of the filtering processing result of the high-frequency amplitude compensation in the transverse space is maintained.
As an optimization, step (3) constructs a high-frequency amplitude compensation filterH(ƒ) the following rationale is followed:W(ƒ)H(ƒ) = 1; ƒ ≧ ƒ when the frequency is greater than or equal to the peak frequency p By solving an inverse problemW(ƒ)H(ƒ) =1 construction of amplitude compensation filterH(ƒ)=1/[W(ƒ)+σ]Where σ is a white noise coefficient that stabilizes the solution problem; when the frequency is less than the peak frequency, 0 is less than or equal to ƒ<ƒ p The amplitude compensation filter is arranged asH(ƒ)=1。
As an optimization, the method for constructing the high-frequency amplitude compensation filter in the step (3) is not the same as that for the high-frequency amplitude compensation filterH(ƒ) each frequency component is calculated separately, but the solution is made from all ƒ ≧ ƒ p A simultaneous equation set consisting of high-frequency component compensation factors, and a stable and smooth filter is constructed through smooth matrix constraint; the invention is represented by a vector HH(ƒ) representing an analytic function of the Gabor amplitude spectrum by a diagonal matrix WW(ƒ), the solution of the amplitude compensation filter H is: h = [ CW + σ ]2(I-C)]-1C, wherein C is a smooth matrix, C = (I + D) T D)-1And D is T D is the second derivative constraint matrix.
As optimization, step (4) is to apply high frequency amplitude compensation filterH(ƒ) application to Gabor spectral slicesS(τƒ), generating a new gabor spectral slice
：
The step (4) comprises phase correction filtering, phase correction is carried out by using a one-dimensional Q model which changes along with the depth, and the one-dimensional Q model is properly adjusted through time matching with the well-side seismic synthetic channel.
And (5) realizing time domain seismic channels after Gabor inverse transformation reconstruction high-frequency amplitude compensation, and realizing the reconstruction in two steps: first, slicing the Gabor spectrum
Performing inverse Fourier transform to obtain Gabor time slice
(ii) a Then, all the gabor slices are integrated
Reconstruction of high frequency amplitude compensationRear seismic trace
：
In the formulah(t) Is a Gabor reconstruction function, which is a Gabor slice generation function in the step (1)g(t) Is the inverse function of (c).
As an optimization, the gabor reconstruction function in step (5) is an inverse function of the gabor slice generation function described in step (1); since the gabor generating function exists in a discrete form in the implementation of step (1), a discrete expression of the gabor reconstruction function must be obtained by discrete numerical calculation of the gabor generating function, thereby ensuring the accuracy of gabor forward-inverse transformation.
After the technical scheme is adopted, the data-driven high-frequency amplitude compensation filter is constructed according to the absorption attenuation characteristics of the underground stratum carried by the seismic signal to the seismic energy, so that the filter with improved resolution can get rid of the dependence on a Q model, can perform self-adaptive high-frequency component compensation on the seismic data, and effectively increases the frequency bandwidth of the seismic data, thereby enhancing the capability of identifying the thin mutual reservoir through stratum imaging and reservoir inversion of the seismic data.
Drawings
FIG. 1 is a block diagram of a flow chart for implementing the seismic data adaptive high frequency compensation method of the present invention; FIG. 2 is a seismic section showing a double-pass time between 3500ms and 4800ms according to an embodiment of the seismic data adaptive high frequency compensation method of the present invention; fig. 3 is a result of adaptive high-frequency amplitude compensation performed on the seismic section of fig. 2 according to the embodiment of the seismic data adaptive high-frequency compensation method of the present invention, and shows an effect of resolution improvement processing on deep reflection seismic by the data driving method.
Detailed Description
The seismic data self-adaptive high-frequency compensation method constructs a data-driven amplitude compensation filter according to the energy absorption attenuation characteristics reflected by the seismic data, and carries out self-adaptive high-frequency component compensation on the actual seismic data.
The method comprises the following steps: (1) realizing Gabor transformation, and constructing Gabor frequency spectrum slices of the seismic channels; (2) constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function; (3) constructing a high-frequency amplitude compensation filter; (4) realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice; (5) and realizing Gabor inverse transformation, and reconstructing the time domain seismic traces after high-frequency amplitude compensation. The invention provides a filter for amplitude compensation constructed according to the self characteristics of seismic data, and further improves the resolution of the seismic data, so the method is a filtering method driven by complete seismic data and is a method for improving the resolution of seismic data in a self-adaptive manner.
And (1) realizing Gabor transformation and constructing a Gabor frequency spectrum slice of the seismic channel. The implementation process comprises the following steps: using Gaussian time window functionsg(t) Setting a Gabor slice generation function; apply it to seismic tracess(t) Construction of Gabor time slicess(τ,t)：s(τ,t)= s(t) g(t-τ) In the formulaτIs the time position of the gabor slice; then using Fourier transform to obtain Gabor frequency spectrum sliceS(τƒ), where ƒ represents frequency.
Step (2) constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function, and realizing the analysis in two steps; carrying out normalization processing on the Gabor frequency spectrum slices of each time window, and fitting the normalized Gabor amplitude spectrum by adopting Wang's generalized wavelet frequency spectrum function:
formula (III) ƒ0Is the natural frequency of the generalized seismic wavelet, anduthen is a fractional order indication of the generalized seismic wavelet; the estimation of the peak frequency is represented in analytical form as follows:
。
in the process of fitting the normalized Gabor amplitude spectrum in the step (2), in order to construct an analytic function of the Gabor amplitude spectrum, Gabor frequency spectrum slices of a plurality of seismic channels can be selected from a transverse space for averaging, and then the normalized Gabor frequency spectrum slice with the average transverse space is obtainedW s (ƒ). The amplitude compensation filter obtained by the method can also be applied to seismic traces within a certain span of the transverse space, so that the continuity of the filtering processing result of the high-frequency amplitude compensation in the transverse space is maintained.
Step (3) constructing a high-frequency amplitude compensation filterH(ƒ) the following rationale is followed:W(ƒ)H(ƒ) = 1; when the frequency is greater than the peak frequency, ƒ is equal to or greater than ƒ p By solving an inverse problemW(ƒ)H(ƒ) =1 construction of amplitude compensation filterH(ƒ)=1/[W(ƒ)+σ]Where σ is a white noise coefficient that stabilizes the solution problem; when the frequency is less than the peak frequency, 0 is less than or equal to ƒ<ƒ p The amplitude compensation filter is arranged asH(ƒ)=1。
A method for constructing the high-frequency amplitude compensation filter in the step (3), which is not a method for constructing the high-frequency amplitude compensation filterH(ƒ) each frequency component is calculated separately, but the solution is made from all ƒ ≧ ƒ p A simultaneous equation set consisting of frequency component compensation factors, and a stable and smooth filter is constructed through the constraint of a smoothing matrix; the invention is represented by a vector HH(ƒ) representing an analytic function of the Gabor amplitude spectrum by a diagonal matrix WW(ƒ), the solution of the amplitude compensation filter H is: h = [ CW + σ ]2(I-C)]-1C, wherein C is a smooth matrix, C = (I + D) T D)-1And D is T D is the second derivative constraint matrix.
Step (4) is to compensate the filter with high frequency amplitudeH(ƒ) application to Gabor spectral slicesS(τƒ), generating a new gabor spectral slice
：
The step (4) comprises phase correction filtering, phase correction is carried out by using a one-dimensional Q model which changes along with the depth, and the one-dimensional Q model is properly adjusted through time matching with the well-side seismic synthetic channel.
Step (5) realizing Gabor inverse transformation, reconstructing a time domain seismic channel after high-frequency amplitude compensation, and realizing by two steps: first, slicing the Gabor spectrum
Performing inverse Fourier transform to obtain Gabor time slice
(ii) a Then, all the gabor slices are integrated
Reconstructing seismic traces after high frequency amplitude compensation
：
In the formulah(t) Is a Gabor reconstruction function, which is a Gabor slice generation function in the step (1)g(t) Is the inverse function of (c).
The Gabor reconstruction function in the step (5) is an inverse function of the Gabor slice generation function in the step (1); since the gabor generating function exists in a discrete form in the implementation of step (1), a discrete expression of the gabor reconstruction function must be obtained by discrete numerical calculation of the gabor generating function, thereby ensuring the accuracy of gabor forward-inverse transformation.
In a word, according to the absorption attenuation characteristics of the underground stratum carried by the seismic signal to the seismic energy, the data-driven high-frequency amplitude compensation filter is constructed, the seismic data are subjected to self-adaptive high-frequency component compensation, the frequency bandwidth of the seismic data is effectively increased, and therefore the capability of identifying the thin mutual reservoir through stratum imaging and reservoir inversion of the seismic data is enhanced.
In order to make the technical solutions and advantages of the present invention more apparent, embodiments of the present invention are specifically described below with reference to the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention and not to limit the present invention.
The invention provides a seismic data self-adaptive high-frequency amplitude compensation method. FIG. 1 is a flow chart of a basic implementation of the method of the present invention.
And S101, realizing Gabor transformation and constructing a Gabor frequency spectrum slice of the seismic channel. The implementation process comprises the following steps: using Gaussian time window functionsg(t) Setting a Gabor slice generation function; apply it to seismic tracess(t) Construction of Gabor time slicess(τ,t)：s(τ,t)= s(t) g(t-τ) In the formulaτIs the time position of the gabor slice; then using Fourier transform to obtain Gabor frequency spectrum sliceS(τƒ), where ƒ represents frequency.
Step S102, constructing an analytic function of the Galois field amplitude spectrum and estimating the peak frequency of the Galois field amplitude spectrum. Fitting the normalized Gabor amplitude spectrum by adopting a generalized wavelet spectrum function, and realizing the method in two steps; gabor spectral slice for each time windowS(τƒ) is subjected to a normalization process,W s(ƒ)=|S(τ,ƒ)|/S max(ii) a Normalized gabor amplitude spectrum fitting by using Wang's generalized wavelet spectral functionW s(ƒ)：
Formula (III) ƒ0Is the natural frequency of the generalized seismic wavelet, anduit is an indication of the fractional order of the generalized seismic wavelet. When the generalized wavelet amplitude spectrum analysis function is used as the fitting function in step S102, the peak frequency is expressed in an analysis form
。
Step S103, a high-frequency amplitude compensation filter is constructed. The basic principle followed is: multiplication of the fitting function of the amplitude compensation filter with the gabor amplitude spectrum is equal to 1, i.e.W(ƒ)H(ƒ) = 1; when the frequency is greater than the peak frequency, ƒ is equal to or greater than ƒ p By solving an inverse problemW(ƒ)H(ƒ) =1 construct amplitude compensation filter:H(ƒ)=1/[W(ƒ)+σ]where σ is a white noise coefficient that stabilizes the solution problem; when the frequency is less than the peak frequency, 0 is less than or equal to ƒ<ƒ p The amplitude compensation filter is arranged asH(ƒ)=1。
And step S104, realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice. Compensating high frequency amplitude for filterH(ƒ) application to Gabor spectral slicesS(τƒ), generating a new gabor spectral slice
：
And step S105, realizing Gabor inverse transformation, and reconstructing the time domain seismic channel after high-frequency amplitude compensation. The method is realized by two steps: first, slicing the Gabor spectrum
Performing inverse Fourier transform to obtain Gabor time slice
(ii) a Then, all the gabor slices are integrated
Reconstructing seismic traces after high frequency amplitude compensation
：
In the formulah(t) Is a Gabor reconstruction function, which is a Gabor slice generation function in step S101g(t) Is the inverse function of (c).
The invention provides a series of preferable schemes based on the basic implementation flow as follows.
Preferably, in the step S102 of fitting the normalized gabor amplitude spectrum, in order to construct an analytic function of the gabor amplitude spectrum, gabor spectrum slices of a plurality of seismic channels may be selected from the transverse space for averaging, and then the normalized gabor spectrum slice with the transverse space average is obtainedW s (ƒ). The amplitude compensation filter obtained by the method can also be applied to seismic traces within a certain span of the transverse space, so that the continuity of the filtering processing result of the high-frequency amplitude compensation in the transverse space is maintained.
Preferably, the high frequency amplitude compensation filter in step S103 is constructed by solving an inverse problem. Amplitude compensation filter is not rightH(ƒ) each frequency component is calculated separately, but the solution is made from all ƒ ≧ ƒ p And a simultaneous equation system formed by the frequency component compensation factors, and a stable and smooth filter is constructed through the constraint of a smoothing matrix. The invention is represented by a vector HH(ƒ) representing an analytic function of the Gabor amplitude spectrum by a diagonal matrix WW(ƒ). The solution of the amplitude compensation filter H is: h = [ CW + σ ]2(I-C)]-1C, wherein C is a smooth constraint matrix, and C = (I + D) T D)-1And D is T D is the second derivative constraint matrix.
Preferably, step S104 includes phase correction filtering, performing phase correction using the one-dimensional Q model that varies with depth, and making appropriate adjustments to the one-dimensional Q model by time matching with the well-side seismic synthetic traces.
Preferably, the gabor reconstruction function in step S105 is an inverse function of the gabor slice generation function described in step S101. Because of the gabor generating functionIn discrete form in the implementation of step S101, it is necessary to generate a function by pairing gaborg(t) Calculating to obtain Gabor reconstruction functionh(t) Thereby ensuring the precision of gabor forward and inverse transformation.
The invention also provides an embodiment [ fig. 2, fig. 3 ]. The two-pass time shown on the deep seismic section of fig. 2 is between 3500ms and 4800ms, and fig. 3 shows that the resolution of the seismic section is significantly improved as a result of adaptive high-frequency amplitude compensation of the seismic section. The embodiment shows the effect of performing resolution improvement processing on deep reflection seismic data by using the data-driven high-frequency amplitude compensation method.
The method has the advantages that the high-frequency amplitude compensation filter driven by the seismic data is constructed, and the stratum Q model does not need to be known in advance, so that the negative influence possibly caused by the estimation error of the stratum Q model can be effectively avoided.
In summary, the seismic data adaptive high-frequency amplitude compensation method of the invention comprises the following steps: realizing Gabor transformation, and constructing Gabor frequency spectrum slices of the seismic channels; constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function; constructing a high-frequency amplitude compensation filter; realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice; and realizing Gabor inverse transformation, and reconstructing the time domain seismic traces after high-frequency amplitude compensation. According to the invention, a high-frequency amplitude compensation filter driven by data is constructed according to the absorption attenuation characteristics of the underground stratum carried by the seismic signal to the seismic energy, and the seismic data is subjected to self-adaptive high-frequency component compensation, so that the frequency bandwidth of the seismic data is effectively increased, and the capability of identifying the thin mutual reservoir through stratum imaging and reservoir inversion of the seismic data is enhanced.
Claims (6)
1. A seismic data self-adaptive high-frequency compensation method is characterized in that a data-driven amplitude compensation filter is constructed according to energy absorption attenuation characteristics reflected by seismic data, and self-adaptive high-frequency component compensation is carried out on actual seismic data; the method comprises the following steps: (1) realizing Gabor transformation, and constructing Gabor frequency spectrum slices of the seismic channels; (2) constructing an analytic function of a Gabor amplitude spectrum and estimating the peak frequency of the analytic function; (3) constructing a high-frequency amplitude compensation filter; (4) realizing high-frequency amplitude compensation filtering of the Gabor frequency spectrum slice; (5) realizing Gabor inverse transformation, and reconstructing a time domain seismic channel after high-frequency amplitude compensation;
the basic principle followed by constructing the high-frequency amplitude compensation filter in the step (3) is that the multiplication of a fitting function of the compensation filter and a Gabor amplitude spectrum is equal to 1; and (3) constructing the high-frequency amplitude compensation filter by using a method of forming a simultaneous equation set by all high-frequency component compensation factors, solving an inverse problem of the simultaneous equation set, and constructing a stable and smooth filter by using a smooth matrix constraint.
2. The seismic data adaptive high frequency compensation method according to claim 1, wherein the step (2) of constructing an analytic function of a gabor amplitude spectrum and estimating the peak frequency thereof is implemented in two steps; carrying out normalization processing on the Gabor frequency spectrum slices of each time window, and fitting the normalized Gabor amplitude spectrum by adopting Wang's generalized wavelet frequency spectrum function:
formula (III) ƒ0Is the natural frequency of the generalized seismic wavelet, and the analytic function of the Galois field amplitude spectrum is expressed by the diagonal matrix WW(ƒ) anduthen is a fractional order indication of the generalized seismic wavelet; the estimation of the peak frequency is represented in analytical form as follows:
。
3. the adaptive high-frequency compensation method for seismic data according to claim 1, wherein the step (3) constructs a high-frequency amplitude compensation filterH(ƒ) the following rationale is followed:W(ƒ)H(ƒ) = 1; ƒ ≧ ƒ when the frequency is greater than or equal to the peak frequency p Disclosure of the inventionOver-solving an inverse problemW(ƒ)H(ƒ) =1 construction of amplitude compensation filterH(ƒ)=1/[W(ƒ)+σ]Where σ is a white noise coefficient that stabilizes the solution problem; when the frequency is less than the peak frequency, 0 is less than or equal to ƒ<ƒ p The amplitude compensation filter is arranged asH(ƒ)=1。
4. The adaptive high-frequency compensation method for seismic data according to claim 1, wherein the high-frequency amplitude compensation filter in the step (3) is not constructed by a method other than the method for constructing the adaptive high-frequency amplitude compensation filterH(ƒ) each frequency component is calculated separately, but the solution is made from all ƒ ≧ ƒ p A simultaneous equation set consisting of high-frequency component compensation factors, and a stable and smooth filter is constructed through smooth matrix constraint; the invention is represented by a vector HH(ƒ) representing an analytic function of the Gabor amplitude spectrum by a diagonal matrix WW(ƒ), the solution of the amplitude compensation filter H is: h = [ CW + σ ]2(I-C)]-1C, wherein C is a smooth matrix, C = (I + D) T D)-1And D is T D is the second derivative constraint matrix.
5. The adaptive high-frequency compensation method for seismic data according to claim 1, wherein the step (4) is to apply a high-frequency amplitude compensation filterH(ƒ) application to Gabor spectral slicesS(τƒ), generating a new gabor spectral slice
：
The step (4) comprises phase correction filtering, phase correction is carried out by using a one-dimensional Q model which changes along with the depth, and the one-dimensional Q model is properly adjusted through time matching with the well-side seismic synthetic channel.
6. The seismic data of claim 1The self-adaptive high-frequency compensation method is characterized in that step (5) realizes inverse Gabor transformation, and the Gabor reconstruction function for reconstructing the time domain seismic channel after high-frequency amplitude compensation is in step (1)GaborFrequency spectrumSlicing Generating a functionThe inverse function of (d); by pairing gabor spectraSlicingAnd calculating the discrete numerical value of the generated function to obtain a discrete expression of the Gabor reconstruction function, and ensuring the precision of forward and inverse transformation of Gabor.
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