A method and system for improving seismic data resolution through frequency extrapolation

Abstract

The present application belongs to the technical field of geophysical exploration, and relates to a method and system for improving seismic data resolution through frequency extrapolation, comprising: collecting a seismic signal, and representing the seismic signal by a reflection coefficient sequence and a seismic wavelet; fitting the reflection coefficient sequence to obtain a plurality of candidate fitting functions, selecting a function having the least influence on the reflection coefficient sequence from the fitting functions, and calculating an entropy norm of the reflection coefficient sequence according to the function having the least influence on the reflection coefficient sequence; converting the reflection coefficient sequence into a reflection coefficient in a frequency domain, performing frequency extrapolation on the reflection coefficient in the frequency domain through the function having the least influence on the reflection coefficient sequence, and solving an optimization problem through iteration; making the reflection coefficient obtained through the frequency extrapolation satisfy a coherence constraint condition, and outputting the frequency extrapolation reflection coefficient meeting the coherence constraint condition. The present application can effectively improve the seismic data resolution while maintaining the continuity of seismic events.

Description

TECHNICAL FIELD

[0001] The present application relates to a method and system for improving seismic data resolution by frequency extrapolation, belonging to the technical field of geophysical exploration. BACKGROUND

[0002] In seismic data processing, resolution is one of the important indicators for evaluating the quality of seismic data. How to effectively improve the resolution of seismic data is a key problem in seismic data processing. However, since the seismic wavelet is band-limited, even if the accurate estimation of the seismic wavelet is obtained, the frequency components outside the effective frequency band of the seismic wavelet cannot be restored by conventional seismic deconvolution techniques. Obviously, without adding other constraints, it is impossible to realize the frequency extrapolation of band-limited signals. Since the seismic signal can be generally assumed to be sparse, frequency extrapolation from the effective frequency band of the sparse signal is possible, and has been studied and applied in different fields, such as ultrasonic nondestructive testing, communication, speech processing and seismic exploration. A typical algorithm for realizing deconvolution by using the sparsity of seismic signals is frequency-constrained minimum entropy deconvolution, which can realize frequency extrapolation of seismic signals. This method has high computational efficiency compared with the method based on L1 norm, but loses weak seismic reflection signals, while the method based on L1 norm can better restore weak reflection signals, but has a large amount of calculation. In addition, frequency extrapolation is a multi-solution problem, and the sparsity constraint of seismic signals can generally obtain a useful solution in single-channel processing, but in actual multi-dimensional seismic signal processing, the multi-solution often leads to poor continuity of seismic events, thereby reducing the interpretability of seismic profiles. SUMMARY

[0003] In view of the above problems, the present application aims to provide a method, system and readable medium for improving seismic data resolution by frequency extrapolation, which can effectively improve the resolution of seismic data while maintaining the continuity of seismic events.

[0004] To achieve the above-mentioned purpose, the present application provides the following technical scheme: a method for improving seismic data resolution by frequency extrapolation, comprising the following steps: acquiring a seismic signal, and representing the seismic signal by a reflection coefficient sequence and a seismic wavelet; fitting the reflection coefficient sequence to obtain a plurality of candidate fitting functions, selecting a function having the least influence on the reflection coefficient sequence from the fitting functions, and calculating the entropy norm of the reflection coefficient sequence according to the function having the least influence on the reflection coefficient sequence; converting the reflection coefficient sequence into a reflection coefficient in the frequency domain, performing frequency extrapolation on the reflection coefficient in the frequency domain by the function having the least influence on the reflection coefficient sequence, and solving an optimization problem by iteration; making the reflection coefficient obtained by frequency extrapolation satisfy a coherence constraint condition, and outputting the frequency extrapolation reflection coefficient meeting the coherence constraint condition.

[0005] Further, the reflection coefficient sequence is a one-dimensional reflection coefficient sequence, and the reflection coefficient sequence is a zero-mean sparse non-Gaussian stationary sequence.

[0006] Further, the function with the least influence on the reflection coefficient sequence is:

[0007]

[0008] wherein cosh is a hyperbolic function, x is a variable of the function F(), and a is a parameter controlling the sparsity of the signal.

[0009] Further, a calculation formula of the entropy norm of the reflection coefficient sequence is:

[0010]

[0011] wherein V(s(i)) is the entropy norm of the reflection coefficient sequence, N is the length of s(i), and q(i) is an amplitude-normalized vector, and a formula of the amplitude-normalized vector is:

[0012]

[0013] wherein s(i) is a reflection coefficient.

[0014] Further, the optimization problem is: the entropy norm of the reflection coefficient sequence Maximize V(s(i)), and

[0015]

[0016] wherein B(ω) is a frequency domain representation of the seismic wavelet b(i), [ω L , ω H ] is an effective frequency band of the seismic wavelet, and ω is a frequency.

[0017] Further, the method of solving the optimization problem by iteration is:

[0018] A solution s k+1 (i) of the reflection coefficient sequence of the k+1th step is:

[0019]

[0020] wherein s(i) is a reflection coefficient, q(i) is an amplitude-normalized vector, G(q(i), a) is a first-order Taylor series of F(q(i), a), s k k(i) is a reflection coefficient sequence obtained by the kth iteration, q k (i) is an amplitude-normalized vector of s k(j) is the amplitude normalized vector of the jth value in the reflection coefficient sequence, a is a parameter controlling the sparsity of the control signal, F(q(i), a) is a function used to calculate the entropy norm of the reflection coefficient sequence, and N is the length of s(i);

[0021] the solution s of the reflection coefficient sequence according to the k+1th step k+1 (i) calculating the frequency domain seismic wavelet of the k+1th step:

[0022]

[0023] B k+1 (ω) is the frequency domain seismic wavelet of the k+1th step, [ω L , ω H ] is the effective frequency band of the seismic wavelet, X(ω, x) is the band-limited seismic signal in the frequency domain, x is the spatial coordinate, ω is the frequency, S k+1 (ω, x) is the frequency domain reflection coefficient obtained by the k+1th iteration;

[0024] updating the emission coefficient according to the frequency domain seismic wavelet of the k+1th step, and the step size of each iteration is:

[0025]

[0026] Further, the optimization objective function of the coherence constraint condition is:

[0027] E = ||X(ω, x)-B(ω, x)S(ω, x)||2+a1f1(s(t, x))+a2f2(s(t, x))

[0028] where X(ω, x) is a band-limited seismic signal in the frequency domain, B(ω, x) is a seismic wavelet in the frequency domain, S(ω, x) is a reflection coefficient in the frequency domain, x is a spatial coordinate, s(t, x) is a reflection coefficient in the time domain, a1 is the weight of f1(s(t, x)), f1(s(t, x)) is a sparsity measure obtained by using the entropy norm of the reflection coefficient sequence; a2 is the weight of f2(s(t, x)), and f2(s(t, x)) is a lateral coherence measure of the reflection coefficient.

[0029] Further, the method for obtaining the lateral coherence measure of the reflection coefficient is: initialization: s0(i, x) = x(i, x), setting parameters a and the maximum number of iterations L; performing inverse Fourier transform on the reflection coefficient in the frequency domain to convert it into a reflection coefficient in the spatial coordinate; constructing a two-dimensional prediction error filter according to the reflection coefficient in the spatial coordinate, and updating the reflection coefficient in the spatial coordinate using the two-dimensional prediction error filter until the number of iterations is reached; and obtaining the lateral coherence measure of the reflection coefficient according to the two-dimensional prediction error filter and the finally obtained reflection coefficient.

[0030] Further, the calculation formula of the transverse coherence measure of the reflection coefficient is:

[0031]

[0032] Wherein, P s is a two-dimensional prediction error filter, and s is a matrix of the finally obtained reflection coefficient.

[0033] The application further discloses a system for improving seismic data resolution through frequency extrapolation, which comprises a signal acquisition module, a fitting function acquisition module, a frequency extrapolation module and a correlation constraint module.

[0034] The application has the following advantages due to the above technical scheme:

[0035] 1. The application effectively improves the resolution of seismic data by recovering weak reflection signals, maintains the continuity of seismic events, and does not reduce the interpretability of seismic profiles, and has very important application value for reducing exploration risk and improving development efficiency of thin oil and gas reservoirs.

[0036] 2. The application analyzes the frequency constraint minimum entropy deconvolution method, finds that the nonlinear function used has a great influence on the processing result of the seismic signal, and therefore proposes a new nonlinear function with an upper limit in the application, and uses a parameter to control the sparsity of the output signal, so that the weak seismic reflection signal can be better recovered, and the calculation speed is faster.

[0037] 3. The application proposes a coherence constraint method, which can reduce the multi-solution of the frequency extrapolation problem and improve the continuity of the seismic profile event. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a schematic view of three different functions varying with the reflection coefficient in an embodiment of the application;

[0039] Figure 2 is a reflectivity plot, Figure 2 (a) is a true reflectivity plot, Figure 2 (b) is a band-limited seismic signal plot; Figure 2 (c) is a reflectivity plot obtained in an embodiment of the present application, Figure 2 (d) is a reflectivity plot obtained based on the L1 norm method, Figure 2 (e) is a reflectivity plot obtained based on the frequency-constrained minimum entropy deconvolution method;

[0040] Figure 3 is a reflectivity plot in the frequency domain, Figure 3 (a) is a true reflectivity plot in the frequency domain, Figure 3 (b) is a band-limited seismic signal plot in the frequency domain; Figure 3 (c) is a reflectivity plot in the frequency domain obtained in an embodiment of the present application, Figure 3 (d) is a reflectivity plot in the frequency domain obtained based on the L1 norm method, Figure 3 (e) is a reflectivity plot in the frequency domain obtained based on the frequency-constrained minimum entropy deconvolution method;

[0041] Figure 4 is a reflectivity profile and a noisy band-limited filtered profile, Figure 4 (a) is a reflectivity profile obtained in the present embodiment, Figure 4 (b) is a noisy band-limited filtered profile obtained in the present embodiment, Figure 4 (c) is a reflectivity profile obtained based on the L1 norm method, Figure 4 (d) is a noisy band-limited filtered profile obtained based on the L1 norm method, Figure 4 (e) is a reflectivity profile obtained based on the frequency-constrained minimum entropy deconvolution method, Figure 4 (f) is a noisy band-limited filtered profile obtained based on the frequency-constrained minimum entropy deconvolution method;

[0042] Figure 5 is a field seismic record and a synthetic record in the present embodiment, Figure 5 (a) is a field seismic record and a synthetic record before frequency extrapolation in the present embodiment, Figure 5 (b) is a field seismic record and a synthetic record after frequency extrapolation;

[0043] Figure 6 is a target layer along layer RMS amplitude slice in a certain oilfield in the present embodiment, Figure 6 (a) is a target layer along layer RMS amplitude slice in a certain oilfield before frequency extrapolation in the present embodiment, Figure 6 (b) is a target layer along layer RMS amplitude slice in a certain oilfield after frequency extrapolation. DETAILED DESCRIPTION

[0044] In order to make the technical personnel of the present application better understand the technical solutions, the present application is described in detail through specific examples. However, it should be understood that the specific embodiments are provided only for better understanding of the present application, and they should not be understood as limiting the present application. In the description of the present application, it is understood that the terms used are only for the purpose of description, and cannot be understood as indicating or implying relative importance.

[0045] In order to solve the problems of the prior art method, such as loss of weak seismic reflection signal, large amount of calculation for recovering weak seismic reflection signal, and multi-solution problem of frequency extrapolation, but in actual multi-dimensional seismic signal processing, the multi-solution often leads to poor continuity of the seismic profile, thereby reducing the interpretability of the seismic profile. The present application provides a method and system for improving seismic data resolution by frequency extrapolation. Through analysis of the frequency constraint minimum entropy deconvolution method, it is found that the nonlinear function used has a great influence on the seismic signal processing result, so a new nonlinear function with an upper limit is proposed, and a parameter of the nonlinear function is used to control the sparsity of the output signal, so that the weak seismic reflection signal can be recovered better, and the calculation speed is faster. At the same time, a coherence constraint method is proposed, which can reduce the multi-solution of the frequency extrapolation problem and improve the continuity of the seismic profile. The processing results of the synthetic data and the actual seismic data show that the present application can effectively improve the resolution of the seismic data, and has very important application value for reducing the exploration risk of thin oil and gas reservoirs and improving the development efficiency. The present application will be described in detail in combination with the drawings and examples.

[0046] Example 1

[0047] The present application discloses a method for improving seismic data resolution by frequency extrapolation, comprising the following steps:

[0048] S1 collects seismic signals, and represents the seismic signals by reflection coefficient sequence and seismic wavelet.

[0049] In the present embodiment, the convolution model of the seismic signal x(i) is represented as x(i)=b(i)*s(i), wherein s(i) is a reflection coefficient sequence, b(i) is a seismic wavelet, the length of which is denoted as q, * is a 1-dimensional convolution operator, and s(i) can be obtained by transforming to the frequency domain; in the present embodiment, the reflection coefficient sequence is a one-dimensional reflection coefficient sequence, and it is assumed that the reflection coefficient sequence is a sparse non-Gaussian stationary sequence with zero mean. Sparse signal refers to a signal with very few non-zero elements, which is a discrete signal. The sparsity of the signal means that the signal can be represented by a linear combination of a few eigenvectors. A stationary signal refers to a signal whose distribution parameters or distribution law do not change with time.

[0050] S2 fits the reflection coefficient sequence to obtain several candidate fitting functions. The function with the least impact on the reflection coefficient sequence is selected, and its entropy norm is calculated based on this function. The entropy norm V(s(i)) of the reflection coefficient sequence is used to measure the sparsity of the reflection coefficient sequence s(i).

[0051] like Figure 1 The diagram shows the variation of three different functions with the reflection coefficient. The three different functions are: F1(x) = x, a linear function; F2(x) = ln(x), the function used in the frequency-constrained minimum entropy deconvolution method; and F3(x, α), which is:

[0052]

[0053] Where cosh is a hyperbolic function, x is the spatial coordinate, and α is the parameter. Figure 1 These three different functions are represented as G1(x), G2(x), and G3(x, α), respectively. From... Figure 1 It can be seen that G1(x) is most sensitive to large reflection coefficients, followed by G2(x), and G3(x, α) is even less sensitive to large reflection coefficients. It can also be seen that different values ​​of the parameter α can control the sensitivity of G3(x, α) to large reflection coefficients; the smaller the parameter α, the less sensitive it is to large reflection coefficients, and the sparser the output signal. Therefore, the fitting function with the least impact on the reflection coefficient sequence is:

[0054]

[0055] This function is a non-linear, monotonically increasing function.

[0056] The formula for calculating the entropy norm of the reflection coefficient sequence is:

[0057]

[0058] Where V(s(i)) is the entropy norm of the reflection coefficient sequence, N is the length of s(i), and q(i) is the amplitude-normalized vector. The formula for the amplitude-normalized vector is:

[0059]

[0060] Where s(i) is the reflection coefficient.

[0061] S3 converts the reflection coefficient sequence into reflection coefficients in the frequency domain, extrapolates the frequency of the reflection coefficients in the frequency domain using the function that has the least impact on the reflection coefficient sequence, and solves the optimization problem iteratively.

[0062] The optimization problem is: to maximize the entropy norm of the reflection coefficient sequence V(s(i)), and

[0063]

[0064] Where B(ω) is the frequency domain representation of the seismic wavelet b(i), [ω L ω H ] is the effective frequency band of the seismic wavelet, and ω is the frequency.

[0065] The method for solving optimization problems iteratively is as follows:

[0066] The solution s of the reflection coefficient sequence at step k+1 k+1 (i) is:

[0067]

[0068] in, s(i) is the reflection coefficient, q(i) is the amplitude-normalized vector, G(q(i), α) is the first-order Taylor series of F(q(i), α), sk(i) is the reflection coefficient sequence obtained in the k-th iteration, and q k (i) is s k The amplitude-normalized vector of (i), q k (j) is the amplitude normalized vector of the j-th value in the reflection coefficient sequence, α is the parameter that controls the sparsity of the signal, F(q(i), α) is the function used to calculate the entropy norm of the reflection coefficient sequence (see F(x, α) above), and N is the length of s(i).

[0069] Based on the solution s of the reflection coefficient sequence at step k+1 k+1 (i) Calculate the frequency domain seismic wavelet at step k+1:

[0070]

[0071] B k+1 (ω) is the frequency-domain seismic wavelet at step k+1, [ω L ω H [ ] represents the effective frequency band of the seismic wavelet, X(ω, x) is the band-limited seismic signal in the frequency domain, x is the spatial coordinate, ω is the frequency, and S k+1 (ω, x) is the frequency domain reflection coefficient obtained in the (k+1)th iteration;

[0072] The emission coefficients are updated based on the frequency domain seismic wavelet in k+1 steps, with the step size for each iteration being:

[0073]

[0074] S4 makes the reflection coefficient obtained by frequency extrapolation satisfy the coherence constraint condition, and outputs the frequency extrapolation reflection coefficient meeting the coherence constraint condition.

[0075] The optimization objective function of the coherence constraint condition is:

[0076] E = ||X(ω, x)-B(ω, x)S(ω, x)||2+a1f1(s(t, x))+a2f2(s(t, x))

[0077] Wherein, X(ω, x) is a band-limited seismic signal in the frequency domain, B(ω, x) is a seismic wavelet in the frequency domain, S(ω, x) is a reflection coefficient in the frequency domain, x is a spatial coordinate, s(t, x) is a reflection coefficient in the time domain, a1 is the weight of f1(s(t, x)), f1(s(t, x)) is a function that has the least impact on the reflection coefficient sequence; a2 is the weight of f2(s(t, x)), and f2(s(t, x)) is a lateral coherence measure of the reflection coefficient.

[0078] The method for obtaining the lateral coherence measure of the reflection coefficient is: initialization: s0(i, x) = x(i, x), set parameters α and the maximum number of iterations L; inverse Fourier transform of the reflection coefficient in the frequency domain to convert the reflection coefficient in the spatial coordinate; construct a two-dimensional prediction error filter according to the reflection coefficient in the spatial coordinate, and update the reflection coefficient in the spatial coordinate using the two-dimensional prediction error filter until the number of iterations is reached; obtain the lateral coherence measure of the reflection coefficient according to the two-dimensional prediction error filter and the finally obtained reflection coefficient.

[0079] In this embodiment, the calculation formula for obtaining the lateral coherence measure of the reflection coefficient is:

[0080]

[0081] Wherein, P s is a two-dimensional prediction error filter, and s is a matrix of the finally obtained reflection coefficient.

[0082] Figure 2 is a reflection coefficient map, Figure 2 (a) is a true reflection coefficient map, Figure 2 (b) is a band-limited seismic signal map; Figure 2 (c) is a reflection coefficient map obtained in this embodiment, Figure 2 (d) is a reflection coefficient map obtained based on the L1 norm method, Figure 2 (e) is a reflection coefficient map obtained by the frequency constraint minimum entropy deconvolution method.

[0083] Figure 3 is a reflection coefficient map in the frequency domain, Figure 3(a) is the reflectivity profile in the frequency domain which is true, Figure 3 (b) is the band-limited seismic signal profile in the frequency domain; Figure 3 (c) is the reflectivity profile in the frequency domain obtained in this embodiment, Figure 3 (d) is the reflectivity profile in the frequency domain obtained based on the L1 norm method, Figure 3 (e) is the transmission coefficient profile in the frequency domain obtained based on the frequency-constrained minimum entropy deconvolution method; from Figure 3 It can be seen from the above that the result of the method in this embodiment is obviously better than that of the frequency-constrained minimum entropy deconvolution method.

[0084] Figure 4 is the reflectivity profile and the band-limited filtered profile with noise added, Figure 4 (a) is the reflectivity profile obtained in this embodiment, Figure 4 (b) is the band-limited filtered profile with noise added obtained in this embodiment, Figure 4 (c) is the reflectivity profile obtained based on the L1 norm method, Figure 4 (d) is the band-limited filtered profile with noise added obtained based on the L1 norm method, Figure 4 (e) is the reflectivity profile obtained based on the frequency-constrained minimum entropy deconvolution method, Figure 4 (f) is the band-limited filtered profile with noise added obtained based on the frequency-constrained minimum entropy deconvolution method. From Figure 4 It can be seen from the above that the method in this embodiment can realize the reconstruction of the missing frequency components outside the effective frequency band.

[0085] Figure 5 is the well seismic record and the synthetic record of a certain oilfield in this embodiment, Figure 5 (a) is the well seismic record and the synthetic record before the frequency extrapolation processing in this embodiment, Figure 5 (b) is the well seismic record and the synthetic record after the frequency extrapolation processing, from Figure 5 It can be seen from the comparison in the vertical direction that the wave group characteristics of the original seismic data are maintained after the high-resolution processing, and the vertical resolution is higher, the well-seismic matching degree is better, which verifies the effectiveness of the method proposed in this embodiment in the application of actual data.

[0086] Figure 6 is the along-layer RMS amplitude slice of the target layer of a certain oilfield in this embodiment, Figure 6 (a) is the along-layer RMS amplitude slice of the target layer of a certain oilfield before the frequency extrapolation processing in this embodiment, Figure 6 (b) is the along-layer RMS amplitude slice of the target layer of a certain oilfield after the frequency extrapolation processing. From Figure 6From the contrast of the plane, the spatial distribution characteristics of the seismic energy after the high resolution processing are kept, and the local characteristics are more fine, which also shows the reliability of the high resolution processing data in the method in the embodiment.

[0087] The calculation speed of the method in the embodiment, the calculation speed of the method based on the L1 norm, and the calculation speed of the frequency constraint minimum entropy deconvolution method are also recorded in the embodiment, and the specific values are shown in Table 1. As can be seen from Table 1, the calculation speed of the frequency constraint minimum entropy deconvolution method is the fastest, the method in the embodiment is the second, and the method based on the L1 norm is the slowest. Compared with the method based on the L1 norm, the method in the embodiment reduces a large amount of calculation, especially when the signal is long.

[0088] Through the seismic data processing method in the embodiment, the frequency band of the seismic data can be widened, and the seismic resolution is obviously improved. Comparing the stratum along the root mean square amplitude slice before and after the high resolution processing, the spatial distribution characteristics of the seismic energy after the processing are kept, and the local characteristics are more fine, which shows the reliability of the high resolution processing data. Compared with the synthetic seismic data generated by the logging data, the data with improved resolution is beneficial to the identification of thin layers. Therefore, the method in the embodiment can effectively realize frequency extrapolation, and the data processed can provide more geological information. Through the synthetic data experiment, the method in the embodiment is compared with the method based on the L1 norm and the frequency constraint minimum entropy deconvolution method: 1) the effect of the method in the embodiment is equivalent to that of the method based on the L1 norm, but is much better than that of the frequency constraint minimum entropy deconvolution algorithm; 2) compared with the method based on the L1 norm, the method in the embodiment reduces the calculation amount.

[0089] Table 1 Calculation speed of the method in the embodiment, the method based on the L1 norm, and the frequency constraint minimum entropy deconvolution method

[0090]

[0091] Embodiment two

[0092] Based on the same inventive concept, the embodiment discloses a system for improving the resolution of seismic data by frequency extrapolation, which comprises:

[0093] The signal acquisition module is used for acquiring the seismic signal and representing the seismic signal by the reflection coefficient sequence and the seismic wavelet.

[0094] The fitting function obtaining module is used for fitting the reflection coefficient sequence to obtain a plurality of candidate fitting functions, selecting a function with the least influence on the reflection coefficient sequence from the fitting functions, and calculating the entropy norm of the reflection coefficient sequence according to the function with the least influence on the reflection coefficient sequence.

[0095] a frequency extrapolation module configured to convert the sequence of reflection coefficients to reflection coefficients in the frequency domain, to frequency extrapolate the reflection coefficients in the frequency domain by a function that has minimal impact on the sequence of reflection coefficients, and to solve an optimization problem iteratively;

[0096] a correlation constraint module configured to cause the reflection coefficients obtained by the frequency extrapolation to satisfy a coherence constraint, and to output the frequency extrapolated reflection coefficients that satisfy the coherence constraint.

[0097] Those skilled in the art will understand that embodiments of the present application can be provided as methods, systems, or computer program products. Thus, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0098] The present application is described in reference to the flowchart and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the present application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 means for implementing one or more functions specified in the flowchart and / or block diagram block or blocks.

[0099] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 means for implementing one or more functions specified in the flowchart and / or block diagram block or blocks.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 Figure 1 means for implementing one or more functions specified in the flowchart and / or block diagram block or blocks.

[0101] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application but not to limit it. Although the present application has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that the specific embodiments of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and any modification or equivalent replacement should be covered in the protection scope of the claims of the present application. The above content is only a specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for improving the resolution of seismic data through frequency extrapolation, characterized in that, Includes the following steps: Seismic signals are acquired and represented by a reflection coefficient sequence and a seismic wavelet; The reflection coefficient sequence is fitted to obtain several candidate fitting functions. The function with the least influence on the reflection coefficient sequence is selected from the fitting functions. The entropy norm of the reflection coefficient sequence is calculated based on the function with the least influence on the reflection coefficient sequence. The reflection coefficient sequence is converted into reflection coefficients in the frequency domain. The frequency coefficients in the frequency domain are extrapolated using the function that has the least impact on the reflection coefficient sequence. The optimization problem is then solved iteratively. Make the reflection coefficient obtained by frequency extrapolation satisfy the coherence constraint condition, and output the frequency extrapolated reflection coefficient that meets the coherence constraint condition.

2. The method for improving seismic data resolution by frequency extrapolation as described in claim 1, characterized in that, The reflection coefficient sequence is a one-dimensional reflection coefficient sequence, and the reflection coefficient sequence is a sparse non-Gaussian stationary sequence with zero mean.

3. The method for improving seismic data resolution by frequency extrapolation as described in claim 1, characterized in that, The function with the least influence on the reflection coefficient sequence is: Where cosh is a hyperbolic function, and x is the spatial coordinate. It is a parameter.

4. The method for improving seismic data resolution by frequency extrapolation as described in claim 3, characterized in that, The formula for calculating the entropy norm of the reflection coefficient sequence is: in, It is the entropy norm of the reflection coefficient sequence, and N is... Length, It is an amplitude-normalized vector, and the formula for the amplitude-normalized vector is: in, It is the reflection coefficient.

5. The method for improving seismic data resolution by frequency extrapolation as described in any one of claims 1-4, characterized in that, The optimization problem is: the entropy norm of the reflection coefficient sequence. ,and ， in, It is a seismic wavelet Frequency domain representation, It is the effective frequency band of the seismic wavelet. It refers to frequency.

6. The method for improving seismic data resolution by frequency extrapolation as described in claim 5, characterized in that, The method for solving the optimization problem iteratively is as follows: Solution of the reflection coefficient sequence at step k+1 for: ， in, , It is the reflection coefficient. It is a vector with normalized amplitude. yes The first-order Taylor series, This is the reflection coefficient sequence obtained from the k-th iteration. yes The amplitude-normalized vector, It is the amplitude-normalized vector of the j-th value in the reflection coefficient sequence. It is a parameter that controls the sparsity of the signal. It is the function used to calculate the entropy norm of the reflection coefficient sequence, where N is... Length; Based on the solution of the reflection coefficient sequence at step k+1 Calculate the frequency domain seismic wavelet at step k+1: ； It is a frequency-domain seismic wavelet of step k+1. It is the effective frequency band of the seismic wavelet. It is a band-limited seismic signal in the frequency domain, where x is the spatial coordinate. It's frequency. It is the frequency domain reflection coefficient obtained in the (k+1)th iteration; The emission coefficients are updated based on the frequency domain seismic wavelet in k+1 steps, with the step size for each iteration being: 。 7. The method for improving seismic data resolution by frequency extrapolation as described in any one of claims 1-4, characterized in that, The objective function for optimizing the coherence constraint is: in, It is a band-limited seismic signal in the frequency domain. It is a seismic wavelet in the frequency domain. It is the reflection coefficient in the frequency domain, where x is the spatial coordinate. It is the reflection coefficient in the time domain. yes The weight, It is the function that has the least impact on the reflection coefficient sequence; yes The weight, It is a measure of the lateral coherence of the reflection coefficient.

8. The method for improving seismic data resolution by frequency extrapolation as described in claim 7, characterized in that, The method for obtaining the lateral coherence measure of the reflection coefficient is as follows: initialization: Set parameters And the maximum number of iterations L; The inverse Fourier transform of the reflection coefficient in the frequency domain is converted into the reflection coefficient in spatial coordinates; A two-dimensional prediction error filter is constructed based on the reflection coefficient in the spatial coordinates, and the reflection coefficient in the spatial coordinates is updated using the two-dimensional prediction error filter until the number of iterations is reached. The transverse coherence measure of the reflection coefficient is obtained based on the two-dimensional prediction error filter and the finally obtained reflection coefficient.

9. The method for improving seismic data resolution by frequency extrapolation as described in claim 7, characterized in that, The formula for calculating the lateral coherence metric of the reflection coefficient is as follows: in, It is a two-dimensional prediction error filter. It is the matrix of reflection coefficients obtained at the end.

10. A system for improving the resolution of seismic data through frequency extrapolation, characterized in that, include: The signal acquisition module is used to acquire seismic signals and represent the seismic signals by a reflection coefficient sequence and a seismic wavelet; The fitting function acquisition module is used to fit the reflection coefficient sequence, obtain several candidate fitting functions, select the function with the least influence on the reflection coefficient sequence from the fitting functions, and calculate the entropy norm of the reflection coefficient sequence based on the function with the least influence on the reflection coefficient sequence. The frequency extrapolation module is used to convert the reflection coefficient sequence into reflection coefficients in the frequency domain. It performs frequency extrapolation of the reflection coefficients in the frequency domain using the function that has the least impact on the reflection coefficient sequence, and solves the optimization problem iteratively. The relevant constraint module is used to ensure that the reflection coefficient obtained by frequency extrapolation meets the coherence constraint conditions, and outputs the frequency extrapolated reflection coefficient that meets the coherence constraint conditions.

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