Irregular seismic data reconstruction method based on multi-domain hybrid optimized 3D curvelet transform

Abstract

The present invention discloses a method for reconstructing irregular seismic data based on multi-domain hybrid optimized three-dimensional curvelet transform, including: collecting irregular seismic data; obtaining a curvelet coefficient threshold value; respectively determining a threshold value and a minimum threshold value for each iteration calculation; then using a time domain reconstruction method and a frequency domain reconstruction method to perform calculations based on the curvelet coefficient threshold value, the threshold value for each iteration calculation, and data characteristics, solving the curvelet coefficient in the iteration, and performing an inverse curvelet transform on the curvelet coefficient to obtain reconstructed seismic data; terminating the iterative calculation until the threshold value for each iteration calculation is less than the minimum threshold value, and obtaining the final high-precision irregular reconstructed data. The present invention utilizes the advantages of full-space data reconstruction by three-dimensional curvelet transform to improve the accuracy of irregular data reconstruction, and at the same time, in view of the problem of low calculation efficiency of three-dimensional curvelet transform reconstruction, improves its calculation speed from two aspects: iterative calculation adaptive threshold model design and mixed use of different transform domain reconstruction methods.

Description

Technical Field

[0001] The invention relates to an irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform, and belongs to the field of high-precision regularized reconstruction of irregular seismic data in seismic exploration. Background Art

[0002] As oil and gas exploration targets become increasingly complex and sophisticated, seismic exploration must not only ensure the quantity and accuracy of collected data, but also save economic costs. "Cost reduction and efficiency improvement" has become a very important goal. In field acquisition, the irregular seismic acquisition method has the advantages of not being restricted by surface obstacles and flexible switching. It can reduce the number of shot points and detection points, improve acquisition efficiency, and save exploration costs. At the same time, complete regular acquisition data can be obtained through indoor regular reconstruction processing, which has obvious advantages.

[0003] Although irregular seismic acquisition has the advantages of flexible field acquisition methods and low sampling density, it can be flexibly changed according to surface obstacles, and sparse spatial sampling density can be used in the field, thereby greatly reducing field acquisition costs, but how to reconstruct irregular seismic data with high precision has always been a difficult problem for the large-scale promotion and application of irregular seismic acquisition. At present, the irregular data reconstruction methods based on Fourier transform and two-dimensional curvelet transform are mainly used, but both have the problem of low reconstruction accuracy. Summary of the invention

[0004] In order to overcome the problems in the prior art, the present invention provides an irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform. The present invention utilizes the advantages of three-dimensional curvelet transform in full space to reconstruct data and improves the reconstruction accuracy of irregular data. At the same time, in order to address the problem of low computational efficiency of three-dimensional curvelet transform reconstruction, the present invention improves its calculation speed from two aspects: iterative calculation threshold model design and mixed use of different transform domain reconstruction methods.

[0005] First, the data is transformed in the frequency domain and the effective bandwidth of the reflected signal is identified. Secondly, the sample data within the effective bandwidth range is selected for frequency domain three-dimensional curvelet transform reconstruction calculation to reconstruct medium and low frequency data. The time domain three-dimensional curvelet transform reconstruction method is then used to reconstruct the high-frequency detail signal, and an adaptive threshold model is constructed to optimize the iterative calculation threshold and automatically find the optimal number of iterative calculations. This forms an irregular seismic data reconstruction technology based on multi-domain hybrid optimized three-dimensional curvelet transform, and finally completes the high-precision regular reconstruction of seismic data, which not only improves the calculation efficiency but also improves the calculation accuracy, providing technical support for irregular seismic acquisition.

[0006] The technical solution provided by the present invention to solve the above technical problems is: a method for reconstructing irregular seismic data based on multi-domain hybrid optimized three-dimensional curvelet transform, comprising:

[0007] Step S1, collecting irregular seismic data;

[0008] Step S2, obtaining a curve coefficient threshold value;

[0009] Step S3, determining the calculation threshold and the minimum threshold for each iteration respectively according to the improved data-driven threshold model and the adaptive minimum threshold calculation model;

[0010] Step S4, calculate the curvelet coefficients in the iteration by mixing the time domain reconstruction method and the frequency domain reconstruction method according to the curvelet coefficient threshold value, the calculation threshold value of each iteration, and the data characteristics, and perform inverse curvelet transformation on the curvelet coefficients to obtain the reconstructed seismic data;

[0011] Step S5, repeating steps S3-S4 until each iterative calculation threshold is less than the minimum threshold and the iterative calculation is terminated, so as to obtain the final high-precision irregular reconstruction data.

[0012] A further technical solution is that in step S2, the curve coefficient threshold value is obtained by the following formula:

[0013]

[0014] Where: mk is the threshold value of the curve coefficient; max is the maximum threshold; ε is the minimum threshold.

[0015] A further technical solution is that the improved data-driven threshold model is:

[0016]

[0017] Where: k Calculate the threshold for each iteration; Idx max is the position of the maximum threshold in ρ; Idx ε is the position of the minimum threshold in ρ; ρ is the sequence of sparse coefficient amplitudes arranged in descending order; k is the number of iterations; I ter is the total number of iterations;

[0018] The adaptive minimum threshold calculation model is:

[0019]

[0020] Where: M size is the size of the matrix involved in the calculation; j is the decomposition scale of the multi-scale transformation; j' is the total decomposition scale of the multi-scale transformation; median is the median function; ε is the minimum threshold.

[0021] A further technical solution is that in step S4, if the threshold of each iterative calculation is greater than the threshold value of the curvelet coefficient, the frequency domain reconstruction method is used; if the threshold of each iterative calculation is less than or equal to the threshold value of the curvelet coefficient, the time domain reconstruction method is used; if the threshold of each iterative calculation is less than the minimum threshold, the iterative calculation is terminated.

[0022] A further technical solution is that the time domain reconstruction method includes: reconstructing the irregular seismic data in the time domain through a fast iterative threshold algorithm according to each iterative calculation threshold, solving the curvelet coefficients in the iteration, and performing inverse curvelet transformation on the curvelet coefficients to obtain reconstructed data.

[0023] A further technical solution is that the frequency domain reconstruction method comprises the following steps:

[0024] Step S411, first perform a one-dimensional Fourier transform on the irregular seismic data along the time direction to transform the irregular seismic data from the time domain to the frequency domain;

[0025] Step S412, using the Fourier coefficients to determine the effective signal bandwidth range and cut out the frequency domain data to be reconstructed;

[0026] Step S413, finally, reconstructing and iterating the frequency domain data to be reconstructed in the frequency domain by using a fast iterative threshold algorithm according to the threshold calculated in each iteration, solving the curvelet coefficients in the iteration, and performing inverse curvelet transform processing on the curvelet coefficients to obtain the reconstructed data.

[0027] A further technical solution is that in step S412, the effective signal bandwidth range is determined by the following formula:

[0028]

[0029] Where: n t is the number of time sampling points; n f is the number of effective frequency samples; To indicate rounding up; f s is the sampling frequency; f c is the cutoff frequency of the seismic signal.

[0030] A further technical solution is that in step S412, the frequency domain data to be reconstructed is cut out by the following formula:

[0031] f′ obs =f obs (n f ×n z )

[0032] Where: n z is the number of channels; n f is the number of effective frequency samples; f obsis the Fourier coefficient; f′ obs is the frequency domain data to be reconstructed.

[0033] A further technical solution is that the iterative process of the fast iterative threshold algorithm is:

[0034] s k+1 =T λ [s k +Θ H (d obs -Θs k )]

[0035] Where: d obs is the incomplete seismic data to be reconstructed; T λ is the threshold function;

[0036] A further technical solution is to use the following hard threshold function to determine the data range involved in each reconstruction calculation;

[0037]

[0038] Where: T hard (x;λ k ) is the hard threshold function; λ is the threshold calculated for each iteration.

[0039] The present invention has the following beneficial effects: the present invention aims at high-precision reconstruction, starts from the characteristics of three-dimensional curvelet transform, makes full use of the characteristics of full-space reconstruction of data by three-dimensional curvelet transform, establishes adaptive threshold model, hybrid utilization of frequency domain and time domain reconstruction methods and other key technologies in iterative calculation, improves the reconstruction accuracy and computational efficiency of irregular seismic data, thereby obtaining high-precision regularized reconstructed data; therefore, the advantage of high reconstruction accuracy of three-dimensional curvelet transform is utilized, and the problem of low computational efficiency is improved, thereby solving the problem of high-precision regularized reconstruction of irregular seismic data and providing technical support for irregular seismic acquisition. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is the original irregular seismic profile;

[0041] Figure 2 It is a profile of seismic data reconstructed based on two-dimensional curvelet transform;

[0042] Figure 3 It is a seismic data profile diagram reconstructed based on the method of the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform of the present invention comprises:

[0045] Step S1, collecting irregular seismic data;

[0046] Step S2, obtaining a curve coefficient threshold value;

[0047] Step S4, then calculate using a time domain reconstruction method and a frequency domain reconstruction method in combination according to the curvelet coefficient threshold value, each iteration calculation threshold value, and data features, wherein if the each iteration calculation threshold value is greater than the curvelet coefficient threshold value, directly start from step S5; if the each iteration calculation threshold value is less than or equal to the curvelet coefficient threshold value, directly start from step S7;

[0048] Step S5, first perform a one-dimensional Fourier transform on the irregular seismic data along the time direction to transform the irregular seismic data from the time domain to the frequency domain;

[0049] Step S6, using the Fourier coefficients to determine the effective signal bandwidth range and cut out the frequency domain data to be reconstructed;

[0050] Step S7, reconstructing and iterating the seismic data by using a fast iterative threshold algorithm according to each iterative calculation threshold, solving the curvelet coefficients in the iteration, and performing inverse curvelet transformation on the curvelet coefficients to obtain reconstructed data;

[0051] Step S8, repeating steps S3-S7 until the iterative calculation threshold value of each iteration is less than the minimum threshold value and the iterative calculation is terminated, so as to obtain the final high-precision irregular reconstruction data.

[0052] Example

[0053] The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform of the present invention specifically includes the following:

[0054] Step 1: According to the basic theory of data reconstruction, the mathematical model for seismic data reconstruction is as follows:

[0055] d obs =Φd = ΦΨ H s (1)

[0056] Θ H =ΦΨ H (2)

[0057] Where, d obs is the incomplete seismic data to be reconstructed; Φ is the sparse sampling matrix; Ψ H is the curvelet transform basis; s is the complete sparse transform coefficient; d is the complete seismic data after reconstruction; Θ H is the perception matrix.

[0058] Step 2: Usually, the data reconstruction can be completed by solving s in equation 1. The present invention adopts a fast iterative threshold algorithm to solve it. The iterative process is as follows:

[0059] s k+1 =T λ [s k +Θ H (d obs -Θs k )] (3)

[0060] Where: d obs is the incomplete seismic data to be reconstructed; T λ is the threshold function;

[0061] Step 3: Establish the multi-domain hybrid optimization calculation method. First, use (Equation 4) to determine the threshold value of the curvelet coefficient λ mk , and then use (Formula 5) to perform partition calculation;

[0062] If the threshold calculated at each iteration is higher than λ mk The frequency domain reconstruction method is used for calculation;

[0063] If the threshold calculated at each iteration is lower than or equal to λ mk The time domain reconstruction method is used for calculation;

[0064] If the threshold of each iteration calculation is lower than ε, the iteration calculation ends;

[0065]

[0066]

[0067] Where: mk is the threshold value of the curve coefficient, λ k is the threshold for each iteration;

[0068] Step 4: Determine the data range involved in each reconstruction calculation based on the threshold, retain the curvelet coefficients that meet the conditions through the threshold, and remove the coefficients that do not participate in the calculation. Use the following hard threshold function to solve this problem:

[0069]

[0070] Step 5: Establishment of an improved data-driven threshold model. According to the characteristics of data reconstruction iterative calculation, the present invention establishes the following improved data-driven threshold model, and uses Formula 7 to determine the threshold of each calculation in Formula 6;

[0071]

[0072] Where: k Calculate the threshold for each iteration; Idx max is the position of the maximum threshold in ρ; Idx ε is the position of the minimum threshold in ρ; ρ is the sequence of sparse coefficient amplitudes arranged in descending order; k is the number of iterations; I ter is the total number of iterations;

[0073] Step 6: Establish the adaptive minimum threshold calculation model and calculate the maximum threshold λ max Usually, the maximum value of the curvelet coefficient is selected, and the selection of the minimum threshold is difficult and critical. If ε is too large, the reconstruction accuracy will be low, and if ε is too small, the number of iterations will increase and the calculation efficiency will decrease. In view of this problem, the present invention starts with the characteristics of the curvelet coefficient and proposes a minimum threshold calculation method. The minimum threshold is related to the noise energy in the sparse domain. At the same time, since the three-dimensional curvelet transform basis is a multi-scale and multi-directional transform basis, the adaptive minimum threshold calculation model of formula (8) is proposed:

[0074]

[0075] Where: M size is the size of the matrix involved in the calculation; j' is the total decomposition scale of the multi-scale transformation, j'=1,2,…,j; median is the median function, which takes the median of the values ​​in each direction of each scale calculated.

[0076] Step 7: Reconstruct the iterative calculation. Use the calculation method and threshold model of steps 4 to 6 to calculate equation (3), solve the curvelet coefficient in the iteration, and perform inverse curvelet transformation on it. rec =Ψ H s k+1 , in this way, the reconstructed data can be obtained. The specific process is as follows.

[0077]

[0078] Step 8: Frequency domain sorting of effective samples. To improve calculation efficiency, the data is sorted and only the data within the effective bandwidth of the reflection wave is calculated. The selection method is as follows: First, one-dimensional Fourier transform is performed on the original seismic data in the time direction to transform the data from the time domain to the frequency domain. The formula is as follows:

[0079] f obs =Fd obs(10)

[0080] Where: F is the Fourier transform basis.

[0081] On this basis, a calculation method for the effective frequency sample points of the reflected wave is constructed, and the effective signal bandwidth range is determined using the Fourier coefficient (Equation 11). The frequency domain data to be reconstructed is cut out using Equation 12. In this way, only about one-third of the data is involved in the calculation of Equation 7, and the calculation efficiency is greatly improved.

[0082]

[0083] f′ obs =f obs (n f ×n z ) (12)

[0084] Where n t is the number of time sampling points; n f is the number of effective frequency samples; To indicate rounding up; f s is the sampling frequency; f c is the cutoff frequency of the seismic signal.

[0085] Step 9, frequency domain reconstruction algorithm. Steps 4 to 7 are still used to calculate the frequency domain data. The threshold processing is the same as the time domain reconstruction. However, the data obtained by calculation at this time is the curvelet coefficient. After the inverse transformation (Formula 13), the seismic data reconstructed in the time domain can be obtained.

[0086] d rec =F H f rec (13)

[0087] Step 10: Repeat steps 3 to 9 to obtain the final high-precision irregular reconstruction data. Figure 2 For the traditional method to reconstruct the profile, there are many high-frequency linear interference waves in the profile. Figure 3 There are no interference waves in Figure 3 The reflection wave continuity is significantly better than Figure 1 Original cross section (black arrow in the figure).

[0088] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for reconstructing irregular seismic data based on multi-domain hybrid optimized three-dimensional curvelet transform, characterized in that: The method comprises: Step S1, collecting irregular seismic data; Step S2, obtaining a curve coefficient threshold value; Step S3, determining the calculation threshold and the minimum threshold for each iteration respectively according to the improved data-driven threshold model and the adaptive minimum threshold calculation model; The improved data-driven threshold model is: Where: k Calculate the threshold for each iteration; Idx max is the position of the maximum threshold in ρ; Idx ε is the position of the minimum threshold in ρ; ρ is the sequence of sparse coefficient amplitudes arranged in descending order; k is the number of iterations; I ter is the total number of iterations; The adaptive minimum threshold calculation model is: Where: M size is the size of the matrix involved in the calculation; j is the decomposition scale of the multi-scale transformation; j' is the total decomposition scale of the multi-scale transformation; median is the median function; ε is the minimum threshold; Step S4, calculate the curvelet coefficients in the iteration by mixing the time domain reconstruction method and the frequency domain reconstruction method according to the curvelet coefficient threshold value, the calculation threshold value of each iteration, and the data characteristics, and perform inverse curvelet transformation on the curvelet coefficients to obtain the reconstructed seismic data; Step S5, repeating steps S3-S4 until the iterative calculation threshold value of each iteration is less than the minimum threshold value, and then the iterative calculation is terminated, so as to obtain the final high-precision irregular reconstruction data.

2. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 1 is characterized in that: In step S2, the curve coefficient threshold value is obtained by the following formula: Where: mk is the threshold value of the curve coefficient; max is the maximum threshold; ε is the minimum threshold.

3. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 1 is characterized in that: In step S4, if the threshold of each iterative calculation is greater than the curve coefficient threshold, the frequency domain reconstruction method is used; if the threshold of each iterative calculation is less than or equal to the curve coefficient threshold, the time domain reconstruction method is used; if the threshold of each iterative calculation is less than the minimum threshold, the iterative calculation is terminated.

4. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 3 is characterized in that: The time domain reconstruction method includes: reconstructing the irregular seismic data in the time domain through a fast iterative threshold algorithm according to each iterative calculation threshold, solving the curvelet coefficients in the iteration, and performing inverse curvelet transformation on the curvelet coefficients to obtain reconstructed data.

5. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 3 is characterized in that: The frequency domain reconstruction method comprises the following steps: Step S411, first perform a one-dimensional Fourier transform on the irregular seismic data along the time direction to transform the irregular seismic data from the time domain to the frequency domain; Step S412, using the Fourier coefficients to determine the effective signal bandwidth range and cut out the frequency domain data to be reconstructed; Step S413, finally, reconstructing and iterating the frequency domain data to be reconstructed in the frequency domain by using a fast iterative threshold algorithm according to the threshold calculated in each iteration, solving the curvelet coefficients in the iteration, and performing inverse curvelet transform processing on the curvelet coefficients to obtain the reconstructed data.

6. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 5 is characterized in that: In step S412, the effective signal bandwidth range is determined by the following formula: Where: n t is the number of time sampling points; n f is the number of effective frequency samples; To indicate rounding up; f s is the sampling frequency; f c is the cutoff frequency of the seismic signal.

7. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 5 is characterized in that: In step S412, the frequency domain data to be reconstructed is cut out by the following formula: f′ obs =f obs (n f ×n z ) Where: n z is the number of channels; n f is the number of effective frequency samples; f obs is the Fourier coefficient; f′ obs is the frequency domain data to be reconstructed.

8. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 4 or 5, characterized in that: The iterative process of the fast iterative threshold algorithm is: s k+1 =T λ [s k +Θ H (d obs -Ths k )] Where: d obs is the incomplete seismic data to be reconstructed; T λ is the threshold function.

9. The irregular seismic data reconstruction method based on multi-domain hybrid optimized three-dimensional curvelet transform according to claim 4 or 5, characterized in that: The following hard threshold function is used to determine the data range involved in each reconstruction calculation; Where: T hard (x;λ k ) is the hard threshold function; λ is the threshold calculated for each iteration.

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