
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

69593
10.1038/s41598-024-69593-z
Article
The application of matching pursuit spectral blueing in post-stack seismic frequency enhancement
Xuebin Jin 12
Bingxi Li 3
Zhenguo Zhang zzg0351@163.com

12
Maosheng Lei 3
Lishuang An 12
Kai Ding 4
1 https://ror.org/01n2bd587 grid.464369.a 0000 0001 1122 661X College of Mining, Liaoning Technical University, Fuxin, 123000 Liaoning China
2 Key Laboratory of Geological Guarantee for Green Development of Mineral Resources of Liaoning Province, Fuxin, 123000 Liaoning China
3 Beijing Tianyuan Yunkai Technology Co., Ltd., Beijing, 100085 China
4 Sinopec Jingwei Zhongyuan Measurement and Control Company, Henan, 457001 China
14 9 2024
14 9 2024
2024
14 2147019 12 2023
7 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The calculation of the spectral blueing operator in the traditional spectral blueing method has singularity, which leads to poor performance in post-stack seimic frequency expansion. To this end, a frequency spreading technique based on matching pursuit (MP) and spectral blueing is proposed. Through time–frequency analysis processing, it is shown that the seismic signal extracted by matching tracking method has good stability and higher resolution. The specific process of the method in this paper firstly uses the matching tracking method to accurately divide the post-stack seismic data into multiple frequency-division seismic bodies; then, in the process of calculating the spectral blueing ization operators for each frequency band, the weighting idea is used to calculate the weights of the optimized spectral blueing ization operators for each frequency band based on the differences in energy in different frequency bands; finally, the optimized spectral blueing operator is convolved with seismic reflection coefficients to obtain high-resolution seismic data. The actual test results of poststack seismic data have proven that the frequency raising method proposed in this paper is superior to the traditional spectral blueing ization algorithm, greatly improving the high-frequency component information of poststack seismic data. After frequency extension, there are more seismic events and higher resolution. Finally, the practicability and rationality of the seismic data after frequency extraction are verified by a series of operations such as attribute extraction, well seismic calibration and inversion.

Keywords

Spectral blueing
Matching pursuit
Poststack seismic
Optimize the spectral blueing operator
Subject terms

Geophysics
Seismology
Supported by Heilongjiang Provincial Natural Science Foundation of ChinaLH2020D008 issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

In the seismic data processing field, high-resolution techniques are crucial for exploring small-scale geological formations such as thin reservoirs, low-amplitude structures, and minor faults. This is particularly vital in developmental seismology where resolution plays a significant role. Commonly employed methods to enhance seismic resolution include deconvolution, Q-value compensation, spectral whitening and spectral blueing1. The sequence of reflection coefficients in actual seismic data typically exhibits ‘blue’ characteristics, meaning there’s a positive correlation between seismic frequency and amplitude—higher frequencies correspond to higher amplitudes2,3. Research indicates that seismic data resolution can be improved by aligning the seismic spectrum with the reflection coefficient spectrum derived from well-log data, a technique known as ‘spectral blueing’4. The process to enhance seismic resolution using spectral blueing starts with a spectral analysis of seismic data to obtain the seismic spectrum, followed by matching this spectrum with the reflection coefficient spectrum from well logging. Then, a spectral blueing operator is calculated. Finally, this operator is convolved with the original seismic reflection coefficients, obtained through recursive deconvolution, to produce high-resolution seismic data. The calculation of the spectral blueing operator is a crucial step in this process5,6.

KAZEMEINI7 and others conducted CO2 content prediction in the Ketzin block using traditional spectral blueing methods, concluding that pre-stack seismic data suppress edge oscillations better than post-stack data and enhance frequency expansion more effectively. BLACHE8 and others discovered that combining traditional spectral blueing with colored inversion not only significantly improves the resolution of post-stack seismic data but also effectively identifies thin layers. In recent years, Chinese scholars such as Yang Ruizhao9, Ji Tiantian10, Liu Jianwei11, and Li Xianbing12 have employed traditional spectral blueing frequency expansion techniques to process seismic data, enhancing the capability to identify thin interbeds in seismic exploration data and achieving high-resolution processing. However, the computation of the spectral blueing operator in traditional methods is too general, as it is derived from the average spectrum of the entire seismic data, not considering the information in different frequency bands of the seismic data. As a result, processed seismic data often suffer from inadequate frequency enhancement and low-frequency signal oscillation. To address this issue, Chen Ping13 and others, under sparse constraints, minimized the impact of wavelets and proposed a spectral inversion-based spectral blueing frequency expansion method. This method combines the advantages of spectral inversion and spectral blueing, introduces prior knowledge from well logs, and improves the descriptiveness of seismic data for thin sand bodies, avoiding interpretative illusions. Xiao Yufeng14 and others proposed a VMD-based frequency division spectral blueing algorithm for pre-stack seismic data, showing that the spectral blueing operators calculated by frequency division are more effective than traditional methods. However, since VMD frequency division cannot specify the decomposition signal’s frequency, Zhang Lu and others used the generalized S-transform method for frequency division of seismic data and optimized the spectral blueing operators for each frequency division through seismic energy calculation, applying them to actual seismic data. Experiments proved that frequency division spectral blueing operators significantly enhance the main frequency of seismic signals and overcome the drawbacks of low-frequency distortion, demonstrating practical utility in improving thin reservoir accuracy.

This paper, building upon previous research, proposes a spectral blueing algorithm based on frequency division using matching pursuit. This method is more stable compared to traditional spectral blueing algorithms, and offers higher resolution than spectral blueing with generalized S-transform frequency division. Additionally, the low-frequency profiles are consistent with the original seismic data.

Matching pursuit

Method and principle

Matching pursuit is a greedy iterative algorithm that adaptively decomposes a signal into a linear combination of a finite number of wavelets, by repeatedly searching for the wavelets in an overcomplete wavelet dictionary that have the highest correlation coefficient with the seismic signal15. In an N-dimensional Hilbert transform space, let D={gγt}γ∈r represent the wavelet dictionary within this space (also known as an overcomplete wavelet library). For any given signal f, it can be decomposed and projected using this overcomplete wavelet library.1 f=<f,gγ1>gγ1+R1f

In Eq. (1), the symbol < · , · > represents the inner product operator.gγ1 denotes the wavelet obtained in the first iteration from the dictionary D, and R1f represents the residual of the signal after decomposition by the wavelet gγ1. Following the principle of energy conservation, the energy relationship satisfied by Eq. (1) is as follows, as expressed in Eq. (2):2 |f|2=||<f,gγ1>||2+|R1f|2

The matching pursuit algorithm requires multiple iterations to find the optimal wavelet. Suppose the iteration has progressed to the n-th step, with the residual after decomposition being Rnf, and the matched wavelet found is gγn. Then, Rnf is further decomposed as follows:3 Rnf=<Rnf,gγn>gγn+Rn+1f

Similarly, Eq. (3) also needs to satisfy the following condition:4 |Rnf|2=||<Rnf,gγn>||2+Rn+1f2

Next, repeat the aforementioned decomposition process until the residual energy of the decomposed original signal becomes minimal and negligible. Assuming a certain signal is decomposed through m iterations of the matching pursuit algorithm, the signal can be expressed as follows:5 f=∑n=1m<Rn-1f,gγn>gγn=∑n=1mangγn

In Eq. (5), a represents the amplitudes of the individual matched wavelets. Therefore, a signal decomposed via the matching pursuit algorithm can be represented as a linear combination of a finite number of matched wavelets, which is a sparse representation.

By employing the aforementioned technique, a signal can be decomposed into signals of various frequency bands, refining each time–frequency baseline, thereby reducing the phenomenon of time–frequency aliasing. Due to the improved energy concentration of the signal after decomposition by matching pursuit, this technique is applied to the frequency division processing of seismic data.

Model testing

Time–frequency analysis

Time–frequency analysis is a technique used to study the characteristics of signals in both time and frequency domains. It combines the advantages of time-domain and frequency-domain analyses, revealing the time-varying nature of signals more comprehensively. Time–frequency analysis can be applied to analyze non-stationary signals, extracting seismic signal features from seismic data, thereby enhancing the ability to identify and interpret special geological bodies16.

To validate the high-resolution characteristics of matching pursuit time–frequency analysis, a synthetic seismic record as shown in Fig. 1a was constructed. This model has a duration of 1000 ms with a sampling interval of 1 ms. When this synthetic seismic record is processed using the generalized S-transform (Fig. 1b) and matching pursuit (Fig. 1c), it is observed that the generalized S-transform cannot separate two closely spaced signals with sufficient distinction. In contrast, the signal processed through matching pursuit not only improves resolution but also distinctly separates adjacent signals in various time segments, yielding better results.Figure 1 Comparison of two time–frequency analysis methods. (a) Synthetic seismic record (b) generalized S-transform (c) matching pursuit.

To further demonstrate the stability of time–frequency analysis using the matching pursuit algorithm, a signal with 30% added Gaussian noise as shown in Fig. 2 was constructed. This signal was then analyzed using the aforementioned two time–frequency analysis methods, with results displayed in Fig. 2b, c. Observation reveals that compared to the generalized S-transform, matching pursuit demonstrates stronger noise resistance, still effectively separating adjacent signals with higher resolution.Figure 2 Comparison of two time–frequency analysis methods (with 30% noise). (a) Synthetic seismic record (b) generalized S-transform (c) matching pursuit.

Seismic data frequency decomposition processing

Firstly, matching pursuit is used to decompose the seismic signal into wavelets and reconstruct the signal, testing the completeness of the reconstructed signal to verify the feasibility and accuracy of the algorithm17.

In this study, a Gabor atom dictionary is employed for designing time–frequency atoms. As the number of iterations increases, the residual between the reconstructed signal and the original signal gradually decreases. We set the residual threshold to be less than 0.3% as the criterion for the final iteration count. Through multiple verifications, it has been observed that when the number of iterations is approximately 50, the average residual falls below 0.3% (Fig. 3b). Therefore, the number of iterations for this study is set to 50.The results are shown in Fig. 3. In Fig. 3a, the blue curve represents the original seismic signal, and the red curve represents the reconstructed signal. Figure 3b shows the reconstruction residue. Figure 4 selects the best atom from the 33rd to the 36th iterations during the matching pursuit process. Figure 5 displays the Wigner–Ville time–frequency diagram corresponding to the atoms in Fig. 4. The reconstruction results prove the effectiveness of decomposition and reconstruction based on the Gabor atom dictionary.Figure 3 MP decomposition and signal reconstruction.

Figure 4 MP wavelet decomposition (selecting four atoms).

Figure 5 MP wavelet TFspectrum (selecting four atoms).

Based on the high-precision time–frequency spectrum obtained through matching pursuit, it’s possible to use matching pursuit wavelets to construct profiles of the same frequency, thereby achieving frequency decomposition of seismic data. To preserve the amplitude of the seismic signal, the spectra of the time–frequency atom Grn(f) are first normalized after decomposition by the matching pursuit method. Then, following Formula (6), the waveforms of all time–frequency atoms gr(t) are weighted in the frequency direction according to their corresponding Gr(f). By extracting according to the given frequency fj,the frequency-decomposed profile DFt,fj can be obtained.6 DFt,fj=∑nangrn(t)Grn(fj)∫Grnλdλ

In the above Formula (6) 18: Grnλ represents the spectrum corresponding to the matching pursuit wavelet grn(t); λ denotes the integration variable; an represents the complex amplitude of the time–frequency atom gr(t). Figure 6 shows a part of the frequency-decomposed seismic volume calculated using matching pursuit, where a is the original seismic profile, b is the frequency-decomposed profile at 20 Hz, c is at 50 Hz, and d is at 80 Hz.Figure 6 The frequency-decomposed seismic volume (partial) obtained through matching pursuit.

Matching pursuit of spectrum blueing technology

Technical principle and process

Traditional spectral blueing methods for frequency expansion primarily utilize the ‘blue spectrum’ characteristic, where seismic frequency and amplitude are positively correlated. Initially, the method involves matching the average seismic spectrum with the reflection coefficient spectrum from well logging to obtain the spectral blueing operator that maximizes the correlation coefficient between the two. Finally, this spectral blueing operator is convolved with the seismic reflection coefficients to obtain the expanded frequency data. However, in traditional spectral blueing methods, the operator is derived by matching the overall average seismic spectrum with the reflection coefficient spectrum from well logging. This approach may not fully utilize the information in each frequency band of the seismic data, leading to potential issues such as loss of low-frequency information and suboptimal frequency expansion effects. Therefore, building on the progress of previous research, this paper introduces the concept of seismic frequency division into the traditional spectral blueing method. Initially, the original seismic volume is decomposed into multiple volumes according to certain frequencies, and a spectral blueing operator is calculated for each decomposed seismic volume. These operators are then averaged to obtain an optimized spectral blueing operator, which is subsequently convolved with seismic reflection coefficients to produce a high-resolution seismic volume. The frequency division of the seismic volume is conducted using matching pursuit, and the entire implementation process follows six steps.Firstly, perform frequency division on the original seismic volume using matching pursuit technology, then calculate the average spectrum Siw¯ for each frequency-divided seismic data volume.

7 Siw¯=∑j=1nSijwn

In Eq. (7): Siw¯ represents the average spectrum of the seismic data volume in the i-th frequency band; Sij(w) represents the seismic spectrum of the j-th trace in the i-th frequency band; n is the sum of the number of seismic traces in that frequency band.(2) Calculate the reflection coefficient spectrum of well logging. For any given well, the reflection coefficient Rj is calculated as follows:

8 Rj=ρj+1vj+1-ρjvjρj+1vj+1+ρjvj

In Eq. (8): ρ represents the density in well logging data; v indicates the velocity in well logging data; j denotes the j-th sampling point in the well logging; Rj represents the reflection coefficient in the well logging data from the top to the j-th sampling point. Then, by applying a Fourier transform, the reflection coefficient spectrum is obtained:9 Rω=∫-∞∞Rt·e-iωtdt

In Eq. (9): Rω represents the reflection coefficient spectrum from well logging; R(t) represents the amplitude spectrum of the reflection coefficient from well logging; i is the imaginary unit, satisfying i2 = −1;ω is the angular frequency, related to frequency f by ω=2πf, and t is the time variable.(3) Calculate the spectral blueing operator for each frequency-divided seismic volume. First, calculate the average spectrum of each frequency-divided seismic volume, aiming to closely approximate the reflection coefficient spectrum of well logging. When the correlation coefficient between the two is at its highest, the spectral blueing operator Bi(ω) is obtained:

10 minTωBiω·Sω¯-Rjω2+RBiω

In Eq. (10) 19: Tω represents the taper function in the optimization algorithm, which helps reduce discontinuities at the edges of the signal, thereby minimizing edge effects in the analysis. Common taper functions include the Hanning window, Hamming window, and Blackman window. In this experiment, the Hanning window is selected for its taper function, characterized by its superior spectral performance and suppression capabilities. Rjω represents the reflection coefficient spectrum of well logging; Sω- denotes the average spectrum of the seismic data volume; R[Bi(ω)] represents the regularization function in the optimization algorithm, used to prevent overfitting of the model to training data. By introducing a regularization function, it’s possible to balance training error and model complexity during model training, thereby enhancing the model’s generalization ability and improving its performance on unseen data. In this experiment, L2 regularization was applied to the spectral blueing operator by adding a regularization term of the sum of operator squares, promoting operator smoothness and slightness, preventing overfitting, and maintaining the model’s generalization ability. Finally, the spectral blueing operator for each frequency-decomposed seismic volume was obtained through Eq. (10).(4) Calculate the weight of the spectral blueing operator for each frequency-divided seismic volume. Firstly, the amplitude energy of each frequency-divided seismic volume must be normalized:

11 Enormi=Ei-EminEmax-Emin

In Eq. (11): Emin and Emax respectively represent the minimum and maximum energy values of the original seismic data; Ei represents the amplitude energy of the i-th frequency-divided seismic volume; Enormi denotes the normalized amplitude energy of the i-th frequency-divided seismic volume. The weight λi of the spectral blueing operator for each frequency-divided seismic volume can be calculated based on the energy proportion of each frequency-divided seismic volume.12 λi=EnormiEnormi∑i=1NEnormi∑i=1NEnormi

In Eq. (12): N represents the number of frequency divisions.(5) Calculate the optimized spectral blueing operator Bopt. By weighted summation of the spectral blueing operators Bi(ω) for each frequency division, the final Bopt can be obtained.

13 Bopt=∑i=1NλiBiω

(6) Compute the high-resolution data. First, extract the wavelet from the original seismic data, then use the recursive deconvolution method to calculate the reflection coefficients on the seismic data, obtaining a reflection coefficient volume RS Finally, perform an inverse Fourier transform on the improved spectral blueing operator to convert it into the time domain, and then convolve it with the reflection coefficient volume RS to obtain the final high-resolution data.14 bopt=12π∫-∞∞Boptωejφωdω

15 Sopt=RS∗bopt

As the spectral blueing operators for different frequency-divided seismic volumes are calculated and averaged, the new spectral blueing operator better represents signals across different frequency bands. The spectral blueing operator derived using the method in this paper, when applied for high-resolution processing of seismic data, results in higher data accuracy. This method not only enhances high-frequency signals but also resolves the issue of low-frequency loss in traditional spectral blueing methods. Therefore, the optimized high-resolution data more accurately represent the reservoir distribution. Below, Fig. 7 shows the flowchart of the frequency division spectral blueing process using matching pursuit.Figure 7 Overall process flowchart.

Process of experiment

Select post-stack seismic data from a certain oil field for analysis. Initially, decompose the post-stack seismic data into various frequency bands using matching pursuit (MP) frequency decomposition; then, resample the well log data according to the original seismic sampling points, ensuring that the number of sampling points in the single trace seismic data matches that of the well log data; finally, obtain the high-resolution seismic data through spectral blueing using the aforementioned formulas. As shown in Fig. 9a, the original seismic bandwidth ranges from 10 to 80 Hz. Therefore, in this experiment, matching pursuit frequency decomposition was employed to obtain frequency-segmented seismic data at intervals of 10 Hz between 10 and 80 Hz. The reflection coefficient spectrum required for well logging was computed as the average reflection coefficient spectrum of all wells in the study area. Seismic spectrum calculation utilized seismic profile data from the wells. The initialization condition for the iterative seismic spectrum approximation to the reflection coefficient spectrum is that the operator is initialized as a full array of ones with the same length as the seismic spectrum. This means that at the beginning of the approximation, the operator’s enhancing or attenuating effect on all frequency components is uniform, without specifically considering any particular frequency range. The initialization operator does not impose any prior assumptions on the optimization results, ensuring that the optimization process is based on maximizing the correlation between seismic and well logging data. The initialization condition for matching pursuit algorithm firstly involves the Gabor dictionary library and initial residuals. Before the algorithm starts, the initial residual is set to the original signal itself because no dictionary atoms are selected to approximate the original signal.

Figure 8 shows the original inter-well seismic profile. Figure 9 details the process for obtaining the spectral blueing operator for the 40 Hz frequency band. Figure 9a represents the seismic spectrum for the frequency band, Fig. 9b shows the average reflection coefficient spectrum from well logging, and Fig. 9c illustrates the matching results for the spectral blueing operator of the frequency band. Inside, the black, blue, and red curves respectively signify the seismic spectrum, the well log’s reflection coefficient spectrum, and the approximated spectral blueing operator. Subsequent steps involve calculating the spectral blueing operators for the remaining seismic frequency bands. Finally, utilizing Formulas (13), (14), (15), the ultimate spectral blueing operator and high-resolution seismic data can be obtained.Figure 8 Original seismic profile.

Figure 9 Process of obtaining spectral blueing operator. (a) Seismic spectrum (b) reflection coefficient spectrum (c) process of obtaining spectral blueing operator.

In this experiment, both traditional spectral blueing and spectral blueing using matching pursuit frequency division were applied to post-stack seismic data for high-resolution processing. The seismic profiles before and after processing, along with the spectral analysis, are shown in Figs. 10, 11.Figure 10 Seismic profiles obtained using traditional spectral blueing method and the method described in this paper. (a) Frequency expansion using traditional spectral blueing method (b) frequency expansion using the method described in this paper.

Figure 11 Seismic spectra obtained using two different spectral blueing frequency expansion techniques.

Observation of the seismic profile reveals that traditional spectral blueing methods only cause slight changes to the post-stack seismic data, without significantly improving resolution. However, the post-stack seismic data processed by the method discussed in this paper shows an increase in the number of phase axes and better continuity, significantly enhancing the resolution of the seismic data. Spectral observation indicates that traditional spectral blueing methods increase the frequency of the original seismic data, notably enhancing high-frequency components but losing low-frequency components. In contrast, the seismic data processed by this paper’s method show a significant increase in high-frequency components and a further broadening of the frequency band. The trend and continuity of the seismic profile, post-frequency enhancement, remain essentially consistent with the original seismic profile, avoiding abnormal jumps in the seismic axis and hence not generating excess noise. Only the overall seismic amplitude undergoes some changes. Employing spectral blueing with matching pursuit broadens the frequency technology, better preserving low-frequency valid signals while increasing high-frequency valid signals, thus ensuring better amplitude preservation.

Results analysis

To further demonstrate the frequency enhancement effect of the processed seismic data, the total energy slice attribute is extracted along the target layer from both the original and frequency-enhanced data, as shown in Fig. 12. Observation reveals that the processed seismic data overall depicts faults more precisely, better reflecting structural characteristics.Figure 12 Total energy slice attribute plane diagram. (a) Total energy attribute of the target layer slice before processing. (b) Total energy attribute of the target layer slice after processing.

Subsequently, the frequency-enhanced data were further analyzed and validated using well-seismic integration. This experiment involved generating synthetic records for the original seismic, frequency-enhanced seismic, and high-frequency component seismic data, with the high-frequency seismic using a frequency-divided seismic volume of 120 Hz. The results are shown in Fig. 13. By comparing drilling data with seismic phases, it is evident that the well-seismic calibration correlation is good both before and after high-resolution processing, accurately reflecting the characteristics of seismic reflection interfaces. The high-frequency components from drilling and seismic correspond well, indicating that the high-frequency parts after processing are geologically significant, and the high-resolution seismic data are reliable.Figure 13 Synthetic record of well 8H29.

Because inversion allows for a better observation of the seismic data’s response to sandstone and mudstone, thereby reflecting reservoir characteristics, waveform inversion was performed on the seismic data before and after processing. This inversion experiment selected seismic profiles passing through the wells 8F4-48, 8F5201, and 8H29, with the results shown in Fig. 14. Among them, a represents the original seismic inversion profile; b represents the seismic inversion profile after processing with the method described in this paper; c shows the local inversion profile for well 8F4-48 before frequency enhancement, while d shows the local inversion profile for well 8F4-48 after frequency enhancement; e shows the local inversion profile for well 8F5201 before frequency enhancement, while f shows the local inversion profile for well 8F5201 after frequency enhancement; g shows the local inversion profile for well 8H29 before frequency enhancement, and h shows the local inversion profile for well 8H29 after frequency enhancement. By comparing the inversion profiles with the well’s sand-mud stratification, it is found that the seismic data after processing have higher inversion resolution and a higher conformity rate to the well logs’ sandstone, which is beneficial for further reservoir prediction work.Figure 14 Seismic inversion profile over the well.

Conclusion

The calculation of the spectral blueing operator is a key step in the spectral blueing method. This paper proposes calculating the spectral blueing operator for each frequency band using matching pursuit frequency decomposition technology, and then obtaining the final optimized and improved spectral blueing operator based on energy weighting. This achieves high-resolution processing of seismic data, enhances the ability of seismic data to identify sand bodies, and addresses the problem of uniformity in the calculation of traditional spectral blueing operators.

The combination of matching pursuit frequency decomposition with the spectral blueing method has to some extent resolved issues found in traditional spectral blueing methods, such as the loss of low-frequency signal and the unreasonable enhancement of high-frequency signal. This approach not only enhances high-frequency components but also preserves low-frequency components well, with better amplitude preservation, making it applicable to multi-well work areas.

The application of spectral blueing broadening technology based on matching pursuit in actual seismic data has proven that this method significantly improves both the vertical and lateral resolution of post-stack seismic data. This improvement is verified through methods such as extracting total energy attributes before and after processing, well-seismic calibration, inversion, etc., demonstrating the rationality of high-resolution seismic data.

Author contributions

J.X.B did all the writing of the paper. L.B.X checked and revised the manuscript content. Z.Z.G checked and revised the manuscript content. L.M.S checked and revised the manuscript content. D.K checked and revised the manuscript content.

Funding

This work was supported by Heilongjiang Provincial Natural Science Foundation of China, LH2020D008.

Data availability

In this paper, a piece of “.sgy ”seismic data is used, and then GeoScope software is used to first obtain the reflection coefficient body of the original seismic, and then the seismic data is divided into different frequency bodies by using the matching pursuit. Finally, the spectral bluing operator is obtained by using the python spectral bluing program written by myself, and the frequency lifting data body is obtained by convolving with the reflection coefficient body.

If anyone wants to reproduce my paper, you can send me an email, and I can send the data and methods to your email.

Email: 964851590@qq.com.

This article initially used a small block of raw seismic data with an ‘sgy’ suffix, then used the matching pursuit feature in GooScope software to divide the seismic data into different frequencies. Using GooScope software, the reflection coefficient volume of the original seismic data was obtained. Subsequently, a Python spectral bluing program written by the author was used to calculate the spectral bluing operators for different frequencies. Finally, these operators were convolved with the reflection coefficient volume to produce a high-resolution seismic volume. If anyone wants to reproduce my paper, you can send me an email, and I can send the data and methods to your email. Thank you! email: 964851590@qq.com.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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