Time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition

Abstract

The invention provides a time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition, and belongs to the field of geophysical exploration and seismic signal processing. Differential compensation of different frequency scales is achieved in time frequency, an effective frequency band is widened after high-frequency compensation, and the purpose of remarkably improving the seismic data resolution is achieved. The method comprises the following steps: firstly, carrying out noise suppression on superposition data through a noise suppression technology to obtain superposition data with a high signal-to-noise ratio, carrying out decomposition on de-noised seismic data based on variational mode decomposition to obtain IMF components with different frequency scales, and carrying out Hilbert transform to obtain corresponding instantaneous amplitude and instantaneous phase; secondly, designing a whitening filter for IMF components with different scales to perform spectrum equalization processing, compensating instantaneous amplitude within a certain frequency range, and obtaining a time-frequency spectrum after spectrum whitening; and finally, combining the processed instantaneous amplitude with the original instantaneous phase to form a new IMF component so as to reconstruct the signal.

Description

Technical Field

[0001] The present application proposes a time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition, belonging to the fields of geophysical exploration and seismic signal processing. Background Art

[0002] With the transfer of exploration targets to deep water, ultra-deep water and complex lithology reservoirs, the refinement degree of resource exploration and development is getting higher and higher, and the existing seismic data are difficult to meet the prediction requirements of fine reservoirs. In order to obtain high-precision and high-resolution data under complex targets, the corresponding high-resolution processing technology is also crucial.

[0003] There are many existing processing technologies for improving the resolution of seismic data, such as spectral whitening, frequency division processing methods, etc. The spectral whitening method performs amplitude equalization on the overall frequency in the time domain; the high-resolution processing method based on frequency division processing is mainly based on algorithms such as wavelet transform, generalized S transform, and empirical mode decomposition (EMD), and uses multi-scale transform to decompose seismic data, and the time-frequency information of different scale components is used for high-resolution processing of the data. In the process of processing actual data, restricted by the theoretical assumptions implicit in different methods themselves, it is difficult to achieve the ideal resolution improvement effect by simply using a certain method. For example, in spectral whitening processing, overall frequency compensation is generally performed, which will affect the fidelity of seismic signals and bring errors to later attribute analysis and inversion. Due to the non-self-adaptive nature of the conventional frequency division compensation method, the selection of scale factors and parameters results in low frequency division accuracy, making it difficult to achieve differential compensation and affecting the high-resolution processing effect. In the joint processing based on EMD and spectral whitening, due to the introduction of false components in the EMD algorithm process, abnormal compensation will occur during the compensation process. For seismic data with low signal-to-noise ratio, the high-frequency noise compensation caused by mode mixing will lead to a decrease in signal-to-noise ratio and affect the imaging quality.

[0004] Currently, it has developed into a joint processing means of two types of methods to form the complementary advantages of the methods. By equalizing and compensating the instantaneous amplitude through the instantaneous frequency value, local details can be effectively compensated and the resolution of seismic data can be improved. At the same time, variational mode decomposition (abbreviation: VMD), as a new adaptive and non-recursive signal decomposition method, is an improvement of the EMD algorithm. This method assumes that each intrinsic mode function (abbreviation: IMF) has a finite bandwidth with different central frequencies, and by transforming to solve the variational problem, the sum of the estimated bandwidths of each IMF is minimized. Compared with the EMD algorithm, it can effectively reduce the probability of problems such as pseudo-components, mode mixing, and end-point effects generated by signal decomposition, and has better noise robustness. Therefore, during the spectral envelope equalization process of each IMF, the accuracy is higher. At the same time, the IMF after eliminating mode mixing is more conducive to identifying high-frequency noise and can effectively avoid compensating for high-frequency noise.

[0005] In view of this, the present application is hereby proposed. Summary of the Invention

[0006] The high-resolution processing method based on variational mode decomposition and time-frequency spectrum whitening of the present invention aims to solve the problems existing in the above-mentioned prior art by proposing a processing scheme that combines variational mode decomposition and spectrum whitening, with the expectation of achieving differential compensation for different frequency scales in the time-frequency domain and significantly improving the resolution of seismic data.

[0007] To achieve the above design objective, the high-resolution processing method based on variational mode decomposition and time-frequency spectrum whitening combines variational mode decomposition technology and spectrum whitening technology to compensate for the high-frequency signals of seismic data in the time-frequency domain to broaden the frequency band; first, noise suppression technology is used to suppress the noise and multiple waves in the stacked data to obtain stacked data with a higher signal-to-noise ratio. Based on variational mode decomposition, the denoised seismic data is decomposed to obtain IMF components with different frequency scales. After Hilbert transform, the corresponding instantaneous amplitude and instantaneous phase are obtained; then, whitening filters are designed for IMF components of different scales for spectral equalization processing, and the instantaneous amplitude within a certain frequency range is compensated to obtain the time-frequency spectrum after spectrum whitening; finally, the processed instantaneous amplitude and the original instantaneous phase are combined to form new IMF components to reconstruct the signal.

[0008] Further, it includes the following steps: Step (1), seismic data denoising processing; The noise and multiple waves in the seismic data are suppressed by noise suppression and signal-to-noise ratio enhancement means to obtain input data with a higher signal-to-noise ratio; Step (2), variational mode decomposition; After obtaining the signal spectrum, Hilbert transform is performed on each IMF to construct an analytic signal, and a tuning index is introduced to multiply with the center frequency to obtain a tuning signal; the estimated modal bandwidth is calculated by the square of the L2 norm of the gradient of the tuning signal, and the calculation formula is as follows: (1) In the formula, f is the original signal, is the set of K IMF components, is the value term added for each mode to adjust its respective center frequency, is each IMF modal component of the center frequency; A quadratic penalty factor and a Lagrange multiplication operator with strong constraint ability are added to the following expression: (2); Among them, is a Dirac distribution, representing the original signal; Decompose the seismic signal based on variational mode decomposition; Step (3), calculate the three instantaneous attributes; Obtain the instantaneous frequency, instantaneous phase, and instantaneous amplitude of the seismic signal through Hilbert transform and complex trace analysis technology, and obtain the time-frequency spectrum reflecting local characteristics; Step (4), spectral whitening and equalization; Obtain the whitening filter according to the reciprocal of the signal spectrum and the white noise factor; Perform the same processing on each IMF to obtain the instantaneous amplitude of the seismic signal after spectral whitening; Reconstruct using the spectral whitened instantaneous amplitude and the original instantaneous phase, and perform selective summation on each IMF component based on signal-to-noise ratio analysis; Step (5), instantaneous amplitude and instantaneous phase reconstruction; Jointly reconstruct the original instantaneous phase and the spectral whitened instantaneous amplitude to form a new seismic signal, thereby obtaining the whitened seismic data. The reconstruction formula is as follows: (12); Sum the IMF terms based on signal-to-noise ratio analysis to obtain the data after spectral whitening with a higher signal-to-noise ratio.

[0009] Furthermore, in the aforementioned step (2), the decomposition process of the seismic signal based on variational mode decomposition includes the following steps. 2.1. Initialize the parameters and n, and the initial value of n is defined as 0; 2.2. Design a loop process such that n = n + 1, and update and ; and The update formulas are as follows: (3); (4); 2.3. Update the multiplication operator as follows: (5); where represents the step size update coefficient; 2.4. Determine whether the component satisfies the constraint condition , and the value of ε is given by testing according to the processing effect and calculation efficiency; if the constraint condition is satisfied, stop the loop and obtain a finite number of IMF components; if the constraint condition is not satisfied, return to step 2.2 and repeat the above steps.

[0010] Further, step (3) includes the following steps: For the seismic signal X ( t ), its Hilbert transform Y ( t ) is: (6); Then, the analytic signal Z(t) can be formed by X(t) and Y(t) through the complex trace technique, and the formula is as follows: (7); Z(t) can be written as: (8); The corresponding instantaneous phase, instantaneous frequency, and instantaneous amplitude can be expressed as: (9).

[0011] Further, step (4) includes the following steps: Assume that the seismic signal sequence is x(t ), and the spectrum of the signal is obtained after Fourier transform X ( ω ). By finding the maximum points of the amplitude spectrum | X ( ω )|, its envelope e ( ω ) is obtained. The whitening filter function is defined as: (10); In the formula, V is the maximum value of the envelope function, that is, ; is the white noise factor; x ( t ) is decomposed by variational mode decomposition to obtain the sum of a series of IMFs; each component contains different local information. For one of the IMFs, c i ( t ), i = 1,..., n, obtained according to formula (9). The corresponding instantaneous frequency and instantaneous amplitude are respectively ω i ( t ) and a i ( t ). By multiplying the whitening filter with the instantaneous amplitude at each time point a i ( t ), the instantaneous amplitude after spectral whitening is obtained, that is: ), (11).

[0012] In summary, the time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition has the following advantages and beneficial effects: 1. This application combines the technical advantages of the joint variational mode decomposition and spectral whitening methods, and thus proposes a high-resolution solution for seismic data processing requirements. It can effectively control the processing effect by selecting the number of IMFs and white noise factors during the decomposition process in the time-frequency domain, realizing differential processing of different frequency scales, that is, compensating for the differences at different frequency scales, and thus has good adaptability to actual data; 2. The IMFs obtained based on variational mode decomposition have good resolution for high-frequency scale noise. In the data reconstruction process of this application, the compensated IMFs are selected according to the signal-to-noise ratio, effectively avoiding the situation of reduced signal-to-noise ratio of seismic data caused by high-frequency noise compensation, and thus obtaining high resolution of seismic data. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition described in this application; Figure 2 is a waveform comparison diagram after single-trace processing; Figure 3 is an original stacked data diagram; Figure 4 is a stacked data diagram after joint variational mode decomposition and spectral whitening processing; Figure 5 is a frequency spectrum diagram of the original stacked data; Figure 6 is a compensated stacked cross-section diagram; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] The present invention will be further described below with reference to the drawings and embodiments.

[0015] Example 1, as Figure 1 shown, in the face of the requirements of fine exploration and development under complex targets, conventional two-dimensional seismic data often has a narrow frequency band, which is not conducive to fine imaging and interpretation, and is difficult to meet the needs of seismic attribute analysis and reservoir prediction of thin interbedded lithologic oil and gas reservoirs.

[0016] The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition proposed in this application, through the joint variational mode decomposition technology and spectral whitening technology, compensates the high-frequency signals of seismic data in the time-frequency domain, thereby broadening the frequency band to achieve high-resolution processing, focusing on solving the problem that the local details and characteristics of the seismic data strata are not clearly depicted, and providing high-fidelity high-resolution seismic data for geological interpreters.

[0017] Specifically, first, noise suppression is performed on the stacked data through noise suppression technology to obtain stacked data with a relatively high signal-to-noise ratio. The denoised seismic data is decomposed based on variational mode decomposition to obtain IMF components with different frequency scales. After Hilbert transform, the corresponding instantaneous amplitude and instantaneous phase are obtained; Then, a whitening filter is designed for the IMF components of different scales for spectral equalization processing, that is, the instantaneous amplitude within a certain frequency range is compensated to obtain the time-frequency spectrum after spectral whitening; Finally, the processed instantaneous amplitude and the original instantaneous phase are combined to form new IMF components, and the signal is reconstructed to achieve the purpose of improving the data resolution.

[0018] The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition includes the following steps: Step (1), seismic data denoising processing; High-resolution seismic data processing has certain requirements for the signal-to-noise ratio of the original data. Due to the existence of high-frequency noise in data with a low signal-to-noise ratio, it is easy to compensate for the noise components. Therefore, noise suppression processing must be performed on the data before high-resolution processing.

[0019] Specifically, the noise and multiple waves in the seismic data are effectively suppressed through noise suppression and signal-to-noise ratio enhancement means to obtain input data with a relatively high signal-to-noise ratio; Step (2), variational mode decomposition; Variational mode decomposition is a non-recursive and fully adaptive variational method that can decompose a signal into multiple IMFs with finite bandwidths, and can clearly depict the local characteristics of seismic signals. Its main advantage is that it can effectively solve the problems of mode mixing and spurious components during the decomposition process. The IMF with a single scale can improve the accuracy of spectral envelope calculation during spectral whitening, and the local characteristics of the signal will be depicted more accurately; Specifically, after obtaining the signal spectrum, Hilbert transform is performed on each IMF to construct an analytic signal; a tuning index is introduced and multiplied by the center frequency to obtain a tuning signal; the estimated modal bandwidth is calculated through the square of the L2 norm of the gradient of the tuning signal, and the calculation formula is as follows: (1) In the formula, f is the original signal, is the set of K IMF components, is the value item added for each mode to adjust its respective center frequency, is each IMF modal component of the center frequency; A quadratic penalty factor is added to the following expression and the Lagrange multiplication with strong constraint ability Operator: (2); Wherein, is the Dirac distribution, represents the original signal; Decompose the seismic signal based on variational mode decomposition; the specific process includes the following steps: 2.1. Initialize the parameters and n, and the initial value of n is defined as 0; 2.2. Design a loop process to make n = n + 1 and update and ; and The update formula is as follows: (3); (4); 2.3. Update the multiplication operator as follows: (5); Wherein, represents the step size update coefficient; 2.4. Judge whether the component satisfies the constraint condition , and the ε value is tested and given according to the processing effect and calculation efficiency; if the constraint condition is satisfied, stop the loop and obtain a finite number of IMF components; if the constraint condition is not satisfied, return to step 2.2 and repeat the above steps.

[0020] Step (3). Calculate the three instantaneous attributes; After the seismic signal is decomposed into multiple different-scale IMFs in step (2), the instantaneous frequency, instantaneous phase, and instantaneous amplitude of the seismic signal are obtained through Hilbert transform and complex trace analysis technology, so as to obtain a time-frequency spectrum that can reflect local characteristics; For the seismic signal X ( t ), its Hilbert transform Y ( t ) is: (6); Then the analytical signal Z(t) can be formed by X(t) and Y(t) through complex trace technology, and the formula is as follows: (7); Z(t) can be written as: (8); The corresponding instantaneous phase, instantaneous frequency, and instantaneous amplitude can be expressed as: (9).

[0021] Step (4), spectral whitening equalization; Based on the obtained time-frequency spectrum, using a whitening filter, optimizing its parameters, and equalizing the instantaneous amplitude at each time point for each component by constraining the instantaneous frequency of the corresponding IMF component; The whitening filter adopted in this application is obtained according to the reciprocal of the signal spectrum and the white noise factor; Specifically, assume the seismic signal sequence is x(t ), and after Fourier transform, the spectrum of the signal is obtained X ( ω ), by finding the maximum points of the amplitude spectrum | X ( ω )| to obtain its envelope e ( ω ), define the whitening filter function as: (10); In the formula, V is the maximum value of the envelope function, that is, ; is the white noise factor; x ( t ) After variational mode decomposition, a series of sums of IMFs are obtained; each component contains different local information. For one of the IMFs, c i ( t ), i = 1, …, n, obtained according to formula (9), the corresponding instantaneous frequency and instantaneous amplitude are respectively ω i ( t ) and a i ( t ), by multiplying the whitening filter with the instantaneous amplitude at each time point a i ( t ), thus obtaining the instantaneous amplitude after spectral whitening, that is: ) (11).

[0022] Perform the same processing on each IMF to obtain the instantaneous amplitude of the seismic signal after spectral whitening; since the IMFs at different scales have different amplitude envelopes and the designed whitening filter has its characteristics, differential processing of different frequencies can be achieved; Each IMF obtained by decomposing this application has good resolution on the high-frequency scale. With the control of the white noise factor of the whitening filter, high-frequency noise can be better identified, and during the compensation process, differential processing can be carried out to avoid the reduction of the data signal-to-noise ratio caused by high-frequency noise compensation.

[0023] Step (5), instantaneous amplitude and instantaneous phase reconstruction; Based on the above steps, it can be seen that the instantaneous phase of each IMF has not changed. Therefore, a new seismic signal is formed by jointly reconstructing the original instantaneous phase and the instantaneous amplitude after spectral whitening, so as to obtain the whitened seismic data. The reconstruction formula is as follows: (12); During the actual data processing process, due to the difference in the signal-to-noise ratio of the data, for the high-frequency IMF after spectral whitening, the sum term of the IMF is controlled based on the signal-to-noise ratio analysis to ensure that the data after spectral whitening has a high signal-to-noise ratio. The IMF components obtained by variational mode decomposition can well reflect the local characteristic information of the seismic signal. During the high-resolution processing of spectral whitening, the seismic data can be effectively identified from both the overall and local aspects, so as to realize the broadening of the frequency band and the fine characterization of the formation.

[0024] Such as Figures 2 to 6 shown, to verify the effectiveness and practicality of the high-resolution processing method of time-frequency spectral whitening based on variational mode decomposition described in this application, the corresponding effect analysis is carried out after processing the actual two-dimensional stacked seismic data in a certain sea area.

[0025] First, use variational mode decomposition to process each trace, and divide the seismic signal into IMF components of different scales; Then, based on the Hilbert transform, construct an analytic signal to obtain the instantaneous frequency and instantaneous phase; Finally, process the time-frequency spectrum by designing a whitening filter. It has a better effect when the white noise factor corresponding to the high-frequency IMF is taken above 0.5, and it has a better effect when the white noise factor corresponding to the low-frequency IMF is taken below 0.5. The high-resolution seismic data is obtained by reconstructing the signal through the amplitude and phase after spectral whitening.

[0026] Such as Figure 2 shown, the comparison diagram of a single trace of the stacked data before and after processing. The waveforms before and after are locally magnified between 0.6 - 1 s. The dotted line is the waveform of the original data, and the solid line is the waveform after being processed by the method of the present invention. It can be seen from the comparison that the waveform after processing has been greatly improved, and the local information of the waveform has become richer.

[0027] Such as Figure 3 and Figure 4As shown, the effects before and after processing the stacked data are presented. By comparison, it can be clearly seen that due to the influence of noise and frequency bandwidth, it is difficult to identify horizons with similar reflection coefficients in the original section. After processing, the horizons are separated, the continuity of the thin-bed reflection event is significantly enhanced, the wave group characteristics are clearer, and the resolution has been greatly improved.

[0028] As Figure 5 and Figure 6 shown, from the spectral comparison, it can be seen that the high-frequency part of the effective signal after processing, 18 Hz - 35 Hz, has been greatly improved, and the broadband data is beneficial to the imaging of the strata.

[0029] After processing the stacked data through the present application, the contact relationships of each structure and the breakpoints of small faults are clearer, the vertical resolution of seismic data is improved, and at the same time, a new method for high-resolution processing of stacked data is provided.

[0030] As described above, combining the content of the solution given in the accompanying drawings and the description, similar technical solutions can be derived, which still fall within the scope of the claims of the technical solution of the present invention.

Claims

1. A time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition, characterized by: Joint Variational Module State decomposition technology and spectrum whitening technology are used to compensate for high-frequency signals of seismic data in the time-frequency domain to broaden the frequency band; Firstly, the noise of stacked data is suppressed by noise suppression technology to obtain stacked data with high signal-to-noise ratio. The denoised seismic data is decomposed based on variational mode decomposition to obtain IMF components with different frequency scales. The corresponding instantaneous amplitude and instantaneous phase are obtained after Hilbert transformation. Then, whitening filters are designed for IMF components of different scales to perform spectrum equalization, compensate for the instantaneous amplitude within a certain frequency range, and obtain the time-frequency spectrum after spectrum whitening; Finally, the processed instantaneous amplitude and the original instantaneous phase are combined to form a new IMF component to reconstruct the signal.

2. The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition according to claim 1, characterized in that In: The following steps are included: Step (1), de-noising of seismic data; The noise and multiple waves in the seismic data are suppressed by noise suppression and signal-to-noise ratio enhancement to obtain input data with a higher signal-to-noise ratio; Step (2), variational mode decomposition; After obtaining the signal spectrum, Hilbert transform is performed on each IMF to construct an analytical signal, and the tuning index is introduced and multiplied by the center frequency to obtain the tuning signal; the estimated modal bandwidth is calculated by the L2 norm square of the tuning signal gradient, and the calculation formula is as follows: （1） Where f is the original signal, is a set of K IMF components, For each mode The added value items are used to adjust the respective center frequencies. is each IMF modal component The center frequency of Add a quadratic penalty factor to the following expression and Lagrange multiplication with strong constraints Operator: （2）； in, is the Dirac distribution, represents the original signal; Decomposing seismic signals based on variational mode decomposition; Step (3), calculating three instant attributes; The instantaneous frequency, instantaneous phase and instantaneous amplitude of the seismic signal are obtained through Hilbert transform and complex channel analysis technology, and the time-frequency spectrum reflecting the local characteristics is obtained; Step (4), spectrum whitening equalization; The whitening filter is obtained according to the inverse of the signal spectrum and the white noise factor; The same processing is performed on each IMF to obtain the instantaneous amplitude of the seismic signal spectrum after whitening; The instantaneous amplitude of spectral whitening and the original instantaneous phase are used for reconstruction, and the various IMF components are selectively summed based on the signal-to-noise ratio analysis; Step (5), instantaneous amplitude and instantaneous phase reconstruction; The new seismic signal is formed by jointly reconstructing the original instantaneous phase and the instantaneous amplitude after spectrum whitening, thereby obtaining the whitened seismic data. The reconstruction formula is as follows: （12）； Based on the signal-to-noise ratio analysis, the IMF summation term is used to obtain the spectrally whitened data with a higher signal-to-noise ratio.

3. The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition according to claim 1, characterized in that In: The step (2), the process of decomposing the seismic signal based on variational mode decomposition comprises the following steps: 2.1、Parameters Initialize with n, the initial value of n is defined as 0; 2.

2. Design a loop process, let n=n+1, update and ; and The update formula is as follows: （3）； （4）； 2.

3. Update the multiplication operator as follows : （5）； in, represents the step size update coefficient; 2.

4. Determine whether the component satisfies the constraints , the ε value is given by testing according to the processing effect and calculation efficiency; if the constraint conditions are met, stop the loop and obtain a finite number of IMF components; if the constraint conditions are not met, return to step 2.2 and repeat the above steps.

4. The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition according to claim 1, characterized in that: The step (3) comprises the following steps: For earthquake signals X ( t ), whose Hilbert transform Y ( t )for: （6）； Then, X(t) and Y(t) can be used to construct the analytical signal Z(t) through complex channel technology. The formula is as follows: （7）； Z(t) can be written as: （8）； The corresponding instantaneous phase, instantaneous frequency and instantaneous amplitude can be expressed as: （9）。 5. The time-frequency spectrum whitening high-resolution processing method based on variational mode decomposition according to claim 1, characterized in that: The step (4) comprises the following steps: Assume that the seismic signal sequence is x(t ), and the spectrum of the signal is obtained after Fourier transform X ( ω ), by the amplitude spectrum | X ( ω )︱Find the maximum point and its envelope e ( ω ), define the whitening filter function as: （10）； In the formula, V is the maximum value of the envelope function, that is ; is the white noise factor; x ( t )After variational mode decomposition, a series of IMFs are obtained; each component contains different local information. For one of the IMFs, c i ( t ), i=1,…,n, according to formula (9), the corresponding instantaneous frequency and instantaneous amplitude are ω i ( t )and a i ( t ), through the whitening filter and the instantaneous amplitude at each time point a i ( t ) to obtain the instantaneous amplitude after spectrum whitening, that is: ) (11).

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