CN108919347A - Seismic signal stochastic noise suppression method based on vmd - Google Patents
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Abstract
The seismic signal stochastic noise suppression method based on vmd that the invention discloses a kind of, this approach includes the following steps：It selects a time window that original noisy two-dimension earthquake signal is made Fourier transformation, is converted into the domain f-x；Mode decomposition is carried out to each frequency slice data；Obtained BIMF component combination will be decomposed and obtain filtered signal；Signal is made into inverse Fourier transform, switches back to the domain t-x；Repetition ibid operates next time window, earthquake record be all disposed after to get to final two-dimension earthquake denoising result.Meanwhile expanding One-Dimensional Variational mode decomposition to two-dimensional complex number form in the present invention, it can be used for 3-D seismics denoising.While seismic signal stochastic noise suppression method based on VMD has excellent noise compacting, amplitude retention property, it is also equipped with higher computational efficiency, the processing requirement of higher-dimension large scale seismic data can be met.
Description
Technical Field
The invention relates to the technical field of seismic data processing of geophysical exploration, in particular to a technology for suppressing random noise and keeping and processing effective energy in seismic signals.
Technical Field
Random noise attenuation of seismic signals is a hot spot and difficult problem in the field of seismic data processing. The method effectively removes random noise interference from observation data, improves signal to noise ratio and resolution ratio, and is a precondition for forward and backward calculation and geological interpretation. At present, the random noise suppression method for seismic signals mainly comprises the following steps: a method based on a filtering theory, a method based on a wavelet domain transformation, a method based on a matrix theory, a method based on a signal decomposition theory, and the like. In recent years, an Empirical Mode Decomposition (EMD) method based on signal Decomposition has become a hot spot in the field of signal Decomposition due to its high signal-to-noise ratio in processing non-stationary and non-linear data.
Complete set empirical mode decomposition (CEEMD) avoids the problem of mode aliasing in the EMD method, effectively improves the defect that random white noise is added in the set empirical mode decomposition (EEMD) method to pollute an original signal, but the CEEMD method still adopts a recursive iterative screening decomposition process, the time consumption of non-stationary seismic signal extreme point interpolation and envelope calculation processes is still too long, and certain limitation exists when multi-dimensional and multi-scale seismic data are processed.
In order to solve the problems and further improve the accuracy of signal Decomposition, the invention provides a seismic signal random noise suppression processing method based on Variational Modal Decomposition (VMD). By converting the modal decomposition process into the optimal solution iterative solution process of the variation model, the minimum sum of the estimated aggregation bandwidths of each component is taken as a constraint, and the dual-dual rising enables the frequency center and the bandwidth of each component to be subjected to self-adaptive separation in a frequency domain. Different from the recursive 'screening' mode of EMD, VMD decomposes and converts signals into non-recursive and variational model functional extremum solving problems, and the variational model optimization objective function solving process can know that the problem is essentially self-adaptive expansion of a plurality of wiener filter sets, has excellent noise robustness and is more suitable for nonstationary time sequence signal decomposition.
Disclosure of Invention
The invention aims to provide a VMD-based seismic signal random noise suppression method to solve the problem that seismic data acquired in a seismic exploration task are interfered by random noise, and the method has excellent noise suppression and amplitude retention performances, has higher calculation efficiency and can meet the processing requirements of high-dimensional and large-scale seismic data.
The technical scheme of the invention is as follows: a seismic signal random noise suppression method based on vmd comprises the following steps:
s1: time domain signals of seismic data are converted into frequency domain signals: selecting a time window to perform Fourier transform on an original noise-containing two-dimensional seismic signal d (x, t) to an f-x domain;
s2: frequency band decomposition of the signal: performing Variable Modal Decomposition (VMD) (variable mode decomposition) on each frequency range data to generate a Band-Limited Intrinsic mode function (BIMF) component for short;
s3: combination of signals: combining the BIMF components obtained by VMD decomposition to obtain a new filtering signal;
s4: frequency domain signals of seismic data are converted into time domain signals: performing inverse Fourier transform on the filtered signal obtained in the step S3, and transforming the signal back to a t-x domain;
s5: and (3) an iterative process: and repeating the same operation on the next time window, and obtaining a final two-dimensional seismic denoising result after all the seismic records are processed.
The VMD decomposition process of the step S2 can be converted into a variational functional optimal solution process, and the decomposition comprises the following steps:
by estimating a Band-Limited Intrinsic mode function (BIMF) component frequency bandwidth objective function in a frequency domain, a mathematical expression thereof is as follows:
wherein K is the number of preset decomposition scales, t is a time variable, ukI.e. the BIMF component, omega, with band-limiting properties after VMD decompositionkFor the center of the frequency of the corresponding mode,is the derivative with respect to time t, δ (t) is the Dirac impulse function, the sign of the convolution, f is the original frequency domain real valued signal,is the squared L2 norm.The meaning of (1) is that each mode function u is transformed by HilbertkConverted into an analytic signal to obtain a real-valued signal ukConversion to complex value to obtain ukThe single-sided spectrum of (1). The variation problem in equation (1) is such that the spectral bandwidth of each BIMF component is at its center frequency ωkNearby, and the bandwidth of BIMF is required to be sparse.
By expanding the variation optimization framework of the VMD method to the complex space, the equation in patent claim 2 is rewritten as follows:
the constrained variation problem is converted into the following unconstrained variation form by introducing a quadratic penalty factor α and a Lagrange multiplier λ:
the Method comprises the following steps of controlling data fidelity, balancing a variational regular term and a quadratic constraint term by a quadratic penalty factor α, ensuring signal reconstruction accuracy in the case of noise, ensuring the strictness of model constraint conditions by a Lagrange multiplier lambda (x), and solving an equation by an alternative Direction multiplier algorithm ADMM (alternative Direction Method of multipliers), wherein the quadratic penalty factor α is a balance parameter for controlling data fidelity, and comprises the following specific steps:
MM _ 1: initializationλ1，n＝0；
MM _ 2: n is n +1, executing the main loop;
MM _ 3: fork is 1: K-1, and a first inner loop update u is performedk：
MM _ 4: k equals K, ending the first inner loop;
MM _ 5: fork is 1: K-1, a second inner loop update ω is performedk：
MM _ 6: k equals K, ending the second inner loop;
MM _ 7: for all ωk> 0, dual rise, update λ:
wherein τ represents a noise margin parameter; in the noise suppression task (instead of the reconstruction of the signal), the update parameter τ is equal to 0 to obtain better denoising effect.
MM _ 8: given a decision accuracy epsilon > 0, repeating steps 2) -7) until an iteration stop condition is met:
and finishing the iteration to obtain K band-limited BIMF components.
The solution process for ADMM involves modal and frequency centric updates of the VMD. Wherein, ω iskThe updating of the frequency center is obtained from the energy spectrum center of gravity of the corresponding mode, ukModal updates correspond to 1/α omega2The Wiener filter structure of (α) is white noise variance, 1/omega2Parameter α controls the width of the Wiener filter, called the fidelity equalization parameter in the present invention increasing α the Wiener filter width narrows to filter more noise but also makes it contain less true peak information, while the algorithm has an increased probability of tending to diverge and not converge, and vice versa.
The value of the number K value of the BIMF component is a key problem of the VMD algorithm, and different modal numbers can influence the solution result, so that the evaluation of the final solution is influenced. The optimal modal decomposition number is determined by calculating the maximum value of the mean value change of the instantaneous frequency of the BIMF component.
The invention has the advantages that: the decomposition process of the VMD method can be converted into an optimal solution process of the variational functional, different from an iteration screening mode of the EMD method, the signal decomposition process is transferred to a variational frame, the minimum sum of the estimation bandwidth of each band-limited BIMF component is taken as a constraint, the variational problem is changed from constraint to non-constraint by an augmented Lagrange objective function, and the optimal solution of the variational functional is searched by adopting an alternative direction multiplier ADMM algorithm to achieve the purpose of signal self-adaptive decomposition. The frequency center and the bandwidth in the ADMM alternately update dual rising, so that the frequency center and the bandwidth simultaneously reach the optimal trend, all BIMF components are obtained at one time, the time efficiency is higher, each modal component has a band-limited characteristic on a frequency spectrum, and the self-adaptive subdivision of a signal frequency band is realized. The update process of the BIMF component has wiener filtering characteristics, so the VMD can be regarded as the multiplexing and adaptive order popularization of wiener filtering, that is, the decomposed energy of each component is subjected to similar wiener filtering operation, and the process has a solid theoretical basis. One-dimensional VMD can be extended to a generalized form of a two-dimensional complex in the frequency domain. The VMD-based seismic signal random noise suppression processing method has excellent noise suppression and amplitude retention performances, has higher calculation efficiency, and can meet the processing requirements of high-dimensional and large-scale seismic data.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required to be used in the description of the embodiments or the prior art will be further described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without any creative effort.
FIG. 1 is a flow chart of an implementation of a VMD-based seismic signal random noise suppression processing method;
FIG. 2 is a diagram of the component signals and the VMD decomposed BIMF component;
FIG. 3 is a graph of the spectral distribution of the synthesized signal of FIG. 2 and the spectra (log-log coordinates) of the 3 BIMF component signals after VMD decomposition;
FIG. 4 is a synthetic seismic record Sigmoid model;
FIG. 5 shows a noisy record of a Sigmoid model and a denoising result thereof by using each method;
FIG. 6a shows the denoising result of the actual noisy seismic data by using a Curvelet 3D method;
FIG. 6b shows the de-noising result of the actual noisy seismic data by using LM3D method;
FIG. 6c is a denoising result of actual noisy seismic data by using BM4D method;
FIG. 6D is a VMD 2D denoising result of actual noisy seismic data;
FIG. 7a is a local similarity graph of a Curvelet 3D denoising result and a noise section of an actual noisy seismic data;
FIG. 7b is a local similarity graph of the de-noising result and the noise section of the actual noisy seismic data NLM 3D;
FIG. 7c is a graph of the local similarity between the de-noising result and the noise profile of the actual noisy seismic data BM 4D;
FIG. 7D is a partial similarity graph of the VMD 2D denoising result and the noise section of the actual noisy seismic data.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The VMD-based two-dimensional seismic signal denoising technical scheme comprises the following specific steps:
step 1: selecting a time window to perform Fourier transform on an original noise-containing two-dimensional seismic signal d (x, t) to an f-x domain;
step 2: and carrying out variation modal decomposition on the data of each frequency band. Firstly, estimating a frequency bandwidth target function of a natural modal function component in a frequency domain; then, expanding a variation optimization framework of the VMD method to a complex space, and converting the constrained variation problem into an unconstrained variation form by adopting an augmented Lagrange function; finally, calculating the optimal solution of the optimal solution by adopting an alternating direction multiplier Algorithm (ADMM) pair to obtain K band-limited BIMF components;
and step 3: and combining the BIMF components obtained by VMD decomposition to generate a filtered signal.
And 4, step 4: the signal is inverse fourier transformed back to the t-x domain.
And 5: and repeating the same operation on the next time window, and obtaining a final two-dimensional seismic denoising result after all the seismic records are processed.
On the basis of the two-dimensional seismic signal denoising method, the invention further provides a three-dimensional seismic signal denoising method. Expanding to a complex value through the two-dimensional VMD, wherein the expanded target optimization function is as follows:
wherein ▽ is a vector gradient operator,is the wavenumber vector of the two-dimensional plane. Similar to the one-dimensional VMD solution, a constraint variational framework is reconstructed by introducing a secondary penalty and a Lagrange multiplier (augmented Lagrange), and the ADMM is used for carrying out optimization solution, wherein the three-dimensional seismic random noise suppression algorithm of the two-dimensional VMD comprises the following specific steps:
d _ 1: selecting a time window to perform Fourier transform on an original noise-containing seismic signal d (m, h, t) to an f-m-h domain;
d _ 2: performing two-dimensional complex VMD decomposition on each frequency slice data;
d _ 3: combining the BIMF components obtained by VMD decomposition to obtain a filtered signal;
d _ 4: performing inverse Fourier transform on the signal, and transforming the signal back to a t-m-h domain;
d _ 5: repeating the same operation on the next time window;
d _ 6: and after the seismic records are completely processed, obtaining a final three-dimensional seismic denoising result.
Fig. 2 shows 3 BIMF component signals obtained by VMD decomposition of the synthesized signal s (t), and in the observation graph (a-c), each BIMF component signal is almost identical to the original component signal, and in the BIMF component partial enlarged graph (a '-c'), only a slight error occurs at two end points of the signal.
Fig. 3 is a graph (log-log coordinates) of the spectrum distribution of the original synthesized signal and the spectrum of the VMD decomposed 3 BIMF component signals, in which each spectrum curve of each reconstructed BIMF modal component has a highest peak value, i.e. corresponding to its center frequency, which is highly consistent with the expected center frequencies of 2, 24 and 288Hz of the original signal, so that the three center frequencies are successfully captured by the 3 BIMF components obtained by VMD decomposition.
FIG. 4 is a theoretical synthetic seismic record Sigmoid model with multi-dip formations, an unconformity surface, a fault and multiple sinusoidal formations, with 256 traces, each trace having 256 time samples, the VMD method with a band-limited BIMF component K of 4, a fidelity equalization parameter α of 2000, and a frequency center ω of 2000kThe initialization adopts a matching tracking method, the length of a time axis window takes 64 sampling points, the length of a space axis window takes 64 channels, and the overlapping degree of sliding steps of the time axis and the space axis is set to be 50 percent.
FIGS. 5(a-f) show the denoising results of the methods after the seismic data are subjected to noise addition, and FIGS. 5(a '-f') show the local similarity graphs among the noise sections corresponding to FIGS. 5 (a-f). Fig. 5(a) shows the data after 20% white gaussian noise is added, and fig. 5 (a') shows the local similarity between the clean signal and the noise. As can be seen from the figure, the five methods all achieve a certain denoising effect, but the denoising result of the Curvelet method in the figure 5(b) has a certain deformation, obvious artifact phenomena occur around a sine-shaped homophase axis, the fault trend basically disappears, the face of the section is fuzzy, and the Curvelet method in the figure 5 (b') can show obvious effective energy leakage; the NLM denoising result shown in fig. 5(c) still retains macroscopic noise information, the corresponding local similarity graph shows that both linear and hyperbolic effective energy is leaked, and the structural information of the original image is not sufficiently protected, which is related to that only the translation characteristic of the block is considered when calculating the similarity of the image block in the non-local Mean (NLM) algorithm; compared with Curvelet and NLM methods, the CEEMD method is slightly improved in SNR value, but part of noise information is still retained in the denoising result in the figure 5(d), and the fault part can be identified; corresponding to the local similarity graph, a little energy loss exists in the sine-shaped same-phase axis area; FIG. 5(e) the method BM3D has better denoising effect, but it can also be seen that part of the low-energy effective signal is removed as noise; in the denoising result of the VMD shown in the attached FIG. 5(f), the signal-to-noise ratio SNR is improved most obviously and is superior to the other four methods, the positions of an inclined stratum, a sinusoidal stratum and a fault in a synthetic model are well reserved, the noise is effectively suppressed, and the original pure model is closest to the visual expression; the comparison of the local similarity graph shows that the effective energy leakage degree of the VMD method is the slightest, and the fidelity performance is the best.
FIG. 6 shows the denoising results of the four methods, respectively, and FIG. 7 shows the local similarity graph of the corresponding denoising results and the noise profile. Comparing the graphs, it can be known that the denoising result of the Curvelet 3D method is too smooth, the details of the edge of the same phase axis are smeared and lost, so that the identification is difficult, and the corresponding local similarity represents more effective energy loss; visible local blocky details disappear in the denoising result of the LM3D method, and the visible partial noise is still distributed in the denoising result and corresponds to a local high abnormal region with more local similarity; the denoising table of BM4D is improved, the section visual effect is better represented, and the local similarity table represents less effective information loss; the VMD 2D method has the advantages that the denoising result is optimal, the details of the homophase axis and the fracture trend of the whole section are clear, the local similarity graph is uniformly distributed in a low energy mode, and the loss of effective homophase axis information is minimum.
Claims (3)
1. A seismic signal random noise suppression method based on VMD comprises the following steps:
s1: selecting a time window to perform Fourier transform on an original noise-containing two-dimensional seismic signal d (x, t) to an f-x domain;
s2: carrying out variation modal decomposition on each frequency band data to generate a band-limited inherent modal function (BIMF) component;
s3: combining the BIMF components obtained by VMD decomposition to generate a filtered signal;
s4: performing inverse Fourier transform on the signal, and transforming the signal back to a t-x domain;
s5: and repeating the same operation on the next time window, and obtaining a final two-dimensional seismic denoising result after all the seismic records are processed.
2. The VMD-based seismic signal random noise suppression method of claim 1, wherein: the VMD decomposition process of the S2 step includes:
firstly, estimating a frequency bandwidth target function of a BIMF component in a frequency domain, wherein the mathematical expression of the frequency bandwidth target function is as follows:
wherein K is the number of preset decomposition scales, t is a time variable, ukI.e. the BIMF component, omega, with band-limiting properties after VMD decompositionkFor the center of the frequency of the corresponding mode,is the derivative with respect to time t, δ (t) is the Dirac impulse function, the sign of the convolution, f is the original frequency domain real valued signal,is the squared L2 norm;the meaning of (1) is that each mode function u is transformed by HilbertkConverted into an analytic signal to obtain a real-valued signal ukConversion to complex value to obtain ukThe single-sided spectrum of (1); the variation problem in equation (1) is such that the spectral bandwidth of each BIMF component is at its center frequency ωkNearby, and the bandwidth of the BIMF is required to have sparsity;
then, by expanding the variation optimization framework of the VMD method to the complex space, the equation in patent claim 2 is rewritten as follows:
and converting the constraint variable problem into the following non-constraint variable form by introducing a secondary penalty factor α and a Lagrange multiplier lambda:
the secondary penalty factor α is a balance parameter for controlling data fidelity, is used for balancing a variation regular term and a secondary constraint term, and can ensure signal reconstruction accuracy in the case of noise, and Lagrange multiplier lambda (x) can ensure the strictness of model constraint conditions;
finally, solving the formula by adopting an alternative direction multiplier algorithm ADMM, which comprises the following specific steps:
MM _ 1: initializationn＝0；
MM _ 2: n is n +1, executing the main loop;
MM _ 3: fork is 1: K-1, and a first inner loop update u is performedk：
MM _ 4: k equals K, ending the first inner loop;
MM _ 5: fork is 1: K-1, a second inner loop update ω is performedk：
MM _ 6: k equals K, ending the second inner loop;
MM _ 7: for all ωk> 0, dual rise, update λ:
wherein τ represents a noise margin parameter; in a noise suppression task, an updating parameter tau is equal to 0 so as to obtain a better denoising effect;
MM _ 8: given a decision accuracy epsilon > 0, repeating steps 2) -7) until an iteration stop condition is met:
finishing iteration to obtain K band-limited BIMF components;
the solution process of the ADMM comprises modal update and frequency center update of the VMD; wherein, ω iskThe updating of the frequency center is obtained from the energy spectrum center of gravity of the corresponding mode, ukModal updates correspond to 1/α omega2The Wiener filter structure of (α) is white noise variance, 1/omega2The parameter α controls the width of a Wiener filter, which is called as a fidelity equalization parameter, the value α is increased, the width of the Wiener filter is narrowed, more noise can be filtered, but the Wiener filter also contains less real peak information, and meanwhile, the probability that the algorithm tends to diverge and not converge is increased, and vice versa;
the value of the number K value of the BIMF components is a key problem of the VMD algorithm, and different modal numbers can influence the solution result, so that the evaluation of the final solution is influenced; the optimal modal decomposition number is determined by calculating the maximum value of the mean value change of the instantaneous frequency of the BIMF component.
3. The VMD-based seismic signal random noise suppression method of claim 1, wherein: applying the two-dimensional VMD to random noise suppression processing of the three-dimensional seismic data; expanding to a complex value through the two-dimensional VMD, wherein the expanded target optimization function is as follows:
wherein,in order to be a vector gradient operator, the vector gradient operator,the wave number vector of the two-dimensional plane is obtained; similar to the one-dimensional VMD solution, a constraint variational framework is reconstructed by introducing a secondary penalty and a Lagrange multiplier (augmented Lagrange), and the ADMM is used for carrying out optimization solution, wherein the three-dimensional seismic random noise suppression algorithm of the two-dimensional VMD comprises the following specific steps:
d _ 1: selecting a time window to perform Fourier transform on an original noise-containing seismic signal d (m, h, t) to an f-m-h domain;
d _ 2: performing two-dimensional complex VMD decomposition on each frequency slice data;
d _ 3: combining the BIMF components obtained by VMD decomposition to obtain a filtered signal;
d _ 4: performing inverse Fourier transform on the signal, and transforming the signal back to a t-m-h domain;
d _ 5: repeating the same operation on the next time window;
d _ 6: and after the seismic records are completely processed, obtaining a final three-dimensional seismic denoising result.
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