An adaptive method and system for suppressing rayleigh wave based on frequency modulation characteristic modal decomposition

Abstract

The application belongs to the technical field of seismic exploration signal processing, and discloses a method and system for suppressing Rayleigh surface waves based on adaptive frequency modulation characteristic mode decomposition, which comprises the following steps: converting a seismic signal to a frequency space domain by using Fourier transform, and extracting an intrinsic modal component by using an adaptive frequency modulation signal mode decomposition method; screening a modal component containing Rayleigh surface waves according to the characteristics of Rayleigh surface waves in the frequency space domain, and performing adaptive filtering to suppress Rayleigh surface waves in the intrinsic modal component; reconstructing signals of the intrinsic modal component after suppression and the remaining components after screening, and performing Fourier inverse transform, so that an effective signal is finally output, which is the result after Rayleigh surface wave suppression.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of seismic exploration signal processing, and particularly relates to an adaptive Rayleigh wave suppression method and system based on frequency modulation characteristic mode decomposition. BACKGROUND

[0002] There are generally surface wave interferences in seismic data, especially land data, which are mainly affected by Rayleigh wave and Love wave noise. The Rayleigh wave has strong amplitude, low frequency, low apparent velocity, serious frequency dispersion, and seriously reduces the signal-to-noise ratio of seismic data. Rayleigh wave suppression, as one of the key links of seismic data processing, has developed from the traditional filter-based method to the data-driven suppression algorithm using deep learning.

[0003] According to the differences in algorithm principles, Rayleigh wave suppression methods can be divided into three categories: filter method, model-driven method and data-driven method. The filter method is to realize effective separation of signal and noise in the transform domain according to the waveform characteristics of Rayleigh wave signal. The model-driven method uses forward simulation to obtain Rayleigh wave data similar to the actual data, and removes Rayleigh wave based on the adaptive subtraction method. The data-driven method learns the characteristics of Rayleigh wave through artificial intelligence, and predicts effective waves according to the nonlinear mapping relationship to suppress Rayleigh wave.

[0004] The linear characteristics of seismic data make it have good predictability in the frequency space domain, while the Rayleigh wave has low apparent velocity and low frequency, and is characterized by aggregation distribution in the frequency space domain. Assuming that each frequency slice of seismic data in the frequency space domain is a multi-component signal along the spatial direction, and effective signals, Rayleigh waves, random noise and the like are different intrinsic modal components, therefore, signal modal decomposition algorithm can be used to realize signal decomposition and complete Rayleigh wave suppression. This type of representative method includes empirical mode decomposition, complete ensemble empirical mode decomposition and the like, which calculates each component according to the upper and lower envelopes of the signal, and considers that each component signal is stationary. The variational mode decomposition realizes the separation of multi-component signals by constructing and optimizing the variational function. It is worth noting that the above signal decomposition methods all assume that the signal is stationary, while the spatial characteristics of Rayleigh wave determine that each frequency component of the signal has frequency modulation characteristics, and its aggregation also proves its non-stationary characteristics. Therefore, the adaptive decomposition method for non-stationary signals needs to be further studied. The time-varying empirical mode decomposition method uses the idea of windowing and dividing the signal, and considers that the signal in the window is stationary, but its parameters are difficult to adjust and have general applicability. SUMMARY

[0005] To solve the problems in the prior art, the application provides a self-adaptive Rayleigh wave suppression method and system based on frequency modulation characteristic modal decomposition, mainly according to the frequency modulation characteristics of Rayleigh waves in the frequency space domain, the apparent velocity of the Rayleigh waves is low, the frequency is low, and the Rayleigh waves show an aggregative distribution characteristic in the frequency space domain, so that the effective signal, Rayleigh waves and random noise and the like can be divided into different intrinsic modal components on each frequency slice of the frequency space domain of the seismic data. Further, the self-adaptive frequency modulation signal modal decomposition method is applied to the signals with the frequency modulation characteristics in the frequency space domain to realize the decomposition of the components, the suppression of the Rayleigh waves is completed, on this basis, the self-adaptive component selection and the filtering strategy are combined to realize the suppression of the Rayleigh wave noise part in the intrinsic modal components in the frequency space domain, that is, the self-adaptive Rayleigh wave suppression technology based on the frequency modulation characteristic modal decomposition.

[0006] To achieve the above object, the application provides the following scheme:

[0007] A self-adaptive Rayleigh wave suppression method based on frequency modulation characteristic modal decomposition, the method comprises:

[0008] The seismic signal is converted to the frequency space domain by using the Fourier transform, and the self-adaptive frequency modulation signal modal decomposition method is used to realize the extraction of the intrinsic modal components;

[0009] The Rayleigh wave modal components containing Rayleigh waves are screened according to the characteristics of the Rayleigh waves in the frequency space domain, and the self-adaptive filtering is performed to realize the suppression of the Rayleigh waves in the intrinsic modal components;

[0010] The intrinsic modal components after the suppression are reconstructed with the components left after the screening, and the Fourier inverse transform is performed, and finally the effective signal is output, that is, the result after the suppression of the Rayleigh waves.

[0011] Preferably, the method for realizing the extraction of the intrinsic modal components by using the self-adaptive frequency modulation signal modal decomposition method comprises:

[0012] ;

[0013] Wherein, the superscript represents an iterative operator, represents a demodulation matrix, is a vector, and represent demodulation signals, is the current estimated component.

[0014] Preferably, the method for realizing the screening of the Rayleigh wave modal components containing Rayleigh waves according to the characteristics of the Rayleigh waves in the frequency space domain comprises:

[0015] The instantaneous frequency is preset, Represents the index on the frequency axis. Represents the maximum frequency value containing Rayleigh surface waves, with each frequency slice being... , in Representative index, set threshold and constant The extracted frequency slices A slice of a certain intrinsic mode component The expression that satisfies this condition is:

[0016] ;

[0017] in, Represents the maximum offset containing Rayleigh surface waves, where As a proportionality coefficient, it is set as a constant, that is... .

[0018] Preferably, the method for suppressing Rayleigh surface waves in intrinsic mode components by performing adaptive filtering includes:

[0019] For each Define the space window , Given the window length, calculate the energy within the window for each spatial point of all IMFs. That is, for the first One IMF:

[0020] ;

[0021] After traversing each window, the energy curve is obtained. By taking the first difference, the position with the largest rate of change can be obtained. That is, the maximum offset of the Rayleigh surface wave, for the first Each IMF Maximum offset Defined as:

[0022] ;

[0023] in, This represents the backward difference operator, which then calculates the maximum offset less than the obtained value. The window at that location is set to 0, which is greater than the calculated maximum offset. The window value is set to 1, which is the window for Rayleigh surface wave suppression. :

[0024] ;

[0025] Each window The IMFs are multiplied by the selected IMFs, that is, the energy of the Rayleigh wave is suppressed from the IMFs containing the Rayleigh wave after screening, to obtain the denoised :

[0026] .

[0027] The application further provides an adaptive Rayleigh wave suppression system based on frequency modulation characteristic modal decomposition, which is used for realizing the method and comprises an extraction module, a suppression module and a reconstruction module.

[0028] The extraction module is used for converting a seismic signal to a frequency space domain by using Fourier transform and extracting intrinsic modal components by using an adaptive frequency modulation signal modal decomposition method.

[0029] The suppression module is used for screening modal components containing Rayleigh waves according to the characteristics of Rayleigh waves in the frequency space domain and performing adaptive filtering to suppress Rayleigh waves in the intrinsic modal components.

[0030] The reconstruction module is used for reconstructing signals of the intrinsic modal components after suppression and the components left after screening, performing Fourier inverse transform and finally outputting effective signals, that is, the results after Rayleigh wave suppression.

[0031] Preferably, the process of extracting intrinsic modal components by using the adaptive frequency modulation signal modal decomposition method comprises:

[0032] ;

[0033] wherein the superscript represents an iteration operator, represents a demodulation matrix, is a vector, and represent demodulation signals, is the current estimated component.

[0034] Preferably, the process of screening modal components containing Rayleigh waves according to the characteristics of Rayleigh waves in the frequency space domain comprises:

[0035] The instantaneous frequency is preset, represents an index on the frequency axis, represents a maximum frequency value containing Rayleigh waves, each frequency slice is , wherein represents a trace index, the threshold and the constant are set, and the frequency slice of the extracted intrinsic modal component slice satisfies the expression:

[0036] ;

[0037] wherein, represents the maximum offset distance containing the Rayleigh wave, wherein is set as a constant, i.e. .

[0038] Preferably, the process of suppressing the Rayleigh wave in the intrinsic mode component by adaptive filtering comprises:

[0039] For each , a spatial window is defined, is the window length, and the energy in the window is calculated for each spatial point of all IMFs , i.e. for the th IMF:

[0040] ;

[0041] After traversing each window, an energy curve is obtained, and by taking the first-order difference, the position with the maximum change rate , i.e. the maximum offset distance of the Rayleigh wave, is obtained, and for the th IMF, each , the maximum offset distance is defined as:

[0042] ;

[0043] wherein, represents a backward difference operator, and then the window at the maximum offset distance obtained is set to 0, and the window at the maximum offset distance obtained is set to 1, i.e. the window for suppressing the Rayleigh wave:

[0044] ;

[0045] Each window is multiplied by the selected IMF, i.e. the energy containing the Rayleigh wave is suppressed from the IMF containing the Rayleigh wave after screening, and the denoised is obtained:

[0046] .

[0047] Compared with the prior art, the present application has the beneficial effects that:

[0048] ​1. The application is based on adaptive Rayleigh wave suppression technology of frequency modulation characteristic modal decomposition, the application adopts time-frequency analysis method to realize Rayleigh wave suppression for non-steady-state seismic signal with frequency modulation characteristics, and good results are obtained in two-dimensional actual seismic data.

[0049] 2. The application realizes screening of Rayleigh wave modal components according to the characteristics of Rayleigh wave in the frequency space domain, and is more suitable for Rayleigh wave suppression of seismic data containing Rayleigh wave noise with frequency modulation characteristics.

[0050] 3. The application realizes the targeted suppression of Rayleigh wave in the intrinsic modal component through adaptive filtering, effectively realizes the amplitude-preserving processing of the seismic signal, and suppresses the surface wave as much as possible under the condition of retaining the seismic effective information, so as to improve the signal-to-noise ratio and retain more low-frequency effective information.

[0051] 4. The application can realize modular processing and has high popularization value. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the application, the following briefly introduces the drawings needed to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0053] Figure 1 A flow chart of a kind of adaptive Rayleigh wave suppression method based on frequency modulation characteristic modal decomposition for the embodiments of the application.

[0054] Figure 2 Synthetic noiseless data and Rayleigh wave data of the embodiments of the application are shown in the schematic diagram, wherein (a) is a schematic diagram of noiseless data; (b) is a schematic diagram of data containing Rayleigh wave and random noise.

[0055] Figure 3 The data and the suppressed noise after Rayleigh wave suppression by different methods of the embodiments of the application are shown in the schematic diagram, wherein (a) is a schematic diagram of frequency space domain Rayleigh wave suppression method based on modal decomposition of frequency modulation signal characteristics; (b) is a schematic diagram of the suppressed noise.

[0056] Figure 4 The IMF and the window function used before and after Rayleigh wave suppression of the embodiments of the application are shown in the schematic diagram, wherein (a) is a schematic diagram of IMF obtained by adaptive frequency modulation signal modal decomposition; (b) is a schematic diagram of Rayleigh wave suppression window function obtained by adaptive filtering strategy; (c) is a schematic diagram of IMF after Rayleigh wave suppression of (a).

[0057] Figure 5The schematic diagram of data and noise after suppressing Rayleigh surface wave by the technology provided in the embodiment of the present application, wherein (a) is the schematic diagram of data after suppressing Rayleigh surface wave; (b) is the schematic diagram of noise after suppressing Rayleigh surface wave.

[0058] Figure 6 The schematic diagram of single shot data containing Rayleigh surface wave in the embodiment of the present application;

[0059] Figure 7 The schematic diagram of profile and noise after suppressing Rayleigh surface wave by the technology provided in the embodiment of the present application, wherein (a) is the schematic diagram of data after suppressing Rayleigh surface wave; (b) is the schematic diagram of noise after suppressing Rayleigh surface wave; (c) is the schematic diagram of low pass filtered data.

[0060] Figure 8 The schematic diagram of amplitude spectrum comparison in the embodiment of the present application;

[0061] Figure 9 The comparison diagram of seismic signal and time-frequency analysis in the embodiment of the present application, wherein (a) is the schematic diagram of single channel time-frequency analysis of original single shot record; (b) is the schematic diagram of single channel time-frequency analysis after suppressing Rayleigh surface wave. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0063] In order to make the above objectives, features and advantages of the present application more apparent, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0064] Embodiment one

[0065] Defects of prior art:

[0066] The existing Rayleigh wave suppression methods based on traditional methods mainly focus on the differences in frequency, energy and speed, and have certain application value. Some methods have been integrated into commercial software. However, these methods still have some technical and methodological shortcomings and challenges. For example, the filtering method is based on the frequency characteristics of noise, and the noise characteristic data is filtered out by means of low-pass filter and other means, so as to obtain the suppressed result. In the process of suppressing the surface wave, the low-frequency effective information may be damaged. The frequency-wavenumber domain filtering method, which also belongs to the filtering method and is integrated into the software, uses the low surface wave apparent velocity feature to suppress the surface wave. The method depends on manual recognition and selection of the cutting area, so its efficiency is limited and depends on manual experience. The adaptive surface wave attenuation method is widely used in actual commercial software. It identifies the surface wave through statistical analysis, and then suppresses the surface wave. The cutting effect is good, but the method still depends on manual picking and parameter testing, and is easy to damage the effective signal. The surface wave suppression technology based on deep learning can construct the training set by simulating the surface wave, and can well realize the network training to obtain the nonlinear mapping relationship to predict the effective wave, so as to realize the suppression of the surface wave. However, it still has problems such as difficulty in training data, single sample, high training cost and high calculation cost.

[0067] In summary, the existing Rayleigh wave suppression method still has the defects of damaging effective signal, relying on manual experience, parameter sensitivity and high calculation cost. These problems limit the amplitude preservation and universality of the Rayleigh wave suppression method, so the Rayleigh wave suppression method still needs to be further improved and optimized.

[0068] The main work of the present application is as follows: 1. The seismic record with frequency modulation characteristics is converted to the frequency space domain, and the adaptive frequency modulation signal modal decomposition algorithm is introduced to realize the complete decomposition of the non-stationary signal (herein, the seismic signal). 2. Considering the characteristics of the data in the frequency space domain, the adaptive component selection method is used to select the modal component containing the surface wave component. 3. The selected modal component is adaptively filtered to obtain the modal component after the surface wave is suppressed. 4. Finally, the effective signal is reconstructed to obtain the frequency space domain signal after the surface wave is suppressed, and the data of the suppressed Rayleigh wave noise is obtained by rotating in the time space domain. The present application reduces the dependence on manual experience in the algorithm, can realize the amplitude-preserving suppression of the modular Rayleigh wave, and has high application value. Specific implementation process:

[0069] As Figure 1As shown, the application provides an adaptive Rayleigh wave suppression method based on frequency modulation characteristic modal decomposition, and the application mainly comprises three modules: one is to convert the seismic signal to the frequency space domain by using Fourier transform, and to realize the extraction of intrinsic modal components by using an adaptive frequency modulation signal modal decomposition method; the second is to realize the screening of the Rayleigh wave modal component according to the characteristics of the Rayleigh wave in the frequency space domain, and to realize the suppression of the Rayleigh wave in the intrinsic modal component by adaptive filtering; the third is to add (signal reconstruction) the intrinsic modal component after suppression and the component left after screening, and to perform Fourier inverse transform, and finally output the effective signal, that is, the result after Rayleigh wave suppression.

[0070] Under the condition of non-uniform elastic medium, f The Rayleigh wave in the frequency domain has the frequency modulation characteristic, and due to the aggregation of the Rayleigh wave in the frequency domain, f The Rayleigh wave-containing signal in the frequency domain has obvious non-steady-state characteristics, so an adaptive decomposition method suitable for the frequency modulation signal is needed to realize the suppression processing of the Rayleigh wave in the frequency domain. The adaptive frequency modulation signal modal decomposition algorithm is based on the variational nonlinear frequency modulation modal decomposition theory, and a time-varying demodulation operator is applied to realize the method of greedy recursive decomposition and adaptive bandwidth update. The method uses a greedy algorithm to extract signal components one by one, and estimates each intrinsic modal component (IMF) by minimizing the bandwidth of the demodulation signal, wherein the first IMF is: f f The adaptive frequency modulation signal modal decomposition algorithm is based on the variational nonlinear frequency modulation modal decomposition theory, and a time-varying demodulation operator is applied to realize the method of greedy recursive decomposition and adaptive bandwidth update. The method uses a greedy algorithm to extract signal components one by one, and estimates each intrinsic modal component (IMF) by minimizing the bandwidth of the demodulation signal, wherein the first IMF is:

[0071] (1) ;

[0072] Wherein, represents the norm, represents the second derivative of the demodulation signal. and represent the demodulation signal, represents the energy remaining after removing the current estimated component from the input signal , is a regularization coefficient. In fact, the signal can be discretized as time sampling , is the total number of sampling points, represents the travel time corresponding to the Nth sampling point, therefore, formula (1) can be discretized as:

[0073] (2) ;

[0074] Wherein,​​​​ , is a diagonal matrix representing a given operator, while is a second-order difference matrix; while vector , , represent two demodulated signals, respectively, while the input signal can be expressed as , and represent the two demodulated signals at travel time corresponding signal values, and similarly, represent the input signal at travel time corresponding signal values, represent the demodulation matrix, constructed from an orthonormal basis derived from the instantaneous phase:

[0075] (3);

[0076] where , while , where represent the phase values corresponding to travel time, while and represent the diagonal matrices of cosine and sine components, respectively, constructed from the instantaneous phase. The discretized formulation of the IMF shows that the vector can be solved iteratively by alternating the update of the demodulated signal and the frequency function. The vector at the th iteration is expressed as:

[0077] (4);

[0078] where the superscript denotes the iteration operator. Essentially, this method acts as a time-frequency bandpass filter, whose bandwidth is determined by . A smaller will result in a narrower filter, i.e., the output IMF will be smoother. Then, the IMF can be estimated as:

[0079] (5);

[0080] Using the demodulated signal obtained in equation (5), the frequency increment can be expressed as:

[0081] (6);

[0082] where representing element-wise product, it is worth noting that the instantaneous frequency is a smooth function, we expect the frequency increment to be smooth enough as well. Therefore, a low-pass filter will be used to pre-process the frequency increment to reduce the introduction of noise during the application. Thus, the instantaneous frequency can be updated as:

[0083] (7) ;

[0084] where, represents the identity matrix, represents the low-pass filter operator, where a larger parameter is more adaptive to the rapidly changing frequency-modulated signal, and the obtained can be calculated to update the matrix , and the iteration stopping condition is set as:

[0085] (8) ;

[0086] When the error ( is the threshold) is satisfied, the iteration is terminated, and the th IMF is obtained. The obtained at this time is assigned to , which is the value of the IMF. Since the seismic signal containing Rayleigh surface wave in the fx domain is a non-stationary signal, according to its low-frequency characteristics in the fx domain, the frequency band of the surface wave can be obtained by spectral analysis of the seismic data, i.e. , represents the index on the frequency axis, represents the maximum frequency value containing the Rayleigh surface wave. The single-frequency signal in the preset frequency range is adaptively decomposed into the frequency-modulated signal mode, i.e., the ACMD algorithm is applied to realize the decomposition of the frequency-modulated signal, and the IMFs corresponding to the single-frequency signal are obtained. When the th IMF is calculated, the th IMF is subtracted from the to-be-decomposed frequency-modulated signal , and is taken as the new input frequency-modulated signal, so as to gradually extract the signal components and update the residual error, realize the recursive decomposition of the IMFs, and prepare for the subsequent suppression of the Rayleigh surface wave. This decomposition method no longer needs to input the number of IMFs, and the iteration ending threshold will affect the total number of IMFs, which is usually set to (the subsequent test is set to ). The regularization parameter in the adaptive frequency-modulated signal mode decomposition algorithm determines the smoothness of the output IMF, and a smaller will get smoother IMF, while larger parameter adapt to the fast changing frequency modulation signal better.

[0087] Since the amplitude of Rayleigh wave is stronger than the effective signal in the decomposed IMF, and the distribution is more concentrated, while the other positions of the IMF are effective signals, using adaptive IMF filter to suppress the locally concentrated distribution of Rayleigh wave in the IMF can reduce the damage to the effective signal.

[0088] First, the screening range of Rayleigh wave is set by using its low frequency characteristics. The threshold is set in advance , where represents the trace index, and the constant and , when the extracted frequency slice satisfies the expression:

[0089] (9);

[0090] where, represents the maximum offset distance containing Rayleigh wave, where is a proportional coefficient, which is set as a constant, i.e. .

[0091] We consider that directly setting IMF to zero may lose the signal at far offset, therefore, we gradually calculate the energy in the sliding window, and then take the point with the largest energy change, which is equivalent to adaptively determining the maximum offset distance where Rayleigh wave may exist, and then set all data less than the offset distance to zero, which can minimize the loss of effective signal.

[0092] For each , define the spatial window , is the window length, and we want to calculate the energy of each spatial point in the window , i.e. for the th IMF,

[0093] (10);

[0094] After traversing each window, the energy curve is obtained. By taking the first difference, the position with the largest change rate is obtained, i.e. the maximum offset distance of Rayleigh wave. For the th IMF, each​ , the maximum offset distance is defined as:

[0095] (11) ;

[0096] wherein, represents the backward difference operator, then the window smaller than the trace position (i.e. the maximum offset distance obtained) is set to 0, and the window larger than the trace position is set to 1, i.e. the window for suppressing the Rayleigh wave :

[0097] (12) ;

[0098] Each window is multiplied by the selected IMF, i.e. the energy of the Rayleigh wave contained in the selected IMF is suppressed, and the denoised :

[0099] (13) ;

[0100] In combination with the foregoing, the method proposed is a Rayleigh wave suppression algorithm combining f the domain adaptive Rayleigh wave identification filter and the adaptive frequency modulation signal modal decomposition method.

[0101] In summary, the implementation steps of the method are as follows:

[0102] 1. The frequency range in which the Rayleigh wave exists is determined by spectrum analysis of the seismic signal, and the offset distance range in which the Rayleigh wave exists is extracted;

[0103] 2. The spatial Fourier transform is performed on the seismic signal to obtain the real part and the imaginary part of the signal in the frequency space domain;

[0104] 3. The adaptive frequency modulation signal modal decomposition algorithm is used to extract the intrinsic modal components by respectively applying the algorithm to each frequency slice of the real part and the imaginary part;

[0105] 4. The maximum offset distance in which the Rayleigh wave exists is calculated and selected by using formulas (9)-(13), and the time window is set to perform adaptive filtering to obtain the IMFs after the Rayleigh wave is suppressed;

[0106] 5. The real part and the imaginary part of the effective signal are reconstructed by accumulating the IMFs after the filtering to obtain the complex form of the effective signal;

[0107] 6. The Fourier inverse transform is performed on the data to convert the data to the time space domain to obtain the final result, i.e. the effective signal after the Rayleigh wave is suppressed.

[0108] Test 1:

[0109] As Figure 2 shown, according to the characteristics of Rayleigh wave, we synthesized a single shot record containing Rayleigh wave, the data is 205 channels, 210 time sampling points, sampling interval is 2ms, the data near offset Rayleigh wave interference is serious, it has obvious dispersion characteristics, the reflection wave form is destroyed. The frequency space domain adaptive Rayleigh wave suppression method based on the mode decomposition of frequency modulation signal characteristics is used for Rayleigh wave suppression test.

[0110] The test results are shown in Figure 3 , the Rayleigh wave suppression effect realized based on the adaptive frequency modulation signal mode decomposition method is very good, which benefits from the good adaptability of the method to the non-steady signal with frequency modulation characteristics. Figure 4 In order to use the adaptive frequency modulation signal mode decomposition in f domain, an intrinsic mode component containing Rayleigh wave is obtained, which can be seen that Rayleigh wave has the characteristics of aggregation distribution and strong energy near offset. We give the window for suppressing Rayleigh wave constructed by the algorithm adaptively, as shown in Figure 4 (b), which is applied to Figure 4 (a) to obtain the IMF after filtering out Rayleigh wave, as shown in Figure 4 (c), which is the schematic diagram of the adaptive filtering process of the proposed technology. The results are shown in Figure 7 , the algorithm suppresses more noise, and the reflection wave phase axis is basically invisible on the noise profile. By comparing the suppression results obtained by the proposed technology without and with adaptive screening and filtering module, as shown in Figure 3 (a) and Figure 5 (a), it can be seen that the adaptive screening and filtering strategy has better amplitude preservation effect in the Rayleigh wave suppression process.

[0111] Test 2:

[0112] The application test of different Rayleigh wave suppression algorithms is carried out on the actual data containing Rayleigh wave. As shown in Figure 6 , it has 1200 sampling points, sampling rate is 4ms, and is seriously affected by the nearly linear Rayleigh wave, its main frequency is low and energy is strong, which leads to the difficulty in identifying the reflection signal.

[0113] Based on the proposed technology, the Rayleigh wave noise is suppressed, and the processing result is shown in Figure 7 (a), which achieves good denoising effect visually, and the residual of effective signal is basically invisible on the noise profile, as shown in Figure 7 (b). Comparing the amplitude spectrum of the original single channel after denoising with the proposed technology and the original single channel, as shown in Figure 8 .As shown, it can be seen that the low-frequency energy of the Rayleigh wave is effectively suppressed, and the low-pass filtered data is combined, as shown in (c) of FIG. 6. Figure 7 As shown in (c) of FIG. 6, it can be seen that the algorithm effectively protects the low frequencies of the remaining data.

[0114] In order to further illustrate the suppression ability of the algorithm on the Rayleigh wave noise, the data of the 8th channel is extracted, as indicated by the black line in (a) of FIG. 7, and their time-frequency spectrum is drawn based on the S transform, as shown in (b) of FIG. 7. Figure 6 Figure 7 As shown in (a) of FIG. 7, it can be seen that the low-frequency energy corresponding to the time in the result obtained by the method is suppressed, and the damage to the remaining signal is small. This further illustrates that the proposed method has good performance in the application of Rayleigh wave suppression, and is especially suitable for the decomposition of non-stationary signals with frequency modulation characteristics. Figure 9

[0115] Embodiment Two

[0116] The application also provides an adaptive Rayleigh wave suppression system based on frequency modulation characteristic modal decomposition, which is used to realize the method of embodiment one, and the system comprises an extraction module, a suppression module and a reconstruction module.

[0117] The extraction module is used to convert the seismic signal to the frequency space domain by using the Fourier transform, and to realize the extraction of the intrinsic modal component by using the adaptive frequency modulation signal modal decomposition method.

[0118] The suppression module is used to realize the screening of the modal component containing the Rayleigh wave according to the characteristics of the Rayleigh wave in the frequency space domain, and to realize the suppression of the Rayleigh wave in the intrinsic modal component by adaptive filtering.

[0119] The reconstruction module is used to reconstruct the signal of the intrinsic modal component after suppression and the component remaining after screening, and to perform Fourier inverse transform, and finally output the effective signal, which is the result after Rayleigh wave suppression.

[0120] In this embodiment, the process of realizing the extraction of the intrinsic modal component by using the adaptive frequency modulation signal modal decomposition method comprises:

[0121] ;

[0122] Wherein, the superscript represents an iteration operator, represents a demodulation matrix, is a vector, and represent demodulated signals, is the current estimated component.

[0123] ​​In this embodiment, the process of filtering Rayleigh surface wave modal components based on the characteristics of Rayleigh surface waves in the frequency spatial domain includes:

[0124] Preset instantaneous frequency , Represents the index on the frequency axis. Represents the maximum frequency value containing Rayleigh surface waves, with each frequency slice being... , in Representative index, set threshold and constant The extracted frequency slices A slice of a certain intrinsic mode component The expression that satisfies this condition is:

[0125] ;

[0126] in, Represents the maximum offset containing Rayleigh surface waves, where As a proportionality coefficient, it is set as a constant, that is... .

[0127] In this embodiment, the process of suppressing Rayleigh surface waves in the intrinsic mode components through adaptive filtering includes:

[0128] For each Define the space window , Given the window length, calculate the energy within the window for each spatial point of all IMFs. That is, for the first One IMF:

[0129] ;

[0130] After traversing each window, the energy curve is obtained. By taking the first difference, the position with the largest rate of change can be obtained. That is, the maximum offset of the Rayleigh surface wave, for the first Each IMF Maximum offset Defined as:

[0131] ;

[0132] in, This indicates a backward difference operator, which then calculates the maximum offset distance less than this path position (the obtained offset). The window for Rayleigh surface wave suppression is set to 0 for positions at (locations not specified in the original text) and 1 for positions larger than this. :

[0133] ;

[0134] Each window is multiplied by the selected IMF, i.e. the energy of the Rayleigh wave is suppressed from the IMF containing the Rayleigh wave after screening, to obtain the denoised IMF :

[0135] .

[0136] The above-described embodiments are merely descriptions of the preferred modes of the present application and are not intended to limit the scope of the present application. Various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art without departing from the design spirit of the present application shall fall within the protection scope of the present application as defined by the claims.​

Claims

1. A method for suppressing adaptive Rayleigh wave based on frequency modulation eigenmode decomposition, characterized in that, The method comprises: The method comprises: The method comprises: The method comprises: The method comprises: Pre-set instantaneous frequency , representing an index on the frequency axis, representing the maximum frequency value containing the Rayleigh wave, each frequency slice is , wherein representing a channel index, setting a threshold value and a constant , the extracted frequency slice one of the intrinsic modal components slices satisfies the expression: ； wherein, represents the maximum offset distance containing the Rayleigh wave, wherein is set as a constant, i.e. ; The method comprises: For each , define spatial window , is the window length, compute the energy within the window for each spatial point for all IMFs , i.e. for the th IMF: ； After traversing each window, the energy curve is obtained By taking the first-order difference, the position of the maximum rate of change is obtained , that is, the maximum offset distance of the Rayleigh wave. For the first IMF, each , the maximum offset distance is defined as: ； wherein, represents a backward difference operator, then the windows smaller than the maximum offset distance sought are set to 0, and the windows larger than the maximum offset distance sought are set to 1, i.e. the windows of the Rayleigh wave suppression : ； Each window The denoised signal is obtained by multiplying each window with the selected IMF, i.e. suppressing the energy of the Rayleigh wave from the selected IMF containing the Rayleigh wave. : 。 2. The method of claim 1, wherein, The method comprises: ； wherein the superscript denotes the iteration operator, represents the demodulation matrix, is a vector, and denotes the demodulated signal, is the current th estimated component.

3. A system for adaptive Rayleigh wave suppression based on frequency- modulated feature mode decomposition, the system being configured to implement the method of any one of claims 1-2, wherein, The system comprises an extraction module, a suppression module and a reconstruction module. The extraction module is configured to use Fourier transform to convert a seismic signal to a frequency space domain, and adopt an adaptive frequency-modulated signal modal decomposition method to extract an intrinsic modal component. The suppression module is configured to perform adaptive filtering to suppress Rayleigh waves in the intrinsic modal component according to characteristics of the Rayleigh waves in the frequency space domain. The reconstruction module is configured to perform signal reconstruction on the intrinsic modal component after suppression and the remaining components after screening, and perform Fourier inverse transform to finally output an effective signal, which is a result after suppression of the Rayleigh waves. The method comprises: The method comprises: The method comprises: The system comprises an extraction module, a suppression module and a reconstruction module. The extraction module is configured to use Fourier transform to convert a seismic signal to a frequency space domain, and adopt an adaptive frequency-modulated signal modal decomposition method to extract an intrinsic modal component. The suppression module is configured to perform adaptive filtering to suppress Rayleigh waves in the intrinsic modal component according to characteristics of the Rayleigh waves in the frequency space domain. The reconstruction module is configured to perform signal reconstruction on the intrinsic modal component after suppression and the remaining components after screening, and perform Fourier inverse transform to finally output an effective signal, which is a result after suppression of the Rayleigh waves.

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