Dynamic polarization window seismic waveform separation method based on time-frequency ridges

Abstract

The present invention discloses a method for separating seismic waveforms of a dynamic polarization window based on time-frequency ridges. The present invention utilizes time-frequency ridge analysis technology and combines a dynamic polarization window calculation method to accurately calculate the polarization characteristics of seismic signals. This method analyzes the dynamic changes of seismic waves in the time-frequency domain, captures the polarization information during the propagation of seismic waves, thereby distinguishing seismic phases and achieving the purpose of waveform separation. Furthermore, it provides more accurate data support and analysis means for application fields such as seismic exploration, earthquake early warning, and earthquake disaster assessment.

Description

Technical Field

[0001] The present invention relates to the field of seismology, and particularly to a method for separating seismic waveforms with a dynamic polarization window based on the time-frequency ridge line. Background Art

[0002] In the field of seismology, the polarization analysis method is an important means to study the vibration state of seismic waves. Through this method, the polarization trajectory or vibration characteristics of seismic waves can be effectively detected. These polarization attributes not only help to determine the seismic phase, but also provide key information for designing filters, thereby further analyzing the seismic source mechanism. However, in the existing time-domain polarization calculation methods, the calculation of polarization parameters usually depends on a specific time window. This approach has the following several significant problems and disadvantages:

[0003] 1. Influence of the time window length on the polarization calculation result: Experimental results show that the choice of the time window length has a significant impact on the accuracy of the polarization calculation result. However, in practical applications, there is no unified criterion for the time window length to guide this choice. This leads to a large uncertainty in the calculation results of polarization parameters.

[0004] 2. Limitations of the constant window: The constant window is a commonly used type of time window, but its fixed property makes it unable to adapt to the dynamic changes that may occur in seismic waves at different time periods. Therefore, using a constant window for polarization calculation may result in information loss or misleading results.

[0005] 3. Limitations of the central frequency window: Although the central frequency window combines frequency characteristics and improves the accuracy of polarization calculation, it still depends on a fixed frequency range. When the frequency characteristics of seismic waves change, the central frequency window may not be able to accurately capture these changes, thus affecting the calculation results of polarization parameters.

[0006] To solve the above problems, researchers have tried to improve the accuracy of polarization calculation by optimizing the choice of the time window length. However, due to the complexity and variability of seismic waves, this method has encountered great difficulties in practice.

[0007] In summary, there is a large uncertainty in the choice of the time window length in the existing time-domain polarization calculation methods, and both the constant window and the central frequency window have limitations. Therefore, there is an urgent need for a new method that can adapt to the dynamic changes of seismic waves and improve the accuracy of polarization calculation. Summary of the Invention

[0008] The object of the present invention is to provide a method for separating seismic waveforms with a dynamic polarization window based on the time-frequency ridge line. The aim is to effectively separate seismic waves of different seismic phases by introducing a dynamic polarization window based on the time-frequency ridge line to solve the problems existing in the prior art.

[0009] To achieve the above object, the present invention is implemented according to the following technical solutions:

[0010] The present invention includes the following steps:

[0011] S1: Use synchronous extraction transformation to convert three-component seismic data into the time-frequency domain, and extract the frequency value with the maximum energy at each moment as the ridge point of the time-frequency ridge line;

[0012] S2: According to the energy distribution in the time-frequency domain, calculate the time-frequency ridge line at each moment, obtain the time-frequency ridge lines of each component and calculate the average value;

[0013] S3: Dynamically adjust the length of the polarization window using the average value of the time-frequency ridge line, thereby generating a dynamic polarization window adapted to the characteristics of seismic waves;

[0014] S4: Use the dynamic polarization window, combine with Hilbert transform to generate an analytic signal, calculate the complex covariance matrix and solve for eigenvalues and eigenvectors, and extract polarization parameters therefrom;

[0015] S5: According to the polarization state, regard the smooth segments of the azimuth curve as the same seismic phase, select the eigenvector with the maximum eigenvalue as the seismic phase base value direction, and use the inner product of the eigenfunctions to separate the waveforms of different seismic phases. The intersection points of the eigenfunctions identify the demarcation points of different seismic phases, thereby realizing waveform separation.

[0016] The beneficial effects of the present invention are:

[0017] The present invention is a method for separating seismic waveforms with a dynamic polarization window based on the time-frequency ridge line. Compared with the prior art, the present invention uses the time-frequency ridge line analysis technology and combines the dynamic polarization window calculation method to accurately calculate the polarization characteristics of seismic signals. This method captures the polarization information during the propagation of seismic waves by analyzing the dynamic changes of seismic waves in the time-frequency domain, thereby distinguishing seismic phases and achieving the purpose of waveform separation. Furthermore, it provides more accurate data support and analysis means for application fields such as seismic exploration, earthquake early warning, and earthquake disaster assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic flowchart of an embodiment of the present invention;

[0019] Figure 2The effect diagram of the embodiment of the present invention; in a, the upper part is the seismic phase characteristic function calculated by the dynamic polarization window based on the time-frequency ridge line of the present invention, and the lower part is the separation result of P and S waves under the dynamic polarization window based on the time-frequency ridge line of the present invention; in b, the upper part is the seismic phase characteristic function calculated by the empirical value (constant window), and the lower part is the separation result of P and S waves under the constant window; in c, the upper part is the seismic phase characteristic function calculated by the central frequency window, and the lower part is the separation result of PS waves under the central frequency window. Detailed implementation manners

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but do not limit the present invention.

[0021] As Figure 1 shown: The present invention includes the following steps:

[0022] S1: Use the synchrosqueezing transform to convert the three-component seismic data into the time-frequency domain, and extract the frequency value with the maximum energy at each moment as the ridge point of the time-frequency ridge line:

[0023] First, use the synchrosqueezing transform (SET) to convert the three-component seismic data u i (t) (i = x, y, z) into the time-frequency domain. According to the energy distribution in the time-frequency domain, select the frequency value corresponding to the maximum energy at each moment as the ridge point at the current moment t n on.

[0024] TFR[u i (t), t] = SET(u i (t)), i = x, y, z (1)

[0025] In formula (1), i represents the x, y, and z components of the three-component data, t represents time, u i (t) represents the seismic data in the time domain, and TFR[] is the time-frequency domain representation of u i (t).

[0026] S2: According to the energy distribution in the time-frequency domain, calculate the time-frequency ridge line at each moment, obtain the time-frequency ridge lines of each component and calculate the average value:

[0027]

[0028] In formula (2), IF i (t n ) represents the extracted time-frequency ridge line, N represents the number of discrete time points in the time-frequency domain, n represents the discrete time point index in the time domain, t n represents the discrete time point in the time-frequency domain, u i (t n ) represents the value in the time-frequency domain at t nFrequency points with discrete time instances, where \(i\) represents the \(x\), \(y\), and \(z\) components of the three-component data. The average value of the time-frequency ridge line is expressed as

[0029]

[0030] In Equation (3), \(mean()\) represents taking the average value, \(N\) represents the number of discrete time points in the time-frequency domain, \(n\) represents the discrete time point index in the time domain, \(t_n\) represents the discrete time point in the time-frequency domain, \(IF x (t n ), \(IF y (t n ), \(IF z (t n ) respectively represent the time-frequency ridges of the \(x\), \(y\), and \(z\) components of the seismic data, represents the average value of the time-frequency ridge line.

[0031] S3: Dynamically adjust the length of the polarization window using the average value of the time-frequency ridge line, thereby generating a dynamic polarization window adapted to the characteristics of seismic waves:

[0032] The length \(L\) of the dynamic polarization window var can be expressed as

[0033]

[0034] where \(f s is the sampling frequency of the signal, \(t n represents the discrete time point, \(N\) represents the number of discrete time points, represents the average value of the time-frequency ridge line. When is the center frequency of this segment of the signal, \(L var is a fixed value that does not change with time, and we call it the time window at the center frequency.

[0035] S4: Use the dynamic polarization window, combine with the Hilbert transform to generate an analytic signal, calculate the complex covariance matrix and solve for the eigenvalues and eigenvectors, and extract the polarization parameters from them:

[0036] When using the dynamic polarization window, construct the analytic signal by selecting the corresponding data according to the window length \(L var (t)\) at each moment

[0037]

[0038] In the above formula, \(H\) represents the Hilbert transform, \(u i (t)(i = x, y, z)\) is the three-component seismic data, \(t\) is the time, and \(i\) is the imaginary unit. Then the complex covariance matrix \(C(t)\) is expressed as:

[0039]

[0040] Where X, Y, and Z respectively represent the three-component analytical signals, and * represents the conjugate. Solve the characteristic equation

[0041]

[0042] Three eigenvalues and eigenvectors can be obtained, where C is the complex covariance matrix, λ i is the eigenvalue to be solved, I is the eigenvector to be solved, and V i x , V i y , V i z are the three components of the eigenvector respectively, and i is the index of the eigenvalue and eigenvector.

[0043] λ i , I i (V i x , V i y , V i z )(i = 1, 2, 3; λ1 > λ2 > λ3)

[0044] The azimuth angle can be defined as:

[0045]

[0046] In the formula, Re() represents taking the real part, and sign() is the sign function. V1 x is the x-component of the largest eigenvalue, and V1 y is the y-component of the largest eigenvalue, and V1 z is the z-component of the largest eigenvalue.

[0047] S5: According to the polarization state, regard the smooth segment of the azimuth curve as the same seismic phase, select the eigenvector corresponding to the largest eigenvalue as the seismic phase base value direction, and use the inner product of the eigenfunctions to separate the waveforms of different seismic phases. The intersection points of the eigenfunctions identify the demarcation points of different seismic phases, thereby realizing waveform separation. Specifically:

[0048] It is considered that the smooth segments of the mutant azimuth curve have the same seismic phase. First, select the eigenvector corresponding to the largest eigenvalue as the base value direction V0 of the seismic phase. The eigenfunction F of the seismic phase can be obtained through the inner product of the base vector and the eigenvector corresponding to the largest eigenvalue of the entire data segment.

[0049]

[0050] Where is the selected base value direction. The intersection points of the two different phase characteristic functions are the demarcation points of different seismic phases, and thus the purpose of seismic waveform separation can be achieved.

[0051] The seismic data used are: the seismic signal of magnitude 7.0 that occurred in Jiuzhaigou County, Aba Prefecture, northern Sichuan Province at 21:19:46 on August 8, 2017, received by the station SEO2 of the network KS. The sampling frequency of this data is 20 Hz, and the number of sampling points is 30,000. The phase characteristic function of the seismic phase calculated based on the dynamic polarization window of the time-frequency ridge line in the present invention is as Figure 2 shown in a. There are obvious differences in different seismic phases, and the intersection points are clear and easy to separate different waveforms. Figure 2 The lower half of a is the separation result. Figure 2 b is the phase characteristic function calculated by the constant window. The intersection points are not clear and the PS waves cannot be effectively separated. Figure 2 c is the phase characteristic function calculated by the central frequency window. Compared with the constant time window, this result has been greatly improved, but the local details are still not well controlled, and it is not easy to make a fine seismic phase division.

[0052] The technical solution of the present invention is not limited to the limitations of the above specific embodiments. Any technical deformation made according to the technical solution of the present invention falls within the protection scope of the present invention.

Claims

1. A dynamic polarization window seismic waveform separation method based on time-frequency ridges, characterized in that Including the following steps: S1: Use synchronous extraction transformation to convert three-component seismic data into the time-frequency domain, and extract the frequency value with the maximum energy at each moment as the ridge point of the time-frequency ridge line; S2: According to the energy distribution in the time-frequency domain, calculate the time-frequency ridge line at each moment, obtain the time-frequency ridge lines of each component and calculate the average value; S3: Dynamically adjust the length of the polarization window using the average value of the time-frequency ridge line, thereby generating a dynamic polarization window adapted to the characteristics of seismic waves; S4: Use the dynamic polarization window, combine with the Hilbert transform to generate an analytic signal, calculate the complex covariance matrix and solve for the eigenvalues and eigenvectors, and extract the polarization parameters from them; S5: According to the polarization state, regard the smooth segments of the azimuth curve as the same seismic phase, select the eigenvector corresponding to the maximum eigenvalue as the seismic phase base value direction, use the inner product of the eigenfunctions to separate the waveforms of different seismic phases, and the intersection points of the eigenfunctions identify the demarcation points of different seismic phases, thereby realizing waveform separation.

2. The method for separating seismic waveforms of a dynamic polarization window based on a time-frequency ridge line according to claim 1, characterized in that: The specific formula of step S1 is as follows: TFR[u i (t),t] = SET(u i (t)), i = x, y, z where: i represents the x, y, and z components of the three-component data, t represents time, and u i (t) represents the time-domain seismic data, and TFR[] is for u i (t) in the time-frequency domain representation.

3. The method for separating seismic waveforms of a dynamic polarization window based on a time-frequency ridge line according to claim 2, characterized in that: The formula of step S2 is as follows: Where: IF i (t n ) represents the extracted time-frequency ridge line, N represents the number of discrete time points in the time-frequency domain, n represents the discrete time point index in the time domain, t n represents the discrete time point in the time-frequency domain, u i (t n ) represents the discrete frequency point at time t n in the time-frequency domain, and i represents the x, y, and z components of the three-component data; The average value of the time-frequency ridge line is expressed as: where: mean() represents calculating the mean value, N represents the number of discrete time points in the time-frequency domain, n represents the discrete time point index in the time domain, and t n represents the discrete time point in the time-frequency domain, and IF x (t n ), IF y (t n ), IF z (t n ) respectively represent the time-frequency ridges of the x, y, and z components of the seismic data, represents the average value of the time-frequency ridges.

4. The method for separating seismic waveforms of a dynamic polarization window based on a time-frequency ridge line according to claim 3, characterized in that: The dynamic polarization window length L in the step S3 var is expressed as: where: f s is the sampling frequency of the signal, t n represents discrete time points, N represents the number of discrete time points, represents the average value of the time-frequency ridge line. When is the center frequency of this section of the signal, L var is a fixed value that does not change with time.

5. The method for separating seismic waveforms of a dynamic polarization window based on a time-frequency ridge line according to claim 4, wherein: When using the dynamic polarization window in step S4, according to the window length L at each moment var select the corresponding data to construct an analytic signal and build a covariance matrix, and solving the characteristic equation can obtain three eigenvalues and eigenvectors: λ i , I i (V i x , V i y , V i z )(i = 1, 2, 3; λ1 > λ2 > λ3) The azimuth angle Azi of the seismic data is defined as: where Re() represents taking the real part, sign() is the sign function, and V1 x is the x-component of the maximum eigenvalue, V1 y is the y-component of the maximum eigenvalue, V1 z is the z-component of the maximum eigenvalue.

6. The method for separating seismic waveforms of a dynamic polarization window based on a time-frequency ridge line according to claim 5, characterized in that: In step S5, first select the eigenvector corresponding to the maximum eigenvalue as the base value direction V0 of the seismic phase. The eigenfunction F of the seismic phase is obtained through the inner product of the base vector and the eigenvector corresponding to the maximum eigenvalue for the entire data segment: wherein is the selected base value direction; the intersection of two different phase characteristic functions is the demarcation point of different seismic phases, and thus the purpose of seismic waveform separation can be achieved.

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