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

Abstract

The invention discloses a dynamic polarization window seismic waveform separation method based on a time-frequency ridge line, which utilizes a time-frequency ridge line analysis technology and combines a dynamic polarization window calculation method to accurately calculate the polarization characteristic of a seismic signal. According to the method, the polarization information in the seismic wave propagation process is captured by analyzing the dynamic change of the seismic wave in the time-frequency domain, so that the seismic phase is distinguished, and the purpose of waveform separation is achieved. And more accurate data support and analysis means are provided for the application fields of seismic exploration, seismic early warning, seismic disaster assessment and the like.

Description

Technical Field

[0001] The invention relates to the field of seismology, and in particular to a dynamic polarization window seismic waveform separation method based on time-frequency ridges. Background Art

[0002] In the field of seismology, polarization analysis is an important means to study the vibration state of seismic waves. This method can effectively detect the polarization trajectory or vibration characteristics of seismic waves. These polarization properties not only help determine the earthquake phase, but also provide key information for designing filters, thereby further analyzing the earthquake 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 significant problems and disadvantages:

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

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

[0005] 3. Limitations of the center frequency window: Although the center frequency window combines frequency characteristics and improves the accuracy of polarization calculation, it still relies on a fixed frequency range. When the frequency characteristics of seismic waves change, the center 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 length of the time window. However, due to the complexity and variability of seismic waves, this method has encountered great difficulties in practice.

[0007] In summary, the existing time-domain polarization calculation methods have great uncertainty in the selection of time window length, and both the constant window and the center 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 purpose of the present invention is to provide a method for separating seismic waveforms using a dynamic polarization window based on time-frequency ridges, and to solve the problems existing in the prior art by introducing a dynamic polarization window based on time-frequency ridges to effectively separate seismic waves of different phases.

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

[0010] The present invention comprises the following steps:

[0011] S1: Use synchronous extraction transformation 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;

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

[0013] S3: The length of the polarization window is dynamically adjusted using the average value of the time-frequency ridges, thereby generating a dynamic polarization window that adapts to the characteristics of seismic waves;

[0014] S4: Use a dynamic polarization window combined with Hilbert transform to generate analytical signals, calculate the complex covariance matrix and solve the eigenvalues ​​and eigenvectors to extract polarization parameters;

[0015] S5: According to the polarization state, the smooth segments of the azimuth curve are regarded as the same seismic phase, and the eigenvector with the largest eigenvalue is selected as the base value direction of the seismic phase. The inner product of the characteristic function is used to separate the waveforms of different seismic phases. The intersection of the characteristic function marks the dividing point of different seismic phases, thereby realizing waveform separation.

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

[0017] The present invention is a dynamic polarization window seismic waveform separation method based on time-frequency ridges. Compared with the prior art, the present invention uses time-frequency ridge analysis technology and combines dynamic polarization window calculation methods to accurately calculate the polarization characteristics of seismic signals. This method analyzes the dynamic changes of seismic waves in the time-frequency domain and captures polarization information during the propagation of seismic waves, thereby distinguishing seismic phases and achieving the purpose of waveform separation. This provides more accurate data support and analysis methods 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 diagram of a flow chart of an embodiment of the present invention;

[0019] Figure 2It is a rendering of an embodiment of the present invention; the upper part of a is the 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 the P and S waves under the dynamic polarization window based on the time-frequency ridge line of the present invention; the upper part of b is the phase characteristic function calculated by the empirical value (constant window), and the lower part is the separation result of the P and S waves under the constant window; the upper part of c is the phase characteristic function calculated by the center frequency window, and the lower part is the separation result of the PS wave under the heart frequency window. DETAILED DESCRIPTION

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

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

[0022] S1: Use synchronous extraction transformation 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, the three-component seismic data u are transformed using the synchronous extraction transform (SET) i (t)(i=x,y,z) is converted to the time-frequency domain, and the frequency value corresponding to the maximum energy at each moment is selected according to the energy distribution in the time-frequency domain. n The ridge point 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, and u i (t) represents the time domain seismic data, TFR[] is u i (t) is represented in the time-frequency domain.

[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 line of each component and calculate the average value:

[0027]

[0028] IF in formula (2) i (t n ) represents the extracted time-frequency ridge, N represents the number of discrete time points in the time-frequency domain, n represents the index of discrete time points in the time domain, and t n represents a discrete time point in the time-frequency domain, u i (t n ) represents the time-frequency domain at t nThe time-frequency ridgeline is expressed as:

[0029]

[0030] In formula (3), mean() represents the mean, N represents the number of discrete time points in the time-frequency domain, n represents the index of the discrete time point in the time domain, tn represents the discrete time point in the time-frequency domain, and IF x (t n ),IF y (t n ),IF z (t n ) table represents the time-frequency ridges of the x, y, and z components of the seismic data. Represents the average value of the time-frequency ridges.

[0031] S3: The length of the polarization window is dynamically adjusted using the average value of the time-frequency ridges to generate a dynamic polarization window that adapts to the characteristics of seismic waves:

[0032] Dynamic polarization window length L var It can be expressed as

[0033]

[0034] where f s is the sampling frequency of the signal, t n represents a discrete time point, N represents the number of discrete time points, represents the average value of the time-frequency ridge. When L is the center frequency of the signal, var It is a fixed value that does not change with time, which we call the center frequency time window.

[0035] S4: Use a dynamic polarization window and Hilbert transform to generate an analytical signal, calculate the complex covariance matrix and solve the eigenvalues ​​and eigenvectors to extract the polarization parameters:

[0036] When using a dynamic polarization window, the window length L at each moment is var (t) Select the corresponding data to construct the analytical signal

[0037]

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

[0039]

[0040] Where X, Y, and Z represent the three-component analytical signals, and * represents conjugation. 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, V i x ,V i y ,V i z The three components of the eigenvector, the eigenvalue i and the index of the eigenvector respectively.

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

[0044] The azimuth can be defined as:

[0045]

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

[0047] S5: According to the polarization state, the smooth segments of the azimuth curve are regarded as the same seismic phase, the eigenvector with the largest eigenvalue is selected as the base value direction of the seismic phase, and the inner product of the characteristic function is used to separate the waveforms of different seismic phases. The intersection of the characteristic function marks the dividing point of different seismic phases, thereby realizing waveform separation. Specifically:

[0048] It is assumed that the smooth segments of the sudden change azimuth curve have the same seismic phase. First, the eigenvector corresponding to the maximum eigenvalue is selected as the base value direction V0 of the seismic phase. The characteristic function F of the seismic phase can be obtained by the inner product of the base vector and the eigenvector corresponding to the maximum eigenvalue of the entire data segment.

[0049]

[0050] in is the selected base value direction. The intersection of two different phase characteristic functions is the dividing point of different seismic phases, thereby achieving the purpose of seismic waveform separation.

[0051] The seismic data used is: the earthquake signal of magnitude 7.0 in Jiuzhaigou County, Aba Prefecture, northern Sichuan Province, received by the station SEO2 of the KS network at 21:19:46 on August 8, 2017. The data sampling frequency is 20Hz, and the sampling points are 30,000. The seismic phase characteristic function calculated by the dynamic polarization window of the time-frequency ridgeline in the present invention is as follows: Figure 2 As shown in a, different earthquake phases are obviously different, and the intersection points are clear, making it easy to separate different waveforms. Figure 2 aThe lower part is the separation result. Figure 2 b is the phase characteristic function calculated by the constant window. The intersection is not clear and the PS wave cannot be effectively separated. Figure 2 c is the seismic phase characteristic function calculated by the center frequency window. Compared with the constant time window, the result is greatly improved, but the local details are still not well controlled, and it is not easy to finely divide the seismic phase.

[0052] The technical solution of the present invention is not limited to the above-mentioned specific embodiments. All technical variations made according to the technical solution of the present invention fall 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: The following steps are involved: S1: Use synchronous extraction transformation 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; S2: According to the energy distribution in the time-frequency domain, the time-frequency ridge line at each moment is calculated, the time-frequency ridge line of each component is obtained and the average value is calculated; S3: The length of the polarization window is dynamically adjusted using the average value of the time-frequency ridges, thereby generating a dynamic polarization window that adapts to the characteristics of seismic waves; S4: Use a dynamic polarization window combined with Hilbert transform to generate analytical signals, calculate the complex covariance matrix and solve the eigenvalues ​​and eigenvectors to extract polarization parameters; S5: According to the polarization state, the smooth segments of the azimuth curve are regarded as the same seismic phase, and the eigenvector with the largest eigenvalue is selected as the base value direction of the seismic phase. The inner product of the characteristic function is used to separate the waveforms of different seismic phases. The intersection of the characteristic function marks the dividing point of different seismic phases, thereby realizing waveform separation.

2. The method for separating seismic waveforms using a dynamic polarization window based on time-frequency ridges according to claim 1, characterized in that: The step S1 is specifically 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, TFR[] is u i (t) is represented in the time-frequency domain.

3. The method for separating seismic waveforms using a dynamic polarization window based on time-frequency ridges according to claim 2, characterized in that: The step S2 is as follows: In the formula: IF i (t n ) represents the extracted time-frequency ridge, N represents the number of discrete time points in the time-frequency domain, n represents the index of discrete time points in the time domain, and t n represents a discrete time point in the time-frequency domain, u i (t n ) represents the time-frequency domain at t n The discrete frequency points at a certain time, i represents the x, y, and z components of the three-component data; The average value of the time-frequency ridge is expressed as: Where: mean() represents the mean, N represents the number of discrete time points in the time-frequency domain, n represents the index of discrete time points in the time domain, tn represents the discrete time points in the time-frequency domain, IF x (t n ),IF y (t n ),IF z (t n ) table represents 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 using a dynamic polarization window based on time-frequency ridges according to claim 3 is characterized by: The dynamic polarization window length L in step S3 var It is expressed as: Where: f s is the sampling frequency of the signal, t n represents a discrete time point, N represents the number of discrete time points, represents the average value of the time-frequency ridge. When L is the center frequency of the signal, var It is a fixed value that does not change over time.

5. The method for separating seismic waveforms using a dynamic polarization window based on time-frequency ridges according to claim 4 is characterized by: When a dynamic polarization window is used in step S4, the window length L at each moment is var Select the corresponding data to construct the analytical signal and build the covariance matrix. Solving the characteristic equation can obtain three eigenvalues ​​and eigenvectors: l i ,I i (V i x ,V i y ,V i z (i=1,2,3;λ1>λ2>λ3) The azimuth Azi of seismic data is defined as: Where Re() represents the real part, sign() is the sign function, and V1 x The x-component of the largest eigenvalue, V1 y is the y component of the maximum eigenvalue, V1 z is the z-component of the largest eigenvalue.

6. The method for separating seismic waveforms using a dynamic polarization window based on time-frequency ridges according to claim 5, characterized in that: In step S5, the eigenvector corresponding to the maximum eigenvalue is first selected as the base value direction V0 of the seismic phase. The characteristic function F of the seismic phase is obtained by the inner product of the base vector and the eigenvector corresponding to the maximum eigenvalue of the entire data segment: in is the selected base value direction; the intersection of two different phase characteristic functions is the dividing point of different seismic phases, thereby achieving the purpose of seismic waveform separation.

Images