Seismic GIT analysis method and apparatus

Abstract

The application provides a seismic GIT analysis method and device, which is used for solving the problem of non-unique solution caused by non-full rank matrix when seismic analysis is performed by using generalized inversion method. The seismic GIT analysis method comprises the following steps: establishing a spectral decomposition equation group according to all seismic records of all stations in data; inducing all unknown path terms to k interval-fixed path intervals according to travel time to form k unknown path interval terms; constructing column vectors according to positions of a seismic source term, a path interval term and a site term in the spectral decomposition equation group, linearly representing part column vectors which do not belong to the same term by remaining column vectors and forming a new spectral decomposition matrix equation; solving the matrix equation by using a least square method to obtain an unconstrained equation solution; and correcting the unconstrained equation solution to obtain a real value of the solution of the matrix equation.

Description

Technical Field

[0001] This invention relates to the field of earthquake analysis, and more specifically, to an earthquake GIT analysis method and apparatus. Background Technology

[0002] The Generalized Inversion Technique (GIT) is a technique that decomposes the Fourier spectrum of a seismic record into source, path, and site terms in the frequency domain. There are two commonly used methods for GIT: nonparametric and parametric methods. Parametric inversion directly provides the models for the source and path attenuation terms. In nonparametric methods, no theoretical model is provided as prior information; the solution is the spectral curves of the source, path attenuation, and site terms.

[0003] Nonparametric methods are divided into single-step and two-step methods. The single-step method can simultaneously obtain all logarithmic source terms, logarithmic site terms, and logarithmic path attenuation terms. The two-step method first calculates the logarithmic path attenuation term, and then calculates the logarithmic source and site terms. Because the matrix used in the calculation is rank-deficient, the solution of the generalized inversion method is not unique, resulting in infinitely many solutions for the required source, site, and path terms. Summary of the Invention

[0004] The purpose of this invention is to provide a seismic GIT analysis method and apparatus that can eliminate the non-uniqueness of solutions in generalized inversion methods and analyze datasets.

[0005] Firstly, this application provides a seismic GIT analysis method, comprising: establishing a spectral decomposition equation set for earthquakes based on all seismic records from all stations in a dataset, wherein each equation in the spectral decomposition equation set represents a seismic record from a station using a source term, a path term, and a site term; summarizing all unknown path terms into k fixed-interval path intervals based on travel time, forming k unknown path interval terms; recording the positions of the source term, the path term, and the site term in the spectral decomposition equation set using column vectors; rewriting the spectral decomposition equation set into a matrix equation; linearly representing the column vectors that do not belong to the same term by removing the remaining column vectors, and substituting them back into the matrix equation to make the matrix equation full rank; solving the matrix equation using the least squares method to obtain an unconstrained solution; and correcting the unconstrained solution to obtain the true value of the solution to the matrix equation.

[0006] The method provided in this application can reverse the true values ​​of the source, site, and path terms of earthquake records in a dataset.

[0007] As an optional approach, the spectral decomposition equations can be transformed into matrix equations as follows: Among them, InS i (f) represents the focal term, InG j (f) represents the site item. For the k unknown path intervals, a1…a m The positions of all InS(f) in the spectral decomposition equations are recorded, a m+1 …a m+n The positions of all InG(f) in the spectral decomposition equations are recorded, a m+n+1 …a m+n+k The positions of all InP(f) in the spectral decomposition equation set are recorded, and b is a vector composed of m seismic records from n stations.

[0008] As an optional approach, the step of linearly representing the portion of the column vectors that do not belong to the same item by the remaining column vectors excluding the portion of the column vectors includes: selecting a site item InG i The corresponding column vector a m+i and a path interval item The corresponding column vector a m+n+j It is then represented linearly by the remaining column vectors.

[0009] As an optional approach, correcting the unconstrained equation solution to obtain the true value of the solution to the matrix equation includes: given the column vector a m+i The corresponding constraint term InG i and the column vector a m+n+j Corresponding constraint terms The accurate values ​​are used to correct for the true solution; among them, the calculated unconstrained source term, site term, and path interval term are respectively offset by -InG i (f), Given site constraint term InG i and path constraint terms After obtaining the accurate value, the true solution is corrected.

[0010] As an alternative approach, the spectral decomposition equations can be modified into matrix equations as follows: Among them, InS i (f) represents the focal term. For the k unknown path intervals, a1…a m ,a m+n+1 …a m+n+k The positions of all InS(f) and InP(f) in the spectral decomposition equation set are recorded respectively, and b is a vector composed of m seismic records from n stations.

[0011] As an optional approach, the step of linearly representing the portion of the column vectors that do not belong to the same item by the remaining column vectors excluding the portion of the column vectors includes: selecting a path interval item. The corresponding column vector a m+n+j It is then represented linearly by the remaining column vectors.

[0012] As an optional approach, correcting the unconstrained equation solution to obtain the true value of the solution to the matrix equation includes: given the column vector a m+n+j Corresponding constraint terms The accurate values ​​are used to correct for the true solution; among them, the calculated unconstrained source term and path interval term are offset by... Given path constraints After obtaining the accurate value, the true solution is corrected.

[0013] As an optional approach, the path interval term that appears most frequently in the spectral decomposition equation set is selected as the constraint term, denoted as... And The corresponding column vector is linearly represented by the remaining column vectors; or the path interval term that appears least frequently in the spectral decomposition equations is selected as the constraint term, denoted as... And The corresponding column vector is linearly represented by the remaining column vectors.

[0014] As an optional approach, correcting the solution of the unconstrained equation to obtain the true value of the solution of the matrix equation includes: given the accurate values ​​of the constraint terms corresponding to the partial column vectors, correcting to obtain the true solution; or using the empirical correction function ECS to correct the solution of the unconstrained equation.

[0015] As an optional approach, after solving the matrix equation using the least squares method to obtain an unconstrained solution, the method further includes: calculating the actual ECS based on the solution of the matrix equation.

[0016] Secondly, an earthquake GIT analysis device is provided, comprising: an equation establishment module, used to establish a spectral decomposition equation set of earthquakes based on all earthquake records from all stations in the dataset, wherein each equation in the spectral decomposition equation set represents an earthquake record from a station using a source term, a path term, and a site term; an induction interval module, used to inductively decompose all unknown path terms into k fixed-interval path intervals based on travel time, forming k unknown path interval terms; a linear transformation module, used to record the positions of the source term, the path term, and the site term in the spectral decomposition equation set using column vectors, rewrite the spectral decomposition equation set into a matrix equation, linearly represent the column vectors of positions that do not belong to the same term by removing the remaining column vectors, and substitute them back into the matrix equation to make the matrix equation full rank; a solution module, used to solve the matrix equation using the least squares method to obtain an unconstrained solution; and a correction module, used to correct the unconstrained solution to obtain the true value of the solution of the matrix equation.

[0017] Thirdly, a computing device is provided, the computing device including a memory and a processor, the processor executing computer instructions stored in the memory, causing the computing device to perform the method for seismic GIT analysis provided in the first aspect and in combination with any implementation of the first aspect.

[0018] Fourthly, a computer-readable storage medium is provided that stores computer instructions, which, when executed by a computer, cause the computer to perform the method for seismic GIT analysis provided in the first aspect and in combination with any implementation of the first aspect. Attached Figure Description

[0019] Figure 1 A schematic flowchart of an earthquake GIT analysis method according to an embodiment of this application is shown;

[0020] Figure 2 The difference at any frequency is shown for all path interval terms calculated by the two methods in two inversions of dataset 1;

[0021] Figure 3 The difference in frequency variation for any path interval term calculated by the two methods in two inversions of dataset 1 is shown;

[0022] Figure 4 This shows the difference between the inverted spectrum of each path interval term and the true spectrum after solving the single-step spectral decomposition matrix equation using the singular value decomposition method (SVD) on dataset 1.

[0023] Figure 5This shows the difference between the inverted spectrum of each path interval term and the true spectrum after solving the two-step spectral decomposition matrix equation using the singular value decomposition (SVD) method on dataset 1.

[0024] Figure 6 The difference at any frequency is shown for all path interval terms calculated by the two methods in two inversions of dataset 2;

[0025] Figure 7 The difference in frequency variation for any path interval term calculated by the two methods in two inversions of dataset 2 is shown;

[0026] Figure 8 It shows that respectively and The results of source terms when performing two single-step inversions on dataset 3 with constraints;

[0027] Figure 9 It shows that respectively and The results of the site terms when performing two single-step inversions on dataset 3 with constraints;

[0028] Figure 10 It shows that respectively and The results of the path interval terms when performing two single-step inversions on dataset 3 with constraints;

[0029] Figure 11 It shows that respectively and The results of performing two single-step inversions on the noise in dataset 3 with constraints and the results of directly performing the inversion using the singular value decomposition (SVD) method for the source term;

[0030] Figure 12 It shows that respectively and The results of performing two single-step inversions on the noise in dataset 3 with constraints and the results of directly inverting the field term using singular value decomposition (SVD) are compared.

[0031] Figure 13 It shows that respectively and The results of the path interval terms when performing two single-step inversions with constraints on the noise in dataset 3 and when performing inversions directly using the singular value decomposition (SVD) method;

[0032] Figure 14 It shows that When performing a single-step inversion on dataset 3 with constraints, the calculated ECS is the same as... Differences;

[0033] Figure 15 It shows that When performing a single-step inversion on dataset 3 with constraints, the calculated ECS is the same as... Differences;

[0034] Figure 16 This demonstrates that, under the condition that the long-period amplitude of the predicted spectrum of the corrected earthquake matches the long-period amplitude of its true source spectrum, ... When performing a single-step inversion on dataset 3 with constraints, the calculated ECS is the same as... Differences;

[0035] Figure 17 This demonstrates that, under the condition that the long-period amplitude of the predicted spectrum of the corrected earthquake matches the long-period amplitude of its true source spectrum, ... When performing a single-step inversion on dataset 3 with constraints, the calculated ECS is the same as... Differences;

[0036] Figure 18 An earthquake GIT analysis apparatus provided in an embodiment of this application is shown. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] This invention provides a generalized seismic inversion method to eliminate the non-uniqueness of solutions caused by incomplete matrix rank during the inversion process. Please refer to [link / reference]. Figure 1 The method includes:

[0039] Step 110: Establish a set of spectral decomposition equations for earthquakes based on all earthquake records from all stations in the dataset. Each equation in the set of spectral decomposition equations represents an earthquake record from a station using source terms, path terms, and site terms.

[0040] Suppose that the number of stations in the dataset used is n, denoted as [InG1,…,InG1]. n The number of earthquakes is m, denoted as [InS1,…,InS]. m In the far-field case, the seismic record of earthquake i obtained by station j can be regarded as a joint effect of the combined influence of the source, path, and site, and the following spectral decomposition equation is obtained:

[0041] InU i,j (f)=InS i (f)+InP k(f)+InG j (f)

[0042] Among them, InU i,j (f) represents the log-Fourier amplitude spectrum of earthquake i recorded at station j, and b is a vector [InU] composed of the log-Fourier amplitude spectra of m earthquake records from n stations in the dataset. 1,1 ,…,InU i,j ] T This corresponds to the set of spectral decomposition equations that make up all earthquake records; InS i (f) represents the focal term, i.e., the logarithmic focal spectrum of earthquake i; InP k (f) represents the path term, describing the sum of attenuation effects of seismic waves at the source distance (viscoelastic attenuation, geometric diffusion, scattering, etc.); InG j (f) is the site term, which describes the site amplification effect at station j.

[0043] Step 120: Summarize all unknown path items into k fixed-interval path intervals based on travel time, forming k unknown path interval items.

[0044] Based on the time it takes for seismic waves to travel from the epicenter to the observation point, InP k (f) Summarize into k path intervals with fixed intervals, forming k unknown path interval items. The interval between path segments can be freely selected, such as 0.1 seconds, 0.5 seconds, 1 second, etc.

[0045] Step 130: Record the positions of the source term, path term, and site term in the spectral decomposition equation system using column vectors. Rewrite the spectral decomposition equation system into a matrix equation. Linearly represent the column vectors that do not belong to the same term by the remaining column vectors after removing the column vectors, and substitute them back into the matrix equation to make the matrix equation full rank.

[0046] The spectral decomposition equations in step 110 contain multiple spectral decomposition equations of consistent form. To facilitate linear algebraic analysis, they are rewritten as a matrix equation containing vectors, with the path terms in the matrix equation replaced by the path interval terms from step 120. The resulting matrix equation is of the form AX = b, where b is a vector composed of the values ​​of the log-Fourier amplitude spectra of all seismic records in the dataset at a specific frequency point, and X is a vector composed of the values ​​of the source term, site term, and path interval term to be solved at the aforementioned specific frequency point. Each column vector in matrix A is used to record the position of a source term, site term, or path term in X within the spectral decomposition equations. Since matrix A is not of full rank, AX = b has an infinite number of least-squares solutions in the rewritten matrix equation.

[0047] To eliminate the non-uniqueness of the solution to the equation, linear algebraic analysis shows that the column vectors recording the positions in A are divided into three groups, recording the positions of the source term, the site term, and the path term, respectively. The column vectors that do not belong to the same group are linearly represented by all the remaining column vectors excluding these parts. Substituting these into the matrix equation, the column vectors that are linearly represented in matrix A no longer exist, and the constraint terms corresponding to these column vectors no longer exist in X. Instead, they are transformed into other terms as part of other terms. After reducing the constraint terms, the solution vector X becomes full rank.

[0048] Step 140: Solve the matrix equation using the least squares method to obtain the unconstrained solution.

[0049] After the processing in step 130, X is full rank, so the least squares method can be used to solve X. Since each term remaining after the transformation of X in step 130 has a constraint term, the obtained X is an unconstrained solution to the equation.

[0050] Step 150: Correct the unconstrained equation solution to obtain the true value of the solution of the matrix equation.

[0051] Step 150 can be used to correct the true solution by giving accurate values ​​of the constraint terms corresponding to the given partial column vectors, or the Empirical Correction Scheme (ECS) can be used to correct the unconstrained equation solution.

[0052] After obtaining the unconstrained solution to the equation, the following two methods can be used to correct it and eliminate the uncertainty of the solution.

[0053] Method 1

[0054] Given the exact values ​​of the constraint terms in the solution of the unconstrained equations, the true solutions for the source, site, and path interval terms are finally obtained. Based on the order in which the terms are solved, earthquake GIT analysis methods can be classified into single-step and two-step methods.

[0055] (1) Single-step method

[0056] The matrix equation after rewriting the spectral decomposition equations is A. onestep x onestep =b:

[0057]

[0058] Among them, InS i (f) represents the focal term, InG j (f) represents the site item. Let there be k unknown path intervals, a1…a m ,a m+1 …am+n ,a m+n+1 …a m+n+k The positions of all InS(f), InG(f), and InP(f) in the spectral decomposition equations are recorded, and b is a vector composed of m seismic records from n stations. Because A onestep Full rank, therefore A onestep x onestep =b has an infinite number of least squares solutions.

[0059] Since each row of the spectral decomposition equations corresponds to one equation, and each equation contains only one InS(f), InG(f), and InP(f), therefore:

[0060]

[0061] This shows that any two column vectors that do not belong to the same group can be linearly represented by all vectors excluding those two vectors. Let's select a field term column vector a. m+i (coefficient is InG) i ) and a path item column vector a m+n+j (coefficient is) If we express it linearly using the remaining column vectors and substitute it back into the matrix equation, then A onestep x onestep =b can be rewritten as

[0062]

[0063]

[0064] because Full rank, therefore the least squares method can be used to... Solve directly, called This is the solution obtained without constraints.

[0065] Among them, the calculated unconstrained source term, site term, and path interval term are compared with x. onestep They were offset respectively -InG i (f), Given site constraint term InG i and path constraint terms After obtaining the accurate value, the true solution x is corrected. onestep The solution x is called the solution x. onestep Based on InG i , The solution is a constraint.

[0066] (2) Two-step method

[0067] The matrix equation after rewriting the spectral decomposition equations is A. twostep x twostep =b:

[0068]

[0069] Still satisfied:

[0070] This shows that any column vector can be linearly represented by the remaining column vectors. Let's select a path term column vector a. m+n+j (coefficient is) If we express it linearly using the remaining column vectors and substitute it back into the matrix equation, then A twostep x twostep =b can be rewritten as

[0071]

[0072]

[0073] Similarly, because Full rank, therefore the least squares method can be used to... Solve directly, called This is the solution obtained without constraints.

[0074] Among them, the calculated unconstrained source term and path interval term were offset by... Given path constraints After obtaining the accurate value, the true solution x is corrected. twostep The solution x is called the solution x. twostep Therefore The solution is a constraint.

[0075] Method 2

[0076] The unconstrained source term derived from the inversion is corrected using an empirical correction function (ECS). This method assumes that the unconstrained source term derived from the inversion (e.g., using singular value decomposition (SVD)) consists of the true source term and an ECS function.

[0077] InS inversion =InS real +ECS

[0078] Corner frequencies of the source spectrum for a given reference magnitude: And according to (Assuming self-similarity) Calculate the corner frequencies of a set of small earthquakes of a specific magnitude, and then calculate their theoretical source spectrum InS. pre(The theoretical source spectrum and the inverted source terms are consistent at long periods), and the ECS is the average of the differences between the predicted spectrum of these small earthquakes and the terms inverted by GIT. After calculating the ECS based on this method, the true solution can be corrected.

[0079] The following table shows three synthetic datasets. The single-step and two-step methods from the previous examples are used to perform two inversions on datasets 1, 2, and 3. Before the inversion, the travel times from all sources to all stations are calculated. Based on the travel times, the path terms are summarized into path intervals with a 0.5s interval: The path interval term that appears most frequently in the spectral decomposition equation system is: (Appearing 496 times), the path interval term with the fewest occurrences is... (Appears once), and the mean of all path spectra contained in each path interval is taken as the true spectrum of that path interval.

[0080] Table 1

[0081]

[0082] Perform two inversions on dataset 1. In the first inversion, both the one-step and two-step methods are used. Apply constraints. In the second inversion, both the one-step and two-step methods use... Make constraints. By As can be seen from the expression, the inverted path term is only related to the path constraint term and is independent of the site constraint term. Therefore, any site term can be chosen to constrain the second degree of freedom. Since this paper performs the inversion on a synthetic dataset, the prior information of the model parameters is known, so the true values ​​are given when the values ​​of the constraint terms are given. Figure 2 For the difference at any frequency among all path interval terms calculated by the two methods in the two inversions, Figure 2 There are a total of 73 path interval items. Figure 3 This represents the difference in frequency variation between any path interval term calculated by the two methods in the two inversions. It can be seen that when using path interval terms that appear more frequently in the spectral decomposition equations... When applying constraints, the differences in path interval terms between the single-step and two-step inversion methods can be systematically reduced. Figure 2 The values ​​at the tail end are more dispersed because these path intervals contain too little data.

[0083] Use SVD to analyze dataset A of dataset 1. onestep x onestep =b and A twostep x twostep =b is solved again (without any constraints). For A onestep x onestep=b After solving using SVD, calculate the difference between the inverted spectrum and the true spectrum for each path interval term, such as Figure 4 As shown, all the difference spectra are equal, indicating that a path interval constraint can be used to correct the inversion spectrum of all path interval terms. For A... twostep x twostep =b After solving using SVD, calculate the difference between the inverted spectrum and the true spectrum for each path interval term, such as Figure 5 As shown, each difference spectrum is not equal. This means that the path interval term calculated using SVD in the first step of the two-step method cannot be corrected using the same constraint term.

[0084] Perform two inversions on dataset 2. In the first inversion, both the one-step and two-step methods are used. Apply constraints. In the second inversion, both the one-step and two-step methods use... Add constraints. The result is as follows: Figure 6 As shown in Figure 7, Figure 6 A total of 73 path interval terms were calculated. In both inversions, the path interval terms calculated by the two methods were equal, with no difference. This indicates that if the site effects of all stations are equal, using the same path constraints, the path interval terms calculated by the single-step and two-step methods are equal.

[0085] Perform two inversions on dataset 3 using a single-step method. In the first inversion, use... Define constraints and provide their true values. Use them in the second inversion. Apply constraints and provide their actual values. Figure 8 Figures 9 and 10 show the results of any earthquake, source term, site term, and path interval term in the two inversions, respectively. Dataset 3 does not directly add noise to the source, site, and path models; instead, noise perturbation is added to each synthetic FAS. In this embodiment, the noise in dataset 3 is inverted separately to observe the impact of the added noise on each source, site, and path interval term. The noise is then used sequentially... and Two single-step inversions are performed with constraints (no need to correct with the true value), and SVD is used to directly invert the noise. The three inversion results are as follows: Figure 11 As shown in Figures 12 and 13, it can be seen that the use of The noise inversion results with path constraints are roughly equivalent to those obtained by direct noise inversion using SVD. The inversion results for dataset 3 show that when using the single-step method for inversion, using path interval terms that appear frequently in the spectral decomposition equation as constraints can systematically reduce the impact of noise on the source and path interval term inversion results. However, the site term inversion results are not affected by the selection of path interval terms.

[0086] Based on the above processing and analysis of the dataset, and in conjunction with the attached figures, it was found that site effects are the cause of the differences between the single-step and two-step methods. When the site effects of all stations are equal and the same path interval term is used as a constraint, the path interval terms calculated by the two methods are equal. Furthermore, it was found that using the path interval term that appears most frequently in spectral decomposition as a constraint can reduce the differences in path interval terms between the single-step and two-step methods, and can also suppress the influence of noise on the inverted source and path interval terms. This measure has the same noise suppression effect as using SVD for inversion.

[0087] In the process of using the Empirical Correction Function (ECS) to eliminate the uncertainty of the equation solution, from The inversion results show that the unconstrained source term consists of the sum of the true source term, a site term, and a path term. Furthermore, since the mainstream empirical correction function (ECS) theory assumes that the inverted unconstrained source term (e.g., using singular value decomposition (SVD)) consists of the true source term and an ECS function, the true ECS function in this embodiment is derived as follows:

[0088] In the previous examples, two inversions were performed on dataset 3 using a single-step method, with the following methods used in each inversion: and Constrain one degree of freedom, and arbitrarily choose a site term to constrain the second degree of freedom. The following section uses mainstream methods to calculate the ECS corresponding to the two inversions and compares it with... Compare with (real ECS). Assume a reference magnitude. Let the corner frequency be set (The corner frequency of earthquakes near the reference magnitude in the composite data is around this value, therefore, taking 60Hz is considered reasonable.) The selected magnitude is... The earthquakes used as correction earthquakes total 134. The actual Mw and M0 values ​​from the dataset are used here. However, in actual inversion, the Mw and M0 values ​​of smaller earthquakes are unknown, requiring the estimation of magnitude and moment. Assuming the earthquakes are self-similar, the f values ​​for the 134 correction earthquakes are calculated using the following formula. c :

[0089]

[0090] To ensure the long-period amplitude of the predicted spectrum of the corrected earthquakes matches the amplitude obtained from the GIT inversion, the average difference between the predicted and inverted spectra of 134 corrected earthquakes is calculated. The ECS values ​​from the two inversion calculations are then compared with... (Real ECS) images, respectively, as shown below Figure 14As shown in Figure 15, the calculated ECS does not match the actual ECS; the difference between the two spectral curves is approximately constant. This is because the long-period amplitude of the GIT inversion spectrum is not equal to the actual amplitude of the small earthquake. Therefore, this difference is transmitted to the calculated ECS through the correction earthquake. By aligning the long-period amplitude of the predicted spectrum of the correction earthquake with the long-period amplitude of its actual source spectrum, and recalculating the ECS, the results are as follows: Figure 16 As shown in Figure 17, it can be seen that the calculated ECS is basically consistent with the actual ECS. It is also observed that when the constraint terms used in the inversion are... When no constraint terms are specified, the calculated ECS is significantly affected by noise. However, when the constraint terms used for inversion are... When the noise level is low, the calculated ECS is significantly less affected.

[0091] In summary, the above embodiments reveal that the ECS calculated by current mainstream methods is not equal to the actual ECS. This is because the long-period amplitude of the corrected earthquake is not equal to the actual amplitude. The path term that appears most frequently in the spectral decomposition equations is used. Applying constraints can suppress the impact of noise on the ECS.

[0092] In summary, this invention provides a seismic GIT analysis method. Using this method, it can be concluded that site effects are the cause of the differences between the two-step and single-step methods. When the site effects of all stations are equal, the path interval terms calculated by the two methods are equal. Using the path term that appears most frequently in the spectral decomposition equations as a constraint can reduce the difference in path interval terms between the single-step and two-step methods, and can also suppress the influence of noise on the inverted source term, path interval term, and ECS. This measure has the same noise suppression effect as using SVD for inversion. Furthermore, it can be concluded that the ECS calculated using the currently mainstream methods is not equal to the true ECS, which is due to the difference between the long-period amplitude of the corrected earthquake and the true amplitude.

[0093] Please refer to Figure 18 This application also provides a seismic GIT analysis apparatus, which includes:

[0094] The equation establishment module 210 is used to establish a set of spectral decomposition equations for earthquakes based on all earthquake records from all stations in the dataset. Each equation in the set of spectral decomposition equations is represented by a source term, a path term, and a site term for an earthquake record from the station.

[0095] The induction interval module 220 is used to inductively summarize all unknown path items into k path intervals with fixed intervals based on travel time, forming k unknown path interval items.

[0096] The linear transformation module 230 is used to record the positions of the source term, path term, and site term in the spectral decomposition equation system using column vectors, rewrite the spectral decomposition equation system into a matrix equation, linearly represent the column vectors that do not belong to the same term by the remaining column vectors after removing the column vectors, and substitute them back into the matrix equation to make the matrix equation full rank.

[0097] Solver module 240 is used to solve matrix equations using the least squares method to obtain unconstrained equation solutions;

[0098] The correction module 250 is used to correct the solution of the matrix equation for the unconstrained equation solution to obtain the true value of the solution.

[0099] The implementation methods of the above modules are the same as those of the corresponding steps described above, and will not be repeated.

[0100] This application also provides a computing device, which includes a memory and a processor, wherein the processor executes computer instructions stored in the memory, causing the computing device to perform some or all of the steps described in any of the above method embodiments.

[0101] This application also provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions that, when executed by a computer, can implement some or all of the steps described in any of the above method embodiments.

[0102] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A seismic GIT analysis method, characterized in that, include: A set of spectral decomposition equations for earthquakes is established based on all earthquake records from all stations in the dataset. Each equation in the set of spectral decomposition equations is represented by a source term, a path term, and a site term for an earthquake record from the aforementioned station. All the unknown path items are categorized into k fixed-interval path intervals based on their travel time, forming k unknown path interval items; The position of the source term, the path term, and the site term in the spectral decomposition equation set is recorded using column vectors. The spectral decomposition equation set is rewritten into a matrix equation. The column vectors that do not belong to the same term are linearly represented by the remaining column vectors after removing the column vectors. The remaining column vectors are then substituted back into the matrix equation to make the matrix equation full rank. The matrix equation is solved using the least squares method to obtain an unconstrained solution. For the unconstrained solution of the equation, the true value of the solution of the matrix equation is obtained by correction.

2. The method according to claim 1, characterized in that, The matrix equations obtained by revising the spectral decomposition equation set are as follows: Among them, InS i (f) represents the focal term, InG j (f) represents the site item. For the k unknown path intervals, a1…a m The positions of all InS(f) in the spectral decomposition equations are recorded, a m+1 …a m+n The positions of all InG(f) in the spectral decomposition equations are recorded, a m+n+1 …a m+n+k The positions of all InP(f) in the spectral decomposition equation set are recorded, and b is a vector composed of m seismic records from n stations.

3. The method according to claim 2, characterized in that, The step of linearly representing the portion of the column vectors that do not belong to the same term by the remaining column vectors excluding the portion of the column vectors includes: Select a site item InG i The corresponding column vector a m+i and a path interval item The corresponding column vector a m+n+j It is then represented linearly by the remaining column vectors.

4. The method according to claim 3, characterized in that, The process of correcting the solution of the unconstrained equation to obtain the true value of the solution to the matrix equation includes: Given the column vector a m+i The corresponding constraint term InG i and the column vector a m+n+j Corresponding constraint terms The accurate value is used to correct the true solution; Among them, the calculated unconstrained source term, site term, and path interval term were offset by... Given site constraint term InG i and path constraint terms After obtaining the accurate value, the true solution is corrected.

5. The method according to claim 1, characterized in that, The matrix equations obtained by revising the spectral decomposition equation set are as follows: Among them, InS i (f) represents the focal term. For the k unknown path intervals, a1…a m ,a m+n+1 …a m+n+k The positions of all InS(f) and InP(f) in the spectral decomposition equation set are recorded respectively, and b is a vector composed of m seismic records from n stations.

6. The method according to claim 5, characterized in that, The step of linearly representing the portion of the column vectors that do not belong to the same term by the remaining column vectors after removing the portion of the column vectors includes: Select a path interval item The corresponding column vector a m+n+j It is then represented linearly by the remaining column vectors.

7. The method according to claim 6, characterized in that, The process of correcting the solution of the unconstrained equation to obtain the true value of the solution to the matrix equation includes: Given the column vector a m+n+j Corresponding constraint terms The accurate value is used to correct the true solution; Among them, the calculated unconstrained source term and path interval term were offset by... Given path constraints After obtaining the accurate value, the true solution is corrected.

8. The method according to any one of claims 3 or 6, characterized in that, The path interval term that appears most frequently in the spectral decomposition equations is selected as the constraint term, denoted as . And The corresponding column vector is linearly represented by the remaining column vectors; or The path interval term that appears least frequently in the spectral decomposition equations is selected as the constraint term, denoted as . And The corresponding column vector is represented linearly by the remaining column vectors.

9. The method according to claim 1, characterized in that, After solving the matrix equation using the least squares method to obtain an unconstrained solution, the method further includes: The actual empirical correction function (ECS) is calculated based on the solution of the matrix equation.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a computer, cause the computer to perform the method as described in any one of claims 1-9.

Images