Unsupervised learning clustering weighted surface peak deformation strong earthquake magnitude estimation method

Abstract

The present application belongs to the technical field of earth observation and data processing, and relates to a surface peak deformation strong earthquake magnitude estimation method based on unsupervised learning clustering weight determination, which solves the problem of insufficient estimation accuracy in the prior art. The method first collects surface peak deformation PGD and PGV data and epicentral distance of the seismic monitoring station; a magnitude regression equation is constructed, the observation characteristics are analyzed by the FCM unsupervised learning clustering algorithm, and the observation weight factor is adaptively determined according to the difference degree of the cluster center and the reference cluster center; then the clustering weight is introduced into the robust estimation model, the sequential weighted least squares solution is solved by combining the IGG3 equivalent weight function, and the fused magnitude is obtained. The present application combines unsupervised clustering adaptive weight determination with robust estimation, and can quickly estimate the magnitude of strong earthquakes with complex fault structures, thereby significantly improving the accuracy, stability and reliability of strong earthquake magnitude estimation.

Description

Technical Field

[0001] This invention belongs to the field of Earth observation and data processing technology, specifically relating to a method for estimating the magnitude of strong earthquakes with surface peak deformation based on unsupervised learning clustering weighting. Background Technology

[0002] Magnitude is a crucial indicator describing the scale and impact of a strong earthquake rupture. Rapid and accurate magnitude determination helps in timely understanding the potential impact range of earthquake disasters. Rapid magnitude estimation methods are mainly divided into empirical scaling methods and rupture feature inversion methods. The rupture feature inversion method uses permanent coseismic deformation variables extracted from the Global Navigation Satellite System (GNSS) to invert an approximate fault slip model to determine the moment magnitude, which has clear physical meaning. However, this method requires a high level of prior fault model and station density, making it difficult to meet the real-time needs of rapid magnitude estimation. The empirical scaling method generally estimates time-frequency characteristic information such as peak ground velocity (PGV) and peak ground displacement (PGD) from high-frequency GNSS or strong-motion seismograph data, and fits this information into an empirical scaling relationship related to the epicentral distance. Such methods do not require an accurate understanding of the focal mechanism; they can quickly estimate the magnitude using only the earthquake location results (epicenter location). The estimated magnitude can avoid the problem of amplitude saturation. However, there is still a lack of a fast magnitude estimation method that combines two empirical models of different scales, PGV and PGD.

[0003] Commonly used magnitude scales include body wave magnitude (Mb), surface wave magnitude (Ms), and moment magnitude (Mw). Traditional rapid magnitude scales for body wave magnitude risk systematically underestimating strong earthquakes with slow rupture characteristics. Surface wave magnitude primarily measures earthquake size by the propagation characteristics of surface waves near the Earth's surface, making it suitable for rapid magnitude warnings with high timeliness. Moment magnitude is directly related to the physical processes of earthquake rupture and is a mechanical quantity describing the absolute magnitude of an earthquake, but it requires precise post-event measurement of the seismic moment for calibration. Using seismograph velocity records from seismological observations to estimate magnitude is a common technique, but the magnitude for early warning during strong earthquakes will be underestimated. Summary of the Invention

[0004] This invention provides an unsupervised learning-based clustering weighting method for estimating the magnitude of strong earthquakes with peak surface deformation, in order to solve the problem of insufficient magnitude estimation accuracy of existing PGD / PGV surface deformation data in the estimation of strong earthquake magnitudes.

[0005] An unsupervised learning-based clustering weighted method for estimating the magnitude of strong earthquakes with peak surface deformation includes the following steps: S1. Collect coseismic deformation observation data, calculate the multi-directional displacement and velocity components of each station, and calculate the peak surface displacement (PGD), peak surface velocity (PGV), and epicentral distance of the station. S2. Construct a magnitude regression equation, use the FCM unsupervised learning clustering algorithm to cluster the dataset to obtain weight factors, construct a fitting weight matrix based on the weight factors, substitute it into PGV and PGD to fit the observation equation, and obtain the fitting empirical coefficients through weighted least squares regression estimation. S3. Based on the empirical coefficients obtained in S2, construct the fusion observation equation, obtain the posterior weights of the two types of observations, PGD and PGV, through the Helmert VCE method, and use the IGG3 equivalent weight criterion to perform robust sequential least squares estimation to obtain the fusion magnitude.

[0006] Furthermore, the calculation formulas for the peak surface displacement (PGD) and peak surface velocity (PGV) are as follows: ; ; In the formula, , and These are expressed as coseismic displacement components in the north, east, and sky directions, respectively, in centimeters. , and These are expressed as coseismic velocity components in the north, east, and sky directions, respectively, in centimeters. The epicenter distance of the station The spherical distance from the station to the epicenter is obtained using the following formula: ; In the formula, This represents the spherical distance from the GNSS / strong-motion meter station to the epicenter, expressed in kilometers. and The latitude and longitude of the station and The coordinates of the epicenter are latitude and longitude. This is the average radius of the Earth.

[0007] Furthermore, in S2, the magnitude regression equation is: ; ; In the formula, , , The PGD magnitude regression coefficient is used. , , The regression coefficient for PGV magnitude. This represents the spherical distance from the GNSS / strong-motion meter station to the epicenter, expressed in kilometers.

[0008] Furthermore, the process of using the FCM unsupervised learning clustering algorithm to cluster the dataset and obtain the weight factors is as follows: the weight factors are derived from PGD, PGV, and epicentral distance. The feature dataset consists of: ; In the formula, , The total number of samples; Set the number of clusters and weighted index Construct the FCM objective function: ; In the formula, , indicating the first The sample belongs to the first The membership degree of each cluster. For the number of clusters, As a weighted index, For the first The feature vector of each sample For the first The characteristic values ​​of each cluster center; To introduce membership constraints, the Lagrange multiplier method is used to construct the Lagrange objective function: ; In the formula, , indicating the first The sample belongs to the first The membership degree of each cluster. For Lagrange multipliers, For the first Cluster centers; Membership degrees satisfy the following constraints: ; Differentiating and iteratively updating the Lagrange function, cluster centers It is calculated using the following formula: ; Let distance For membership function Taking the derivative, we get: ; In the formula, For the first Sample With the Cluster centers The distance between them For the first Sample With the Cluster centers The distance between them; After iterating until the objective function converges, the cluster centers are obtained. And the corresponding objective function is calculated in each iteration. This minimizes the objective function; after iteration, the FCM model obtains... Cluster centers, including the baseline cluster center , and the epicenter distance for each group and and The corresponding cluster centers are and Based on the degree of feature difference between each cluster center and the baseline cluster center, the FCM clustering weight factors corresponding to the PGD and PGV observations are constructed: ; ; In the formula, and These are the FCM clustering weight factors corresponding to the PGD and PGV observations, respectively. For the first Cluster centers, For the first The epicentral distance corresponding to each cluster center For the first The PGD value corresponding to each cluster center The epicentral distance corresponding to the reference center. The epicentral distance corresponding to the reference center. The PGD value corresponding to the reference center. For the first The PGV value corresponding to each cluster center The PGV value corresponding to the reference center. For the first A measure of the difference between each cluster center and the baseline cluster center.

[0009] Furthermore, the process of constructing a fitting weight matrix based on weight factors, substituting it into the PGV / PGD fitting observation equation, and obtaining the fitting empirical coefficients through weighted least squares regression includes constructing the fitting observation equations for PGV and PGD based on the magnitude regression equation: ; ; In the formula, To design the matrix, , These are the regression coefficient vectors for the PGD and PGV magnitude regression models, respectively; Based on FCM clustering weight factor Constructed weight matrix for: ; In the formula, The observation weights for each station are determined based on the FCM clustering weight factor; Fitting weight matrix Substituting the observation equations for PGD and PGV into the fitted equations, and using weighted least squares regression estimation, we obtain the fitted empirical coefficient vectors of the PGD and PGV magnitude regression models. and : ; ; In the formula, The logarithmic matrix of PGD observations, The logarithmic matrix of PGV observations. To design the matrix, For FCM-based clustering weight factors The constructed weight matrix, , These are the regression coefficient vectors for the PGD and PGV magnitude regression models, respectively; The fitted empirical coefficient vector is represented as follows: ; ; In the formula, , , These are the empirical coefficients of the PGD magnitude regression equation obtained by weighted least squares regression. , , These are the empirical coefficients of the PGV magnitude regression equation obtained by weighted least squares regression. Design Matrix for: ; In the formula, The known moment magnitudes of historical earthquakes. For the first Epicentral distance of each station; PGD ​​observation logarithmic matrix for: ; PGV observation logarithmic matrix for: ; Calculate the residuals between the observed PGD / PGV values ​​and the regression predictions: ; In the formula, The predicted residuals for PGD / PGV, These are PGD / PGV observations; These are the predicted values ​​for PGD / PGV.

[0010] Furthermore, in S3, the fusion observation equation is constructed based on empirical coefficients as follows: ; ; In the formula, , , These are the empirical coefficients of the PGD magnitude regression equation obtained by weighted least squares regression. , , These are the empirical coefficients of the PGV magnitude regression equation obtained by weighted least squares regression. and The first The first observation station was at the first Peak surface displacement and peak surface velocity observations for each observation epoch. For the first The first observation station was at the first Epicentral distance at each observation epoch, To estimate the strong earthquake moment and magnitude during the observation epoch; The regression magnitude of the observed epoch is calculated using the least squares criterion: ; In the formula, To integrate the overall design matrix, The prior weight matrix for PGD / PGV observations. This represents the overall observation vector; Fusion Design Matrix for: ; Overall observation vector for: ; Weight matrix of PGD / PGV observations for: ; In the formula, and Let be the prior weight matrices for PGD and PGV.

[0011] Furthermore, the specific process of obtaining the posterior weights of the two types of observations, PGD and PGV, through the Helmert VCE method is as follows: the two types of magnitude fitted observations, PGD and PGV, are incorporated into the Helmert variance component equation as two types of weights for variance component estimation. A joint observation model, a stochastic model, a population error equation, and a population normal equation are constructed. The unit weight variances of the PGD and PGV observations are estimated iteratively using the Helmert estimation formula. The posterior weight matrices of the two types of observations are updated. The iteration continues until the unit weight variances of the two types are equal or the hypothesis testing requirements are met. The joint observation model for PGD and PGV observations is expressed as follows: ; ; In the formula, and For observation vectors of PGD and PGV class observations, and The design matrices are for PGD and PGV type observations. and For PGD and PGV type observations, ; Design matrices for PGD and PGV type observations and for: ; ; Error terms for PGD and PGV type observations and for: ; ; In the formula, For the first PGD ​​error of each station For the first PGV error of each station; No. PGD ​​error at individual stations for: ; No. PGV error of individual stations for: ; The stochastic models for the two types of observations, PGD and PGV, are as follows: ; ; ; In the formula, For variance, and For observation vectors of PGD and PGV class observations, and For PGD and PGV type observations, the unit weight variance is given. and Let be the inverse of the prior weight matrices of PGD and PGV. PGD ​​observation vector With PGV observation vector Covariance between PGD ​​error Error with PGV Covariance between them; The overall error equations for PGD and PGV observations are as follows: ; In the formula, For the total residual vector, To integrate the magnitude estimates, To integrate the overall design matrix, For the overall observation vector, ; Estimation of combined magnitude : ; In the formula, For matrix The transpose of the matrix; The overall normal equations for the two types of peak deformation observations, PGD and PGV, are as follows: ; In the formula, The coefficient matrix of the overall normal equation. The coefficient matrix of the overall normal equation. Coefficient matrix The inverse matrix; Overall normal equation coefficient matrix for: ; Overall normal equation coefficient matrix for: ; Variance component estimation is performed on the two types of observations, PGD and PGV. The estimated solution for the variance components is as follows: ; In the formula, This is a vector of unit-weighted variance estimates for the two classes of observations, PGD and PGV. Coefficient matrix The inverse matrix, A constant vector is constructed from the residuals and prior weights; The unit weighted variance estimate vectors of the two types of observations, PGD and PGV. for: ; coefficient matrix for: ; In the formula, This indicates finding the trace of a matrix. and These represent the number of observations for the two categories, PGD and PGV, respectively. The constant vector constructed from residuals and prior weights for: ; Post-verification rights are updated to: ; In the formula, For the first The posterior weight matrix of the observations, It is a constant. For the first The unit weighted variance estimate is obtained by estimating the variance components of the observations.

[0012] Furthermore, the robust sequential least squares estimation using the IGG3 equivalent weight criterion to obtain the fused magnitude includes constructing a robust estimation objective function: ; In the formula, For the first One observation right, For the first The square of each residual; The weights of the observations are adjusted using the IGG3 equivalent weight function, which is as follows: ; In the formula, The equivalent weight function value, To standardize the residuals, For variance factor, This is the normal observation threshold. This is the threshold for abnormal observations. For weighting coefficients, , , , , The smoothing coefficients for the robustness weights of IGG3 are given. The value ranges from 1.0 to 1.5. The value ranges from 2.5 to 3.0; Based on the IGG3 equivalent weight function, normal observations retain their original weights, suspicious observations are weighted down, and abnormal observations are set to zero and removed, thus completing robust estimation and obtaining the fused magnitude.

[0013] Compared with the prior art, the present invention has the following technical effects: This invention achieves adaptive weighting of seismic observation data through FCM unsupervised clustering, with weight allocation more closely matching the actual data characteristics, effectively avoiding the problem of strong subjectivity in traditional empirical weighting. At the same time, combined with IGG3 robust sequential least squares estimation, it can significantly suppress the impact of observational gross errors on magnitude estimation results, improving the stability and reliability of magnitude inversion. The overall algorithm has a high degree of automation and stronger applicability, and can achieve more accurate, efficient, and robust estimation of strong earthquake magnitudes. Attached Figure Description

[0014] Figure 1 This is a flowchart of the technology of the present invention; Figure 2 The PGD fitting plot for the equal weight model; Figure 3 The PGV fitting plot for the equal weight model; Figure 4 The PGD fitting plot for the FCM (Fuzzy C-Means) weighted model; Figure 5 The PGV fitting plot for the FCM weighted model; Figure 6 This is a residual distribution diagram of the PGD empirical coefficients after least squares fitting; Figure 7 The residual distribution of the PGV empirical coefficients after least squares fitting is shown in the figure. Figure 8 The image shows the real-time magnitude estimation results of the improved algorithm under the PGD / PGV fusion model in the Tohoku 2011 earthquake case. Figure 9 The figure shows the real-time magnitude estimation results of the improved algorithm under the PGD / PGV fusion model in the Tokachi 2003 earthquake case. Figure 10The figure shows the real-time magnitude estimation results of the improved algorithm under the PGD / PGV fusion model in the case of the Kumamoto 2016 earthquake. Figure 11 The image shows the real-time magnitude estimation results of the improved algorithm under the PGD / PGV fusion model in the case of the Kilauea 2018 earthquake. Figure 12 This is a graph showing the real-time magnitude estimation results of the improved algorithm under the PGD / PGV fusion model in the Napa2014 earthquake case. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0016] like Figure 1 As shown, the method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering includes the following steps: S1. Collect coseismic deformation observation data, calculate the multi-directional displacement and velocity components of each station, and calculate the peak surface displacement (PGD), peak surface velocity (PGV), and epicentral distance of the station. S2. Construct a magnitude regression equation, use the FCM unsupervised learning clustering algorithm to cluster the dataset to obtain weight factors, construct a fitting weight matrix based on the weight factors, substitute it into the PGV / PGD fitting observation equation, and obtain the fitting empirical coefficients through weighted least squares regression estimation. S3. Based on the empirical coefficients obtained in S2, construct the fusion observation equation, obtain the posterior weights of the two types of observations, PGD and PGV, through the Helmert VCE method, and use the IGG3 equivalent weight criterion to perform robust sequential least squares estimation to obtain the fusion magnitude.

[0017] This embodiment uses a GNSS / strong motion meter fused coseismic deformation dataset. The dataset contains five earthquake examples from the past 20 years worldwide, with magnitudes ranging from Mw6.0 to Mw9.0, epicentral distances between 1 km and 1000 km, and focal depths less than 60 km. The five earthquake examples are shown in Table 1.

[0018] Table 1. Detailed information for each earthquake case. .

[0019] The five selected typical earthquakes are clearly representative: Tohoku 2011 (Mw 9.0) off the coast of northeastern Japan is a super earthquake with a large number of stations, which can be used to demonstrate the estimation accuracy of this method under large earthquake conditions; Tokachi 2003 (Mw 8.3) in Hokkaido, Japan is a typical tsunami earthquake and is highly representative, which can be used to verify the applicability of the method in strong tsunami earthquake scenarios; Kumamoto 2016 (Mw 7.0) in Kyushu, Japan is a moderate earthquake with a moderate number of stations, which can reflect the performance of the method under common observation conditions; Kilauea 2018 (Mw 6.9) in the Hawaiian Islands has very few available stations, which is suitable for verifying the stability of the method under extreme conditions such as sparse stations; Napa 2014 (Mw 6.1) in California, USA is at the lower limit of the selected magnitude range and can be used to cover lower magnitude scenarios.

[0020] Next, we will estimate the empirical coefficients of the magnitude regression model. Figure 2 , Figure 3 , Figure 4 and Figure 5 This paper presents the results of fitting all PGD and PGV observations for five earthquake events using both the Equal Weighted Model and the FCM (Fuzzy C-Means) model. Figure 2 , Figure 3 , Figure 4 and Figure 5 It can be seen that the measured data of PGD and PGV under the Equal model have large dispersion, significant deviation in high-magnitude areas, and poor model stability; while after unsupervised clustering weighting under the FCM model, the dispersion of the data is significantly reduced, the measured points fit the fitted curve better, and the model accuracy and robustness are significantly improved.

[0021] Weighted least squares fitting was performed using the FCM weight matrix of this invention to obtain the PGD regression coefficients. Under the equal weight scheme, the regression coefficients of the PGD model are A = –4.366, B = 1.021, and C = –0.130, while the regression coefficients of the PGV model are A = –2.902, B = 0.795, and C = –0.143. After weighted least squares fitting using the weight matrix constructed by unsupervised clustering weighting, the regression coefficients obtained are: A = –4.341, B = 1.033, and C = –0.136 for the PGD model, and A = –3.005, B = 0.818, and C = –0.147 for the PGV model. The empirical coefficients fitted by the Equal model and the FCM clustering weighting model are on the same order of magnitude, differing only in two decimal places.

[0022] Depend on Figure 2 , Figure 3 , Figure 4and Figure 5 It can be seen that PGD and PGV exhibit a clear scale dependence with epicentral distance, meaning that the response to near-field earthquake events is stronger and gradually decreases with increasing epicentral distance, and their linear variation trend reflects the magnitude of the earthquake. This indicates that the surface peak deformation parameter obtained by fusing PGD and PGV can effectively characterize the spatial distribution characteristics of earthquake magnitude, which is consistent with the observational patterns of real earthquake events.

[0023] The fitting residuals of the magnitude fitting model based on the FCM weighting scheme, such as Figure 6 and Figure 7 As shown, although the differences in empirical coefficients are not significant, the residual sequence of the least squares model in the FCM clustering weighted model is more compact than that in the equal-weight model, with less overall fluctuation in the fitted residuals, fewer spikes in the residuals, and a more uniform distribution. The results show that the average absolute value of the residuals in the equal-weight model is approximately 0.312 cm / s, with a maximum absolute error of 0.60 cm / s; while the numerical distribution of the unsupervised clustering weighted model is more stable (average absolute value approximately 0.281 cm / s, maximum absolute error only 0.50 cm / s), with an overall error reduction of approximately 10%. In PGD estimation, the residuals of the traditional equal-weight model return to zero or jump across multiple stations, exhibiting significant dispersion; while the absolute value of the residuals in the unsupervised clustering weighted model remains stable between 0.10 and 0.30 cm, with variations between adjacent stations not exceeding 0.20 cm, resulting in a more compact and smoother residual sequence. Therefore, the proposed unsupervised clustering weighting model can effectively constrain the dispersion of the residuals, making the estimation results more closely clustered within the physically reasonable range, and significantly improving the accuracy and consistency of ground motion parameter estimation. Table 1 shows that the PGD and PGV of each seismic event have a significant scale correlation with the epicentral distance, exhibiting a strong response to near-field seismic events, which gradually decreases with increasing epicentral distance; the linear trend reflects the magnitude. This indicates that the peak surface deformation parameters obtained through the PGD and PGV fusion method can effectively reflect the spatial distribution characteristics of earthquake magnitude, consistent with actual observation patterns.

[0024] Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 This paper compares the performance of the traditional least squares method and the robust variance component estimation method (hereinafter referred to as the improved method) in real-time magnitude estimation for five earthquake events. The upper and lower limits of the error bars represent the unit weighted mean square error of the magnitude estimation per epoch, i.e., the internal consistency accuracy. Using the absolute magnitude deviation of less than one magnitude unit for 10 consecutive epochs as the convergence criterion, the convergence observation epoch time and convergence magnitude for each earthquake case were calculated. The results show that for all five earthquake cases, the improved method exhibits a smaller internal consistency accuracy before magnitude convergence, and its overall convergence trend is slightly faster than that of the least squares method.

[0025] As shown in Table 1, Napa 2014 (California, USA) and Kilauea 2018 (Hawaii) are located on the eastern and central Pacific coasts, with relatively dense station deployments and some co-located stations close to the epicenter. Therefore, the initial magnitude estimation time was less than 50 seconds, resulting in the fastest convergence speed. Kumamoto 2016 (Kyushu, Japan) and Tokachi 2003 (Hokkaido, Japan) are located in the western Pacific subduction zone. The station distribution is limited by topography and land-sea conditions, and there is a lack of deformation data for some GNSS and strong-motion seismograph co-located stations. This directly led to abrupt changes in the magnitude time series of these two earthquakes in the middle and end. Tohoku 2011 (offshore in northeastern Japan) has a sufficient number of co-located stations with even spatial distribution. Therefore, its merged magnitude is in extremely high agreement with the reference moment magnitude released by the USGS after the event. Differences in geographical distribution and station configuration provide an intuitive basis for understanding the differences in magnitude estimation performance across earthquake cases. The denser and more uniformly distributed the co-located stations, the lower the ill-conditioned nature of the observation equations, resulting in faster magnitude convergence and tighter residuals. The improved method proposed in this application can adaptively adjust weights under non-ideal observation conditions, thus achieving lower internal consistency accuracy and faster convergence than the traditional least squares method in events such as Kumamoto and Tokachi, verifying the robustness and universality of this method under different observation conditions.

[0026] Compared to the reference magnitude, the magnitude results of some selected earthquakes showed slight fluctuations in the middle or end of the time series. This was mainly due to the lack of deformation data from GNSS and strong-motion seismograph stations located together, resulting in a reduction in the available PGD and PGV observations. In addition, some earthquakes showed a slight underestimation of magnitude, which was related to the direction of the rupture propagation and the uneven distribution of stations. When the source ruptured in a certain direction, stations in that direction usually recorded higher PGD and PGV, while the peak values ​​of stations in the opposite direction were relatively lower, thus having a slight impact on the magnitude estimation.

[0027] Among the five selected earthquake cases, those with evenly distributed and sufficient stations showed extremely high agreement between their combined magnitude and the reference magnitude. While the magnitude estimation accuracy slightly decreased for cases with unevenly distributed stations or larger epicentral distances, it still generally met the requirements for practical applications. These experimental results demonstrate that the rapid magnitude estimation method based on robust variance component estimation can be effectively used to quickly determine the magnitude of major earthquakes corresponding to the five selected earthquake cases.

[0028] Using the moment magnitude Mw published by the USGS as a reference, Table 2 statistically analyzes the average magnitude deviation of all five earthquake examples to assess the reliability of the magnitude model. Table 2 shows that under the Equal weighting scheme, the traditional least squares method has an average magnitude deviation of 0.299 and a convergence magnitude deviation of 0.324; the improved method of this invention has an average magnitude deviation of 0.317 and a convergence magnitude deviation of 0.255. Under the FCM clustering weighting scheme, the traditional least squares method has an average magnitude deviation of 0.286 and a convergence magnitude deviation of 0.315; the improved method of this invention reduces the average magnitude deviation to 0.224 and the convergence magnitude deviation to 0.229. The comparison demonstrates that the improved method of this invention can effectively reduce magnitude estimation deviation and improve estimation accuracy and stability. This indicates that the magnitude obtained by the improved method is in very good agreement with the subsequently published reference moment magnitude. Compared with the traditional least squares method, the accuracy of the average magnitude estimation is improved by 29.3%, and the accuracy of the convergent magnitude estimation is improved by 10.2%.

[0029] Table 2. Accuracy of Magnitude Estimation by the Improved Method under the PGD / PGV Fusion Model .

[0030] This invention constructs a PGD / PGV magnitude fitting model based on unsupervised learning clustering weighting using fused coseismic deformation information, and develops a rapid PGD / PGV fusion magnitude estimation method based on robust variance component estimation. This overcomes the influence of integral drift of broadband velocity or acceleration from the regional to the teleseismic range, and solves the limitations of insufficient sampling rate and low vertical displacement accuracy caused by single GNSS deformation. This method effectively weakens the influence of spurious peak surface deformation signals caused by interference factors such as instrument response and background noise in actual observations, significantly improving the fitting accuracy of the PGD / PGV magnitude regression model and the accuracy of the rapid magnitude estimation results, providing technical support for rapid earthquake situation assessment. Experimental results show that the proposed method can estimate stable convergent magnitude results within 50 seconds after the earthquake, with a final magnitude deviation better than 0.25 magnitude units, enabling rapid magnitude estimation for tsunami earthquakes with complex fault structures.

[0031] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering and weighting, characterized in that... Includes the following steps: S1. Collect coseismic deformation observation data, calculate the multi-directional displacement and velocity components of each station, and calculate the peak surface displacement (PGD), peak surface velocity (PGV), and epicentral distance of the station. S2. Construct a magnitude regression equation, use the FCM unsupervised learning clustering algorithm to cluster the dataset to obtain weight factors, construct a fitting weight matrix based on the weight factors, substitute it into PGV and PGD to fit the observation equation, and obtain the fitting empirical coefficients through weighted least squares regression estimation. The FCM unsupervised learning clustering algorithm is used to cluster the dataset and obtain the weight factors, specifically PGD, PGV, and epicentral distance. The feature dataset consists of: ； In the formula, , The total number of samples; Set the number of clusters and weighted index Construct the FCM objective function: ； In the formula, , indicating the first The sample belongs to the first The membership degree of each cluster. For the number of clusters, As a weighted index, For the first The feature vector of each sample For the first The feature values ​​of each cluster center; To introduce membership constraints, the Lagrange multiplier method is used to construct the Lagrange objective function: ； In the formula, , indicating the first The sample belongs to the first The membership degree of each cluster. For Lagrange multipliers, For the first Cluster centers; Membership degrees satisfy the following constraints: ； Differentiating and iteratively updating the Lagrange function, cluster centers It is calculated using the following formula: ； Let distance For membership function Taking the derivative, we get: ； In the formula, For the first Sample With the Cluster centers The distance between them For the first Sample With the Cluster centers The distance between them; After iterating until the objective function converges, the cluster centers are obtained. And the corresponding objective function is calculated in each iteration. This minimizes the objective function. After the iteration is completed, the FCM model obtains Cluster centers, including the baseline cluster center , and the epicenter distance for each group and and The corresponding cluster centers are and Based on the degree of feature difference between each cluster center and the baseline cluster center, the FCM clustering weight factors corresponding to the PGD and PGV observations are constructed: ； ； In the formula, and These are the FCM clustering weight factors corresponding to the PGD and PGV observations, respectively. For the first Cluster centers, For the first The epicentral distance corresponding to each cluster center For the first The PGD value corresponding to each cluster center The epicentral distance corresponding to the reference center. The epicentral distance corresponding to the reference center. The PGD value corresponding to the reference center. For the first The PGV value corresponding to each cluster center The PGV value corresponding to the reference center. For the first A measure of the difference between each cluster center and the baseline cluster center; S3. Based on the empirical coefficients obtained in S2, construct the fusion observation equation, obtain the posterior weights of the two types of observations, PGD and PGV, through the Helmert VCE method, and use the IGG3 equivalent weight criterion to perform robust sequential least squares estimation to obtain the fusion magnitude.

2. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The formulas for calculating the peak surface displacement (PGD) and peak surface velocity (PGV) are as follows: ； ； In the formula, , and These are expressed as coseismic displacement components in the north, east, and sky directions, respectively, in centimeters. , and These are expressed as coseismic velocity components in the north, east, and sky directions, respectively, in centimeters. In S1, the epicentral distance of the station The spherical distance from the station to the epicenter is obtained using the following formula: ； In the formula, This represents the spherical distance from the GNSS / strong-motion meter station to the epicenter, expressed in kilometers. and The latitude and longitude of the station and The coordinates of the epicenter are latitude and longitude. This is the average radius of the Earth.

3. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The magnitude regression equation is: ； ； In the formula, , , The PGD magnitude regression coefficient is used. , , The regression coefficient for PGV magnitude. This represents the spherical distance from the GNSS / strong-motion meter station to the epicenter, expressed in kilometers.

4. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The process involves constructing a fitting weight matrix based on weight factors, substituting it into the PGV / PGD fitting observation equation, and obtaining the fitting empirical coefficients through weighted least squares regression estimation. This includes constructing the fitting observation equations for PGV and PGD based on the magnitude regression equation. ； ； In the formula, To design the matrix, , These are the regression coefficient vectors for the PGD and PGV magnitude regression models, respectively; Based on FCM clustering weight factor Constructed weight matrix for: ； In the formula, The observation weights for each station are determined based on the FCM clustering weight factor; Fitting weight matrix Substituting the observation equations for PGD and PGV into the fitted equations, and using weighted least squares regression estimation, we obtain the fitted empirical coefficient vectors of the PGD and PGV magnitude regression models. and : ； ； In the formula, The logarithmic matrix of PGD observations, The logarithmic matrix of PGV observations. To design the matrix, For FCM-based clustering weight factors The constructed weight matrix, , These are the regression coefficient vectors for the PGD and PGV magnitude regression models, respectively; The fitted empirical coefficient vector is represented as follows: ； ； In the formula, , , These are the empirical coefficients of the PGD magnitude regression equation obtained by weighted least squares regression. , , These are the empirical coefficients of the PGV magnitude regression equation obtained by weighted least squares regression. Design Matrix for: ； In the formula, The known moment magnitudes of historical earthquakes. For the first Epicentral distance of each station; PGD ​​observation logarithmic matrix for: ； PGV observation logarithmic matrix for: ； Calculate the residuals between the observed PGD / PGV values ​​and the regression predictions: ； In the formula, The predicted residuals for PGD / PGV, These are PGD / PGV observations; These are the predicted values ​​for PGD / PGV.

5. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The fusion observation equation constructed based on empirical coefficients is as follows: ； ； In the formula, , , These are the empirical coefficients of the PGD magnitude regression equation obtained by weighted least squares regression. , , These are the empirical coefficients of the PGV magnitude regression equation obtained by weighted least squares regression. and The first The first observation station was at the first Peak surface displacement and peak surface velocity observations for each observation epoch. For the first The first observation station was at the first Epicentral distance at each observation epoch, To estimate the strong earthquake moment and magnitude during the observation epoch; The regression magnitude of the observed epoch is calculated using the least squares criterion: ； In the formula, To integrate the overall design matrix, The prior weight matrix for PGD / PGV observations. This represents the overall observation vector; Fusion Design Matrix for: ； Overall observation vector for: ； Weight matrix of PGD / PGV observations for: ； In the formula, and Let be the prior weight matrices for PGD and PGV.

6. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The specific process of obtaining the posterior weights of the two types of observations, PGD and PGV, using the Helmert VCE method is as follows: the two types of magnitude fitted observations, PGD and PGV, are incorporated into the Helmert variance component equation as two types of weights for variance component estimation. A joint observation model, a stochastic model, a population error equation, and a population normal equation are constructed. The unit weight variances of the PGD and PGV observations are estimated iteratively using the Helmert estimation formula. The posterior weight matrices of the two types of observations are updated. The iteration continues until the unit weight variances of the two types are equal or the hypothesis testing requirements are met. The joint observation model for PGD and PGV observations is expressed as follows: ； ； In the formula, and For observation vectors of PGD and PGV class observations, and The design matrices are for PGD and PGV type observations. and For PGD and PGV type observations, ; Design matrices for PGD and PGV type observations and for: ； ； Error terms for PGD and PGV type observations and for: ； ； In the formula, For the first PGD ​​error of each station For the first PGV error of each station; No. PGD ​​error at individual stations for: ； No. PGV error of individual stations for: ； The stochastic models for the two types of observations, PGD and PGV, are as follows: ； ； ； In the formula, For variance, and For observation vectors of PGD and PGV class observations, and For PGD and PGV type observations, the unit weight variance is given. and Let be the inverse of the prior weight matrices of PGD and PGV. PGD ​​observation vector With PGV observation vector Covariance between PGD ​​error Error with PGV Covariance between them; The overall error equations for PGD and PGV observations are as follows: ； In the formula, For the total residual vector, To integrate the magnitude estimates, To integrate the overall design matrix, For the overall observation vector, ; Estimation of combined magnitude : ； In the formula, For matrix The transpose of the matrix; The overall normal equations for the two types of peak deformation observations, PGD and PGV, are as follows: ； In the formula, The coefficient matrix of the overall normal equation. The coefficient matrix of the overall normal equation. Coefficient matrix The inverse matrix; Overall normal equation coefficient matrix for: ； Overall normal equation coefficient matrix for: ； Variance component estimation is performed on the two types of observations, PGD and PGV. The estimated solution for the variance components is as follows: ； In the formula, This is a vector of unit-weighted variance estimates for the two classes of observations, PGD and PGV. Coefficient matrix The inverse matrix, A constant vector is constructed from the residuals and prior weights; The unit weighted variance estimate vectors of the two types of observations, PGD and PGV. for: ； coefficient matrix for: ； In the formula, This indicates finding the trace of a matrix. and These represent the number of observations for the two categories, PGD and PGV, respectively. The constant vector constructed from residuals and prior weights for: ； Post-verification rights are updated to: ； In the formula, For the first The posterior weight matrix of the observations, It is a constant. For the first The unit weighted variance estimate is obtained by estimating the variance components of the observations.

7. The method for estimating the magnitude of strong earthquakes with peak surface deformation based on unsupervised learning clustering weighting according to claim 1, characterized in that, The method of using the IGG3 equivalent weight criterion for robust sequential least squares estimation to obtain the fused magnitude includes constructing a robust estimation objective function: ； In the formula, For the first One observation right, For the first The square of each residual; The weights of the observations are adjusted using the IGG3 equivalent weight function, which is as follows: ； In the formula, The equivalent weight function value, To standardize the residuals, For variance factor, This is the normal observation threshold. This is the threshold for abnormal observations. For weighting coefficients, , , , , The smoothing coefficients for the robustness weights of IGG3 are given. The value ranges from 1.0 to 1.

5. The value ranges from 2.5 to 3.0; Based on the IGG3 equivalent weight function, normal observations retain their original weights, suspicious observations are weighted down, and abnormal observations are set to zero and removed, thus completing robust estimation and obtaining the fused magnitude.

Images